drgeo-doc-1.5/0002777000175000017500000000000010117134567006776 5drgeo-doc-1.5/README0000644000175000017500000002246107716177153007606 This is the module with the sources of the DrGeo manual. If you wish to work on or to participate in the translation of a manual, you are suggested to entirely read this document. Also you may want to read part of this document from time to time. The various sections of this document explain how is set up the translation procedure within this module. Some of the paragraphs below may look a bit difficult to follow, however translating the manual is one step but keeping a translated version up to date with the source manual is more difficult. The main purpose of this CVS module organisation is to have a consistent way to keep track of the update in the source manual and to apply it to the translated manual. HOW TO COMPILE MANUAL --------------------- In top directory: aclocal automake autoconf ./configure --prefix=/usr cd fr (up to you) make drgenius.pdf make drgenius.html make install (it will install the .html so that Dr.Geo can found it) DOCUMENT TO TRANSLATE --------------------- To translate the Dr Geo manual, one file need to get translated: o the drgenius.tex file, it is the manual source; LATEX & HYPERLATEX ------------------ LaTeX & HyperLaTeX are used to produce from a single .tex document a paper version and a html version used as an online help. Common macros to all the manuals are placed in the drgeniusCommon.tex file. This file is included near the top of the drgenius.tex document. The drgenius.tex is the manual. Each national manual has its own directory -- generally a two letters directory name. PICTURES -------- In the manual, the pictures are located in the "figures" directories of the various manual version. However, while translating the manual, the c/figures can be used for all manual versions by setting the LaTeX macro \drgeniusImagePath to the appropriate relative path "../c/figures". If you want to get localised pictures as well, create a 'figures' directory in your locale directory, for example it/figures. Into that directory copy the c/figures/Makefile. Then in the it/Makefile.am change '../c/figures' to 'figures'. Then you need to get all the new shot as .png images into it/figures. SOURCE MANUAL ------------- The source manual is the French version -- in the fr directory. This means this is the version where new stuff is written first. The international version -- in English -- is in the c directory, we keep it as best as we can up to date with the French version. In short, if you can read French, you should update your national manual from this manual. Otherwise, use the international version in the C directory. DR GEO MANUAL VERSION ------------------------ When a manual version is ready (i.e. to be translated to other languages or up to date with the original version) it is tagged in the CVS. The tag names are of the form version-X_X where X are numbers. The first version is always version-1_0. Examples: To mark the fr/drgenius.tex ready to be translated to other language we mark it with the following command: cvs tag version-1_0 fr/drgenius.tex To mark the it/drgenius.tex as up to date to the version-1_1 of the French manual we use the following command: cvs tag version-1_1 it/drgenius.tex IMPORTANT NOTE FOR TRANSLATOR ----------------------------- \xname{} instructions must not be translated. These commands set hooks for the Dr. Geo on-line help manual. Translating the commands will just broke the Dr. Geo on-line help system (i.e. the user will not get the required help section). STARTING THE TRANSLATION ------------------------ Let's see with an example: Let's say you want to create a new Dutch version of the manual. The country code is nl (you may want to have nl_BE and nl_NL) 1. fetch the whole drgenius-man module from the OFSET CVS cvs -d:ext:hilaire@cvs.sourceforge.net:/cvsroot/ofset co drgenius-man 2. create the manual directory and related data cd drgenius-man mkdir nl 3. edit the following files, necessary to resp. autoconf and automake. a. In configure.ac, add nl/Makefile to the list of AC_CONFIG_FILES: AC_CONFIG_FILES([ Makefile c/Makefile fr/Makefile ... nl/Makefile)] b. In Makefile.am, add nl to the list of subdirectories: SUBDIRS = c es fr ... nl 4. fetch the last stable manual version you want to translate from. Let's say you want to translate from the French version. a. First see what the latest stable version of the French manual is cvs update cat fr/version Let's say the previous command returns version-1_2 b. Fetch the French version-1_2 from the CVS and commit cvs add nl cd nl cp ../fr/Makefile.am . (edit the file to set the appropriate path) (just replace fr by nl) touch ChangeLog version cvs get -r version-1_2 -p drgenius-man/fr/drgenius.tex > drgenius.tex cvs get -r version-1_2 -p drgenius-man/fr/topic.dat > topic.dat You are ready to translate the drgenius.tex and topic.dat to Dutch. When translations are done, commit the files to the CVS server: cvs add drgenius.tex Makefile.am ChangeLog version topic.dat cvs -z3 commit -m "Initial set-up of the manual." The add operation is only need once, then updates to the files can be commited with the commit command. 5. Once the translation is up to date and you are sure about that, mark it as version-1_2 (do not forget to commit once more before tagging): echo "version-1_2" > nl/version cvs -z3 commit "Updated version." cvs tag version-1_2 nl/drgenius.tex UPDATING A TRANSLATION ---------------------- The updates of the translated manuals are organised with the TAG system which comes with CVS. We use this system to mark new manual version ready to be translated. The last stable version can be found from the version file within the respective directory of the manual. In a few words, to update a translated manual from one stable version to the next stable one of the source language manual, we look at the differences between the last two stable versions of the source language manual, then apply this differences to our translated manual. In the following we will take an example to explain further how to proceed. Let's say we have the Dutch manual version-1_1 up to date while the release version-1_2 of the French source manual is committed into the CVS. Note: To know what is the latest stable version of the French source manual proceed as: cd your-working-copy cvs update cat fr/version The Dutch maintainer will want to apply to its manual the differences between the version-1_1 and version-1_2 in the French manual. All this means the maintainer will need: - the Dutch manual version-1_1 - the French manual version-1_1 - the French manual version-1_2 Here how we proceed: cd nl cvs get -r version-1_1 -p drgenius-man/fr/drgenius.tex > drgenius-1_1.tex cvs get -r version-1_2 -p drgenius-man/fr/drgenius.tex > drgenius-1_2.tex Then look at differences with a command like diff -u drgenius-1_1.tex drgenius-1_2.tex | less or diff -u drgenius-1_1.tex drgenius-1_2.tex > diff.txt Lines deleted from drgenius-1_1.tex begin with the sign '-' and lines added to drgenius-1_2.tex begin with the sign '+'. Some lines before and after these changes are the same. The diff document produced with the diff command may not always be easy to read. There is an alternative tool to look at the differences. The section UPDATING A TRANSLATION WITH EMACS explains this tool. UPDATING A TRANSLATION WITH EMACS --------------------------------- You can use the GNU Emacs Ediff (Menu Tools->Compare->..) to look at the differences. Start Emacs, then go to the menu Tools->Compare->Two Files... (or use M-x ediff-files). Select the files nl/drgenius-1_1.tex nl/drgenius-1_2.tex (Note: Remember, those drgenius-1_1.tex and drgenius-1_2.tex files are the French versions we fetch from the CVS into the nl directory) Emacs will show you the differences between these two versions. You can browse them with 'n' and 'p' ('?' toggle key for help). You can now open in a third view (C-x 4 f or open a new frame with C-x 5 f) the source of the Dutch source manual (nl/drgenius.tex) When the translation is up to date, mark it as version-1_2 (do not forget to commit it a very last time before tagging) echo "version-1_2" > nl/version cvs -z3 commit "Updated version." cvs tag version-1_2 nl/drgenius.tex Then you can safely delete the drgenius-1_1.tex and drgenius-1_2.tex file rm nl/drgenius-1_1.tex rm nl/drgenius-1_2.tex NOTE: Of course, if you translated from the international version, you just need to replace every 'fr' by 'c'. Comment, remarks, proofreading are very welcome to enhance this document. IN PROGRESS ----------- DO NOT READ HERE. Documented function may not work for now. A more easy way for comparing two versions is to use vc-minor-mode. With an updated working directory, you have to edit the last version of drgenius.tex. For example, the mode line contains somethinglike CVS-1.2 for drgenius-1_2.tex. Then use : C-x v ~ and type 1.1 to obtain the previous version of the file (see C-h m and Version Control in the Emacs manual for more help on VC minor mode). A new buffer is created. Then use : M-x ediff-buffers and validate two times (Emacs should propose the correct buffers). You have now previous version of the file (v1.1) at the top and the last one (v1.2) at the bottom of the frame. 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When coming back to configure, we # need to make the FD available again. if test "$no_create" != yes; then ac_cs_success=: ac_config_status_args= test "$silent" = yes && ac_config_status_args="$ac_config_status_args --quiet" exec 5>/dev/null $SHELL $CONFIG_STATUS $ac_config_status_args || ac_cs_success=false exec 5>>config.log # Use ||, not &&, to avoid exiting from the if with $? = 1, which # would make configure fail if this is the last instruction. $ac_cs_success || { (exit 1); exit 1; } fi drgeo-doc-1.5/AUTHORS0000644000175000017500000000042507712435306007763 Copyright 2001-2003 Hilaire Fernandes (original document in French & English) Copyright 2002-2003 Andrea Centomo (Italian version) Copyright 2002 Jean-Philippe Georget (French version) Copyright 2001 Adrian Soto (Spanish version) Copyright 2003 Tobias Verbeke (Dutch version) drgeo-doc-1.5/COPYING0000644000175000017500000004765707622213464007767 GNU Free Documentation License Version 1.2, November 2002 Copyright (C) 2000,2001,2002 Free Software Foundation, Inc. 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 0. 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If the Document specifies that a particular numbered version of this License "or any later version" applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation. ADDENDUM: How to use this License for your documents To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page: Copyright (c) YEAR YOUR NAME. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the "with...Texts." line with this: with the Invariant Sections being LIST THEIR TITLES, with the Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST. If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation. If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software. drgeo-doc-1.5/ChangeLog0000644000175000017500000000142110113164053010445 2004-06-08 Hilaire Fernandes * Makefile.am (EXTRA_DIST): Add fdl.tex. 2003-10-30 Hilaire Fernandes * nl/drgenius.tex: Fixed to get it compile with HyperLatex. (chapter{GNU Free Documentation License}): Add reference to the GFDL. (chapter*{Copyright}): Add Copyright notice. Add the translator name. 2003-09-16 Hilaire Fernandes * nl/drgenius.tex: Change \drgeniusApi to \drgeoApi. * drgeniusCommon.tex: Change \drgeniusApi to \drgeoApi, please update it in the source document. 2003-07-28 Hilaire Fernandes * drgeniusCommon.tex: Rename \toppanel to \HlxTopPanel. 2003-02-11 Hilaire Fernandes * configure.ac: Add the fr and es directory to the AC_OUTPUT drgeo-doc-1.5/INSTALL0000644000175000017500000000004607710556436007751 ./configure --prefix=/usr make installdrgeo-doc-1.5/Makefile.am0000644000175000017500000000024210113164053010727 CLEANFILES= *~ SUBDIRS = c es fr it nl EXTRA_DIST = \ drgeniusCommon.tex COPYING README NEWS INSTALL fdl.tex uninstall-local: rm -rf $(datadir)/drgeo/help/ drgeo-doc-1.5/NEWS0000644000175000017500000000030207710556167007413 Dr. Geo manual 0.2.0 * Updated Italian manual. 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IFS='%' set - `echo ${dstdir} | sed -e 's@/@%@g' -e 's@^%@/@'` IFS="${oIFS}" pathcomp='' while [ $# -ne 0 ] ; do pathcomp="${pathcomp}${1}" shift if [ ! -d "${pathcomp}" ] ; then $mkdirprog "${pathcomp}" else true fi pathcomp="${pathcomp}/" done fi if [ x"$dir_arg" != x ] then $doit $instcmd $dst && if [ x"$chowncmd" != x ]; then $doit $chowncmd $dst; else true ; fi && if [ x"$chgrpcmd" != x ]; then $doit $chgrpcmd $dst; else true ; fi && if [ x"$stripcmd" != x ]; then $doit $stripcmd $dst; else true ; fi && if [ x"$chmodcmd" != x ]; then $doit $chmodcmd $dst; else true ; fi else # If we're going to rename the final executable, determine the name now. if [ x"$transformarg" = x ] then dstfile=`basename $dst` else dstfile=`basename $dst $transformbasename | sed $transformarg`$transformbasename fi # don't allow the sed command to completely eliminate the filename if [ x"$dstfile" = x ] then dstfile=`basename $dst` else true fi # Make a temp file name in the proper directory. dsttmp=$dstdir/#inst.$$# # Move or copy the file name to the temp name $doit $instcmd $src $dsttmp && trap "rm -f ${dsttmp}" 0 && # and set any options; do chmod last to preserve setuid bits # If any of these fail, we abort the whole thing. If we want to # ignore errors from any of these, just make sure not to ignore # errors from the above "$doit $instcmd $src $dsttmp" command. if [ x"$chowncmd" != x ]; then $doit $chowncmd $dsttmp; else true;fi && if [ x"$chgrpcmd" != x ]; then $doit $chgrpcmd $dsttmp; else true;fi && if [ x"$stripcmd" != x ]; then $doit $stripcmd $dsttmp; else true;fi && if [ x"$chmodcmd" != x ]; then $doit $chmodcmd $dsttmp; else true;fi && # Now rename the file to the real destination. $doit $rmcmd -f $dstdir/$dstfile && $doit $mvcmd $dsttmp $dstdir/$dstfile fi && exit 0 drgeo-doc-1.5/missing0000755000175000017500000001451007624116420010305 #! /bin/sh # Common stub for a few missing GNU programs while installing. # Copyright (C) 1996, 1997, 2001 Free Software Foundation, Inc. # Franc,ois Pinard , 1996. # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 2, or (at your option) # any later version. # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # You should have received a copy of the GNU General Public License # along with this program; if not, write to the Free Software # Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA # 02111-1307, USA. if test $# -eq 0; then echo 1>&2 "Try \`$0 --help' for more information" exit 1 fi # In the cases where this matters, `missing' is being run in the # srcdir already. if test -f configure.in; then configure_ac=configure.ac else configure_ac=configure.in fi case "$1" in -h|--h|--he|--hel|--help) echo "\ $0 [OPTION]... PROGRAM [ARGUMENT]... Handle \`PROGRAM [ARGUMENT]...' for when PROGRAM is missing, or return an error status if there is no known handling for PROGRAM. Options: -h, --help display this help and exit -v, --version output version information and exit Supported PROGRAM values: aclocal touch file \`aclocal.m4' autoconf touch file \`configure' autoheader touch file \`config.h.in' automake touch all \`Makefile.in' files bison create \`y.tab.[ch]', if possible, from existing .[ch] flex create \`lex.yy.c', if possible, from existing .c lex create \`lex.yy.c', if possible, from existing .c makeinfo touch the output file yacc create \`y.tab.[ch]', if possible, from existing .[ch]" ;; -v|--v|--ve|--ver|--vers|--versi|--versio|--version) echo "missing - GNU libit 0.0" ;; -*) echo 1>&2 "$0: Unknown \`$1' option" echo 1>&2 "Try \`$0 --help' for more information" exit 1 ;; aclocal) echo 1>&2 "\ WARNING: \`$1' is missing on your system. You should only need it if you modified \`acinclude.m4' or \`$configure_ac'. You might want to install the \`Automake' and \`Perl' packages. Grab them from any GNU archive site." touch aclocal.m4 ;; autoconf) echo 1>&2 "\ WARNING: \`$1' is missing on your system. You should only need it if you modified \`$configure_ac'. You might want to install the \`Autoconf' and \`GNU m4' packages. Grab them from any GNU archive site." touch configure ;; autoheader) echo 1>&2 "\ WARNING: \`$1' is missing on your system. You should only need it if you modified \`acconfig.h' or \`$configure_ac'. You might want to install the \`Autoconf' and \`GNU m4' packages. Grab them from any GNU archive site." files=`sed -n 's/^[ ]*A[CM]_CONFIG_HEADER(\([^)]*\)).*/\1/p' $configure_ac` test -z "$files" && files="config.h" touch_files= for f in $files; do case "$f" in *:*) touch_files="$touch_files "`echo "$f" | sed -e 's/^[^:]*://' -e 's/:.*//'`;; *) touch_files="$touch_files $f.in";; esac done touch $touch_files ;; automake) echo 1>&2 "\ WARNING: \`$1' is missing on your system. You should only need it if you modified \`Makefile.am', \`acinclude.m4' or \`$configure_ac'. You might want to install the \`Automake' and \`Perl' packages. Grab them from any GNU archive site." find . -type f -name Makefile.am -print | sed 's/\.am$/.in/' | while read f; do touch "$f"; done ;; bison|yacc) echo 1>&2 "\ WARNING: \`$1' is missing on your system. You should only need it if you modified a \`.y' file. You may need the \`Bison' package in order for those modifications to take effect. You can get \`Bison' from any GNU archive site." rm -f y.tab.c y.tab.h if [ $# -ne 1 ]; then eval LASTARG="\${$#}" case "$LASTARG" in *.y) SRCFILE=`echo "$LASTARG" | sed 's/y$/c/'` if [ -f "$SRCFILE" ]; then cp "$SRCFILE" y.tab.c fi SRCFILE=`echo "$LASTARG" | sed 's/y$/h/'` if [ -f "$SRCFILE" ]; then cp "$SRCFILE" y.tab.h fi ;; esac fi if [ ! -f y.tab.h ]; then echo >y.tab.h fi if [ ! -f y.tab.c ]; then echo 'main() { return 0; }' >y.tab.c fi ;; lex|flex) echo 1>&2 "\ WARNING: \`$1' is missing on your system. You should only need it if you modified a \`.l' file. You may need the \`Flex' package in order for those modifications to take effect. You can get \`Flex' from any GNU archive site." rm -f lex.yy.c if [ $# -ne 1 ]; then eval LASTARG="\${$#}" case "$LASTARG" in *.l) SRCFILE=`echo "$LASTARG" | sed 's/l$/c/'` if [ -f "$SRCFILE" ]; then cp "$SRCFILE" lex.yy.c fi ;; esac fi if [ ! -f lex.yy.c ]; then echo 'main() { return 0; }' >lex.yy.c fi ;; makeinfo) echo 1>&2 "\ WARNING: \`$1' is missing on your system. You should only need it if you modified a \`.texi' or \`.texinfo' file, or any other file indirectly affecting the aspect of the manual. The spurious call might also be the consequence of using a buggy \`make' (AIX, DU, IRIX). You might want to install the \`Texinfo' package or the \`GNU make' package. Grab either from any GNU archive site." file=`echo "$*" | sed -n 's/.*-o \([^ ]*\).*/\1/p'` if test -z "$file"; then file=`echo "$*" | sed 's/.* \([^ ]*\) *$/\1/'` file=`sed -n '/^@setfilename/ { s/.* \([^ ]*\) *$/\1/; p; q; }' $file` fi touch $file ;; *) echo 1>&2 "\ WARNING: \`$1' is needed, and you do not seem to have it handy on your system. You might have modified some files without having the proper tools for further handling them. Check the \`README' file, it often tells you about the needed prerequirements for installing this package. You may also peek at any GNU archive site, in case some other package would contain this missing \`$1' program." exit 1 ;; esac exit 0 drgeo-doc-1.5/mkinstalldirs0000755000175000017500000000132507624117454011524 #! /bin/sh # mkinstalldirs --- make directory hierarchy # Author: Noah Friedman # Created: 1993-05-16 # Public domain # $Id: mkinstalldirs,v 1.1 2003/02/17 08:37:41 hilaire Exp $ errstatus=0 for file do set fnord `echo ":$file" | sed -ne 's/^:\//#/;s/^://;s/\// /g;s/^#/\//;p'` shift pathcomp= for d do pathcomp="$pathcomp$d" case "$pathcomp" in -* ) pathcomp=./$pathcomp ;; esac if test ! -d "$pathcomp"; then echo "mkdir $pathcomp" mkdir "$pathcomp" || lasterr=$? if test ! -d "$pathcomp"; then errstatus=$lasterr fi fi pathcomp="$pathcomp/" done done exit $errstatus # mkinstalldirs ends here drgeo-doc-1.5/drgeniusCommon.tex0000644000175000017500000000701310114442166012416 % This is common part to all native language % of the DrGenius documentation % % % Copyright 2002 Hilaire Fernandes % Licensed under the terms of the FDL % Set constants \setcounter{htmldepth}{5} % Spanish accent \W \HlxAccent{'i}{\xmlsym{iacute}} % Define some macro \newcommand{\HlxIcons}{\drgeniusImagePath/} % First redefine some HyperLatex command \begin{ifhtml} \newcommand{\HlxTopPanel}{\EmptyP{\HlxSeqPrevUrl\HlxUpUrl\HlxSeqNextUrl}{% \xml*{table width="100%" cellpadding=0 cellspacing=2}\xml{tr} \xml*{td bgcolor="##99ccff"}% \EmptyP{\HlxSeqNextUrl} {\xlink{\HlxCallEval{\HlxImage}{\HlxPure{\HlxSeqNextTitle}}{next.png}}% {\HlxSeqNextUrl}}% {\htmlimage[alt=""]{\HlxIcons{}blank.png}}% \xml*{/td}% \xml*{td bgcolor="##99ccff"}% \EmptyP{\HlxUpUrl} {\xlink{\HlxCallEval{\HlxImage}{\HlxPure{\HlxUpTitle}}{up.png}}% {\HlxUpUrl}}% {\htmlimage[alt=""]{\HlxIcons{}blank.png}}% \xml*{/td}% \xml*{td bgcolor="##99ccff"}% \EmptyP{\HlxSeqPrevUrl} {\xlink{\HlxCallEval{\HlxImage}{\HlxPure{\HlxSeqPrevTitle}}{previous.png}}% {\HlxSeqPrevUrl}}% {\htmlimage[alt=""]{\HlxIcons{}blank.png}}% \xml*{/td}% \xml*{td align="center" bgcolor="##99ccff" width="100%"}% \textbf{\HlxThisTitle}% \xml*{/td}% \HlxPanelFields \xml*{/tr}% \xml*{/table}}} \end{ifhtml} % Up to three key word to set an index entry % FIXME: I do not remember what is for the fourth one % index macro for both \newcommand{\drgeniusIndex}[4]{ \texorhtml{\index{#1!#2!#3|#4}} {\index{#1 - #2 - #3}} } % insert a figure (tex and html) \newcommand{\drgeniusFigure}[2]{ \begin{figure}[!ht] \caption{#1} \begin{center}% 5cm \texorhtml{\includegraphics[width=5cm,keepaspectratio=true]{\drgeniusImagePath/#2}} {\htmlimage{./\drgeniusImagePath/#2.png}} \end{center} \end{figure} } \newcommand{\drgeniusFigureSize}[3]{ \begin{figure}[!ht] \caption{#1} \begin{center} \texorhtml{\includegraphics[width=#3cm,keepaspectratio=true]{\drgeniusImagePath/#2}} {\htmlimage{./\drgeniusImagePath/#2.png}} \end{center} \end{figure} } % insert an icon (tex and html) \newcommand{\drgeniusIcon}[1]{ \texorhtml{\includegraphics[width=1cm,keepaspectratio=true]{\drgeniusImagePath/#1}} {\htmlimage{./\drgeniusImagePath/#1.png}} } % insert an image (tex and html) \newcommand{\drgeniusImage}[1]{ \texorhtml{\includegraphics{\drgeniusImagePath/#1}} {\htmlimage{./\drgeniusImagePath/#1.png}} } \newcommand{\drgeoMenu}[1]{\texttt{#1}} \newcommand{\drgeniusMenu}{\drgeoMenu} \newcommand{\drgeniusNote}[1]{\texorhtml{ \begin{center}\begin{tabular}{lp{10cm}} \hline \textbf{\Large (!)} & #1 \\ \hline \end{tabular}\end{center}} {\htmlrule \textbf{\Large (!)} #1 \htmlrule} } \newcommand{\drgenius}[0]{\textsc{Dr.~Geo}} \newcommand{\drgeo}[0]{\textsc{Dr.~Geo}} % Arguments are: % #1 function name \newenvironment{drgeoApi}[1]{\texorhtml{\vspace{0.3cm}\noindent{\fbox{\large \texttt{#1}}}} {{\large \texttt{#1}}}\\\noindent} {\texorhtml{\bigskip}{\htmlrule}} % #1 argument name % #2 argument explanation \newcommand{\drgeoApiIn}[2]{\noindent\texttt{\textit{#1}}: #2 \\ } % #1 explain returned value \newcommand{\drgeoApiOut}[1]{\noindent\textit{\drgeoApiOutLocale}: #1 \\ } \newcommand{\drgeoApiExample}[1]{\noindent\textbf{\drgeoApiExampleLocale}: \\ \noindent\texttt{#1} } \W\begin{iftex} \sloppy %% These definitions work reasonably for A4 and letter paper \oddsidemargin 10mm \evensidemargin 10mm \topmargin 0mm \headsep 10mm \textwidth 14cm \textheight 23cm \footskip 2cm \W\end{iftex} drgeo-doc-1.5/fdl.tex0000664000175000017500000004775607740335755010236 \begin{verbatim} GNU Free Documentation License Version 1.2, November 2002 Copyright (C) 2000,2001,2002 Free Software Foundation, Inc. 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 0. PREAMBLE The purpose of this License is to make a manual, textbook, or other functional and useful document "free" in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others. This License is a kind of "copyleft", which means that derivative works of the document must themselves be free in the same sense. It complements the GNU General Public License, which is a copyleft license designed for free software. We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should come with manuals providing the same freedoms that the software does. 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It allows users to create geometric figures that can be manipulated with respect to geometric rules. The program is useable with students from the primary through secondary levels. \drgeniusFigureSize{\drgeo welcome screen}{fig1}{8} To create a new empty geometric figure, the user clicks on the first (on the left) button in the toolbar. Alternatively, a new figure can be created using the menu item \drgeniusMenu{File->New->Figure} from the menu bar. When a new figure is created, a new toolbar with a set of six icons appears. The last item (on the right) in the toolbar is an option menu; it is used to adjust the scale of the current geometric figure. \drgeniusFigureSize{An empty geometric figure}{fig2}{6} The six icons correspond to different types of functions. These functions are described in the next chapter. \drgeniusFigureSize{A \drgeo figure and its description}{fig50}{8} With each figure, a pane is available. By default the pane is pushed to the extreme left so that only the representation of the figure is visible. At any moment, the user can push the pane to the right to make visible the figure description. A figure description is a tree list. The tree is composed of all the elements of the figure. The elements relative to other elements can be expanded by pressing the '+' sign, that way the user can visualize the parents of this element. \chapter{Basic Functions} This chapter describes the tools used to construct geometric figure. At the end of this chapter, customisation is presented. \section{Construction Tools} These tools are split into six groups available from the second toolbar of \drgenius. \drgeniusFigureSize{\drgeo{}'s tool categories and their descriptions}{fig3}{12} \xname{point_tools} \subsection{Point Tools} \subsubsection{Free Point} \drgeniusIcon{fig4} Create a free point on an area or a free point on an uni-dimensional object. In the first case, the created point can be moved anywhere in the figure area. To build the point the user just clicks on the background. In the latter case, it is constrained to the uni-dimensional object (line); it is stuck to the object. To build this kind of point the user clicks over a line (i.e. straight line, ray, segment, circle, arc, etc.). \subsubsection{Midpoint} \drgeniusIcon{fig5} Create the middle of two points or the middle of a segment. In the first case, the user selects two points. In the latter case the user just selects a segment. \subsubsection{Intersection} \drgeniusIcon{fig6} Create the intersection point(s) of two line objects. The user needs to select two line objects. \subsubsection{Point by its Coordinates} \drgeniusIcon{fig7} Create a point defined by its coordinates. The user needs to select two numbers, the first selected number is the abscissa; the second one is the ordinate. \xname{line_tools} \subsection{Line Tools} \subsubsection{Straight Line} \drgeniusIcon{fig8} Create a straight line defined by two points. The user selects two points. \subsubsection{Ray} \drgeniusIcon{fig9} Create a ray (half-line) defined by two points. The user selects two points; the first point is the origin, the second one belongs to the ray. \subsubsection{Segment} \drgeniusIcon{fig10} Create a segment given by two points. \subsubsection{Vector} \drgeniusIcon{fig11} Create a vector given by two points. The user selects two points. The first point is the origin; the second one is the extremity. \subsubsection{Circle} \drgeniusIcon{fig12} Create a circle. The user can create a circle from different selections: \begin{enumerate} \item the centre and a point on the circle; \item the centre and a number (the radius of the circle); \item the centre and a segment which length is the radius of the circle. \end{enumerate} \subsubsection{Arc Circle} \drgeniusIcon{fig13} Create an arc defined by three points. The first selected point is the origin of the arc; the third one is the extremity and the second one is a point on the arc. \subsubsection{Locus} \drgeniusIcon{fig14} Create a locus defined by two points. The user selects two points, one is a free point on a line and the other one is a constrained point of the first one (i.e. when one moves, the other one does as well). \subsubsection{Polygon} \drgeniusIcon{fig15} Create a polygon defined by n points. The user selects n+1 points delimiting the polygon. The first and last selected points are the same; this tells \drgenius that the selection is over. The polygon object is not an object like the other lines; it is not possible to place a point on it or to construct an intersection between a polygon and another line object. \xname{transformation_tools} \subsection{Transformation Tools} \subsubsection{Parallel Line} \drgeniusIcon{fig16} Create a line passing through a point and parallel to a "direction" (another line or line segment moving in a "direction"). The user selects a point and a direction (i.e. a straight line, a ray, a segment or a vector). \subsubsection{Perpendicular Line} \drgeniusIcon{fig17} Create a line perpendicular to a direction and passing through a point. The user selects a point and a direction (i.e. straight line, a ray, a segment or a vector). \subsubsection{Axial symmetry} \drgeniusIcon{fig18} Create the image of an object by an axial symmetry. The user selects an object to transform and the axis of symmetry (a straight line). When the user wants to construct the image of a straight line, s/he must first select it with the mouse; the first selected line is the line that which will be transformed. \subsubsection{Central Symmetry} \drgeniusIcon{fig19} Create the image of an object by a central symmetry. The user selects the object to transform and the centre of its symmetry (a point). When the user wants to construct the image of a point, s/he must first select it (with the mouse). The transformation will then be performed on this point. \subsubsection{Translation} \drgeniusIcon{fig20} Create the image of an object by translation. The user selects the object to transform and the vector of translation. When the user wants to construct the image of a vector, s/he must select it (with the mouse). The transformation will then be performed on this vector. \subsubsection{Rotation} \drgeniusIcon{fig21} Create the image of an object by a rotation. The user selects the point to transform, the centre and the angle of the rotation. When the user wants to create the image of a point, s/he must first select it (with the mouse). The transformation will then be performed on this selected point. The angle can be selected from different type of value: \begin{itemize} \item \textbf{numeric value}: in this case the angle is expressed in radians. Examples of numeric values are: free value, distance between two points, a segment length, a coordinate, a value returned by a Dr.~Genius Guile Script, etc.; \item \textbf{a geometric angle formed by three points}: in this case the angle is expressed in degrees. Be aware that in this case the angle can only fall within [0~;~180]; \item \textbf{an oriented angle formed by two vectors}: in this case the angle is expressed in degrees between [0~;~360[. \end{itemize} \subsubsection{Scale} \drgeniusIcon{fig22} Create the image of a an object by a scale transformation (homothetie). The user selects the point to transform, the centre and the factor (i.e. a number). When the user wants to create an image of a point, s/he must first select it; the transformation will be performed on this selected point. \xname{numeric_tools} \subsection{Numeric Tools} \subsubsection{Distance, Length \& Number} \drgeniusIcon{fig23} Create a numeric value. The numeric value can be computed or user- edited depending on the user's selections: \begin{enumerate} \item two points: distance between these two points; \item a segment: the length of this segment; \item a vector: the vector's magnitude; \item a circle: the length of the circle; \item an arc circle: the length of the arc; \item a straight line: the slope of the line; \item a straight line and a point: the distance between the line and the point; \item a click on the background permits the user to enter a new value (i.e. a free value). \end{enumerate} \subsubsection{Angle} \drgeniusIcon{fig24} Create an angle defined by three point or two vectors. In the first case, the resulting angle is non oriented (i.e. a geometric angle in the range [0~;~180]. In the second case, the angle is oriented and it is within the range ]-180~;~180]. \subsubsection{Coordinates} \drgeniusIcon{fig25} Create the coordinates of a point or a vector. This tool creates both the abscissa and the coordinate. \subsubsection{\drgenius Guile Script} \drgeniusIcon{fig49} Create a \drgenius Guile Script. The script receives input of n objects. It eventually returns a number, printed in the figure. A script can be used for its side effects or for its returned value. The \drgenius Guile Scripts are covered in details in the \link{Chapter Advanced Features}[ Chapter \Ref]{advancedFeatures} and exactly at \link{Section Script}[ Section \Ref, page \Pageref]{script}. \xname{macroconstruction_tools} \subsection{Macro-Construction Tools} \subsubsection{Setting a Macro-Construction} \drgeniusIcon{fig26} Extract a construction sequence of a figure and turn it as a macro-construction. \subsubsection{Executing a Macro-Construction} \drgeniusIcon{fig27} Execute (i.e. ``run'' or ``play'') a pre-built macro-construction. The macro-construction can be either newly created or loaded from file. \drgeniusNote{Macro-Constructions are exposed in \link{Section Macro-Construction}[Section \Ref, page \Pageref]{macroConstruction}.} \xname{other_tools} \section{Other functions} \subsection{Moving figure} Figure can be moved by pressing CONTROL key and button 1 of the mouse. \subsection{Moving object} \drgeniusIcon{fig28} An object can be moved by draggin it. The figure is then recomputed according to its properties. Almost every type of geometric object can be moved. When necessary, \drgenius performs a reverse dragging. For example, this occurs when the user moves a line defined by two points, \drgenius will move the two points according to the desired line position. \subsection{Deleting Objects} \drgeniusIcon{fig30} An object on the figure can be deleted when activating this menu. Eventually, the user can undelete using the undo function from the toolbar or application menu. By default the undo level is set to 10 but the user can adjust this value from the preference dialog. \xname{editing_object_styles} \subsection{Editing Object Styles} \drgeniusIcon{fig29} Each object owns such style attributes as colour, thickness, label, size or shape. Additionally, it is possible to hide an object temporarily without deleting it. For example, it can be useful to hide intermediate constructions without deleting them. All these attributes can be adjusted from a dialog activated when the user selects an object in the figure. The point style dialog concerns any kind of point object. From it, it is possible to adjust its color, shape, size, name and visibility. \drgeniusFigure{The style dialog for point object}{fig31} The line style dialog concerns straight line, ray, segment, vector, circle, arc circle, locus. From it, it is possible to adjust the color, style, name and visibility. \drgeniusFigure{The style dialog for line object}{fig32} The numeric \& polygon style dialog concerns all kind of values (user edited, computed by user's \drgenius Guile Script or representing geometric measure) and polygon shape. \drgeniusFigure{The style dialog for numeric \& polygon objects}{fig33} \subsection{Editing Object Properties} \drgeniusIcon{fig52} Some objects own properties adjustable by the user. When the user clicks on such objects, an appropriate dialog appears. Actually the following objects own user adjustable properties: \begin{enumerate} \item Free point on the area: abscissa and coordinate can be edited;\\ \drgeniusFigure{Edit free point coordinates}{fig34} \item Free value: its value can be edited;\\ \drgeniusFigure{Edit free value}{fig36} \item Script: its code can be edited.\\ \drgeniusFigure{Edit a script}{fig35} \end{enumerate} \section{User's Preferences} \xname{default_behaviour} \subsection{Default Behaviour} \label{default_behaviour} \drgenius default behaviour can be customised in several ways. To adjust the preferences, the user goes to the menu item \drgeniusMenu{Edit->Preferences...} to open the preferences dialog. The dialog is composed of a notebook with two pages: \begin{enumerate} \item The first page concerns global preferences:\\ \drgeniusFigureSize{Global preferences}{fig37}{8} Actually, the user can only adjust the default name of a session to be saved on disk. \item The second page is about geometric figure preferences:\\ \drgeniusFigureSize{Geometric figure preferences}{fig38}{8} From this page, a wide range of option can be adjusted: \begin{itemize} \item The number of Undo/Redo level; \item The default figure name to be used when a new figure is created. The \%d is replaced by an integer value handled by \drgenius, this value is incremented at each newly created figure; \item Several default name for single figure file and LaTeX/PostScript export; \item In the superior area of the page, another notebook allows the user to adjust the default object style of each figure item (geometric or numeric ones). The concerned styles are colour, shape, size and style. \end{itemize} \end{enumerate} \subsection{Other Preferences} In addition to changing the default behaviour of \drgenius, the user can change the name of a figure from the menu item \drgeniusMenu{Edit->Rename}. \drgeniusFigure{Renaming a figure view}{fig39} \chapter{Advanced Features} \label{advancedFeatures} In this chapter we present features used to extend the cabilities of \drgenius in various ways. The first is macro-construction; it allows the extraction of a construction logic in a record. Then, this record can be repeated or saved as a file. The \drgenius Guile Script features are the other means for extending \drgenius. These scripts are really figure items like the other geometric items. They receive as input, user selected figure item references and they return values, plugged into figures. \drgenius Guile Scripts can be useful for their returned values or their side effects; which really depends on what the user wants to achieve. The last feature is user-interface customisability. The idea is to give the teacher the cability to prepare geometric figure files with tools taken from the Dr.~Genius toolbar and contextual menu. This capability may help in achieving a desired ``pedagogical effect'' \xname{using_macro} \section{Macro-Construction} \label{macroConstruction} Macro-constructions are a bit like a procedure which receives as input figure items and then returns one or more figure items, constructed by the macro-construction. They are built on a model defined by the user. This means that the user has to build a construction sequence only once. Then she can tell \drgenius that she wants this sequence to be recorded in a macro-construction. To record a construction sequence, \drgenius needs to know which are the initial items of the sequence and the resulting items. Of course the resulting items must depend \textit{only} on the initial items; otherwise Dr.~Genius would not be able to deduce the resulting items from the initial ones. Using its knowledge of the initial and resulting items, \drgenius deduces the construction sequence and saves it in a macro-construction. The user can then execute this macro-construction simply by inputting (initial) items (they must match the type) in the figure. The macro-construction can then build the resulting items. \drgeniusNote{Invisible intermediate figure items are also built by the macro-construction. These items are necessary to build the resulting items.} To illustrate the macro-construction feature, we will use an example in which the user wants to record the construction of a circle with a given center which passes through three points, also given. \drgeniusFigureSize{Our initial figure}{fig40}{4} Before constructing the macro-construction, the user needs to construct the final figure; it is used as a pattern from which to build the macro-construction. \drgeniusFigureSize{Our figure with the resulting construction}{fig41}{4} \subsection{Constructing a Macro-Construction} At this point, the construction sequence is done. Now, the user needs to tell Dr.~Genius that she wants to create a macro-construction from this sequence. She can call the \drgeniusMenu{Construct a macro} function from the icon \drgeniusIcon{fig26} or from the contextual menu in the figure view. From the wizard dialog, the user selects the input \& output parameters, the name and description of the macro-construction. \drgeniusFigureSize{The 1st page of the wizard dialog to construct a macro-construction}{fig42}{6} The second page of the dialog is used to select the input parameters. In our example, these are the three initial points. The user just needs to go to this second page and she can select the three points in the figure. The selected items will blink. \drgeniusFigureSize{The 2nd page, the three points are already selected}{fig43}{6} From the 3rd page, she selects the output parameters. In our example, we want the circle and its centre as the result of the macro-construction. She proceeds as in the case of the input parameters to select them. \drgeniusFigureSize{The 3rd page, the circle and its centre are already selected}{fig44}{6} In the 4th page, the user enters the name and the description of the macro-construction. This information is displayed when the user executes a macro-construction, so it helps to distinguish macro-construction between them. \drgeniusFigureSize{The 4th page, the name and description of the macro-construction}{fig45}{6} From the last page of the wizard dialog (the 5th one), the user can terminate the creation by pressing the \texttt{Finish} button. Alternatively, she can return to previous pages to adjust the macro-construction parameters. \drgeniusNote{If the input \& output parameters selections do not match (\drgenius cannot extract the logic of the construction), the macro-construction cannot be built. In such a case, the user needs to reconsider the input and output parameters selection. She can go back to the 2nd and 3rd page of the wizard dialog to adjust her choices.} At this point the macro-construction is built and recorded in \drgenius. In the next section, we will see how to use this macro-construction. \subsection{Executing a Macro-Construction} To execute a macro-construction, the user calls the \drgeniusMenu{Execute pre-build macro} function from the icon \drgeniusIcon{fig27} or from the contextual menu in the figure view. From the wizard dialog, the user selects the macro-construction. In the 2nd page, she selects the macro-construction from the list in the top area of the dialog. Once a macro-construction is selected, she can directly click on the input parameters in the figure. As soon as all the necessary input parameters are selected, the macro-construction is executed and the final parameters appear. \drgeniusFigureSize{The user selects the input parameters directly in the figure}{fig46}{6} In our example, the macro-construction needs three input parameters (three points) and it builds a point and a circle. To execute our macro-construction, we need a figure with a least three points. \drgeniusFigureSize{A figure with three points}{fig47}{4} Once our macro-construction is applied to these three points, we get the desired circle and its centre. \drgeniusFigureSize{The resulting figure with the circle and its centre}{fig48}{4} \xname{drgenius_guile_script} \section{\drgenius Guile Script} \label{script} \drgenius is Guile aware. This means it is possible to execute Guile scripts within \drgenius. But what is Guile? From the Guile manual: \begin{quote}{\em Guile is an interpreter for the Scheme programming language, packaged for use in a wide variety of environments.} \end{quote} The following citation describes accurately how is used Guile within \drgenius: \begin{quote}{\em Like a shell, Guile can run interactively, reading expressions from the user, evaluating them, and displaying the results, or as a script interpreter, reading and executing Scheme code from a file. However, Guile is also packaged as an object library, allowing other applications to easily incorporate a complete Scheme interpreter. An application can use Guile as an extension language, a clean and powerful configuration language, or as multi-purpose "glue", connecting primitives provided by the application.} \end{quote} In \drgenius, an API is available from the Guile interpretor. This API is a set of hooks in the geometric engine. Therefore the user can write scripts to manipulate figure items (geometric and numeric). Also, as scripts are figure items like any other, they do not need to be saved as separate files. They are saved in the figure file. In the following, we will use the DGS acronym for \drgenius Guile Script. \subsection{Creating a DGS} \subsection{More about DGS} \section{User interface customisation} \label{user_interface-custome} \chapter{Saving and Loading Constructions} Constructions can be saved in two ways. One construction per file or a construction set per file (i.e. a Dr.~Genius session). \section{Saving one construction} From the menu \drgeniusMenu{File->Save} or \drgeniusMenu{File->Save As...}, a file can be saved containing the figure under the active view. \drgeniusNote{Dr.~Genius can work with several figures at the same time. The user can switch from one figure to another one by clicking on the corresponding tabs.} With the second menu, the user can change the name of the saved document. \drgeniusNote{The default file name proposed to the user by Dr.~Genius can be changed from the \drgeniusMenu{Edit->Preferences...} menu. For more information see \link{Section Defaut Behaviour}[Section \Ref, page \Pageref]{default_behaviour}.} \section{Saving a Session} A session is a set of Dr.~Genius data the user wants to save in one shot in a file. It allows teacher to organise a set of data (figure, macro-construction, note) in one file, so it is more convenient to re-open such data. From the \drgeniusMenu{File->Save Multiple} menu, the user can display the session dialog. \drgeniusFigureSize{The Dr.~Genius session dialog}{fig51}{8} The list of all active data is saved in this file and presented in a table. The first colon represents the type of data contained in Dr.~Genius. The second one represents the name of the data. \drgeniusNote{Actually, a session can contain three kinds of data: 2D interactive figure, macro-construction and text.} Then users can decide to select one by one the data to save from the list. Then she can press the \drgeniusMenu{Save Session} button. Alternatively, she can save all the data by pressing the \drgeniusMenu{Save All} button. \drgeniusNote{\drgeniusMenu{File->Save Multiple} menu is the only way to save macro-constrcutions to a file.} \section{Loading Constructions} \chapter{Cook Book} \W \begin{iftex} \appendix \listoffigures \W \end{iftex} \end{document} drgeo-doc-1.5/c/figures/0002777000175000017500000000000010117134566010663 5drgeo-doc-1.5/c/figures/blank.png0000644000175000017500000000012410117134566012367 ‰PNG  IHDR I´è·PLTE™ÌÿõÉj IDATxÚc`Ü Žû±´IEND®B`‚drgeo-doc-1.5/c/figures/fig0.png0000644000175000017500000007240310117134566012136 ‰PNG  IHDR³ È4Ê‘bKGDÿÿÿ ½§“ pHYs  d_‘tIMEÓ&ü„– IDATxœì½wxœÕ•?~ÛÛ¦fFeÔ,É–ä"¹÷Ží˜n!›LØ$¦6›ÝR d³dɆ$” $SŒ1 6î½È²%Ëê½4ým·üþÛqØ<ùfÇüøÂ_ÆGÌø1ã#üe|ؘÁ9¸ðÊáÇ>|©ä¹|ñ¡bÆñ57ßò‰›nºé[ßú–mÛ™‹Ï<óÌ÷¿ÿý§žzêÒÊvÙáÃÃŒD"ñô“OÍ›3÷¡‡hlnÊ\衇îºë®;w&‰K+áåøaÊŽ äää\øæüõÚÚÚ+¯¼òÒ‰vùáCÅŒ0†øðŒ&‚snYæ{.Rj_a.SK-À£¿¿÷¹çžkmkP¸œîk®º¶  àåW^lnn‚¹Ýî©S¦¯Y³Æëõ_jIÿÞñ¡MÎœ9}ßO~‹GfÏ¥ªRKK[_wÄét%“±IUåD!‘H¤¥±uÁÜÅßýÎ/µ°ïøð0£¯¯ç»ßùV Û»dùlM.lÓ xrã™ÓM?øñ·Ý~udt@×SÉ„ùîÛûnýäçnºñS—Zä¿k|xüŒD"!\¹òŠPv@V°nÅ©0ŠÇå]uÍê²²¯×ð¨Nâñ)ÅeáÝ{v^jyÿÞñáñ3„’"»]~¯ÛIB¹‰Œ®¼ryQa™×ë§$„‚r46\X”÷Ö«û¾õí„愲?ñ‰[¦Lžv©[ð÷…3"‘Ñd"½gÏ>ÀãÏvyü~R=ý½1„,ËãJ <îc¶Ó%Fã©á¬€ on;uÇ?~jé’•·ß~ÇÄÊêKÝŽ¿|x˜±cÇŽÚÚSýýý²*Åâ#·®ÿTý©†mïìÊÍÎ#„! b7ÜxMYe8++kê´I Móg9t;5›Nloéرýà·¾{æþ?X>aÒ¥nÊß><èg?ûÙÆÆƯ}íkN·kË–Ímm-½½½_üÂÅÅ%ŠT*µk÷Ž={ßýç¯~®¨´ÐH¥N9iDt#)£6ˆÇÌw·îK%Ù·¾ù½Ù³\êÖ\zàï}ï{—Z†1Àƒ>ø‡?üᦛÖÍ™3@dšÖ[o¼¹há¢õë?ëñxœN‡Óéôû³âñÄ›o¾½`Þ‚‚‚°¬`9BÀ•\\’ß?0°åõ-¥%¥…Å—ºM—†Øä¿ø¯‡~xÎœ9«V­R… Ì9×4ç²eWhš&˲ªª²,{½þysø|Á]»ö:.EQTÅ¡(ª¢(ªªb"\°hª' Ý÷À÷jOþÿ}âþòf†a¦ùðÏ{üY&÷Üsw87_’EQ¡‚‚¡$I„ȪêPUc\TX<44dsf3†‘$E²DEQ 7Z¼t†' }ûÞoœª;z©Ûw)q3£ ë'÷ïwOþ&;Ç»tÙ¢@ €8çc‡ÃÀsÎcœsιmÛœsjš†a˜¦Éƒ$IDÓdcèp“EKfÊNñÃûî=^sà7òÒáreü÷xòù¿|ÕlÕÅ|~—®ë6£Î9åŒB)5mË´-˲’Éd$‰Åb–irÎ`€S!c !Œ!Q$Õ¡:5Uv¸Ñ‚ESu:òí{¿14Ü{©Ûzip¹2ãñ'~ùäÓ¿^´|f0×Mn3+wuuõ÷÷'‰ÑÑQ˲úúú Ãhkkkmmíëëëíí6 =c<!IRÙ©ÈNB‰hªêrh.‡C æx–^1_ë«_¿³«»õR7÷à²dÆ™¦úGýå‚¥ÓÆ@bkNµ¹¹©££ã_¾~ÏW¾ò•‘‘‘¡A!„®ë=]½ýü÷ßÿ¶mÛ¢Ñ.hÚÐ Á€ÆcB°"Ëš,9’dIÓ4·Óéu¹\9¹¾ÕkÇC÷=ðýÖö¦KÝè—%3žþýo]~¥¸," P<®°³«5tvv¶µµõööú|žd2žJ%º»;kkk;;Û-Ûõöµå™Ô›AŒ%Œ$YV$¢!(¬¨ŠKSÝN—z,yºáø?ýÑ¥nôË/ŸÑÑÙü³Ÿÿhî‚j‡ "yÝþžž!·Ë³öª«gL›ÑÛÛÓÞÞætiû÷ï›4qREE¹Ã¡ù³¼”[=½ý»fuV–c„‘Dˆ,!LA#Œ Œ1ÁA P5œÎݳk_4Ÿ?oÑ¥ný‡Ë/;^S{"Èöx¼VDf¢Ùs¦Ö>ØÛÛ‰ ¬Ïœ3Û¶mïl=''ÇëWû{bm# ÚËV.ôg9`K@P†"X  sN$!ãvv^ÖŠÕK^ßòò‚yóçÍ]z©ðáòcÆÉ“'‚!Ÿ¦©‡Óár9‡aØ „ ûzãñ¤ìó'WM˜œëË^uòøé涓”RÍ­L™Q’›*..öxœA!„”S*øYf@…àcBUÓ”3”_ÌÎu¿øÒs“ü¾Ð%VÁ‚ËŒ==]5'Žåå{½^§ÃéÔ\NÍåuŸ7+”J¤-‹ Á$IÂ2 dû|^K79’„eUr{œ>W’±¶-!„ŒsN™ÅÃc$Aˆ€a…D4Ue¶ÍÜ>6±ª|÷ö£;vl»áú[.µ>\f̈ÅGS©d(T ˲ªjÑ$¢I’¬9¼^O¶eê–eÙ¶Å9å@pN1$ÂåÀcŒ%;Y–‡3„”65,ۦ̢”bŒâÔÓv*n„ó 4·"Ë’B¶ÂlÛ„|E¥ù^~vöì¹ù%—Z—3âñX<Íä¹eÉ‘ @"H6L“`Õå÷!·cœ3ÛmsΡÌxÁ¸Í˜Å˜mz* Ô2m˶¥\UUE²ëëkŽž ç-[¶¤¸´˜H’CuÚÔt¹\EŹGÕ=þÄ#_øÜ—òr /µ2...³ØäLsýþƒ»ª¦•û³|)¶Åd,˪–™Qˆ 8”ˆ,aEŠ*«šâЧ¢j’D„Œ[5 3HÆâ‘T:•LêñQ½¥©ûõMÛª ý^Ÿ;¿ (Ož®oÊËÉw{]D" Î)‚RVêt]}CaQAv(÷Rëã"â2³”ZŠCQU!ÔÞÖµmÛ΂܂Ûo¿b(8ºíri¶m"Â’$qAMªs.8§¦i–‘HDÉX:‰uvô ôŽ Æ#I¿ß×ÚÒ³`ál╼žÀÞ‡b±d˜$€,«N‡›@åDèTÜõu?þ›»ïþFQ~iF0ÃLÇF#CCC###étú|šB …æ̽üÂÝËŒ¡ÌP‚‘4<=S×ÜÕÖ{Ûmë%Žc±øÛoîØ·oÿ-ÿpó´éS€ ‹ J-.lÛ¶lféf:L¦zg{ÿ‰š“}}}n·¯8\ù©_ýü³/66ŸqÈÞ¢p™i¥Ç’sóp¤ÉàF Œ‘ê’î©ùå/ÿë‹_¸«¥¥uÇöí­mÌN§õ¸L$ιeQ!d˜ö¤IU[{ÃÇÖ^w©õ÷¿ÀeÆ a*•JºÂçó„óó  PwwO[[[SSÓÌYSdBpjÛ”ZŒ[–ÖÍt2™Œ ;VS_×àr;æ/˜[_²÷ÝšS§ê¿ÿý|ñ‹ÿ´tÑŠP0lÙ©TRBpÊB„%EAK…¢(ÅñÚ«[OÔÔôt÷MžTîrJŒ@VÀëò:‚e AÀ°¬¡Ú‡jkjêNž¸ç_¿{©Uø·âòc†aŒ1ˆDiYÑ_Xïqz§Çyõµk'M©œ6} ƈAA™I™E™iØ)]O§“é¾Á£·u¶M®ï¸ ¤ç.šñÎ{®»æú%K–nÙòæç oW4G*±m3Ó"ʉH.q. 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IntroductionTopContents

Contents

Any comments/remarks?
Or you are volunteer to write part of the manual.
-> Contact Hilaire Fernandes at OFSET ( ) or join the DR. GEOmailing list.

IntroductionTopContents
drgeo-doc-1.5/c/default_behaviour.html0000644000175000017500000000623210117134566013512 Dr. Geo User's Manual -- Default Behaviour
Other PreferencesUser's PreferencesDefault Behaviour

Default Behaviour

DR. GEOdefault behaviour can be customised in several ways. To adjust the preferences, the user goes to the menu item Edit->Preferences... to open the preferences dialog.

The dialog is composed of a notebook with two pages:

  1. The first page concerns global preferences:

    Global preferences

    Actually, the user can only adjust the default name of a session to be saved on disk.
  2. The second page is about geometric figure preferences:

    Geometric figure preferences

    From this page, a wide range of option can be adjusted:
    • The number of Undo/Redo level;
    • The default figure name to be used when a new figure is created. The %d is replaced by an integer value handled by DR. GEO, this value is incremented at each newly created figure;
    • Several default name for single figure file and LaTeX/PostScript export;
    • In the superior area of the page, another notebook allows the user to adjust the default object style of each figure item (geometric or numeric ones). The concerned styles are colour, shape, size and style.
Any comments/remarks?
Or you are volunteer to write part of the manual.
-> Contact Hilaire Fernandes at OFSET ( ) or join the DR. GEOmailing list.

Other PreferencesUser's PreferencesDefault Behaviour
drgeo-doc-1.5/c/drgenius_11.html0000644000175000017500000000360610117134566012145 Dr. Geo User's Manual -- Straight Line
RayLine ToolsStraight Line

Straight Line

Create a straight line defined by two points. The user selects two points.

Any comments/remarks?
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-> Contact Hilaire Fernandes at OFSET ( ) or join the DR. GEOmailing list.

RayLine ToolsStraight Line
drgeo-doc-1.5/c/drgenius_12.html0000644000175000017500000000402010117134566012135 Dr. Geo User's Manual -- Ray
SegmentLine ToolsStraight LineRay

Ray

Create a ray (half-line) defined by two points. The user selects two points; the first point is the origin, the second one belongs to the ray.

Any comments/remarks?
Or you are volunteer to write part of the manual.
-> Contact Hilaire Fernandes at OFSET ( ) or join the DR. GEOmailing list.

SegmentLine ToolsStraight LineRay
drgeo-doc-1.5/c/drgenius_13.html0000644000175000017500000000364210117134566012147 Dr. Geo User's Manual -- Segment
VectorLine ToolsRaySegment

Segment

Create a segment given by two points.

Any comments/remarks?
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VectorLine ToolsRaySegment
drgeo-doc-1.5/c/drgenius_14.html0000644000175000017500000000400210117134566012137 Dr. Geo User's Manual -- Vector
CircleLine ToolsSegmentVector

Vector

Create a vector given by two points. The user selects two points. The first point is the origin; the second one is the extremity.

Any comments/remarks?
Or you are volunteer to write part of the manual.
-> Contact Hilaire Fernandes at OFSET ( ) or join the DR. GEOmailing list.

CircleLine ToolsSegmentVector
drgeo-doc-1.5/c/drgenius_15.html0000644000175000017500000000420510117134566012145 Dr. Geo User's Manual -- Circle
Arc CircleLine ToolsVectorCircle

Circle

Create a circle. The user can create a circle from different selections:

  1. the centre and a point on the circle;
  2. the centre and a number (the radius of the circle);
  3. the centre and a segment which length is the radius of the circle.
Any comments/remarks?
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Arc CircleLine ToolsVectorCircle
drgeo-doc-1.5/c/drgenius_16.html0000644000175000017500000000405710117134566012153 Dr. Geo User's Manual -- Arc Circle
LocusLine ToolsCircleArc Circle

Arc Circle

Create an arc defined by three points. The first selected point is the origin of the arc; the third one is the extremity and the second one is a point on the arc.

Any comments/remarks?
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LocusLine ToolsCircleArc Circle
drgeo-doc-1.5/c/drgenius_17.html0000644000175000017500000000412210117134566012145 Dr. Geo User's Manual -- Locus
PolygonLine ToolsArc CircleLocus

Locus

Create a locus defined by two points. The user selects two points, one is a free point on a line and the other one is a constrained point of the first one (i.e. when one moves, the other one does as well).

Any comments/remarks?
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PolygonLine ToolsArc CircleLocus
drgeo-doc-1.5/c/drgenius_18.html0000644000175000017500000000423510117134566012153 Dr. Geo User's Manual -- Polygon
Line ToolsLocusPolygon

Polygon

Create a polygon defined by n points. The user selects n+1 points delimiting the polygon. The first and last selected points are the same; this tells DR. GEOthat the selection is over. The polygon object is not an object like the other lines; it is not possible to place a point on it or to construct an intersection between a polygon and another line object.

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Line ToolsLocusPolygon
drgeo-doc-1.5/c/drgenius_20.html0000644000175000017500000000413510117134566012143 Dr. Geo User's Manual -- Parallel Line
Perpendicular LineTransformation ToolsParallel Line

Parallel Line

Create a line passing through a point and parallel to a "direction" (another line or line segment moving in a "direction"). The user selects a point and a direction (i.e. a straight line, a ray, a segment or a vector).

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Perpendicular LineTransformation ToolsParallel Line
drgeo-doc-1.5/c/drgenius_21.html0000644000175000017500000000423110117134566012141 Dr. Geo User's Manual -- Perpendicular Line
Axial symmetryTransformation ToolsParallel LinePerpendicular Line

Perpendicular Line

Create a line perpendicular to a direction and passing through a point. The user selects a point and a direction (i.e. straight line, a ray, a segment or a vector).

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Axial symmetryTransformation ToolsParallel LinePerpendicular Line
drgeo-doc-1.5/c/drgenius_22.html0000644000175000017500000000444710117134566012153 Dr. Geo User's Manual -- Axial symmetry
Central SymmetryTransformation ToolsPerpendicular LineAxial symmetry

Axial symmetry

Create the image of an object by an axial symmetry. The user selects an object to transform and the axis of symmetry (a straight line). When the user wants to construct the image of a straight line, s/he must first select it with the mouse; the first selected line is the line that which will be transformed.

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Central SymmetryTransformation ToolsPerpendicular LineAxial symmetry
drgeo-doc-1.5/c/drgenius_23.html0000644000175000017500000000441410117134566012146 Dr. Geo User's Manual -- Central Symmetry
TranslationTransformation ToolsAxial symmetryCentral Symmetry

Central Symmetry

Create the image of an object by a central symmetry. The user selects the object to transform and the centre of its symmetry (a point). When the user wants to construct the image of a point, s/he must first select it (with the mouse). The transformation will then be performed on this point.

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TranslationTransformation ToolsAxial symmetryCentral Symmetry
drgeo-doc-1.5/c/drgenius_24.html0000644000175000017500000000434010117134566012145 Dr. Geo User's Manual -- Translation
RotationTransformation ToolsCentral SymmetryTranslation

Translation

Create the image of an object by translation. The user selects the object to transform and the vector of translation. When the user wants to construct the image of a vector, s/he must select it (with the mouse). The transformation will then be performed on this vector.

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RotationTransformation ToolsCentral SymmetryTranslation
drgeo-doc-1.5/c/drgenius_25.html0000644000175000017500000000551410117134566012152 Dr. Geo User's Manual -- Rotation
ScaleTransformation ToolsTranslationRotation

Rotation

Create the image of an object by a rotation. The user selects the point to transform, the centre and the angle of the rotation. When the user wants to create the image of a point, s/he must first select it (with the mouse). The transformation will then be performed on this selected point.

The angle can be selected from different type of value:

  • numeric value: in this case the angle is expressed in radians. Examples of numeric values are: free value, distance between two points, a segment length, a coordinate, a value returned by a Dr. Genius Guile Script, etc.;
  • a geometric angle formed by three points: in this case the angle is expressed in degrees. Be aware that in this case the angle can only fall within [0 ; 180];
  • an oriented angle formed by two vectors: in this case the angle is expressed in degrees between [0 ; 360[.
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ScaleTransformation ToolsTranslationRotation
drgeo-doc-1.5/c/drgenius_26.html0000644000175000017500000000417510117134566012155 Dr. Geo User's Manual -- Scale
Transformation ToolsRotationScale

Scale

Create the image of a an object by a scale transformation (homothetie). The user selects the point to transform, the centre and the factor (i.e. a number). When the user wants to create an image of a point, s/he must first select it; the transformation will be performed on this selected point.

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Transformation ToolsRotationScale
drgeo-doc-1.5/c/drgenius_28.html0000644000175000017500000000466610117134566012164 Dr. Geo User's Manual -- Distance, Length & Number
AngleNumeric ToolsDistance, Length & Number

Distance, Length & Number

Create a numeric value. The numeric value can be computed or user- edited depending on the user's selections:

  1. two points: distance between these two points;
  2. a segment: the length of this segment;
  3. a vector: the vector's magnitude;
  4. a circle: the length of the circle;
  5. an arc circle: the length of the arc;
  6. a straight line: the slope of the line;
  7. a straight line and a point: the distance between the line and the point;
  8. a click on the background permits the user to enter a new value (i.e. a free value).
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AngleNumeric ToolsDistance, Length & Number
drgeo-doc-1.5/c/drgenius_29.html0000644000175000017500000000430310117134566012151 Dr. Geo User's Manual -- Angle
CoordinatesNumeric ToolsDistance, Length & NumberAngle

Angle

Create an angle defined by three point or two vectors. In the first case, the resulting angle is non oriented (i.e. a geometric angle in the range [0 ; 180]. In the second case, the angle is oriented and it is within the range ]-180 ; 180].

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CoordinatesNumeric ToolsDistance, Length & NumberAngle
drgeo-doc-1.5/c/drgenius_30.html0000644000175000017500000000404710117134566012146 Dr. Geo User's Manual -- Coordinates
DR. GEOGuile ScriptNumeric ToolsAngleCoordinates

Coordinates

Create the coordinates of a point or a vector. This tool creates both the abscissa and the coordinate.

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DR. GEOGuile ScriptNumeric ToolsAngleCoordinates
drgeo-doc-1.5/c/drgenius_31.html0000644000175000017500000000442110117134566012143 Dr. Geo User's Manual -- DR. GEOGuile Script
Numeric ToolsCoordinatesDR. GEOGuile Script

DR. GEOGuile Script

Create a DR. GEOGuile Script. The script receives input of n objects. It eventually returns a number, printed in the figure. A script can be used for its side effects or for its returned value. The DR. GEOGuile Scripts are covered in details in the Chapter Advanced Features and exactly at Section Script.

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Numeric ToolsCoordinatesDR. GEOGuile Script
drgeo-doc-1.5/c/drgenius_33.html0000644000175000017500000000406610117134566012152 Dr. Geo User's Manual -- Setting a Macro-Construction
Executing a Macro-ConstructionMacro-Construction ToolsSetting a Macro-Construction

Setting a Macro-Construction

Extract a construction sequence of a figure and turn it as a macro-construction.

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Executing a Macro-ConstructionMacro-Construction ToolsSetting a Macro-Construction
drgeo-doc-1.5/c/drgenius_34.html0000644000175000017500000000441210117134566012146 Dr. Geo User's Manual -- Executing a Macro-Construction
Macro-Construction ToolsSetting a Macro-ConstructionExecuting a Macro-Construction

Executing a Macro-Construction

Execute (i.e. "run" or "play") a pre-built macro-construction. The macro-construction can be either newly created or loaded from file.

(!) Macro-Constructions are exposed in Section Macro-Construction.
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Macro-Construction ToolsSetting a Macro-ConstructionExecuting a Macro-Construction
drgeo-doc-1.5/c/drgenius_36.html0000644000175000017500000000356610117134566012161 Dr. Geo User's Manual -- Moving figure
Moving objectOther functionsMoving figure

Moving figure

Figure can be moved by pressing CONTROL key and button 1 of the mouse.

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Moving objectOther functionsMoving figure
drgeo-doc-1.5/c/drgenius_37.html0000644000175000017500000000445710117134566012162 Dr. Geo User's Manual -- Moving object
Deleting ObjectsOther functionsMoving figureMoving object

Moving object

An object can be moved by draggin it. The figure is then recomputed according to its properties. Almost every type of geometric object can be moved. When necessary, DR. GEOperforms a reverse dragging. For example, this occurs when the user moves a line defined by two points, DR. GEOwill move the two points according to the desired line position.

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Deleting ObjectsOther functionsMoving figureMoving object
drgeo-doc-1.5/c/drgenius_38.html0000644000175000017500000000437310117134566012160 Dr. Geo User's Manual -- Deleting Objects
Editing Object StylesOther functionsMoving objectDeleting Objects

Deleting Objects

An object on the figure can be deleted when activating this menu. Eventually, the user can undelete using the undo function from the toolbar or application menu. By default the undo level is set to 10 but the user can adjust this value from the preference dialog.

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Editing Object StylesOther functionsMoving objectDeleting Objects
drgeo-doc-1.5/c/drgenius_39.html0000644000175000017500000000437310117134566012161 Dr. Geo User's Manual -- Deleting Objects
Editing Object StylesOther functionsMoving objectDeleting Objects

Deleting Objects

An object on the figure can be deleted when activating this menu. Eventually, the user can undelete using the undo function from the toolbar or application menu. By default the undo level is set to 10 but the user can adjust this value from the preference dialog.

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Editing Object StylesOther functionsMoving objectDeleting Objects
drgeo-doc-1.5/c/drgenius_3.html0000644000175000017500000000425510117134566012067 Dr. Geo User's Manual -- Basic Functions
Advanced FeaturesTopIntroductionBasic Functions

Basic Functions

This chapter describes the tools used to construct geometric figure. At the end of this chapter, customisation is presented.

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Advanced FeaturesTopIntroductionBasic Functions
drgeo-doc-1.5/c/drgenius_40.html0000644000175000017500000000527310117134566012151 Dr. Geo User's Manual -- Editing Object Properties
Other functionsEditing Object StylesEditing Object Properties

Editing Object Properties

Some objects own properties adjustable by the user. When the user clicks on such objects, an appropriate dialog appears. Actually the following objects own user adjustable properties:
  1. Free point on the area: abscissa and coordinate can be edited;

    Edit free point coordinates

  2. Free value: its value can be edited;

    Edit free value

  3. Script: its code can be edited.

    Edit a script

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Other functionsEditing Object StylesEditing Object Properties
drgeo-doc-1.5/c/drgenius_41.html0000644000175000017500000000370610117134566012151 Dr. Geo User's Manual -- User's Preferences
Basic FunctionsOther functionsUser's Preferences

User's Preferences

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Basic FunctionsOther functionsUser's Preferences
drgeo-doc-1.5/c/drgenius_42.html0000644000175000017500000000441410117134566012147 Dr. Geo User's Manual -- Display grid
Other functionsEditing Object PropertiesDisplay grid

Display grid

It is possible to display a unit grid under each DR. GEO figure. The corresponding command can be accessed from the Edition->Show or hide grid menu. It can also be activated from the Ctrl-G shortcut. If the command is activated again, the grid is hidden. The grid is a unit grid: each subdivision corresponts to one unit. Also, if the grid is apparent when the figure is being saved, then the grid is saved too.

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Other functionsEditing Object PropertiesDisplay grid
drgeo-doc-1.5/c/drgenius_43.html0000644000175000017500000000420710117134566012150 Dr. Geo User's Manual -- Other Preferences
User's PreferencesDefault BehaviourOther Preferences

Other Preferences

In addition to changing the default behaviour of DR. GEO, the user can change the name of a figure from the menu item Edit->Rename.

Renaming a figure view

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User's PreferencesDefault BehaviourOther Preferences
drgeo-doc-1.5/c/drgenius_44.html0000644000175000017500000000604110117134566012147 Dr. Geo User's Manual -- Advanced Features
Saving and Loading ConstructionsTopBasic FunctionsAdvanced Features

Advanced Features

In this chapter we present features used to extend the cabilities of DR. GEOin various ways.

The first is macro-construction; it allows the extraction of a construction logic in a record. Then, this record can be repeated or saved as a file.

The DR. GEOGuile Script features are the other means for extending DR. GEO. These scripts are really figure items like the other geometric items. They receive as input, user selected figure item references and they return values, plugged into figures.

DR. GEOGuile Scripts can be useful for their returned values or their side effects; which really depends on what the user wants to achieve.

The last feature is user-interface customisability. The idea is to give the teacher the cability to prepare geometric figure files with tools taken from the Dr. Genius toolbar and contextual menu. This capability may help in achieving a desired "pedagogical effect"

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Saving and Loading ConstructionsTopBasic FunctionsAdvanced Features
drgeo-doc-1.5/c/drgenius_45.html0000644000175000017500000000421010117134566012144 Dr. Geo User's Manual -- Other Preferences
User's PreferencesDefault BehaviourOther Preferences

Other Preferences

In addition to changing the default behaviour of DR. GEO, the user can change the name of a figure from the Edit->Rename menu item.

Renaming a figure view

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User's PreferencesDefault BehaviourOther Preferences
drgeo-doc-1.5/c/drgenius_46.html0000644000175000017500000001102510117134566012147 Dr. Geo User's Manual -- Constructing a Macro-Construction
Executing a Macro-ConstructionMacro-ConstructionConstructing a Macro-Construction

Constructing a Macro-Construction

At this point, the construction sequence is done. Now, the user needs to tell Dr. Genius that she wants to create a macro-construction from this sequence. She can call the Construct a macro function from the icon or from the contextual menu in the figure view.

From the wizard dialog, the user selects the input & output parameters, the name and description of the macro-construction.

The 1st page of the wizard dialog to construct a macro-construction

The second page of the dialog is used to select the input parameters. In our example, these are the three initial points. The user just needs to go to this second page and she can select the three points in the figure. The selected items will blink.

The 2nd page, the three points are already selected

From the 3rd page, she selects the output parameters. In our example, we want the circle and its centre as the result of the macro-construction. She proceeds as in the case of the input parameters to select them.

The 3rd page, the circle and its centre are already selected

In the 4th page, the user enters the name and the description of the macro-construction. This information is displayed when the user executes a macro-construction, so it helps to distinguish macro-construction between them.

The 4th page, the name and description of the macro-construction

From the last page of the wizard dialog (the 5th one), the user can terminate the creation by pressing the Finish button. Alternatively, she can return to previous pages to adjust the macro-construction parameters.

(!) If the input & output parameters selections do not match (DR. GEOcannot extract the logic of the construction), the macro-construction cannot be built. In such a case, the user needs to reconsider the input and output parameters selection. She can go back to the 2nd and 3rd page of the wizard dialog to adjust her choices.

At this point the macro-construction is built and recorded in DR. GEO. In the next section, we will see how to use this macro-construction.

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Executing a Macro-ConstructionMacro-ConstructionConstructing a Macro-Construction
drgeo-doc-1.5/c/drgenius_47.html0000644000175000017500000000647410117134566012164 Dr. Geo User's Manual -- Executing a Macro-Construction
Macro-ConstructionConstructing a Macro-ConstructionExecuting a Macro-Construction

Executing a Macro-Construction

To execute a macro-construction, the user calls the Execute pre-build macro function from the icon or from the contextual menu in the figure view.

From the wizard dialog, the user selects the macro-construction. In the 2nd page, she selects the macro-construction from the list in the top area of the dialog. Once a macro-construction is selected, she can directly click on the input parameters in the figure. As soon as all the necessary input parameters are selected, the macro-construction is executed and the final parameters appear.

The user selects the input parameters directly in the figure

In our example, the macro-construction needs three input parameters (three points) and it builds a point and a circle. To execute our macro-construction, we need a figure with a least three points.

A figure with three points

Once our macro-construction is applied to these three points, we get the desired circle and its centre.

The resulting figure with the circle and its centre

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Macro-ConstructionConstructing a Macro-ConstructionExecuting a Macro-Construction
drgeo-doc-1.5/c/drgenius_48.html0000644000175000017500000001104110117134566012147 Dr. Geo User's Manual -- Constructing a Macro-Construction
Executing a Macro-ConstructionMacro-ConstructionConstructing a Macro-Construction

Constructing a Macro-Construction

At this point, the construction sequence is done. Now, the user needs to tell Dr. Genius that she wants to create a macro-construction from this sequence. She can call the Construct a macro function from the icon or from the contextual menu in the figure view.

>From the wizard dialog, the user selects the input & output parameters, the name and description of the macro-construction.

The 1st page of the wizard dialog to construct a macro-construction

The second page of the dialog is used to select the input parameters. In our example, these are the three initial points. The user just needs to go to this second page and she can select the three points in the figure. The selected items will blink.

The 2nd page, the three points are already selected

>From the 3rd page, she selects the output parameters. In our example, we want the circle and its centre as the result of the macro-construction. She proceeds as in the case of the input parameters to select them.

The 3rd page, the circle and its centre are already selected

In the 4th page, the user enters the name and the description of the macro-construction. This information is displayed when the user executes a macro-construction, so it helps to distinguish macro-construction between them.

The 4th page, the name and description of the macro-construction

>From the last page of the wizard dialog (the 5th one), the user can terminate the creation by pressing the Finish button. Alternatively, she can return to previous pages to adjust the macro-construction parameters.

(!) If the input & output parameters selections do not match (DR. GEOcannot extract the logic of the construction), the macro-construction cannot be built. In such a case, the user needs to reconsider the input and output parameters selection. She can go back to the 2nd and 3rd page of the wizard dialog to adjust her choices.

At this point the macro-construction is built and recorded in DR. GEO. In the next section, we will see how to use this macro-construction.

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Executing a Macro-ConstructionMacro-ConstructionConstructing a Macro-Construction
drgeo-doc-1.5/c/drgenius_49.html0000644000175000017500000000353010117134566012154 Dr. Geo User's Manual -- Creating a DGS
More about DGSDR. GEOGuile ScriptCreating a DGS

Creating a DGS

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More about DGSDR. GEOGuile ScriptCreating a DGS
drgeo-doc-1.5/c/drgenius_4.html0000644000175000017500000000456710117134566012076 Dr. Geo User's Manual -- Construction Tools
Other functionsBasic FunctionsConstruction Tools

Construction Tools

These tools are split into six groups available from the second toolbar of DR. GEO.

DR. GEO's tool categories and their descriptions

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Other functionsBasic FunctionsConstruction Tools
drgeo-doc-1.5/c/drgenius_50.html0000644000175000017500000000354010117134566012145 Dr. Geo User's Manual -- More about DGS
DR. GEOGuile ScriptCreating a DGSMore about DGS

More about DGS

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DR. GEOGuile ScriptCreating a DGSMore about DGS
drgeo-doc-1.5/c/drgenius_51.html0000644000175000017500000000363710117134566012155 Dr. Geo User's Manual -- User interface customisation
Advanced FeaturesDR. GEOGuile ScriptUser interface customisation

User interface customisation

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Advanced FeaturesDR. GEOGuile ScriptUser interface customisation
drgeo-doc-1.5/c/drgenius_52.html0000644000175000017500000000437110117134566012152 Dr. Geo User's Manual -- Saving and Loading Constructions
Cook BookTopAdvanced FeaturesSaving and Loading Constructions

Saving and Loading Constructions

Constructions can be saved in two ways. One construction per file or a construction set per file (i.e. a Dr. Genius session).

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Cook BookTopAdvanced FeaturesSaving and Loading Constructions
drgeo-doc-1.5/c/drgenius_53.html0000644000175000017500000000506210117134566012151 Dr. Geo User's Manual -- Saving one construction
Saving a SessionSaving and Loading ConstructionsSaving one construction

Saving one construction

From the menu File->Save or File->Save As..., a file can be saved containing the figure under the active view.

(!) Dr. Genius can work with several figures at the same time. The user can switch from one figure to another one by clicking on the corresponding tabs.

With the second menu, the user can change the name of the saved document.

(!) The default file name proposed to the user by Dr. Genius can be changed from the Edit->Preferences... menu. For more information see Section Defaut Behaviour.
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Saving a SessionSaving and Loading ConstructionsSaving one construction
drgeo-doc-1.5/c/drgenius_54.html0000644000175000017500000000622710117134566012156 Dr. Geo User's Manual -- Saving a Session
Loading ConstructionsSaving and Loading ConstructionsSaving one constructionSaving a Session

Saving a Session

A session is a set of Dr. Genius data the user wants to save in one shot in a file. It allows teacher to organise a set of data (figure, macro-construction, note) in one file, so it is more convenient to re-open such data.

From the File->Save Multiple menu, the user can display the session dialog.

The Dr. Genius session dialog

The list of all active data is saved in this file and presented in a table. The first colon represents the type of data contained in Dr. Genius. The second one represents the name of the data.

(!) Actually, a session can contain three kinds of data: 2D interactive figure, macro-construction and text.

Then users can decide to select one by one the data to save from the list. Then she can press the Save Session button. Alternatively, she can save all the data by pressing the Save All button.

(!) File->Save Multiple menu is the only way to save macro-constrcutions to a file.
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Loading ConstructionsSaving and Loading ConstructionsSaving one constructionSaving a Session
drgeo-doc-1.5/c/drgenius_55.html0000644000175000017500000000357410117134566012161 Dr. Geo User's Manual -- Loading Constructions
Saving and Loading ConstructionsSaving a SessionLoading Constructions

Loading Constructions

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Saving and Loading ConstructionsSaving a SessionLoading Constructions
drgeo-doc-1.5/c/drgenius_56.html0000644000175000017500000000510510117134566012152 Dr. Geo User's Manual -- Cook Book
TopSaving and Loading ConstructionsCook Book

Cook Book

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TopSaving and Loading ConstructionsCook Book
drgeo-doc-1.5/c/drgenius_57.html0000644000175000017500000000357410117134566012163 Dr. Geo User's Manual -- Loading Constructions
Saving and Loading ConstructionsSaving a SessionLoading Constructions

Loading Constructions

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Saving and Loading ConstructionsSaving a SessionLoading Constructions
drgeo-doc-1.5/c/drgenius_58.html0000644000175000017500000000527010117134566012157 Dr. Geo User's Manual -- Cook Book
FootnotesTopSaving and Loading ConstructionsCook Book

Cook Book

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FootnotesTopSaving and Loading ConstructionsCook Book
drgeo-doc-1.5/c/drgenius_59.html0000644000175000017500000000451710117134566012163 Dr. Geo User's Manual -- Footnotes
TopCook BookFootnotes

Footnotes

 (1)
That means, being able to create some type of object from a single command but through different modalities. For instance, with the circle-building command, the user can create a circle from its center and another point or a length, or from a segment, etc. Of course, this command is represented by a single icon, and DR. GEO is expected to anticipate the user's construction. The immediate consequence is a reduction of the interface-learning burden for the user, while a large number of construction modes are offered.
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TopCook BookFootnotes
drgeo-doc-1.5/c/drgenius_6.html0000644000175000017500000000435010117134566012066 Dr. Geo User's Manual -- Free Point
MidpointPoint ToolsFree Point

Free Point

Create a free point on an area or a free point on an uni-dimensional object. In the first case, the created point can be moved anywhere in the figure area. To build the point the user just clicks on the background. In the latter case, it is constrained to the uni-dimensional object (line); it is stuck to the object. To build this kind of point the user clicks over a line (i.e. straight line, ray, segment, circle, arc, etc.).

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MidpointPoint ToolsFree Point
drgeo-doc-1.5/c/drgenius_7.html0000644000175000017500000000407110117134566012067 Dr. Geo User's Manual -- Midpoint
IntersectionPoint ToolsFree PointMidpoint

Midpoint

Create the middle of two points or the middle of a segment. In the first case, the user selects two points. In the latter case the user just selects a segment.

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IntersectionPoint ToolsFree PointMidpoint
drgeo-doc-1.5/c/drgenius_8.html0000644000175000017500000000403610117134566012071 Dr. Geo User's Manual -- Intersection
Point by its CoordinatesPoint ToolsMidpointIntersection

Intersection

Create the intersection point(s) of two line objects. The user needs to select two line objects.

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Point by its CoordinatesPoint ToolsMidpointIntersection
drgeo-doc-1.5/c/drgenius_9.html0000644000175000017500000000403710117134566012073 Dr. Geo User's Manual -- Point by its Coordinates
Point ToolsIntersectionPoint by its Coordinates

Point by its Coordinates

Create a point defined by its coordinates. The user needs to select two numbers, the first selected number is the abscissa; the second one is the ordinate.

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Point ToolsIntersectionPoint by its Coordinates
drgeo-doc-1.5/c/drgenius_guile_script.html0000644000175000017500000000671710117134566014423 Dr. Geo User's Manual -- DR. GEOGuile Script
User interface customisationAdvanced FeaturesMacro-ConstructionDR. GEOGuile Script

DR. GEOGuile Script

DR. GEOis Guile aware. This means it is possible to execute Guile scripts within DR. GEO. But what is Guile? From the Guile manual:

Guile is an interpreter for the Scheme programming language, packaged for use in a wide variety of environments.

The following citation describes accurately how is used Guile within DR. GEO:

Like a shell, Guile can run interactively, reading expressions from the user, evaluating them, and displaying the results, or as a script interpreter, reading and executing Scheme code from a file. However, Guile is also packaged as an object library, allowing other applications to easily incorporate a complete Scheme interpreter. An application can use Guile as an extension language, a clean and powerful configuration language, or as multi-purpose "glue", connecting primitives provided by the application.

In DR. GEO, an API is available from the Guile interpretor. This API is a set of hooks in the geometric engine. Therefore the user can write scripts to manipulate figure items (geometric and numeric). Also, as scripts are figure items like any other, they do not need to be saved as separate files. They are saved in the figure file. In the following, we will use the DGS acronym for DR. GEOGuile Script.

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User interface customisationAdvanced FeaturesMacro-ConstructionDR. GEOGuile Script
drgeo-doc-1.5/c/drgenius.html0000644000175000017500000000270610117134566011644 Dr. Geo User's Manual

Dr. Genius User's Manual

Hilaire Fernandes
With contributions from David Bucknell
OFSET
http://www.ofset.org

August 29, 2004

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drgeo-doc-1.5/c/editing_object_styles.html0000644000175000017500000000646510117134566014406 Dr. Geo User's Manual -- Editing Object Styles
Editing Object PropertiesOther functionsDeleting ObjectsEditing Object Styles

Editing Object Styles

Each object owns such style attributes as colour, thickness, label, size or shape. Additionally, it is possible to hide an object temporarily without deleting it. For example, it can be useful to hide intermediate constructions without deleting them. All these attributes can be adjusted from a dialog activated when the user selects an object in the figure.

The point style dialog concerns any kind of point object. From it, it is possible to adjust its color, shape, size, name and visibility.

The style dialog for point object

The line style dialog concerns straight line, ray, segment, vector, circle, arc circle, locus. From it, it is possible to adjust the color, style, name and visibility.

The style dialog for line object

The numeric & polygon style dialog concerns all kind of values (user edited, computed by user's DR. GEOGuile Script or representing geometric measure) and polygon shape.

The style dialog for numeric & polygon objects

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Editing Object PropertiesOther functionsDeleting ObjectsEditing Object Styles
drgeo-doc-1.5/c/introduction.html0000644000175000017500000000706410117134566012547 Dr. Geo User's Manual -- Introduction
Basic FunctionsTopContentsIntroduction

Introduction

Dr. Genius is the interactive geometry package for the Gnome Desktop. It allows users to create geometric figures that can be manipulated with respect to geometric rules. The program is useable with students from the primary through secondary levels.

DR. GEOwelcome screen

To create a new empty geometric figure, the user clicks on the first (on the left) button in the toolbar. Alternatively, a new figure can be created using the menu item File->New->Figure from the menu bar. When a new figure is created, a new toolbar with a set of six icons appears. The last item (on the right) in the toolbar is an option menu; it is used to adjust the scale of the current geometric figure.

An empty geometric figure

The six icons correspond to different types of functions. These functions are described in the next chapter.

A DR. GEOfigure and its description

With each figure, a pane is available. By default the pane is pushed to the extreme left so that only the representation of the figure is visible. At any moment, the user can push the pane to the right to make visible the figure description. A figure description is a tree list. The tree is composed of all the elements of the figure. The elements relative to other elements can be expanded by pressing the '+' sign, that way the user can visualize the parents of this element.
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Basic FunctionsTopContentsIntroduction
drgeo-doc-1.5/c/line_tools.html0000644000175000017500000000441210117134566012167 Dr. Geo User's Manual -- Line Tools
Transformation ToolsConstruction ToolsPoint ToolsLine Tools

Line Tools

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Transformation ToolsConstruction ToolsPoint ToolsLine Tools
drgeo-doc-1.5/c/macroconstruction_tools.html0000644000175000017500000000376510117134566015026 Dr. Geo User's Manual -- Macro-Construction Tools
Construction ToolsNumeric ToolsMacro-Construction Tools

Macro-Construction Tools

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Construction ToolsNumeric ToolsMacro-Construction Tools
drgeo-doc-1.5/c/numeric_tools.html0000644000175000017500000000430410117134566012702 Dr. Geo User's Manual -- Numeric Tools
Macro-Construction ToolsConstruction ToolsTransformation ToolsNumeric Tools

Numeric Tools

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Macro-Construction ToolsConstruction ToolsTransformation ToolsNumeric Tools
drgeo-doc-1.5/c/other_tools.html0000644000175000017500000000431310117134566012361 Dr. Geo User's Manual -- Other functions
User's PreferencesBasic FunctionsConstruction ToolsOther functions

Other functions

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User's PreferencesBasic FunctionsConstruction ToolsOther functions
drgeo-doc-1.5/c/point_tools.html0000644000175000017500000000375510117134566012402 Dr. Geo User's Manual -- Point Tools
Line ToolsConstruction ToolsPoint Tools

Point Tools

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Line ToolsConstruction ToolsPoint Tools
drgeo-doc-1.5/c/transformation_tools.html0000644000175000017500000000441210117134566014306 Dr. Geo User's Manual -- Transformation Tools
Numeric ToolsConstruction ToolsLine ToolsTransformation Tools

Transformation Tools

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Numeric ToolsConstruction ToolsLine ToolsTransformation Tools
drgeo-doc-1.5/c/using_macro.html0000644000175000017500000000754610117134566012341 Dr. Geo User's Manual -- Macro-Construction
DR. GEOGuile ScriptAdvanced FeaturesMacro-Construction

Macro-Construction

Macro-constructions are a bit like a procedure which receives as input figure items and then returns one or more figure items, constructed by the macro-construction. They are built on a model defined by the user. This means that the user has to build a construction sequence only once. Then she can tell DR. GEOthat she wants this sequence to be recorded in a macro-construction. To record a construction sequence, DR. GEOneeds to know which are the initial items of the sequence and the resulting items. Of course the resulting items must depend only on the initial items; otherwise Dr. Genius would not be able to deduce the resulting items from the initial ones.

Using its knowledge of the initial and resulting items, DR. GEOdeduces the construction sequence and saves it in a macro-construction. The user can then execute this macro-construction simply by inputting (initial) items (they must match the type) in the figure. The macro-construction can then build the resulting items.

(!) Invisible intermediate figure items are also built by the macro-construction. These items are necessary to build the resulting items.

To illustrate the macro-construction feature, we will use an example in which the user wants to record the construction of a circle with a given center which passes through three points, also given.

Our initial figure

Before constructing the macro-construction, the user needs to construct the final figure; it is used as a pattern from which to build the macro-construction.

Our figure with the resulting construction

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DR. GEOGuile ScriptAdvanced FeaturesMacro-Construction
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Other copyright apply to the respective owners of the modified documentations. See the section history for the complet list. \xname{introduction} \chapter{Introducción} \section{Preliminares} \drgeo\ es un programa tanto de geometría interactiva como de programación en el lenguaje Scheme. Permite crear figuras geométricas, así como manipularlas interactivamente respetando sus restricciones geométricas. Ofrece igualmente la posibilidad de introducirse gradualmente en la programación. Es útil para la enseñanza a estudiantes de nivel básico o superior. La interfaz de usuario de \drgeo\ ha sido concebida para dar, dentro de un conjunto armónico, a la vez sencillez en su operación, ergonomía y funcionalidades avanzadas. Así la interfaz de \drgeo\ , con una gran sencillez, permite al neófito la familiarización con las funciones básicas del programa. Posteriormente, a medida que lo conozca más, el usuario conocerá los aspectos más avanzados de la interfaz y del funcionamiento de \drgeo\ : múltiples modos para la construcción de objetos \footnote{ Se trata de poder, a partir de un mismo comando, crear un tipo de objeto según se requiera. Por ejemplo, a partir del comando para la construcción de un círculo, el usuario puede crear un círculo a partir de su centro y de ya sea un punto, una longitud, un segmento, etc. Con todo, este comando es representado por un solo icono, y \drgeo\ se anticipa para ofrecer al usuario la construcción deseada. El efecto inmediato es que existe una disminución en el tiempo de aprendizaje de la interfaz, al proponer un número importante de modos de construcción}, macros de construcciones, sesiones, adaptabilidad de la interfaz, uso de scripts y de Figuras Scheme de \drgeo (i.e. \drgeo\ es programable en dos modos distintos). Estas funciones avanzadas generan muy poca sobrecarga a la interfaz, por lo que \drgeo\ es utilizado con entusiasmo en la enseñanza primaria, lo que no resta su uso en el nivel medio. En las secciones siguientes, expondremos las herramientas básicas. Posteriormente las funciones avanzadas serán presentadas en detalle. \drgeniusFigureSize{Pantalla de Bienvenida de \drgeo\ }{fig1}{8} La estructura de la interfaz es la siguiente~: \begin{enumerate} \item la \textit{barra de menú} característica con \drgeoMenu{Archivo}, \drgeoMenu{Editar}, \drgeoMenu{Macros}, \drgeoMenu{Ventanas}, \drgeoMenu{Ayuda} ; \item la \textit{barra de acciones} para crear una nueva figura o un texto explicativo; contiene también las herramientas de hacer/deshacer y la rejilla . \end{enumerate} Para crear una figura geométrica nueva, el usuario debe hacer click en el primer botón de la barra de herramientas. De manera alternativa, una nueva figura puede ser creada usando el elemento de la barra del menú \drgeniusMenu{Archivo->Nuevo->Figura}. Cuando una nueva figura es creada, una nueva \textit{barra de íconos} formada por seis iconos aparece. Esta barra de íconos termina con un menú que permite ajustar la escala de la figura geométrica actual. Además, una barra de íconos vertical, a la izquierda de la figura, ofrece un rápido acceso a las herramientas más utilizadas. \drgeniusFigureSize{Una figura geométrica vacía}{fig2}{8} Los seis iconos de la barra de íconos son entradas de menú generales desde donde se llaman a funciones específicas. Estas funciones son descritas en el siguiente capítulo. \drgeniusFigureSize{Una figura de \drgeo\ y su descripción}{fig50}{8} Para cada figura, un \textit{árbol sinóptico} está disponible. Inicialmente este panel está oculto en el extremo izquierdo de modo que sólo la representación de la figura es visible. En cualquier momento, el usuario puede empujar el panel hacia la derecha como sigue: Lleve el ratón a la parte izquierda de la figura, justo a la izquierda de donde está la regla; cuando el puntero del ratón cambie de forma, presione el botón y continúe presionando mientras mueve el ratón a la derecha. Con ello, será visible la descripción de la figura. La descripción de una figura es un árbol formado con todos los elementos de la figura. Los elementos que dependen de otros elementos pueden ser revelados al hacer click sobre el símbolo `+'. Con ello, se mostrarán los elementos que dieron origen (v.g. los que dieron origen a una línea pueden ser dos puntos; aunque pueden ser otros originadores. También se les llama elementos antecedentes o elementos padre). \section{\drgeo\ en la red} \drgeo\ dispone de su propio espacio en la red en el sitio \textsc{ofset} en la dirección~: \xlink{http://www.ofset.org/drgeo}. En este espacio, el usuario encontrará la siguiente información~: \begin{itemize} \item la información para obtener \drgeo{}~; \item la documentación del programa; \item algunas indicaciones para involucrarse en el proyecto \drgeo{}~; \item algunas referencias para el uso pedagógico del programa. \end{itemize} \chapter{Funciones Básicas} Este capítulo describe las herramientas usadas para construir figuras geométricas. Al final del capítulo, la configuración de las preferencias del usuario es también presentada. \section{Herramientas de Construcción} Estas herramientas están separadas en seis grupos disponibles desde la segunda barra de herramientas de \drgeo\ . \drgeniusFigureSize{Categorías de herramientas de \drgeo\ y sus descripciones}{fig3}{12} Cuando el usuario hace click sobre uno de los iconos decorados con un triangulito verde, una nueva barra vertical de iconos aparece inmediatamente. En ella se agrupan funciones de una misma familia. De izquierda a derecha, tenemos acceso a las barras de herramientas verticales para: construir puntos, construir líneas, realizar transformaciones geométricas, calcular valores numéricos, generar macros de construcciones, y utilizar las herramientas de edición -- \emph{Otras herramientas} Estas funciones también aparecen dentro del menú contextual de una figura, que es llamado haciendo click con el botón derecho en el fondo de la figura. \xname{point_tools} \subsection{Herramientas de puntos} \subsubsection{Punto Libre} \drgeniusIcon{fig4} \label{free_point} \drgeniusIndex{Punto}{Libre}{}{} Crear un punto libre en el área o un punto libre en un objeto unidimensional(segmento, semirrecta,recta, arco de círculo, círculo, lugar geométrico). \begin{enumerate} \item En el primer caso, el punto creado puede moverse a cualquier lugar del fondo de la figura; para construirlo, el usuario simplemente hace click en cualquier parte del fondo. \item En el segundo caso, el punto está limitado a moverse en el objeto unidimensional (línea o círculo); esta pegado al objeto. Para construir este tipo de punto el usuario hace click sobre una línea (i.e. una línea recta, una semirrecta, un segmento, un círculo, un arco de círculo, etc.). \end{enumerate} \paragraph{¿Cómo ubicar un punto dadas sus coordenadas~?} La solución más simple consiste en colocar un punto libre y luego editar sus propiedades --~herramienta \link{Propiedades}[ Sección \Ref, página \Pageref]{property-item}~-- ajustando sus coordenadas a voluntad.. Otra posibilidad --~menos flexible para este tipo de figura~-- consiste en colocar dos valores libres en la figura --~herramienta \link{Valor Numérico}[Sección \Ref, página \Pageref]{numeric_tool}~-- y luego construir el punto con coordenadas dadas por esos dos valores --~herramienta \link{Punto definido por sus coordenadas}[ Sección \Ref, página \Pageref]{coordinate_point} Cette possibilité a un avantage sur la Este procedimiento tiene una ventaja sobre el precedente: el punto construido no puede ser ya movido con el ratón; el punto está inexorablemente atado a su posición. \subsubsection{Punto Medio} \drgeniusIcon{fig5} \drgeniusIndex{Punto}{Medio}{}{} Crear el punto medio de un par de puntos o la mitad de un segmento. \begin{enumerate} \item En el primer caso, el usuario selecciona dos puntos. \item En el segundo caso, el usuario simplemente selecciona un segmento \end{enumerate}. \subsubsection{Intersección} \drgeniusIcon{fig6} \drgeniusIndex{Punto}{Intersección}{}{} Crear el(los) punto(s) de intersección de dos líneas (objetos unidimensionales, i.e. recta, semirrecta, segmento, arco de círculo, círculo o lugar geométrico). El usuario necesita seleccionar dos líneas (v.g arco de círculo y semirrecta). \subsubsection{Punto definido por sus coordenadas} \drgeniusIcon{fig7} \label{coordinate_point} \drgeniusIndex{Punto}{Definido por sus coordenadas}{}{} Crear un punto definido por sus coordenadas. El usuario necesita seleccionar dos números, el primer número seleccionado es la abscisa, el segundo la ordenada. \paragraph{¿Cómo colocar un punto con restricciones a sus coordenadas?} Esta funcion es muy utilizada cuando deseamos, por ejemplo, construir el lugar geométrico de un punto. Esta construcción supone la existencia de dos valores --~ver \link{Sección Valores Numéricos}[ Sección \Ref, página \Pageref]{numeric_tool} -- el punto es construidoluego de seleccionar esos dos valores. Los valores pueden ser independientes o uno depender del otro. \xname{line_tools} \subsection{Herramientas de líneas} \subsubsection{Recta} \drgeniusIcon{fig8} \drgeniusIndex{Recta}{}{}{} \drgeniusIndex{Línea}{}{}{} Crear una línea recta definida por sus dos puntos. El usuario selecciona dos puntos. \subsubsection{Semirrecta} \drgeniusIcon{fig9} \drgeniusIndex{Semirrecta}{}{}{} \drgeniusIndex{Rayo}{}{}{} % FIXME: NO ESTOY SEGURO SI PONER RAYO ES BUENO. HAY QUE CAMBIAR Crea una semirrecta (también llamada rayo) definida por dos puntos. El usuario selecciona dos puntos, el primero es el origen, el segundo pertenece a la semirrecta. \subsubsection{Segmento} \drgeniusIcon{fig10} \drgeniusIndex{Segmento}{}{}{} Crea un segmento definido por dos puntos. \subsubsection{Vector} \drgeniusIcon{fig11} \drgeniusIndex{Vector}{}{}{} Crea un vector definido por dos puntos. El usuario selecciona dos puntos, el primer punto es el origen, el segundo es el extremo. Una vez que el vector es creado, éste puede ser desplazado independientemente de los dos puntos que le dieron origen. Esto sigue siendo cierto para vectores construidos a través de una transformación. (Ver la sección de Transformaciones en este manual). \subsubsection{Círculo} \drgeniusIcon{fig12} \drgeniusIndex{Círculo}{}{}{} Crea un círculo. El usuario puede crear un círculo a partir de varias opciones: \begin{enumerate} \item el centro y un punto del círculo; \item el centro y un número (el radio del círculo); \item el centro y un segmento cuya longitud es el radio del círculo. \end{enumerate} \subsubsection{Arco de Círculo} \drgeniusIcon{fig13} \drgeniusIndex{Arco de círculo}{}{}{} Crea un arco de círculo definido por tres puntos. El primer punto seleccionado es el origen del arco, el tercero es su extremo, el segundo es un punto sobre el arco. Los tres puntos seleccionados formarán parte del arco. \subsubsection{Lugar geométrico} \drgeniusIcon{fig14} \drgeniusIndex{Lugar Geométrico}{}{}{} \drgeniusIndex{Locus}{}{}{} Crea un lugar geométrico (locus en latín) dados dos puntos. El usuario selecciona dos puntos; uno es un punto libre sobre una línea (linea o círculo); el otro es un punto que depende del primero (i.e. cuando uno mueve el primero, el segundo también tiene que moverse). \subsubsection{Polígono} \drgeniusIcon{fig15} \drgeniusIndex{Polígono}{}{}{} Crea un polígono definido por n puntos. El usuario selecciona n+1 puntos delimitando el polígono. El primero y el último seleccionado deben ser los mismos, esto indica a \drgeo\ que la selección esta terminada. El objeto polígono no es un objeto como los objetos unidimensionales, no es posible colocar un punto sobre él o calcular la intersección entre un polígono y otro objeto unidimensional. Por otro lado, es posible aplicar a un polígono una transformación geométrica (rotación, reflexión, homotecia, etc.) \xname{transformation_tools} \subsection{Herramientas de Transformación} \subsubsection{Línea Paralela} \drgeniusIcon{fig16} \drgeniusIndex{Recta}{Paralela}{}{} \drgeniusIndex{Línea}{Paralela}{}{} Crea una línea paralela a una dirección y que pase a través de un punto. El usuario selecciona un punto y una dirección (i.e. una línea recta, una semirrecta, un segmento o un vector). \subsubsection{Línea Perpendicular} \drgeniusIcon{fig17} \drgeniusIndex{Recta}{Perpendicular}{}{} \drgeniusIndex{Línea}{Perpendicular}{}{} \drgeniusIndex{Recta}{Ortogonal}{}{} Crea una línea perpendicular a una dirección y que pasa a través de un punto. El usuario selecciona un punto y una dirección (i.e. una línea recta, una semirrecta, un segmento o un vector). (Ortogonal es un sinónimo de Perpendicular) \subsubsection{Simetría Axial (Reflexión)} \drgeniusIcon{fig18} \drgeniusIndex{Transformación del plano}{Simetría}{Axial}{} \drgeniusIndex{Transformación del plano}{Reflexión}{}{} Crea la imagen de un objeto a través de una simetría axial (reflexión en una recta). El usuario selecciona el objeto a transformar y el eje de simetría (que debe ser una recta). Cuando el usuario quiere construir la imagen de una línea recta, la primera línea recta seleccionada por el usuario será la recta a reflejar. \subsubsection{Simetría Central } \drgeniusIcon{fig19} \drgeniusIndex{Transformación del plano}{Simetría}{Central}{} \drgeniusIndex{Rotación}{De 180 grados}{}{} Crea la imagen de un objeto a través de una simetría central. El usuario selecciona los objetos que serán transformados y el centro de simetría (un punto). Cuando el usuario quiere construir la imagen de un punto, el primer punto seleccionado es el punto a transformar.(La simetría central es equivalente a una rotación de 180 grados). \subsubsection{Traslación} \drgeniusIcon{fig20} \drgeniusIndex{Transformación del plano}{Traslación}{}{} Crear la imagen de un objeto a través de una traslación. El usuario selecciona el objeto que será transformado y el vector de traslación. Cuando el usuario quiere construir la imagen de un vector, el primer vector seleccionado es el vector que será trasladado. \subsubsection{Rotación} \drgeniusIcon{fig21} \drgeniusIndex{Transformación del plano}{Rotación}{General}{} Crea la imagen de un objeto a través de una rotación. El usuario selecciona el punto que será rotado, el centro y el ángulo de la rotación. Cuando el usuario quiere crear la imagen de un punto, el primer punto seleccionado es el punto a transformar. El ángulo puede ser seleccionado a partir de varios tipos de valores~: \begin{itemize} \item \textbf{valor numérico}~: el ángulo es expresado en radianes. Ejemplos de valores numéricos~: valor libre, un valor devuelto por un script Guile de \drgenius, etc.~; \item \textbf{la medida de un ángulo geométrico formado por tres puntos}~: su medida es entonces expresada en grados. Atención, pues en este caso la medida estará en el intervalo [0~;~180]~; \item \textbf{la medida de un ángulo orientado entre dos vectores}~: esta medida es expresada en grados y cubre el intervalo ]-180~;~180]. \end{itemize} \subsubsection{Escala (Homotecia)} \drgeniusIcon{fig22} \drgeniusIndex{Transformación del plano}{Homotecia}{}{} \drgeniusIndex{Transformación del plano}{Escala}{}{} Crea la imagen de un objeto a través de una transformación de escala (es decir, homotecia). El usuario selecciona el objeto a transformar, el centro de homotecia, y el factor (i.e. un número). Cuando el usuario quiera crear la imagen de un punto, el primer punto seleccionado es el punto a transformar. (Por ejemplo, si se desea hacer un polígono un tercio de grande, se selecciona un punto --centro de homotecia--, el polígono, y el valor 0.33333 ) \xname{numeric_tools} \subsection{Herramientas Numéricas} \subsubsection{Distancias, longitudes \& Números} \drgeniusIcon{fig23} \label{numeric_tool} \drgeniusIndex{Número}{}{}{} \drgeniusIndex{Recta}{Pendiente}{}{} \drgeniusIndex{Línea}{Pendiente}{}{} \drgeniusIndex{Recta}{Distancia}{}{} \drgeniusIndex{Línea}{Distancia}{}{} \drgeniusIndex{Círculo}{Perímetro}{}{} \drgeniusIndex{Segmento}{Longitud}{}{} \drgeniusIndex{Vector}{Norma}{}{} \drgeniusIndex{Vector}{Longitud}{}{} \drgeniusIndex{Arco de círculo}{Longitud}{}{} \drgeniusIndex{Número}{Valor libre}{}{} Crea un valor numérico. El valor numérico puede ser computado o editado por el usuario dependiendo de las selecciones que haga el usuario: \begin{enumerate} \item dos puntos: la distancia entre dos puntos; \item un segmento: la longitud de este segmento; \item un vector; la magnitud de ese vector (también llamada norma del vector); \item un círculo: el perímetro del círculo; \item un arco de círculo; la longitud del arco; \item una línea recta: la pendiente de la recta; \item una línea recta y un punto: la distancia entre la línea y el punto \item un click sobre el fondo permite al usuario entrar un valor nuevo (i.e. un valor numérico libre) \end{enumerate} Esta última posibilidad es muy intenresante en ciertas situaciones. Por ejemplo, ella permite fijar una longitud, el radio de un círculo, la medida de un ángulo (en radianes) o las coordenadas de un punto. Estos valores numéricos pueden ser enseguida utilizados por las herramientas de construcción de círculos, de rotación de objetos o para la creación de puntos dadas sus coordenadas. \subsubsection{Ángulo} \drgeniusIcon{fig24} \drgeniusIndex{Ángulo}{Geométrico}{}{}{} \drgeniusIndex{Ángulo}{Orientado}{}{}{} Calcula la magnitud de un ángulo definido por tres puntos o dos vectores. En el primer caso, el ángulo se considera no orientado (i.e. un ángulo geométrico con valores en el intervalo [0~;~180°]. En el segundo caso, el ángulo se considera orientado y toma valores en el rango ]-180~;~180]. \subsubsection{Coordenadas} \drgeniusIcon{fig25} \drgeniusIndex{Punto}{Coordenadas}{}{} \drgeniusIndex{Vector}{Coordenadas}{}{} Al selecciona un punto o un vector, nos da como resultado las coordenadas del punto o nos da las coordenadas del vector (coordenadas del punto final menos coordenadas del punto inicial). Esta herramienta crea tanto a la abscisa como a la ordenada. \subsubsection{Script Guile de \drgenius} \label{script-tool} \drgeniusIcon{fig49} \drgeniusIndex{Script}{}{}{} Crea un script Scheme de \drgeo (i.e. un script en el lenguaje Scheme). El script recibe una entrada de \emph{n} objetos. Siempre dará como resultado un número, que será presentado en la figura. Un script puede ser usado para obtener efectos colaterales o por el valor que da como resultado. Los Scripts Scheme de \drgeo\ están cubiertos en detalle en el \link{Capítulo Construcciones Avanzadas }[Capítulo \Ref]{advancedFeatures} y exactamente en la \link{Sección Script}[Sección \Ref, página \Pageref]{script}. \xname{macroconstruction_tools} \subsection{Herramientas para Macros de construcciones} \drgeniusIndex{Macro}{}{}{} \subsubsection{Crear una Macro} \drgeniusIcon{fig26} Extrae una secuencia de construcción dada en una figura y la convierte en la macro de una construcción. \subsubsection{Ejecutar una Macro} \drgeniusIcon{fig27} Ejecuta (i.e. ``lanza'' o ``corre'') una macro previamente construida. La macro puede haber sido recién creada o puede ser cargada desde un archivo. \drgeniusNote{Las construcciones de Macro están expuestas en la\link{Sección Construcción de Macros }[\Ref, página \Pageref]{macroConstruction}.} \xname{other_tools} \section{Otras herramientas} \subsection{Árbol lógico de construcción} \drgeniusIndex{Histórico}{Árbol lógico}{}{} Cada figura esta asociada a un árbol lógico de construcción. Este árbol es cronológico; es decir que recuerda, desde la parte alta hasta la parte baja, el orden de construcción de la figura. Ciertas entradas del árbol pueden ser desplegadas para que aparezcan los antecedentes --es decir, los objetos originadores (objetos padres)-- utilizados en la definición del objeto. Inicialmente el árbol esta oculto (enmascarado); de hecho está replegado en el borde izquierdo de la ventana. Para hacerlo aparecer hace falta desplegarlo con la ayuda del ratón. Mover el puntero del ratón hacia el borde izquierdo de la ventana de \drgeo\, cuando éste se transforme en ``<->'', presionar el botón del ratón y manteniéndolo presionado mueva el ratón a la derecha. \subsection{Mover la figura} \drgeniusIndex{Figura}{Mover}{}{} La figura puede ser movida presionando al mismo tiempo la tecla Control y el botón izquierdo del ratón al moverlo hacia donde se desea mover la figura. \subsubsection{Mover un Objeto} \drgeniusIcon{fig28} \drgeniusIndex{Objeto}{Mover}{}{} Un objeto puede ser movido al jalarlo con el ratón. La figura es redibujada con respecto a las nuevas posiciones. Casi cualquier tipo de objeto geométrico puede ser movido. Cuando es necesario, \drgenius\ mueve los puntos libres asociados con la figura. Por ejemplo, cuando el usuario mueve una línea definida por dos puntos libres, \drgenius\ moverá los dos puntos simultáneamente.. \subsection{Borrar un objeto} \drgeniusIcon{fig30} \drgeniusIndex{Objeto}{Borrar}{}{} Los objetos en la figura pueden ser borrados cuando se activa este menú. En cualquier momento posterior, el usuario puede anular el borrado usando la función ``deshacer'' de la bara de íconos o del menú editar->deshacer. Inicialmente el número de anulaciones posibles es de 10, pero el usuario puede ajustar este valor a través del diálogo de preferencias (Editar ->preferencias). \xname{editing_object_styles} \subsection{Editar la Apariencia de un Objeto} \drgeniusIcon{fig29} \drgeniusIndex{Editar}{Apariencia}{}{} \drgeniusIndex{Objeto}{Renombrar}{}{} \drgeniusIndex{Objeto}{Ocultar}{}{} \drgeniusIndex{Objeto}{Enmascarar}{}{} Cada objeto geométrico posee atributos de apariencia como son el color, el grosor, el nombre, el tamaño o la forma. Además, es posible ocultar temporalmente un objeto sin borrarlo. Por ejemplo, puede ser útil ocultar construcciones intermedias sin borrarlas. Todos estos atributos puedes ser ajustados desde un diálogo activado cuando el usuario selecciona un objeto en la figura. \drgeniusIndex{Punto}{Renombrar}{}{} El diálogo de apariencia para puntos se relaciona con cualquier tipo de objeto de punto. Desde él es posible ajustar el color, la forma, el tamaño, nombre y visibilidad. \drgeniusFigure{El diálogo de estilo para un objeto tipo punto}{fig31} El diálogo de apariencia para líneas se refiere a líneas rectas, semirrectas (rayos), segmentos, vectores, círculos, arcos de círculos, lugares geométricos. Desde él, es posible ajustar el color, el grosor, el nombre y su visibilidad. Cuando una recta, una semirrecta, un vector o un segmento son definidos por dos puntos que tienen nombres no vacíos, entonces el nombre de la recta es automáticamente deducido a partir de los nombres de los puntos que la originan. En este caso el usuario no puede renombrar a la recta. \drgeniusFigure{El diálogo de apariencia para objetos tipo línea}{fig32} El diálogo de estilo para los objetos tipo numérico y tipo polígono se refiere a todo tipo de valores (editados por el usuario, calculados por un Script Scheme de \drgeo\ o valores que representan una medida de un objeto geométrico) y de formas de polígono. (Notar que dos polígonos pueden tener colores distintos; podemos cambiarles el color) \drgeniusFigure{El diálogo de estilo para objetos numéricos y tipo polígono.}{fig33} \T \clearpage \subsection{Editando Propiedades de Objetos} \label{property-item} \drgeniusIcon{fig52} \drgeniusIndex{Editar}{Propiedades}{}{} \drgeniusIndex{Editar}{Punto}{}{} \drgeniusIndex{Editar}{Script}{}{} \drgeniusIndex{Editar}{Valor}{}{} Ciertas propiedades de los objetos son ajustables por el usuario. Cuando el usuario hace click en tales objetos, un diálogo apropiado aparece. De hecho, los siguientes objetos poseen propiedades ajustables por el usuario: \begin{enumerate} \item punto libre~: la abscisa y la ordenada pueden ser editadas;\\ \drgeniusFigure{Editar las coordenadas de un punto libre}{fig34} \item valor libre~: su valor puede ser editado\\ \drgeniusFigure{Editar valor libre}{fig36} \item script~: su código puede ser editado (El código esta en el lenguaje Scheme, que es un dialecto del lenguaje Lisp)\\ \drgeniusFigure{Editando un script}{fig35} \end{enumerate} \T \clearpage \subsection{Activar un enrejado} \drgeniusIndex{Figura}{Activar}{Enrejado(rejilla)}{} \drgeniusIndex{Enrejado}{Activar}{}{} \drgeniusIndex{Rejilla}{Activar}{}{} Es posible mostrar un enrejado unitario dentro de cualquier figura de \drgeo. El comando es accesible desde el menú \drgeniusMenu{Editar->Mostrar u ocultar rejilla}. Puede ser también activado con la tecla \drgeniusMenu{Ctrl-G}. Si el comando es reactivado, el enrejado es ocultado. El enrejado es unitario: cada subdivisión representa una unidad. Por último, si el enrejado esta activado al momento de guardar la figura; éste también será guardado junto con ella. \section{Preferencias de Usuario} \xname{default_behaviour} \subsection{Comportamiento Predeterminado} \label{default_behaviour} \drgeniusIndex{Editar}{Preferencias predeterminadas(default)}{}{} El comportamiento predeterminado de \drgenius\ puede ser modificado de varias maneras. Para ajustar las preferencias, el usuario va al elemento del menú \drgeniusMenu{Editar->Preferencias...} para abrir el diálogo de preferencias. \drgeniusFigureSize{Preferencias de las figuras geométricas}{fig38}{8} El diálogo se compone de dos partes~:: \begin{enumerate} \item La primera parte trata sobre propiedades de las figuras geométricas. Las distintas opciones permiten al usuario dar las reglas predeterminadas para cada tipo de objeto (geométrico o numérico). Estas reglas se refieren a la apariencia de los objetos. \item La segunda parte trata sobre preferencias globales~: \begin{itemize} \item El nivel para Deshacer/Rehacer; \item El nombre de la figura predeterminado que se usará cuando una nueva figura es creada. El \%d es remplazado por un valor entero que es manejado por \drgeo, este valor es incrementado con cada nueva figura creada; \item El navegador de internet predeterminado para visualisar la ayuda en línea~; \item Los nombres predeterminadas para ser utilizados cuando se guarde una figura o una sesión~; \item Los nombres predeterminados para exportar en los formatos \LaTeX~ y PostScript~; \end{itemize} \end{enumerate} \drgeniusIndex{Editar}{Estilo predeterminado (por default)}{}{} \drgeniusIndex{Editar}{Preferencias predeterminadas (por default)}{Deshacer/Hacer}{} \drgeniusIndex{Editar}{Preferencias predeterminadas}{Nombres}{} \drgeniusIndex{Ayuda}{Preferencias predeterminadas}{Navegador}{} \subsection{Otras Preferencias} Además del comportamiento predeterminada de \drgenius, el usuario puede cambiar el nombre de una figura desde el elemento menú \drgeniusMenu{Editar->Renombrar}. \drgeniusFigure{Renombrar la vista de una figura}{fig39} \chapter{Características Avanzadas} \label{advancedFeatures} En este capítulo presentamos características usadas para extender las características de \drgenius\ o adaptarlo a una situación pedagógica dada. La primera es la macro de una construcción geométrica. Ella permite la extracción de la lógica de una construcción en un registro. Ya hecho esto, este registro se puede repetir o guardar en un archivo que lleve la extensión \textbf{.mgeo}, y puede ser abierto cuando sea necesario.. Los Scripts Scheme de \drgeo\ --~\drgeo\ Script en inglés; abreviado DGS ~-representan otra forma de extender \drgenius. Estos scripts son en realidad elementos de figuras como cualquier otro elemento geométrico. Ellos reciben como entrada las referencias a los elementos de figura seleccionados por el usuario y dan como resultado un valor numérico, que se inserta en la figura . Son, en efecto, funciones \footnote{O procedimientos para los que se iniciaron en el lenguaje Pascal.} injertadas en una figura, y son evaluadas en cada actualización de la figura (i.e. cada vez que el programa requiere volver a dibujar la figura) Los Scripts Guile de \drgeo\ pueden ser útiles por el valor que dan como resultado o por sus efectos colaterales, dependiendo de lo que el usuario desee hacer. Extendiendo la funcionalidad de los Scripts de DrGeo, \drgeo\ puede ir todavía más allá, con la Figura Scheme de \drgeo: Ésta consiste en un archivo de texto que contiene una figura geométrica completamente escrita en el lenguaje de programación Scheme. La potencia de este modo de crear una figura radica en permitir una construcción usando el tipo de programación llamado funcional \footnote{Por ejemplo, permite la recursión.}, y no solamente declarativo, como es el caso de la interfaz gráfica. De este modo, \drgeo\ se convierte en un programa que puede ser utilizado para la introducción a la programación. Por último, la adaptación de la interfaz de usuario de \drgeo\ permite al maestro preparar una sesión de trabajo con varios documentos en los que ciertas funciones han sido bloqueadas a través de una contraseña (password). El objetivo de esto es permitir el uso del programa en ciertas situaciones pedagógicas dadas. \xname{using_macro} \section{Macros de Construcciones} \label{macroConstruction} Una Macro para una una construcción es una especie de procedimiento que recibe como entrada a elementos de figuras y devuelve uno o más elementos de figuras, construidas por la macro. Ellas son construidas en un modelo definido por el usuario. Esto significa que ella (o él) tiene que elaborar la serie de pasos para la construcción sólo una vez, a partir de entonces ordena a \drgenius\ grabar esta serie de pasos en una macro (macro-construction). Esta macro puede ser entonces guardada en un archivo con extensión \textbf{.mgeo}. Para grabar una serie de pasos para la construcción, \drgeo\ necesita saber cuáles son los elementos iniciales de la serie y los elementos que se van a dar como resultado. Desde luego que los elementos que se den como resultado deben depender \textit{solamente} de los elementos iniciales, \footnote{Esta restricción ha sido posteriormente flexibilizada, lo cual permite ir más allá con las macors. Ver \link{Crear un polígono regular}[ Sección \Ref, página \Pageref]{polygon_macro}.}, de otro modo \drgenius\ no podría deducir los elementos producidos a partir de los dados. De este modo, \drgenius\ deduce la lógica de la serie de pasos de la construcción y la guarde en una macro. El usuario puede ejecutar esta macro con sólo especificar los elementos de entrada (que deben coincidir con los parámetros que necesita la macro) en la figura. Entonces la macro crealos elementos especificados como resultado. \drgeniusNote{Los elementos invisibles de las figuras intermedias también son construidos por la macro. Estos elementos son necesarios para crear los elementos resultantes} Para ilustrar la característica de macros para construcciones, supondremos que el usuario desea grabar la construcción de un círculo que pasa por tres puntos. Supondremos, además, que se desea obtener el centro del círculo. \drgeniusFigureSize{Nuestra figura inicial}{fig40}{4} \drgeniusIndex{Macro}{Crear}{}{} Antes de la creación de la macro, el usuario necesita construir la figura final, ésta es usada como un molde con el cual se crea la macro. \drgeniusFigure{Nuestra figura con la construcción resultante}{fig41} \subsection{Crear una Macro} En esta etapa, la serie de pasos para la construcción ya está hecha. Ahora el usuario necesita ordenar a \drgeo\ que quiere una macro a partir de esta serie de pasos. Puede llamar la función \drgeniusMenu{Construir una macro} de la barra de íconos \drgeniusIcon{fig26} o del menú contextual que aparece al pulsar el botón derecho sobre el fondo de la figura.. Desde el menú de creación de la macro, el usuario selecciona los parámetros de entrada y de salida, el nombre y la descripción de la macro. \drgeniusFigureSize{La primera parte del menú de creación de la macro}{fig42}{6} La segunda parte del diálogo sirve para seleccionar los parámetros de entrada. En nuestro ejemplo, estos son los tres puntos iniciales. El usuario sólo necesita llegar a este lugar y seleccionar los tres puntos en la figura. Los elementos seleccionados parpadearán. \drgeniusFigureSize{Segunda parte, los tres puntos ya están seleccionados}{fig43}{6} En la tercera parte del diálogo, el usuario selecciona los parámetros de salida. En nuestro ejemplo, deseamos que el círculo y el centro sean los parámetros de salida para la macro. El usuario procede entonces como en el caso de los parámetros de entrada par seleccionarlos. \drgeniusFigureSize{La tercera página, el círculo y su centro ya están seleccionados}{fig44}{6} En la cuarta parte del diálogo, el usuario escribe el nombre y la descripción de la macro. Estos datos son desplegados cuando el usuario ejecuta una macro, de modo que ayuda a distinguir una macro de otra. \drgeniusFigureSize{La cuarta parte, el nombre y la descripción de la macro}{fig45}{6} En la última parte del diálogo (la quinta), el usuario crea la macro haciendo click sobre el botón \texttt{Aplicar}(finalizar la construcción). Alternativamente, el usuario puede regresar a las partes previas para ajustar los parámetros de la macro. \drgeniusNote{Si los parámetros de entrada y de salida no coinciden (\drgenius\ no puede extraer la lógica de la construcción), la macro no puede ser construida. En este caso, el usuario necesita reconsiderar la selección de los parámetros de entrada y de salida. Puede regresar a la segunda o a la tercera parte del menú de creación para ajustar sus elecciones.} En este momento la macro está construida y grabada en \drgenius. En la siguiente sección, veremos cómo usarla. \subsection{Ejecutar una Macro} \drgeniusIndex{Macro}{Ejecutar}{}{} Para ejecutar la macro de una construcción, el usuario llama la función \drgeniusMenu{Ejecutar macro previamente construida} de la barra de íconos \drgeniusIcon{fig27} o desde el menú contextual que se obtiene pulsando el boton derecho. Una ventana de diálogo que describe el procedimiento se inserta entonces. Desde la ventana de diálogo, el usuario selecciona la macro. En la segunda parte, selecciona la macro de la lista en la parte más alta del diálogo. Una vez que la macro fue seleccionada, puede hacer click directamente en los parámetros de entrada en la figura. Tan pronto como todos los parámetros de entrada sean seleccionados, la macro es ejecutada y los elementos de salida aparecen. \drgeniusFigureSize{El usuario selecciona los parámetros de entrada directamente en la figura}{fig46}{6} En nuestro ejemplo, la macro necesita tres parámetros de entrada (tres puntos) y crea a partir de ellos un círculo y un punto. Para ejecutar nuestra macro, necesitamos una figura con al menos tres puntos. \drgeniusFigureSize{Una figura con tres puntos}{fig47}{4} Una vez que nuestra macro es ejecutada usando esos tres puntos, obtenemos el círculo deseado y también su centro. \drgeniusFigureSize{La figura resultante con el círculo y su centro}{fig48}{4} \subsubsection{Con la ayuda del menú Macros} \drgeniusIndex{Macro}{Ejecutar}{Menu}{} Existe otro procedimiento --más rápido-- para ejecutar una macro. La barra de menú principal de \drgeo\ contiene un menú \drgeoMenu{Macro-constructions}. Este menú esta poblado con los nombres de las macros cargadas en la memoria del programa. Para ejecutar una macro, el usuario selecciona directamente la macro de su preferencia. En outre un passage du pointeur souris au dessus de chaque item de menu fait apparaître une info-bulle de la description de la macro. L'utilisateur peut ainsi avoir rapidement une explication sur l'ensemble des macro-constructions. \drgeniusFigureSize{Ejecutar una macro directamente desde el menú \drgeoMenu{Macro-constructions}}{fig62}{6} \T \clearpage \xname{drgenius_guile_script} \section{Script Scheme de \drgeo} \label{script} \drgeniusIndex{Script}{Introducción}{}{} \drgenius\ es compatible con Guile. Esto quiere decir que es posible ejecutar un script del lenguaje Scheme en \drgeo. Pero ¿qué es Guile? Leemos en el manual de Guile~: \begin{quote}{\em Guile es un intérprete del lenguaje de programación Scheme, concebida para su uso en una gran variedad de ambientes } \end{quote} Las siguientes citas describen de modo preciso como es Guile usado dentro de \drgenius: \begin{quote}{\em Como un shell, Guile puede correr interactivamente, leyendo expresiones del usuario, evaluándolas, y mostrando los resultados, o como un intérprete para un script, leyendo y ejecutando código de Scheme a partir de un archivo. Por otro lado, Guile también está disponible como una biblioteca (library) de objetos, lo que permite a otras aplicaciones fácilmente incorporar un intérprete de Scheme completo. Un programa puede usar Guile como un lenguaje de extensión, un lenguaje de configuración simple y poderoso, o como un ``pegamento'' multipropósito que conecta primitivas elaboradas dentro del programa. } \end{quote} En \drgenius, una API (Interfaz de programa para una aplicación, --Application Program Interface-- en Inglés) está disponible a partir del intérprete Guile. Esta API es un conjunto de ``enlaces'' en la maquinaria geométrica. Por lo tanto el usuario puede escribir un script para manipular elementos de figuras (geométricas y numéricas). Asimismo, ya que los scripts son figuras como cualquier otra, los scripts no necesitan ser guardados en un archivo separado; son guardados en el archivo de la figura. En lo que sigue usaremos el acrónimo DGS para referirnos a un Script Scheme de \drgenius\ (``\drgenius\ Script''). \subsection{DGS a través de ejemplos} \drgeniusIndex{Script}{Ejemplos}{}{} La herramienta para crear un DGS esta disponibe al seleccionar la sección Valor Numérico dentro del menú contextual que se obtiene al hacer click con el botón derecho del ratón en el fondo de la figura. Un DGS puede recibir de 0 a \textit{n} parámetros de entrada. Después de haber escogido el DGS, basta hacer click en los objetos geométricos (o numéricos) que constituirán los parámetros de entrada. Al terminar de escoger los parámetros de entrada, se debe hacer click en un área libre del fondo de la figura; con ello, el script sera visible. En lo que sigue nos proponemos trabajar con algunos ejemplos de DGS que permitirán comprender fácilmente su uso y su potencialidad. Los DGS, como las macros, dan una dimensión particular a \drgenius, Le permiten, junto con las macros\footnote{Las macros constituyen el aspecto geométrico, en tanto que los DGS abarcan también el aspecto numérico; pero no sólo eso, pues nos permiten utilizarlos con un espíritu de programador (``hacker'', en inglés, sería un término más apropiado)}, llevar a cabo cosas que los autores del programa no incorporaron o no quisieron incorporar: ``Ir hacia donde ellos no fueron o no quisieron ir''. Es también importante comprender que la mayor parte de las funciones del intérprete GNU Guile están disponibles a través del DGS. Esto es particularmente cierto para las librerías de funciones\footnote{En particular, las funciones matemáticas} que utilizaremos ampliamente. \paragraph{DGS sin parámetros de entrada} El procedimiento para crear un script sin parámetros de entrada es el siguiente~: \begin{enumerate} \item Después de haber escogido \link{Script Guile de \drgenius\ }[ Sección \Ref, página \Pageref]{script-tool}, hacer click en el lugar de la figura donde se desee colocar el script. Como deseamos que el script no tenga parámetros de entrada, debemos prestar atención y no hacer click erróneamente en algún objeto geométrico; no sea que \drgenius\ considere ese objeto como un parámetro de entrada \footnote{Si por accidente hacemos click sobre un objeto, el seleccionar de nuevo la herramienta Script en el menú bastará para anular nuestro error}. \item Una vez que el DGS ha sido creado, aparece en la figura la cadena de caracteres ``Dr.~Genius''. Todo script recién creado contiene un comando predeterminado que muestra ese mensaje. Usted puede editarlo seleccionando \link{propiedades del objeto}[ Sección \Ref, página \Pageref]{property-item}. \item Una vez que esta herramienta ha sido seleccionada, hacer click sobre el script --o para ser más precisos sobre su valor~-- de su elección. Una ventana se abrirá con el contenido del script y le permitirá editarlo. En lo que sigue, usaremos ese diálogo para escribir nuestros ejemplos. \end{enumerate} \subparagraph{Un generador de números aleatorios y otros ejemplos} \drgeniusIndex{Script}{\texttt{números aleatorios}}{}{} Si usted desea un generador de números aleatorios, nada es más simple: simplemente su script contiene únicamente la siguiente línea (recuerde hacer click en aplicar y luego cerrar...): \begin{verbatim} (random 10) \end{verbatim} Así, cada vez que se dibuja la figura, este script devuelve un número entero aleatorio en el intervalo [0~;~10[ (es decir, [0~;~10) ) Si usted prefiere un número real en el intervalo [0~,~1), utilice el siguiente script: \begin{verbatim} (random:uniform) \end{verbatim} \drgeniusNote{Algunas precisiones~: \begin{itemize} \item El valor devuelto por el script es el valor calculado por la última línea del script. En nuestros ejemplos, se trata del valor devuelto por la función que usamos. \item La última línea debe devolver un número real; de otro modo \drgenius\ imprimirá ``Resultado no imprimible''. \item Si lo que se desea es mostrar el valor de una variable, basta poner esa variable en la última línea. \end{itemize} } \subparagraph{Cálculo de algunas constantes comunes} Para calcular el valor aproximado de $\pi$~: \begin{verbatim} (acos -1) \end{verbatim} O de $e$~: \begin{verbatim} (exp 1) \end{verbatim} Los valores devueltos por estos DGS pueden ser inmediatamente utilizados como todos los demás valores numéricos que \drgenius\ genera. Por todo lo anterior, los DGS son verdaderamente nuestros aliados. Pero eso no es todo, los DGS pueden hacer muchas más cosas interesantes cuando reciben parámetros de entrada. Enseguida veremos cómo. \paragraph{DGS con al menos un parámetro de entrada} \drgeniusIndex{Script}{Con parámetros de entrada}{}{} El procedimiento para crear un DGS con un parámetro de entrada es esencialmente el mismo. Justo después de haber seleccionado la herramienta script, basta hacer click sobre el objeto que será el parámetro de entrada y enseguida hacer click sobre el fondo de la figura, en el lugar donde se desee tener al nuevo script. Enseguida, dentro del script, el parametro de entrada será referido por la variable $a1$. En caso de tengamos dos o más parámetros de entrada, utilizaremos, respetando el orden en que fueron seleccionados, las variables $a1, a2, a3, a4,$ etc. dependiendo del número de objetos seleccionados. Dependiendo del objeto que seleccionemos, diversos métodos estarán disponibles para obtener valores, como pueden ser coordenadas, longitud, etc. Estos métodos son mostrados en la Sección \link{Métodos de referencia para un DGS}[ \Ref, página \Pageref]{api-dgs}. En lo que sigue, expondremos gradualmente un ejemplo no muy complicado en que construiremos la curva de una función así como la tangente en un punto de la curva que podremos mover. La figura final es mostrada por \drgeo. Esta se llama \xlink{slope.fgeo}[(/usr/share/drgeo/examples/figures/slope.fgeo)]{/usr/share/drgeo/examples/figures/slope.fgeo} \drgeniusFigureSize{La figura que obtendremos}{fig55}{8} \subparagraph{Definir un valor en un intervalo dado.} \drgeniusIndex{Script}{Intervalo}{}{} En una nueva figura, empezamos colocando dos puntos y el segmento que ellos determinan. Sobre este segmento colocamos un punto libre al que llamaremos ``¡Muéveme!''(``Move me!'' en inglés). Este punto nos sirve para determinar un valor numérico que identifica la posición del punto dentro del segmento; esto lo lograremos dentro del script. En seguida crearemos un script que tiene como único parámetro de entrada el punto ``¡Muéveme!''. Ya que $a1$ es la variable en el script del punto ``¡Muéveme!'', el script siguiente (que llamaremos Xo) nos dará un valor decimal comprendido entre [-10~;~10]~. \begin{verbatim} (define x (getAbscissa a1)) (* 20 (- x 0.5)) \end{verbatim} % I FOLLOWED THE ITALIAN VERSION IN THE FOOTNOTE HERE. Cabe aclarar algunas cosas. En la primera línea, \texttt{(getAbscissa a1)} permite obtener la ``abscisa curvilínea'' del objeto al que se refiere $a1$\footnote{En este punto $x$ toma un valor entre 0 y 1 inclusive. La ``abscisa curvilínea'' del objeto es 0 en un extremo, y va creciendo hasta ser 1 en el otro extremo; es 0.5 en la mitad, 0.25 a un cuarto, etc. } . En la segunda línea calibramos el valor. En este caso la expresión significa $20 \times ( x -0.5)$. Dado que ésta es la última línea del script, el resultado de esta última operación será el valor que el script devuelva, y será un número decimal en el intervalo $[-10;+10]$ como se deseaba\footnote{Ya que $x$ estaba entre 0 y 1, $20 \times ( x -0.5)$ estará entre -10 y 10.}. Finalmente, llamemos este script Xo. (Esto se puede hacer en el menú contextual: seleccione otros, luego apariencia, y haga click en el script para ponerle nombre). \subparagraph{Dibujar la gráfica de una función.} \drgeniusIndex{Lugar geométrico}{Script}{}{} % I DECIDED NOT TO TRANSLATE nous servira d'abscisse BECAUSE IT COULD % LEAD TO SOME CONFUSSION WITH THE CURVILÍNEAR ABSCISSA. % I FOLLOWED THE ITALIAN VERSION HERE El valor obtenido por el script precedente nos servirá, a través de otro script, para calcular la imagen del punto bajo la función $x \rightarrow cos(x)$. Este segundo script tiene como parámetro de entrada al script Xo. \begin{verbatim} (define x (getValue a1)) (cos x) \end{verbatim} Subrayemos que en \texttt{(getValue a1)} el objeto al que se refiere $a1$ no es el punto ``¡Muéveme!'', sino el script Xo, y que no estamos obteniendo la ``abscisa curvilínea'' de un punto, sino el valor de un número (en este caso del script Xo, que dentro del segundo script es llamado $a1$). Llamamos a este script Yo % I ADDED THE NEXT PARAGRAPH. Por ejemplo, si el punto ``¡Muéveme!'' estaba a la mitad entonces su ``abscisa curvilínea'' es 0.5, de modo que Xo toma el valor $20 \times ( 0.5 -0.5)=0$, y Yo toma el valor cos(0)=1. % I ADDED SOME SENTENCES IN PARENTHESIS TO CLARIFY SOME THINGS AND % TO REMIND THE READER HOW TO CREATE Mo AND THE LOCUS. Enseguida crearemos el punto Mo de coordenadas (Xo~;~Yo). Es un punto de la curva de la función $x \rightarrow cos(x)$. Para dibujar la porción de la gráfica con dominio [-10~;~10], crearemos el lugar geométrico del punto Mo cuando el punto ``¡Muéveme'' describe el segmento. Con ello obtendremos la gráfica!(Recordar que para crear Mo, hay que seleccionar, en el menú contextual, punto, coordenadas y luego hacer click en los scripts que dan las coordenadas. Para lograr el lugar geométrico, recordar seleccionar en el menú contextual curva, lugar geométrico y luego seleccionar los puntos ``¡Muéveme!'' y Mo.) \subparagraph{Calcular y dibujar la tangente a la gráfica en un punto} \drgeniusIndex{Script}{Ejemplos}{Tangente a una curva}{} Para dibujar la tangente en Mo=(Xo,Yo), hace falta tener la pendiente en ese punto. Usando Cálculo Diferencial, sabemos que la pendiente esta dada por la derivada, que en este caso es $x \rightarrow -sin(x)$ evaluada en el punto Xo. De modo que crearemos un script que tiene como parámetro de entrada al script Xo~: \begin{verbatim} (- 0 (sin (getValue a1))) \end{verbatim} La notación prefija (i.e ``* 2 3'' en vez de ``2 * 3'') utilizada por Scheme/Guile puede parecer poco intuitiva, pero es cuestión de simplemente acostumbrarse a ella; es simplemente decir ``El producto de dos y tres'' en lugar de ``dos por tres''. Llamemos al script recién creado ``Pendiente en el punto Mo''. Resta, pues dibujar la tangente. Para esto calcularemos, primero, las coordenadas de un segundo punto --~M1~-- de esa recta. Comencemos por su abscisa (No confundir con la ``abscisa geométrica''); por ejemplo: $X_{1} = X_{0} + 2$. Para hacer esto crearemos un script que tendrá como parámetro de entrada al script Xo~, y al que llamaremos X1: \begin{verbatim} (define x1 (getValue a1)) (+ x1 2) \end{verbatim} Encontremos en este momento la ordenada del punto M1. Para ello necesitamos: \begin{itemize} \item Mo (referencia $a1$)~; \item la pendiente en Mo ($a2$)~; \item la abscisa X1 ($a3$).(No confundir con ``la abscisa geométrica'') \end{itemize} Después de seleccionar como parámetros de entrada al punto Mo, a la pendiente en Mo(que llamamos ``Pendiente en el punto Mo'', ``Slope at Mo'' en inglés), y a X1, determinamos la ordenada de M1, que llamaremos Y1, a través del siguiente cálculo: $Yo + m \times (X1 - X0)$~: \begin{verbatim} (define x0 (car (getCoordinates a1))) (define y0 (cadr (getCoordinates a1))) (define m (getValue a2)) (define x1 (getValue a3)) (+ (* m (- x1 x0)) y0) \end{verbatim} En relación con la función \texttt{(getCoordinates a1)} en la que $a1$ debe ser una referencia a un objeto de tipo punto, el método devuelve una lista que contiene las coordenadas del punto, en este caso Mo. La instrucción \texttt{car} permite extraer el primer elemento de esta lista; la instrucción \texttt{cadr}, el segundo. El resto del script debe resultar claro. Habiendo nombrado este último script Y1, construimos el punto M1=(X1~;~Y1), y, para terminar, construimos la tangente (MoM1). (Para esto ya no necesitamos scripts; podemos usar el menú, escogiendo punto dadas sus coordenadas y la recta dados dos puntos). Por supuesto, habría sido posible utilizar unos dos o tres scripts en lugar de la gran cantidad que usamos. Sin embargo, esperamos que estos pequeños ejemplos logren en usted el deseo de experimentar por usted mismo los DGS. \subsection{Métodos de referencia para los scripts de \drgeo\ } \label{api-dgs} Las secciones siguientes contienen la descripción de los métodos disponibles para los DGS. Estos métodos están clasificados de acuerdo al tipo de objeto geométrico o numérico. % I FOLLOWED THE ITALIAN VERSION IN TERMS OF THE SYNTAX. \subsubsection{Punto} \drgeniusIndex{Script}{\texttt{getAbscissa}}{}{}{} \begin{drgeoApi}{valor (getAbscissa punto)} \drgeoApiIn{punto}{Referencia a un punto sobre una curva} \drgeoApiOut{La ``abscisa geométrica'' del punto sobre la curva.El valor pertenece al intervalo [0~;~1]} \drgeoApiExample{(define x (getAbscissa a1))\\ (* x 10)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{setAbscissa}}{}{}{} \begin{drgeoApi}{(setAbscissa punto x)} \drgeoApiIn{punto}{Referencia a un punto libre sobre una línea} \drgeoApiIn{x}{Valor decimal en el intervalo [0~;~1] que representa a la nueva ``abscisa geométrica''} \drgeoApiExample{(setAbscissa a1 0.5)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getCoordinates}}{}{} \begin{drgeoApi}{lista (getCoordinates punto|vector)} Devuelve las coordenadas de un punto o de un vector.\\ \drgeoApiIn{punto|vector}{Referencia a un punto o un vector} \drgeoApiOut{Lista que contiene las coordenadas del punto o del vector} \drgeoApiExample{(define c (getCoordinates a1))\\ (define x (car c))\\ (define y (cadr c))\\ (+ (* x x) (* y y))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{setCoordinates}}{}{} \begin{drgeoApi}{(setCoordinates punto coord)} Asigna coordenadas a un punto\\ \drgeoApiIn{punto}{Referencia a un punto libre en el plano} \drgeoApiIn{coord}{Lista de dos números decimales} \drgeoApiExample{(define l (list 1.4 (random 5)))\\ (setCoordinate a1 l)} \end{drgeoApi} \subsubsection{Recta, Semirrecta, Segmento, Vector} \drgeniusIndex{Script}{\texttt{getSlope}}{}{}{} \begin{drgeoApi}{valor (getSlope dirección)} \drgeoApiIn{dirección}{Referencia a un objeto de tipo recta, semirrecta, segmento o vector} \drgeoApiOut{La pendiente en esa dirección} \drgeoApiExample{(define p (getSlope a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getUnit}}{}{}{} \begin{drgeoApi}{valor (getUnit dirección)} \drgeoApiIn{dirección}{Referencia a un objeto de tipo recta, semirrecta, segmento o vector} \drgeoApiOut{Una lista que contiene las coordenadas de un vector unitario en la dirección dada} \drgeoApiExample{(define v (getUnit a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getNormal}}{}{}{} \begin{drgeoApi}{valor (getNormal dirección)} \drgeoApiIn{dirección}{Referencia a un objeto de tipo recta, semirrecta segmento o vector} \drgeoApiOut{Una lista que contiene las coordenadas de un vector normal a la dirección dada} \drgeoApiExample{(define n (getNormal a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getNorm}}{}{} \begin{drgeoApi}{valor (getNorm vector)} \drgeoApiIn{vector}{Referencia a un vector} \drgeoApiOut{La norma (i.e., magnitud, longitud) de ese vector} \drgeoApiExample{(define n (getNorm a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getLength}}{}{} \begin{drgeoApi}{valor (getLength segmento)} \drgeoApiIn{segmento}{Referencia a un segmento} \drgeoApiOut{La longitud de ese segmento} \drgeoApiExample{(define l (getLength a1))} \end{drgeoApi} \subsubsection{Círculo, Arco de círculo} \drgeniusIndex{Script}{\texttt{getCenter}}{}{} \begin{drgeoApi}{lista (getCenter círculo|arco)} \drgeoApiIn{círculo|arco}{Referencia a un círculo o un arco de círculo} \drgeoApiOut{Lista que contiene las coordenadas del centro de un círculo o de un arco de círculo} \drgeoApiExample{(define c (getCenter a1))\\ (car c)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getRadius}}{}{} \begin{drgeoApi}{valor (getRadius círculo|arco)} \drgeoApiIn{círculo|arco}{Referencia a un círculo o un arco de círculo} \drgeoApiOut{Radio del círculo o del arco de círculo} \drgeoApiExample{(define r (getRadius a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getLength}}{}{} \begin{drgeoApi}{valor (getLength círculo|arco)} \drgeoApiIn{círculo|arco}{Referencia a un círculo o un arco de círculo} \drgeoApiOut{Perímetro del círculo o longitud del arco de círculo} \drgeoApiExample{(define l (getLength a1))} \end{drgeoApi} \subsubsection{Funciones Numéricas} \drgeniusIndex{Script}{\texttt{getValue}}{}{} \begin{drgeoApi}{valor (getValue número)} \drgeoApiIn{número}{Referencia a un número} \drgeoApiOut{Valor de ese número} \drgeoApiExample{(define a (getValue a1))\\ (define b (getValue a2))\\ (+ a b)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{setValue}}{}{} \begin{drgeoApi}{(setValue número v)} \drgeoApiIn{número}{Referencia a un número} \drgeoApiIn{v}{Valor decimal} \drgeoApiExample{(define v (getValue a1))\\ (setValue a2 v)} \end{drgeoApi} \subsubsection{Ángulo} \drgeniusIndex{Script}{\texttt{getAngle}}{}{} \begin{drgeoApi}{valor (getAngle ángulo)} \drgeoApiIn{ángulo}{Referencia a un ángulo orientado o geométrico} \drgeoApiOut{La medida de ese ángulo en grados. Para obtener la medida en radianes, utilice la función \texttt{getValue}} \drgeoApiExample{(define angle1 (getAngle a1))\\ (define angle2 (getAngle2))\\ (define angle3 (getAngle a3))\\ (+ angle1 angle2 angle3)} \end{drgeoApi} \subsubsection{Otros} % THERE IS A TYPO IN THE FRENCH VERSION!!!! % WARNING SINCE THE SCRIPT IS EXECUTED LOTS OF TIMES THE FIGURE WILL MOVE A LOT. \drgeniusIndex{Script}{\texttt{move}}{}{} \begin{drgeoApi}{(move item t)} \drgeoApiIn{item}{Referencia a un objeto de la figura} \drgeoApiIn{t}{vector de dos dimensiones} \drgeoApiExample{(define v (vector .1 0))\\ (move a1 v)} \end{drgeoApi} \section{Figura Scheme de \drgeo} \drgeniusIndex{Figura Scheme de \drgeo}{Introducción}{}{} Las \emph{Figuras Scheme de \drgeo} -- (FSD) -- son figuras escritas en un lenguaje relativamente natural. No se trata entonces de construir una figura con la ayuda de la interfaz gráfica de \drgeo\ sino más bien de describir una figura dentro del lenguaje Scheme(Una variante de Lisp). Hemos cuidado mucho que la sintaxis utilizada sea fácil y concisa. Además, el conjunto de palabras clave utilizadas en Scheme para para describir una figura simple son adaptables de modo que aparezcan en Español, Francés, Inglés, etc. . Una combinación de varios idiomas es también posible; pero no es deseable.(N. del T. es por ello que varias palabras clave en este manual aparecen en Español. Basta con traducir un archivo en el directorio scm donde \drgeo\ está instalado; notar que en la traducción hecha del archivo, se incluyó una versión de los comandos con acentos y eñes, así como otra sin acentos y sin eñes. Las palabras clave no traducidas seran escritas en inglés.) \subsection{Algunos Ejemplos} \drgeniusIndex{Figura Scheme de \drgeo}{Ejemplos}{}{} (N.del T. En lo que sigue se usarán las palabras ``referencia'' y ``nombre''. ``referencia'' es una variable que apunta a un objeto. ``nombre'' es el rótulo que aparece en la figura. A veces se usará el termino variable; pero ``referencia'' es más preciso en otros casos.) En sí, Scheme es un lenguaje de muy alto nivel. Cuando una figura es definida en este lenguaje, disponemos también de todo su poder para, por ejemplo, definir recursivamente alguna parte de la figura o bien para colocar aleatoriamente ciertos objetos de tal suerte que, cada vez que se cargue la figura, los objetos aparecerán ligeramente distintos. En pocas palabras, los FSD no están atados a las limitantes de la interfaz gráfica, y además poseen todo el poder del lenguaje Scheme. \drgeniusIndex{Figura Scheme de \drgeo{}}{Evaluar}{}{}Un FSD es entonces un archivo con extension \textbf{.scm} creado con la ayuda de un editor de texto, el cual es abierto en \drgeo\ con la ayuda del comando \drgeniusMenu{Archivo->Evaluar}. \drgeniusIndex{Figura Scheme de \drgeo}{Nueva figura}{}{} Comencemos por estudiar un ejemplo sencillo de FSD~: \begin{verbatim} (nueva-figura "Mi figura") \end{verbatim} Este es el script más pequeño que podemos definir. Después de ser cargado en \drgeo, simplemente crea una nueva figura vacía con el nombre ``Mi figura''. Podemos escribir comandos \texttt{(nueva-figura "{}Mi figura"{})} tantas veces como deseemos. Veamos ahora un segundo ejemplo~: \begin{verbatim} (nueva-figura "Mi figura") (sea Punto "A" libre 1.2 -2) \end{verbatim} Este FSD define una figura con un punto libre $A$ de coordenadas iniciales $(1,2~;~-2)$. Como podemos ver la sintaxis de la definición de un objeto geométrico es relativamente cómoda, a tal grado que esa expresada en nuestra lengua madre. Esto es de interés especial para la enseñanza secundaria. De hecho, todos los comandos de definición de objeto tienen una sintaxis común. Tal sintaxis es como sigue: \begin{enumerate} \item Se comienza siempre con la palabra clave \texttt{sea}, la cual indica que deseamos definir un nuevo objeto \item Inmediatamente le sigue la clase de objeto; en este caso \texttt{Punto}. \item El nombre del objeto va enseguida, $A$, debe siempre estar entre dos comillas "{}. Si no deseamos nombrar al objeto, de todos modos es necesario dar un nombre vacío como sigue: "{}"{}. \item Para terminar, necesitamos precisar, dentro de la clase, qué tipo de objeto, en nuestro ejemplo, la clase es punto, y el tipo es \texttt{libre}. Esto significa que el punto $A$ es libre. \item El tipo de objeto es seguido por una lista de argumentos que depende de la clase de objeto y de que tipo de objeto. En nuestro ejemplo, esta lista se compone de dos números, las coordenadas del punto libre $A$. \end{enumerate} Prosigamos con un tercer ejemplo~: \begin{verbatim} (define (triángulo p1 p2 p3) (Segmento "" extremos p1 p2) (Segmento "" extremos p2 p3) (Segmento "" extremos p1 p3)) (define (azar) (- 8 (* 16 (random:uniform)))) (nueva-figura "Mi figura") (sea Punto "A" libre (azar) 0) (sea Punto "B" libre 5 0) (sea Punto "C" libre (azar) 5) (triángulo A B C) \end{verbatim} (N. del T. En este ejemplo, dos palabras están en inglés: ``random'' que significa ``azar'', y ``uniform'' que significa ``uniforme''. Como se comentó antes es posible traducirlas modificando el archivo dentro del directorio scm donde \drgeo\ esté instalado. El archivo para español es: \texttt{/usr/share/drgeo/scm/drgeo\_scm\_interface\_constant\_es.scm}). Este ejemplo es particularmente interesante, nos muestra tres cosas importantes~: \begin{enumerate} \item La definición de una construcción de alto nivel no prevista por los autores de \drgeo. En el programa que acabamos de ver hemos definido la función \texttt{triángulo} la cual, a partir de tres puntos construye el triángulo que pasa por esos tres puntos. Podemos comparar esto con las macros; pero con un grado de libertad mucho más amplio e importante. \item La definición de las funciones asociadas, en este caso definimos la función \texttt{azar} que devuelve un número decimal comprendido entre -8 y 8. Utilizamos esta función para añadir un elemento de azar en ciertos puntos en nuestra figura. De este modo cada vez que se cargue la figura, ésta será ligeramente distinta. \item En efecto, la utilización de la palabra clave \texttt{sea} no es obligatoria; nosotros la utilizamos para guardar una referencia al objeto creado. Por ejemplo, dentro de la función \texttt{triángulo} no guardamos referencias para los segmentos creados. Por otro lado, cuando definimos los puntos $A$, $B$ y $C$ necesitamos guardar una referencia para ellos, estas referencias se llamarán igual\footnote{Desde el punto de vista del lenguaje Scheme, estas referencias son símbolos que apuntan hacia una estructura interna del objeto --un prototipo-- mientras que los nombres son simplemente cadenas de caracteres.}; pero sin las comillas; así nuestras referencias son: \texttt{A}, \texttt{B} y \texttt{C}. En lo que sigue llamaremos \textbf{símbolos} a esas variables, esta es la terminología precisa del lenguaje Scheme. De este modo, al llamar a la función \texttt{triángulo}, pasamos como parámetros a los símbolos \texttt{A}, \texttt{B} y \texttt{C} que son utilizados para definir nuestros tres segmentos. \end{enumerate} Notar que cuando definimos los segmentos, no les dimos ningún nombre; en ese caso \drgeo\ les dará un nombre que está determinado a partir del nombre de sus extremos. Nuestros tres segmentos tendrán entonces los nombres $[AB]$, $[BC]$ y $[AC]$. Para concluir esta sección, veamos un último ejemplo~: \begin{verbatim} (sea Punto "A" libre 1 0) (sea Punto "B" libre 5 0) (sea Recta "d1" 2puntos A B) (envía A color amarillo) (envía A forma redonda) (envía A tamaño grande) (envía B oculto) (envía d1 grosor punteado) \end{verbatim} Los tres primeros comandos crean dos puntos y una recta. La parte que nos interesa particularmente es la serie de comandos \texttt{envía}. Estos comandos permiten la comunicación con un objeto cuyo símbolo hemos guardado; en este caso tenemos los símbolos \texttt{A}, \texttt{B} y \texttt{d1}. El comando consiste en enviar un mensaje a un objeto. Su primer parámetro de entrada es el objeto con el que deseamos comunicarnos, el segundo argumento es el mensaje, los restantes argumentos están determinados por tipo de mensaje que es enviado. Por ejemplo \texttt{(envía A color amarillo)} envía el mensaje \texttt{color} con parámetro de entrada \texttt{amarillo}. El punto A toma entonces el color amarillo. Es fácil comprender el sentido de los otros comandos \texttt{envía}. Estos serán explicadosen la sección siguiente. Hemos terminado nuestra pequeña visita guiada a las \emph{Figuras Scheme de Dr. Geo, FSD}. En las secciones siguientes expondremos el conjunto de comandos disponibles para definir las FSD. \subsection{Métodos de referencia para las figuras Scheme de \drgeo} La definición de los objetos en un documento FSD se hace a través de prototipos. Los prototipos son en cierto sentido objetos a los que podemos interrogar y modificar como veremos en lo que sigue. Empero, antes de la definición de objeto alguno en un FSD, el FSD debe ser creado con el comando \texttt{nueva-figura} en el principio del archivo. \subsubsection{Comandos generales} \begin{drgeoApi}{(nueva-figura nombre)} \drgeoApiIn{nombre}{Cadena de caracteres} \drgeoApiOut{No devuelve ningún valor. Es llamada por el efecto que produce, no por el valor que devuelve. Este comando crea una figura nueva. Los objetos creados posteriormente se crean dentro de esta figura hasta que se vuelva a llamar este comando.} \drgeoApiExample{(nueva-figura "{}Mi 1er figura"{})} \end{drgeoApi} \subsubsection{Definición de objetos en una figura} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{}{} Un objeto puede ser definido a través de varias sintaxis~: \begin{itemize} \item \texttt{(sea Punto "{}p1"{} tipo args)} El punto es creado y su referencia guardada en la variable \texttt{p1}. Esta sintaxis utiliza una macro Scheme. \item \texttt{(Punto "{}Nombre"{} tipo args)} El punto es creado pero ninguna referencia al punto es conservada. \item \texttt{(define p1 (Punto "{}Nombre"{} tipo args))} El punto es creado y su referencia guardada en la variable \texttt{p1}. \item \texttt{(set! p1 (Punto "{}Nombre"{} tipo args))} El punto es creado y su referencia es copiada en la variable, ya existente, \texttt{p1}. \end{itemize} Si unos objetos son creados después del cuerpo de una función, utilice ya sea la forma \texttt{set!} o la forma especial de Scheme \texttt{let}. Es importante subrayar que la llamada se hace a una función que devuelve una referencia al objeto creado. Para saber más sobre la correspondencia entre los nombres de los comandos Scheme en Español y en Inglés, vea el archivo \texttt{/usr/share/drgeo/scm/drgeo\_scm\_interface\_constant\_es.scm}. \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Punto}{} \paragraph{Punto} \T ~\\ \begin{drgeoApi}{prototipo (Punto nombre libre x y)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{x}{La abscisa del punto} \drgeoApiIn{y}{La ordenada del punto} \drgeoApiOut{Referencia a un punto libre del plano con coordenadas iniciales \texttt{x} y \texttt{y}.} \drgeoApiExample{(define p1 (Punto "{}A"{} libre 1.2 (acos -1)))} \end{drgeoApi} \begin{drgeoApi}{prototipo (Punto nombre sobre-la-curva curva x)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{curva}{Referencia a una curva (recta, semirrecta, segmento, arco, círculo, etc..)} \drgeoApiIn{x}{Abscisa curvilínea (la ``abscisa geométrica'') del punto libre; el valor pertenece al intervalo [0~;~1]} \drgeoApiOut{Referencia a un punto libre sobre la curva} \drgeoApiExample{(Punto "{}M"{} sobre-la-curva s1 0.5)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Punto nombre mitad-2pts p1 p2)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{p1}{Referencia a un punto} \drgeoApiIn{p2}{Referencia a un punto} \drgeoApiOut{Referencia al punto medio de los dos puntos.} \drgeoApiExample{(sea Punto "{}A"{} libre 1 1)\\ (sea Punto "{}B"{} libre 4 4)\\ (Punto "{}I"{} mitad-2pts A B)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Punto nombre mitad-segmento s)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{s}{Referencia a un segmento} \drgeoApiOut{Referencia a la mitad de un segmento.} \drgeoApiExample{(Punto "{}L"{} mitad-segmento s)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Punto nombre intersección l1 l2)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{l1}{Referencia a una línea(recta o curva)} \drgeoApiIn{l2}{Referencia a una línea(recta o curva)} \drgeoApiOut{Referencia al punto de intersección de las dos líneas} \drgeoApiExample{(Punto "{}I"{} intersección recta segmento)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Punto nombre intersección2 l1 l2)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{l1}{Referencia a una línea(recta o curva)} \drgeoApiIn{l2}{Referencia a una línea(recta o curva)} \drgeoApiOut{Referencia al segundo punto de intersección de las dos líneas cuando una de las dos líneas es del tipo arco de círculo o del tipo círculo.} \drgeoApiExample{(Punto "{}I"{} intersección2 recta círculo)} \end{drgeoApi} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Recta}{} \paragraph{Recta} \T ~\\ \begin{drgeoApi}{prototipo (Recta nombre 2puntos p1 p2)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{l1}{Referencia a un punto} \drgeoApiIn{l2}{Referencia a un punto} \drgeoApiOut{Referencia a una recta que pasa por los dos puntos.} \drgeoApiExample{(sea Punto "{}A"{} libre 0 0)\\ (sea Punto "{}M"{} libre 1 2)\\ (Recta "{}"{} 2puntos A M)} \end{drgeoApi} % HERE AN EXPLICIT EXAMPLE MIGHT BE USEFUL. d WAS NOT DEFINED. \begin{drgeoApi}{prototipo (Recta nombre paralela p d)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{p}{Referencia a un punto} \drgeoApiIn{d}{Referencia a una dirección (recta, segmento, vector,...)} \drgeoApiOut{Referencia a una recta paralela a la dirección \texttt{d} y que pasa por el punto \texttt{p}.} \drgeoApiExample{(sea Punto "{}A"{} libre 1 5)\\ (sea Recta "{}d1"{} paralela A d)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Recta nombre perpendicular p d)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{p}{Referencia a un punto} \drgeoApiIn{d}{Referencia a una dirección (recta, segmento, vector, ...)} \drgeoApiOut{Referencia a una recta perpendicular à la dirección de \texttt{d} y que pasa por por \texttt{p}.} \drgeoApiExample{(sea Punto "{}A"{} libre 1 5)\\ (sea Recta "{}d1"{} perpendicular A d)} \end{drgeoApi} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Semirrecta}{} \paragraph{Semirrecta} \T ~\\ \begin{drgeoApi}{prototipo (Semirrecta nombre 2puntos o p)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{o}{Referencia a un punto, origen de la semirrecta} \drgeoApiIn{p}{Referencia a un punto, punto de la semirrecta} \drgeoApiOut{Referencia a una semirrecta definida por su origen y por un punto.} \drgeoApiExample{(sea Punto "{}A"{} libre 1 5)\\ (sea Punto "{}O"{} libre 0 0)\\ (sea Semirrecta "{}dd1"{} 2puntos A 0)} \end{drgeoApi} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Segmento}{} \paragraph{Segmento} \T ~\\ \begin{drgeoApi}{prototipo (Segmento nombre extremos p1 p2)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{p1}{Referencia a un punto} \drgeoApiIn{p2}{Referencia a un punto} \drgeoApiOut{Referencia a un segmento definido por sus extremos} \drgeoApiExample{(sea Punto "{}A"{} libre 1 5)\\ (sea Punto "{}B"{} libre 10 4)\\ (sea Segmento "{}"{} extremos A B)} \end{drgeoApi} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Círculo}{} \paragraph{Círculo} \T ~\\ \begin{drgeoApi}{prototipo (Círculo nombre 2puntos c p)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{c}{Referencia a un punto, centro del círculo} \drgeoApiIn{p}{Referencia a un punto sobre el círculo} \drgeoApiOut{Referencia a un círculo definido por su centro y por un punto.} \drgeoApiExample{(sea Punto "{}A"{} libre 1 5)\\ (sea Punto "{}B"{} libre 10 4)\\ (sea Círculo "{}C1"{} 2puntos A B)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Círculo nombre centro-radio c r)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{c}{Referencia a un punto, centro del círculo} \drgeoApiIn{r}{Referencia a una valor numérico, radio del círculo} \drgeoApiOut{Referencia a un círculo definido por su centro y por su radio} \drgeoApiExample{(sea Punto "{}A"{} libre 1 5)\\ (sea Número "{}r"{} libre 10)\\ (sea Círculo "{}C1"{} centro-radio A r)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Círculo nombre centro-segmento c s)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{c}{Referencia a un punto, centro del círculo} \drgeoApiIn{s}{Referencia a un segmento dada la donde la longitud del segmento será el radio del círculo} \drgeoApiOut{Referencia a un círculo definido por su centro y por un segmento cuya longitud es su radio.} \drgeoApiExample{(sea Punto "{}A"{} libre 1 5)\\ (sea Círculo "{}C1"{} centro-segmento A s)} \end{drgeoApi} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Arco}{} \paragraph{Arco de círculo} \T ~\\ \begin{drgeoApi}{prototipo (Arco nombre 3puntos p1 p2 p3)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{p1}{Referencia a un punto, 1$^{er}$ extremo del arco de círculo} \drgeoApiIn{p2}{Referencia a un punto del arco} \drgeoApiIn{p3}{Referencia a un punto, 2$^{o}$ extremo del arco de círculo} \drgeoApiOut{Referencia a un arco de círculo definido por sus extremos y por un punto interno.} \drgeoApiExample{(sea Punto "{}A"{} libre 1 5)\\ (sea Punto "{}B"{} libre 0 5)\\ (sea Punto "{}C"{} libre -1 -2)\\ (sea Arco "{}arc"{} 3puntos A B C)} \end{drgeoApi} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Polígono}{} \paragraph{Polígono} \T ~\\ \begin{drgeoApi}{prototipo (Polígono nombre npuntos args)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto.} \drgeoApiIn{args}{Una lista de referencias de puntos~; vértices del polígono.} \drgeoApiOut{Referencia a un polígono definido por sus vértices.} \drgeoApiExample{(sea Polígono "{}quad"{} npuntos A B C D)} \end{drgeoApi} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Transformaciones geométricas}{} \paragraph{Las transformaciones geométricas} \T ~\\ Los prototipos de las transformaciones geométricas permiten la obtención de objetos rotados, reflejados, trasladados, a escala, etc.. Estos prototipos usan como referencia a los tipos punto, recta, semirrecta, vector, círculo, arco de círculo y polígono. \begin{drgeoApi}{prototipo (TipoDeObjeto nombre rotación objeto centro ángulo)} \drgeoApiIn{TipoDeObjeto}{Punto, Segmento, Recta, Semirrecta, Vector, Círculo, Arco, Polígono} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{objeto}{Referencia del objeto a transformar} \drgeoApiIn{centro}{Referencia a un punto, centro de la rotación} \drgeoApiIn{ángulo}{Referencia a un valor numérico, ángulo de la rotación} \drgeoApiOut{Referencia del objeto ya transformado.} \drgeoApiExample{(sea Punto "{}I1"{} rotación I C a)} \end{drgeoApi} \begin{drgeoApi}{prototipo (TipoDeObjeto nombre escala objeto centro k)} \drgeoApiIn{TipoDeObjeto}{Punto, Segmento, Recta, Semirrecta, Vector, Círculo, Arco, Polígono} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{objeto}{Referencia del objeto a transformar} \drgeoApiIn{centro}{Referencia a un punto, centro de la escala (centro de homotecia)} \drgeoApiIn{k}{Referencia a un valor numérico, factor de la escala (homotecia)} \drgeoApiOut{Referencia del objeto transformado.} \drgeoApiExample{(sea Polígono "{}P1"{} escala P C k1)} \end{drgeoApi} \begin{drgeoApi}{prototipo (TipoDeObjeto nombre simetría objeto centro)} \drgeoApiIn{TipoDeObjeto}{Punto, Segmento, Recta, Semirrecta, Vector, Círculo, Arco, Polígono} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{objeto}{Referencia del objeto a transformar} \drgeoApiIn{centro}{Referencia a un punto, centro de la simetría (esto es, una rotación de 180 grados)} \drgeoApiOut{Referencia del objeto ya transformado.} \drgeoApiExample{(sea Segmento "{}S1"{} simetría S C)} \end{drgeoApi} \begin{drgeoApi}{prototipo (TipoDeObjeto nombre reflexión objeto eje)} \drgeoApiIn{TipoDeObjeto}{Punto, Segmento, Recta, Semirrecta, Vector, Círculo, Arco, Polígono} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{objeto}{Referencia del objeto a transformar} \drgeoApiIn{eje}{Referencia a una recta, eje de la reflexión} \drgeoApiOut{Referencia del objeto ya transformado} \drgeoApiExample{(sea Polígono "{}P1"{} reflexión P d1)} \end{drgeoApi} \begin{drgeoApi}{prototipo (TipoDeObjeto nombre traslación objeto vector)} \drgeoApiIn{TipoDeObjeto}{Punto, Segmento, Recta, Semirrecta, Vector, Círculo, Arco, Polígono} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{objeto}{Referencia del objeto a transformar} \drgeoApiIn{vector}{Referencia a un vector} \drgeoApiOut{Referencia del objeto ya transformado} \drgeoApiExample{(sea Círculo "{}C1"{} traslación C v)} \end{drgeoApi} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Lugar Geométrico}{} \paragraph{Lugar geométrico} \T ~\\ \begin{drgeoApi}{prototipo (Lugar-geométrico nombre 2puntos m c)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{m}{Referencia a un punto móvil sobre una línea (recta, círculo, etc.)} \drgeoApiIn{c}{Referencia a un punto fijo que depende del punto \texttt{m}} \drgeoApiOut{Referencia al lugar geométrico de \texttt{c} cuando \texttt{m} se mueve sobre la línea (recta, círculo, etc.) } \drgeoApiExample{(Lugar-geométrico "{}locus1"{} 2puntos M I)} \end{drgeoApi} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Vector}{} \paragraph{Vector} \T ~\\ \begin{drgeoApi}{prototipo (Vector nombre 2puntos o e)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{o}{Referencia a un punto, origen del vector} \drgeoApiIn{e}{Referencia a un punto, extremo del vector} \drgeoApiOut{Referencia a un vector.} \drgeoApiExample{(sea Punto "{}B"{} libre 0 5)\\ (sea Punto "{}C"{} libre -1 -2)\\ (Vector "{}"{} 2puntos C B)} \end{drgeoApi} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Número}{} \paragraph{Número} \T ~\\ \begin{drgeoApi}{prototipo (Número nombre libre x y v)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{x,y}{Las coordenadas del número} \drgeoApiIn{v}{El valor inicial del número} \drgeoApiOut{Referencia a un número libre.} \drgeoApiExample{(sea Número "{}pi"{} libre 5 5 (acos -1))} \end{drgeoApi} \begin{drgeoApi}{prototipo (Número nombre longitud-segmento x y s)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{x,y}{Las coordenadas del número} \drgeoApiIn{s}{Referencia a un segmento} \drgeoApiOut{Referencia a un número, longitud de un segmento.} \drgeoApiExample{(sea Número "{}l"{} longitud-segmento 5 5 S)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Número nombre norma-vector x y v)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{x,y}{Las coordenadas del número} \drgeoApiIn{s}{Referencia a un vector} \drgeoApiOut{Referencia a un número, norma(longitud) de un vector.} \drgeoApiExample{(sea Número "{}l"{} norma-vector 5 5 V)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Número nombre punto-círculo x y p c)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{x,y}{Las coordenadas del número} \drgeoApiIn{p}{Referencia a un punto} \drgeoApiIn{c}{Referencia a un círculo} \drgeoApiOut{Referencia a un número, distancia entre el punto y el círculo.} \drgeoApiExample{(sea Número "{}l"{} punto-círculo 5 5 P C)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Número nombre punto-recta x y p d)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{x,y}{Las coordenadas del número} \drgeoApiIn{p}{Referencia a un punto} \drgeoApiIn{c}{Referencia a una recta} \drgeoApiOut{Referencia a un número, distancia entre el punto y la recta.} \drgeoApiExample{(sea Número "{}d"{} punto-recta 5 5 M D1)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Número nombre punto-punto x y p1 p2)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{x,y}{Las coordenadas del número} \drgeoApiIn{p1}{Referencia a un punto} \drgeoApiIn{p2}{Referencia a un punto} \drgeoApiOut{Referencia a un número, distancia entre los dos puntos.} \drgeoApiExample{(sea Número "{}d"{} punto-punto 5 5 A B)} \end{drgeoApi} \begin{drgeoApi}{prototype (Número nombre longitud-círculo x y c)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto.} \drgeoApiIn{x,y}{Las coordenadas del número.} \drgeoApiIn{c}{Referencia a un círculo.} \drgeoApiOut{Referencia a un número, perímetro del círculo.} \drgeoApiExample{(sea Número "{}p"{} longitud-círculo 5 5 C)} \end{drgeoApi} \begin{drgeoApi}{prototype (Número nombre pendiente-línea x y d)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto.} \drgeoApiIn{x,y}{Las coordenadas del número.} \drgeoApiIn{d}{Referencia a una recta.} \drgeoApiOut{Referencia a un número, pendiente de la recta dada.} \drgeoApiExample{(sea Número "{}p"{} pendiente-línea 5 5 d1)} \end{drgeoApi} \begin{drgeoApi}{prototype (Número nombre longitud-arco x y arc)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto.} \drgeoApiIn{x,y}{Las coordenadas del número.} \drgeoApiIn{arc}{Referencia a un arco de círculo.} \drgeoApiOut{Referencia a un número, longitud del arco de círculo dado.} \drgeoApiExample{(sea Número "l" longitud-arco 5 5 ABC)} \end{drgeoApi} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Ángulo}{} \paragraph{Ángulo} \T ~\\ \begin{drgeoApi}{prototipo (Ángulo nombre geométrico A B C)} \drgeoApiIn{nombre}{Cadena de caracteres que designa al nombre del objeto} \drgeoApiIn{A}{Referencia a un punto} \drgeoApiIn{B}{Referencia a un punto, vértice del ángulo} \drgeoApiIn{C}{Referencia a un punto} \drgeoApiOut{Referencia a un ángulo geométrico} \drgeoApiExample{(sea Ángulo "{}a"{} geométrico A B C)} \end{drgeoApi} \subsubsection{Modificación de los atributos(Apariencia) de los objetos} \drgeniusIndex{Figura Scheme de \drgeo}{Creación de objetos}{Atributos(Apariencia) de los objetos}{} Para modificar los atributos de un objeto ya creado, utilizamos un sistema de envío de mensajes directamente al prototipo que representa al objeto en cuestión. La modificación de sus atributos(apariencia) es resultado de este proceso, y se hace ya que los objetos han sido creados. % I COULD NOT TRANSLATE ``bordeaux'' \begin{drgeoApi}{(envía objeto color valor)} \drgeoApiIn{objeto}{Referencia a un objeto} \drgeoApiIn{valor}{El color; los valores posibles son: \texttt{negro, gris-oscuro, gris, blanco, verde-oscuro, verde, azul-oscuro, azul, rojo, bordeaux, amarillo, naranja}} \drgeoApiExample{(sea Punto "{}A"{} libre 1 2)\\ (envía A color verde)} \end{drgeoApi} \begin{drgeoApi}{(envía línea grosor valor)} \drgeoApiIn{línea}{Referencia a una línea (recta, semirrecta, círculo, lugar geométrico, etc.)} \drgeoApiIn{valor}{El grosor, los valores posibles son: \texttt{punteado, pequeño, grande}} \drgeoApiExample{(sea Punto "{}A"{} libre 1 2)\\ (sea Punto "{}O"{} libre 0 0)\\ (sea Recta "{}d"{} 2puntos A B)\\ (envía d grosor punteado)} \end{drgeoApi} \begin{drgeoApi}{(envía punto tamaño valor)} \drgeoApiIn{punto}{Referencia a un punto} \drgeoApiIn{valor}{El tamaño del punto, los valores posibles son: \texttt{pequeño, normal, grande}} \drgeoApiExample{(sea Punto "{}A"{} libre 1 2)\\ (envía A tamaño pequeño)} \end{drgeoApi} \begin{drgeoApi}{(envía punto forma valor)} \drgeoApiIn{punto}{Referencia a un punto} \drgeoApiIn{valor}{La forma del punto, los valores posibles son: \texttt{redondo , cruz, redondo-vacío,rec, rec-vacío}} \drgeoApiExample{(sea Punto "{}A"{} libre 1 2)\\ (envía A forma redondo)} \end{drgeoApi} \begin{drgeoApi}{(envía objeto oculto)} \drgeoApiIn{objeto}{Referencia a un objeto que va a ser ocultado} \drgeoApiExample{(sea Punto "{}A"{} libre 1 2)\\ (envía A oculto)} \end{drgeoApi} % IT WOULD BE BETTER TO INCLUDE THE SYNONIMS IN THE DEFINITION % OF EACH COMMAND IN ADDITION TO PUTTING THEM IN A SEPARATE SECTION % IT WOULD BE NICE TO HAVE IT IN TWO COLUMNS. \subsection{Sinónimos en DGS} \drgeniusIndex{Figura Scheme de \drgeo}{Sinónimos}{}{} Esta sección consta de una transcripción ligeramente modificada del archivo \texttt{/usr/share/drgeo/scm/drgeo\_scm\_interface\_constant\_es.scm}) Modificando este archivo se pueden obtener sinónimos para escribir en el lenguaje Scheme como si fuera Español. Esta sección ayudara a comprender programas escritos en Inglés. Aunque es posible combinar código en Inglés con codigo con sinónimos en Español, francés o lo que se desee, convendría hacer todo el código en Inglés para asegurar su lectura por usuarios de todo el mundo. Por ejemplo, los siguientes comandos son sinónimos: \begin{verbatim} (lets Point "P" free 3 3)(send A 'color bordeaux) (sea Punto ¨P¨ libre 3 3)(env~a A color rojo-oscuro) \end{verbatim} Notar que se han traducido varias versiones, de modo que es posible evitar escribir eñes o acentos. \T \begin{multicols}{2}[][0.1cm] \begin{verbatim} COLORES: negro black gris-oscuro dark-grey gris-obscuro dark-grey gris grey blanco white verde-oscuro dark-green verde-obscuro dark-green verde green azul-oscuro dark-blue azul-obscuro dark-blue azul blue rojo red rojo-oscuro bordeaux rojo-obscuro bordeaux amarillo yellow anaranjado orange naranja orange GROSORES: punteado dashed pequeño small pequeno small grande large PUNTOS redondo round redonda round cruz cross redondo-vacío round-empty redondo-vacio round-empty redonda-vacía round-empty redonda-vacia round-empty cuadrado-vacío rec-empty cuadrado-vacio rec-empty cuadrada-vacía rec-empty cuadrada-vacia rec-empty rec-vacía rec-empty rec-vacia rec-empty ESTILO color 'color grosor 'thickness forma 'shape tamaño 'size tamano 'size enmascarado 'masked oculto 'masked ocultar 'masked PUNTOS libre 'free sobre-la-curva 'on-curve sobre-curva 'on-curve en-curva 'on-curve mitad-2pts 'middle-2pts mitad-segmento 'middle-segment intersección 'intersection intersección2 'intersection2 SEGMENTOS extremos 'extremities 2puntos '2points RECTAS paralela 'parallel ortogonal 'orthogonal perpendicular 'orthogonal 2puntos '2points CÍRCULOS centro-radio 'center-radius centro-segmento 'center-segment ARCOS 3puntos '3points POLÍGONOS npuntos 'npoints NÚMEROS longitud-segmento 'segment-length norma-vector 'vector-norm longitud-vector 'vector-norm punto-recta 'point-line punto-círculo 'point-circle punto-circulo 'point-circle punto-punto 'point-point perímetro-círculo 'circle-length perimetro-circulo 'circle-length longitud-círculo 'circle-length longitud-circulo 'circle-length pendiente-línea 'line-slope pendiente-linea 'line-slope longitud-arco 'arc-length ÁNGULOS geométrico 'geometric geometrico 'geometric TRANSFORMACIONES rotación 'rotation rotacion 'rotation homotecia 'scale escala 'scale simetría 'symmetry simetria 'symmetry translación 'translation translación 'translation traslación 'translation traslacion 'translation GENERALES sea lets nueva-figura new-figure figura-nueva new-figure enviar send envía send envia send Punto Point Recta Line Línea Line Linea Line Segmento Segment Semirrecta Ray Rayo Ray Círculo Circle Circulo Circle Arco Arc Arco Arc Lugar-geométrico Locus Lugar-geometrico Locus Vector Vector Numérico Numeric Numerico Numeric Número Numeric Numero Numeric Ángulo Angle Angulo Angle Polígono Polygon Poligono Polygon \end{verbatim} \T \end{multicols} \subsection{Galería de Ejemplos} \drgeniusIndex{Figura Scheme de \drgeo}{Ejemplos}{}{} Para ilustrar la utilización de las Figuras Scheme de \drgeo, proponemos una breve serie de ejemplos. En ellos mostraremos el potencial de las FSD y esperamos igualmente que le sean una fuente de inspiración. Para cada uno de estos ejemplos, damos el código fuente en Scheme de la figura, y en seguida el resultado. El código fuente puede ser copiado dentro de un archivo de texto con un editor, y luego guardado con la extensión \textbf{.scm} con lo que podrá ser evaluado después por \drgeo. % AGRUGUÉ EL SIGUIENTE PÁRRAFO. El código siguiente se encuentra en inglés. Favor de ver la seccion Sinónimos para poder escribir la mayor parte del código en Español. \subsubsection{Polígono regular} \drgeniusIndex{Figura Scheme de \drgeo}{Ejemplos}{Polígono regular}{} Para construir un polígono regular, con un número arbitrario de lados, podemos hacer uso de una función recursiva en Scheme. Construire un polygone régulier, avec un nombre de coté arbitraire, peut se faire par l'intermédiaire d'une fonction récursive Scheme. \begin{verbatim} (define pi (acos -1)) (define n 15) (define x0 0) (define y0 0) (define p1 0) (define (polygon center p a n) (if (> n 0) (begin (set! p1 (Point "" rotation p center a)) (send p1 masked) (Segment "" extremities p p1) (polygon center p1 a (- n 1))))) (new-figure "Regular Polygon!") (lets Point "C" free x0 y0) (lets Numeric "a" free 0 0 (* 2 (/ pi n))) (send a masked) (set! p1 (Point "I" free 5 0)) (lets Segment "S" extremities C p1) (Segment "" rotation S C a) (polygon C p1 a n) \end{verbatim} \drgeniusFigureSize{Un polígono regular de 15 lados}{fig59}{6} \subsubsection{Fractal} \drgeniusIndex{Figura Scheme de \drgeo}{Ejemplos}{Fractal}{} La construcción de una curva fractal con la forma de un árbol se logra fácilmente con una Figura Scheme. El código fuente de la figura es sorprendentemente breve, sobre todo cuando lo comparamos con la construcción ``a mano'' usando la interfaz gráfica. \begin{verbatim} (new-figure "Baum") (lets Numeric "A1" free 2 2 +3.4) (lets Numeric "A2" free 2 3 -3.7) (lets Numeric "S1" free 2 4 +0.5) (lets Numeric "S2" free 2 5 +0.9) (define (dec n) (- n 1)) (define (inc n) (+ n 1)) (define (invisible p) (send p masked) p) (define (scalerot oP C a s) (let* ((sP (invisible (Point "" scale oP C s))) (rP (invisible (Point "" rotation sP C a))) ) rP)) (define (Zweig p0 p1 n) (Segment "" extremities p0 p1) (let* ((left-scale (if (odd? n) S1 S2)) (left-angle A1) (right-scale (if (odd? n) S2 S1)) (right-angle A2) ) (if (> n 0) (begin (Zweig p1 (scalerot p0 p1 left-angle left-scale) (dec n)) (Zweig p1 (scalerot p0 p1 right-angle right-scale) (dec n)))))) (lets Point "A" free -3 0) (lets Point "B" free -3 2) (Zweig A B 6) \end{verbatim} \drgeniusFigureSize{Una curva fractal que simula la representación de un árbol}{fig60}{8} \section{Bloquear las herramientas de la interfaz} \label{ui-lock} \drgeo\ ofrece la posibilidad de preparar sesiones\footnote{Archivos que contienen varios documentos de \drgeo\ (i.e. figuras y/o texto)} dentro de los cuales el maestro puede decidir, para ciertas figuras, impedir el acceso a ciertas herramientas, el bloqueo se realiza utilizando una contraseña distinta para cada figura. Esto da al maestro flexibilidad al preparar una actividad con distintas figuras, y diversas herramientas disponibles en cada figura. \subsection{Bloqueo de las herramientas} \drgeniusIndex{Herramientas}{Bloquear}{}{} % I FOLLOWED THE ITALIAN, THE FIRST LINE IS CRYPTIC. Para impedir el acceso a las herramientas de construcción recurrimos al comando \drgeniusMenu{Editar->Interfaz personalizado}. Después de haberlo seleccionado se abre una gran ventana de diálogo con todos los iconos de los instrumentos de \drgenius. Allí, podemos hacer click sobre los iconos para activarlos o desactivarlos. Cuando una herramienta está desactivada, el icono que la representa aparece ligeramente desvanecido. Es igualmente posible desactivar todas las herramientas en una misma columna haciendo click en el icono principal del menú (que se reconoce por tener un pequeño triángulo verde en la parte inferior derecha). \drgeniusFigureSize{Ventana de diálogo para bloquear algunas herramientas de la interfaz}{fig53}{8} Cuando el usuario ha terminado de seleccionar los iconos que han de ser bloqueados, se procede al bloqueo propiamente dicho haciendo click sobre el botón \drgeniusMenu{bloqueo} en la ventana de diálogo. En este momento, \drgenius\ pedirá una contraseña. \drgeniusNote{Cuando se guarda una figura o una sesión en que se impide el acceso a ciertas herramientas, las contraseñas son igualmente guardadas, de forma encriptada, en el archivo} \subsection{Desbloqueo de las herramientas} \drgeniusIndex{Herramientas}{Desbloqueo}{}{} % I AM NOT SURE !! I SKIPPED ONE COMMENT IN THE TRANSLATION!!! Es por supuesto posible desbloquear la interfaz, ya sea para dar acceso progresivo a las herramientas --~estando en la clase con los estudiantes-- o para volver a diseñar la figura. Para ello, se necesita escoger dentro de la ventana de diálogo el botón \drgeniusMenu{Desbloquear}. \drgenius\ pide entonces la contraseña que se ingresó previamente. \drgeniusFigure{La ventana de diálogo para desbloquear la interfaz de una figura.}{fig54} \chapter{Archivos y documentos} Las construcciones pueden ser guardadas de dos maneras. Una construcción por archivo o un conjunto de construcciones por archivo (i.e. una sesión de \drgenius). Le recordamos que los documentos que con tienen las figuras debes ser guardados con una extensión \textbf{.fgeo} y que aquellos que contengan sólo macros que sean guardados con la extensión \textbf{.mgeo}. Para los documentos que contienen varias figuras, construcciones de macros y textos explicativos, utilizar la extensión \textbf{.fgeo} Lo anterior es sólo indicativo, pero seguir estas reglas permitirá identificar y volver a cargar los archivos más fácilmente. \section{Guardar una construcción} \drgeniusIndex{Figura}{Guardar}{}{} A partir del menú \drgeniusMenu{Archivo->Guardar} o del menú \drgeniusMenu{Archivo->Guardar como...}, un archivo que contiene la figura de la vista activa puede ser guardada. \drgeniusNote{\drgenius\ puede trabajar con varias figuras al mismo tiempo. El usuario puede pasar de una figura a otra haciendo click sobre el nombre de la figura (ubicado en la parte baja de la figura).}. Con el segundo menú, el usuario puede cambiar el nombre del documento a guardar. \drgeniusNote{El nombre del archivo inicialmente propuesto puede ser cambiado con el menú\drgeniusMenu{Editar->Preferencias...}. Para más información ver la \link{sección comportamiento predeterminado}[ Sección \Ref, página \Pageref]{default_behaviour}.} \section{Guardar una sesión} \drgeniusIndex{Macro}{Guardar}{}{} \drgeniusIndex{Sesión}{Guardar}{}{} Una sesión es un conjunto de objetos de \drgenius\ que el usuario desea guardar de un solo golpe en un archivo. Esto permite al maestro organizar un conjunto de objetos (figuras, macros y notas de clase) en un solo archivo con el fin de facilitar su uso. A partir del menú \drgeniusMenu{->Guardar múltiple}, el usuario puede abrir la ventana de diálogo de la sesión. \drgeniusFigureSize{La ventana de diálogo de la sesión \drgenius}{fig51}{8} En esta ventana de diálogo, la lista de todos los objetos activos está presente en una tabla. La primera columna muestra los tipos de objetos contenidos en la sesión de \drgenius, la segunda muestra los nombres de los objetos. \drgeniusNote{De hecho, una sesión puede contener tres tipos de objetos~: figuras interactivas en dos dimensiones, macros y textos.} El usuario puede seleccionar uno por uno los objetos a guardar y después hacer click en el botón\drgeniusMenu{Guardar selección}. Alternativamente, puede guardar todos los objetos haciendo click sobre el botón \drgeniusMenu{Guardar todo}. \drgeniusNote{El menú \drgeniusMenu{Archivo->Guardar múltiple} es el único medio de guardar una macro en un archivo.} \section{Guardar una Macro} \drgeniusIndex{Macro}{Guardar}{}{} Para guardar una o varias macros en un archivo. es necesario proceder como cuando uno desea guardar una sesión --guardar múltiple--. Posteriormente , en la ventana para guardar una sesión, seleccionar la o las macros que se desea guardar. En seguida guárdelas en un archivo que contenga la extensión \textbf{.mgeo}. ¡Eso es todo! Es de este modo posible crear bibliotecas de macros, una por archivo, o varias agrupadas por temas en un sólo archivo. \section{Abrir un archivo} \drgeniusIndex{Macro}{Abrir}{}{} \drgeniusIndex{Sesión}{Abrir}{}{} \drgeniusIndex{Figura}{Abrir}{}{} Ya sea que el usuario haya guardado una sola figura o una sesión con los distintos objetos, el procedimiento para la apertura de cualquier tipo de archivo es siempre a través del menú \drgeniusMenu{Archivo->Abrir}. Si la sesión recién abierta contiene macros, estas están directamente disponibles a partir de que la herramienta para ejecutar macros esté disponible para la ejecución. Las macros están disponibles para todas las figuras abiertas. \section{Exportar una figura} \drgeo\ ofrece la posibilidad de exportar una figura geométrica a un documento \LaTeX o PostScript. Estos dos formatos de exportación son de tipo vectorial, a diferencia de las imágenes de mapas de bits que son de menor calidad para una impresión. Los comandos de exportación son accesibles a través del menú \drgeniusMenu{Archivo->Exportar como...} \subsection{Exportar a \LaTeX} \drgeniusIndex{Figura}{Exportar}{\LaTeX}{} En el caso de una exportación al formato \LaTeX, el documento exportado necesita el paquete \texttt{pstricks}. Éste es en general distribuido con \LaTeX. Típicamente un documento exportado en \LaTeX\ podrá ser integrado dentro de otro documento \LaTeX\ o bien directamente compilado con los comandos: \begin{verbatim} latex figure.tex dvips figure.dvi \end{verbatim} Esta serie de comandos permite obtener el documento figure.ps, el cual puede ser abierto por el programa GhostView\footnote{GhostView es un programa que permita visualizar documentos PostScript (.ps o .eps) así como documentosPDF} \texttt{gv}. \subsection{Exportar a PostScript} \label{exporter-ps} \drgeniusIndex{Figura}{Exportar}{PostScript}{} La exportación al formato PostScript -- extensión \texttt{eps} -- ofrece la ventaja de ser fácilmente utilizable por diversos programas \footnote{Este formato es reconocido por TeXmacs, OpenOffice.org, Lyx, \LaTeX\, Xfig, el Gimp y muchos más.}. En efecto, el formato \textsc{eps} es cercano a ser un estandard en lo que se refiere a imágenes vectoriales. Para visualizar rápidamente este tipo de imágenes,utilizamos, como ya antes mencionamos, el programa GhostView; en una terminal se invoca escribiendo \texttt{gv}. \subsection{Exportar a \textsc{png}} \drgeniusIndex{Figura}{Exportar}{PNG}{} Ciertos programas como OpenOffice.org sólo explotan parcialmente el formato \textsc{eps}\footnote{OpenOffice.org permite integrar una imagen \textsc{eps} pero no la puede mostrar. Únicamente en la impresión en papel aparecerá la imagen}. Es posible, afortunadamente, exportar al formato \textsc{png}. La imagen exportada bajo este formato tiene una alta definición y posee un fondo transparente. Esto puede permitir escribir un texto a lo largo de la figura. \subsection{Exportar Fly Draw} \drgeniusIndex{Figura}{Exportar}{Fly Draw/WIMS}{} El servidor de ejercicios WIMS desarrollado por el Dr. Xiao Gang en la universidad de Nice dispone de un formato de descripción de figuras llamado Fly Draw. \drgeo\ puede exportar hacia ese formato. \subsection{Definir el área de exportación} \drgeniusIndex{Figura}{Exportar}{Definir el área de exportación}{} Inicialmente, \drgeo\ exporta la zona visible de la figura. Por lo anterior, si deseamos exportar una zona precisa de la figura, una manera de hacerlo es redimensionar la ventana de \drgeo\ hasta obtener la zona deseada \footnote{Cuando lo deseemos, el panel lateral que contiene el árbol lógico de la figura, puede ser desplegado reduciendo aún más la zona visible, y, en consecuencia, el área de exportación.}. Esta solución, empero, aunque rápida y simple, no es lo suficientemente flexible. Además, el área de exportación no queda guardada junto con la figura. Afortunadamente, existe otro modo de definirla usando el comando \drgeniusMenu{Definir el área de exportación} el cual es accesible desde el menú \drgeniusMenu{Archivo->Preferencias de Exportación} Habiendo seleccionado el comando, podemos seleccionar un rectángulo en la figura que corresponderá con el área de exportación. Esta área puede ser redefinida tantas veces como sea necesario. En la figura estará representada por un rectángulo gris claro. Cuando la figura sea guardada, esta zona lo será también. Para suprimir el área de exportación y regresar al comportamiento inicial de \drgeo\ use el comando \drgeniusMenu{Eliminar área de exportación}, el cual, por supuesto, no borra ningún objeto de la figura. \drgeniusFigureSize{Una figura con un área de exportación definida}{fig56}{7} \drgeniusFigureSize{El área de exportación ha sido exportada a un documento PostScript; es visible con el programa GhostView}{fig57}{7} \chapter{Aplicaciones Didácticas} Este capítulo constituye una ayuda para el usuario que desea familiarisarse con \drgeo{} a través de ejemplos. A diferencia de los capítulos precedentes, el enfoque es más concreto, y es orientado a situaciones precisas. El capítulo consiste en diversas aplicaciones pedagógicas. \section{Pitágoras y scripts} Una de las aplicaciones didácticas en \drgeo{} consiste en la utilización de los \link{scripts Scheme}[ Seccióon \Ref, página \Pageref]{script} para resolver ejercicios de Geometría. Como ejemplo, vamos a mostrar la solución a un problema clásico en cuya solución se usa el teorema de Pitágoras. El texto es el siguiente~: \begin{quote} \em Sea un trapecio rectángulo $ABCD$ del que son conocidas las bases y la altura. Calcular el perímetro y el área del trapecio. \end{quote} No es difícil, siguiendo el mismo modelo, desarrollar otros ejemplos semejantes. \textbf{Solución~:} Comencemos por construir la figura en \drgeo{}, la cual debe ser como sigue~: \drgeniusFigureSize{Trapecio Rectángulo}{dafig1}{8} La figura contiene los datos a partir de los cuales podemos resolver el problema. Podemos contestar enseguida la pregunta relacionada con el área, para ello podemos escribir el script Scheme sigueinte que tiene como entradas las dos bases y la altura del trapecio~: \drgeniusIndex{Script}{Ejemplos}{Área de un trapecio}{} \begin{quote}{\begin{verbatim} define AB (getLength a1)) (define DC (getLength a2)) (define AD (getLength a3)) (/ ( * AD (+ AB DC )) 2 ) \end{verbatim} } \end{quote} \drgeniusIndex{Script}{Ejemplos}{Diferencia en la longitud de dos segmentos}{} Calculamos la longitud del segmento $BH$ escribiendo un script Scheme que tiene por parámetros de entrada a los segmentos $AB$ y $CD$. El texto del script es el siguiente~: \begin{quote}{\begin{verbatim} (define AB (getLength a1)) (define CD (getLength a2)) (- AB CD) \end{verbatim} } \end{quote} \drgeniusIndex{Script}{Ejemplos}{Teorema de Pitágoras}{} En este momento, podemos aplicar el Teorema de Pitágoras al triángulo rectángulo $CHB$. Aquí también utilizamos un script Scheme que tiene por parámetros de entrada al segmento $CH$ y al script $BH$~: \begin{quote} { \begin{verbatim} (define CH (getLength a1)) (define BH (getValue a2)) (+ (* CH CH) (* BH BH)) \end{verbatim} } \end{quote} \drgeniusIndex{Script}{Ejemplos}{Raíz cuadrada}{} Finalmente, podemos obtener el valor del segmento $BC$ calculando la raiz cuadrada del valor devuelto por el script anterior~: \begin{quote} { \begin{verbatim} (define q (getValue a1)) ( sqrt q ) \end{verbatim} } \end{quote} Los dos scripts anteriores pueden ser combinados en un solo script un poco más elaborado. \drgeniusIndex{Script}{Ejemplos}{Perímetro}{} Ahora podemos concluir el ejercicio calculando el perímetro con un script Scheme~: \begin{quote} { \begin{verbatim} (define AB (getLength a1)) (define CB (getValue a2)) (define DC (getLength a3)) (define AD (getLength a4)) (+ (+ AB CB )(+ DC AD )) \end{verbatim} } \end{quote} \section{Teoremas y conjeturas} Los \link{scripts Scheme}[ Secciónn \Ref, página \Pageref]{script} permiten no sólo resolver ejercicios, sino también comprender mejor el enunciado de los teoremas (y las hipótesis de los mismos) asi como corroborar o descartar conjeturas. En esta sección comenzaremos analizando el enunciado del Teorema de Ptolomeo~: \begin{quote} \em Dado un cuadrilátero inscrito en una circunferencia, la suma de los productos de los lados opuestos es igual al producto de las diagonales. \end{quote} Podemos construir la figura con \drgeo{} como abajo~: \drgeniusFigureSize{Teorema de Ptolomeo: cuadrilátero convexo}{dafig2}{8} En la figura, hemos implementado dos scripts que calculan, respectivamente, la suma del producto de los lados opuestos, y el producto de las diagonales. \drgeniusIndex{Script}{Ejemplos}{Teorema de Ptolomeo}{} El primer script es el siguiente~: \begin{quote} { \begin{verbatim} (define AB (getLength a1)) (define DC (getLength a2)) (define BC (getLength a3)) (define AD (getLength a4)) (+ (* AB DC )(* BC AD )) \end{verbatim} } \end{quote} El segundo script es~. \begin{quote} { \begin{verbatim} (define DB (getLength a1)) (define AC (getLength a2)) (* DB AC ) \end{verbatim} } \end{quote} Como podemos ver, los valores devueltos por los dos scripts, en conformidad con el Teorema de Ptolomeo, son iguales \footnote{Esto es una verificación numérica; no una prueba}. Cuando modificamos dinámicamente la figura, los valores de los scripts son idénticos, salvo en el caso siguiente~: \drgeniusFigureSize{Teorema de Ptolomeo: cuadrilátero no convexo}{dafig3}{8} Vemos en la figura que el cuadrilátero ya no es convexo. En este caso el enunciado del Teorema es falso. Por lo tanto, para contemplar ese caso, debemos reformular el enunciado como sigue~: \begin{quote} \em Dado un cuadrilátero CONVEXO inscrito en una circunferencia, la suma del producto de lados opuestos es igual al producto de las diagonales.. \end{quote} En este momento las conjeturas aparecen de modo natural~: ¿es acaso valida la conclusión del teorema de Ptolomeo también valida para un cuadrilátero convexo no inscrito en un círculo~?(i.e. ¿es cierto el recíproco?) Con \drgeo{} podemos ver que dicha conjetura es falsa como muestra la figura siguiente~: \drgeniusFigureSize{Refutación de la conjetura}{dafig4}{8} El lector no tendrá problemas en utilizar \drgeo{} para la construcción de ejemplos didácticos, relacionados probablemente con teoremas más conocidos, como el Teorema de Pitágoras o alguno de los teoremas de Euclides. \section{Números irracionales} \drgeniusIndex{Figura Scheme de \drgeo}{Ejemplos}{Espiral de Teodoro}{} Una construcción clásica, relacionada con los números irracionales, conocida bajo el nombre de ``Espiral de Teodoro'' permite construir geométricamente la raíz cuadrada de números enteros a partir de un triángulo isósceles. Consideremos el triángulo $OAB$ donde $OA=1$~: \drgeniusFigureSize{Construción de la raíz cuadrada de 2}{dafig7}{8} Por el teorema de Pitágoras, tenemos que $OB$ es igual a la raíz cuadrada de 2. Si, ahora, con la figura, construímos un nuevo triángulo rectángulo en $B$, con lados $OB$ y $BC$ tal que $BC=1$. \drgeniusFigureSize{Construcción de la raíz de 3}{dafig8}{8} Nuevamente, por el teorema de Pitágoras, es claro que la hipotenusa $OC$ del triángulo $OBC$ tiene por longitud la raíz cuadrada de 3. Repitiendo este proceso obtenemos todas las raíces cuadradas de los números naturales. La naturaleza repetitiva de la construcción se presta perfectamente para la utilización de un FSD. Consideremos el código siguiente~: \begin{quote} { \begin{verbatim} (new-figure "Triangle") (define (triangle p1 p2 p3 n) (let* ((s1 (Segment "" extremities p1 p2)) (s2 (Segment "" extremities p2 p3)) (s3 (Segment "" extremities p3 p1)) (pe (Line "" orthogonal p3 s3)) (ci (Circle "" center-segment p3 s2)) (p4 (Point "" intersection2 pe ci))) (send pe masked) (send ci masked) (send p4 masked) (if (> n 0) (triangle p1 p3 p4 (- n 1))))) (lets Point "O" free 0 0) (lets Point "A" free -1 0) (lets Point "B" free -1 1) (triangle O A B 15) \end{verbatim} } \end{quote} El triángulo inicial está definido a través de coordenadas por comodidad unicamente. El código es la transcripción literal del procedimiento repetitivo previamente descrito. Una vez evaluado por \drgeo{}, el código nos da la siguiente figura~: \drgeniusFigureSize{Espiral de Teodoro}{dafig9}{8} Las hipotenusas de cada triángulo tienen por longitud las raíces cuadradas de los números enteros naturales entre 2 y 17. \section{Espiral de Baravelle} \drgeniusIndex{Figura Scheme de \drgeo}{Ejemplos}{Espiral de Baravelle}{} Como vimos anteriormente, con la ayuda de una FSD es posible construir de manera intuitiva y simple figuras que permiten visualizar situaciones que en un programa son ya sea iterativas o recursivas. Profundicemos un poco más en este aspecto. Modificando el código Scheme utilizado para la construcción de los números irracionales, podemos obtener una figura famosa en la literatura matemática: la espiral de Baravelle. El código Scheme que define la espiral es el siguiente~: \begin{quote} \begin{verbatim} (new-figure "Baravelle") (define (triangle p1 p2 p3 n) (let* ((s1 (Segment "" extremities p1 p2)) (s2 (Segment "" extremities p2 p3)) (s3 (Segment "" extremities p3 p1)) (m (Point "" middle-2pts p1 p3)) (r (Segment "" extremities m p3)) (pe (Line "" orthogonal p3 s3)) (ci (Circle "" center-segment p3 r )) (p4 (Point "" intersection2 pe ci))) (send pe masked) (send ci masked) (send p4 masked) (send m masked) (if (> n 0) (triangle m p3 p4 (- n 1))))) (lets Point "A" free 0 5) (lets Point "B" free 5 5) (lets Point "C" free 5 0) (triangle A B C 9) (lets Point "D" free 0 -5) (lets Point "E" free -5 -5) (lets Point "F" free -5 0) (triangle D E F 9) \end{verbatim} \end{quote} \drgeniusFigureSize{La espiral de Baravelle obtenida al evaluar el código Scheme}{dafig10}{8} Con base en la figura y en el código Scheme correspondiente, vemos claramente la naturaleza iterativa del mecanismo de construcción de la figura. Un problema interesante, que dejamos al lector, consiste en establecer cuándo las dos ramas de la espiral convergen. Una pequeña variación al codigo precedente~: \begin{quote} \begin{verbatim} (new-figure "Spirale") (define (square p1 p2 p3 p4 n) (let* ((s1 (Segment "" extremities p1 p2)) (s2 (Segment "" extremities p2 p3)) (s3 (Segment "" extremities p3 p4)) (s4 (Segment "" extremities p4 p1)) (A (Point "" on-curve s1 1/10)) (B (Point "" on-curve s2 1/10)) (C (Point "" on-curve s3 1/10)) (D (Point "" on-curve s4 1/10))) (send A masked) (send B masked) (send C masked) (send D masked) (if (> n 0) (square A B C D (- n 1))))) (lets Point "M" free 5 5) (lets Point "N" free -5 5) (lets Point "O" free -5 -5) (lets Point "P" free 5 -5) (square M N O P 30) \end{verbatim} \end{quote} Obtenemos, pues, una espiral simplificada. \drgeniusFigureSize{Espiral simplificada}{dafig11}{8} El lector está invitado a divertirse creando nuevas variaciones. \T \clearpage \section{Cadena de Papus} \drgeniusIndex{Figura Scheme de \drgeo}{Ejemplos}{Cadena de Papus}{} Una aplicación de las Figuras Scheme de \drgeo\ consiste en la reproducción de una figura cuando sólo conocemos sus características analíticas. Nos proponemos desarrollar un ejemplo famoso: ``La Cadena de Papus''. \drgeniusFigureSize{Cadena de Papus}{dafig12}{8} Los centros y los radios de los círculos que la constituyen tienen una expresión analitica conocida, y es sencillo implementar la expresión analítica en una FSD que reproducirá la figura. \begin{quote} \begin{verbatim} (new-figure "Pappo") (define (circle n) (let*( (r (Numeric "" free 0 0 (/ 15 ( + 6 (* n n ))))) (c (Point "" free (* 5 (/ 15 ( + 6 (* n n )))) (* 2 (* n (/ 15 ( + 6 (* n n ))))))) (p (Circle "" center-radius c r ))) (send r masked) (if (> n 0) (circle (- n 1))))) (circle 8) (lets Point "A" free 5 0) (lets Point "O" free 0 0) (lets Point "B" free 15 0) (lets Point "M" middle-2pts B O) (lets Circle "" 2points M O) (lets Circle "" 2points A O) (lets Line "" 2points A O) \end{verbatim} \end{quote} El código de la figura es relativamente intuitivo y no necesita mayor comentario. Un ejercicio no trivial, que dejamos al lector, consiste en determinar una construcción con regla y compás que conduzca a una implementación iterativa. (la implementación dada es recursiva). \section{Cálculo de $\pi$} El cálculo aproximado de $\pi$ ha tenido un papel importante en la historia de las Matemáticas. Los métodos para su cálculo son diversos, teniendo mejoras de uno a otro método. Nos proponemos atacar el problema con un método que llamaremos, aunque no sea del todo apropiado, \textbf{Método de Exhaución}. Éste método tiene la ventaja de mostrar la esencia misma del problema. (El método siguiente fue desarrollado por Arquímides usando el método de Exhaución desarrollado por Eudoxo, el cual fue precursor de la teoría de límites). Comenzaremos con la construcción de un hexágono regular inscrito en una circunferencia a partir de su lado $BC$. Notemos de paso que es posible a partir de esta construcción crear y memorizar una macro que llamaremos \textit{Hexágono} \drgeniusFigureSize{Hexágono regular inscrito}{dafig5}{8} La idea del método de exhaución consiste en primero aproximar la longitud del círculo con el perímetro $P_(0)$ del hexágono y de calcular una aproximación de $\pi$ dividiendo $P_(0)$ por el diámetro del círculo. Claramente, la aproximación obtenida sera de 3. En una segunda etapa podemos, utilizando \drgeo{}, construir dentro de la misma circunferencia, un dodecágono regular. Calculemos su perímetro,$P_(1)$, y dividamos por el diámetro de la circunferencia. Esto nos dará una mejor aproximación. \drgeniusFigureSize{Aproximación de $\pi$}{dafig6}{8} Duplicando en cada paso el número de lados del polígono regular inscrito obtenemos mejores aproximaciones. \chapter{Libro de recetas} Este capítulo constituye una ayuda para el usuario que desea realizar construcciones geométricas con \drgeo. Contrariamente a los capítulos precedentes, el enfoque es hacia problemas precisos. El contenido de este capítulo es fruto del uso que los usuarios han hecho del programa, y responde a algunas peticiones de los mismos. \section{Crear un polígono regular} \label{polygon_macro} \drgeniusIndex{Macro}{Polígono}{}{} \drgeniusIndex{Polígono}{Macro}{}{} \drgeniusIndex{Macro}{Script}{}{} \drgeo\ puede crear varias macros con elementos independientes (i.e. varios puntos libres, valores libres o scripts independientes). Para hacer esto drgeo dota de valores a los parámetros libres de esos objetos \footnote{Si no, las macros no podrían ser llamadas. Por ejemplo,¿qué valor debemos dar a un objeto tipo valor libre que interviene dentro de la construcción de una figura?}. \drgeo\ puede crear varias macros. El o los valores escogidos son, en efecto, los valores del objeto que sirvió de modelo durante la creación de la macro. En lo que sigue, un pequeño ejemplo que permite crear polígonos regulares de cualquier número de lados es presentado. En varias de las macros, un script Scheme interviene en el proceso. El ejemplo es mostrado paso a paso, aunque el lector no familiarizado con las macros, los scripts o más generalmente el funcionamiento de \drgeo\ está invitado a leer las secciones anteriores. \subsection{El modelo del polígono} Para comenzar, crearemos un punto libro, en seguida un Script que no toma parámetros de entrada (para crear el script, seleccionar la herramienta script y hacer enseguida click sobre el fondo de la figura). Editar el script y escribir lo siguiente~: \begin{verbatim} (/ (* 2 (acos -1)) 7) \end{verbatim} El resultado de este script es el valor del script y servirá para construir, a través de una rotación un polígono regular de 7 lados. Colocar enseguida un valor libre con valor 2. Éste será el radio de nuestro polígono. Construir un círculo de centro el punto y de radio el valor recién creado. Sobre este círculo colocar un punto. Llamemos a este punto $O$. Ahora utilicemos la herramienta rotación para crear la imágen del punto $O$ bajo la rotación con centro de rotación en el centro del círculo, y con un ángulo de rotación cuyo valor es el valor del script. Continuar sucesivamente hasta obtener los siete vértices del polígono. Unir los vertices con los segmentos hasta obtener el polígono. \drgeniusFigureSize{Resultado de construir un polígono regular de 7 lados.}{fig61}{8} \subsection{La macro del polígono} Abrir el diálogo para la creación de la macro y crearla como se indica a continuación~: \begin{enumerate} \item \textbf{parámetro de entrada~:} el centro del círculoe~; \item \textbf{paramètres de sortie~:} el punto $O$ y los 7 lados del polígono. \end{enumerate} Listo, la macro ha sido creada. Para crear un polígono regulara de 7 lados, abrir la ventana de diálogo para ejecutar una macro. Basta seleccionar un punto de la figura para crear un polígono de 7 lados. \subsection{Algunas consideraciones} Cuando \drgeo\ encuentra los elementos libres en una macro, fija sus valores toamndo a la figura como modelo. En nuestro ejemplo, el script, el valor del radio y el punto $O$ son los elementos libres de los que hablamos. Cuando la macro es ejecutada, sus valores se fijan como sigue~: \begin{itemize} \item El valor se fija 2~; \item el script se fija en \texttt{(/ (* 2 (acos -1)) 7)}~; \item el punto sobre el círculo se fija con la misma abscisa curvilínea que la que tenía el punto $O$.. \end{itemize} Es esto último lo que da sentido a la utilización conjunta de macros con scripts u otros elementos libres. En otras palabras, por ejemplo, si para construir una figura necesitamos 7 elementos libres al empezar, y al crear la macro sólo damos 1, el resto de los elementos libres necesarios para la figura se toman de la figura que sirvió de modelo. \section{Imprimir una figura} \drgeniusIndex{Figura}{Imprimir}{}{} \drgeniusIndex{Imprimir}{Figura}{}{} Lo más sencillo es exportar la figura al formato PostScript -- \link{Exportar a PostScript}[ Sección \Ref, página \Pageref]{exporter-ps}. En seguida es posible usar un programa que permita visualizar los documentos e imprimirlos. El documento, de calidad vectorial, puede ser abierto e impreso por programas como GhostView, Gnome GhostView o incluso K GhostView, por citar algunos. \section{Colocar un párrafo de texto en la figura} \drgeniusIndex{Colocar}{Texto}{}{} \drgeniusIndex{Figura}{Colocar}{Texto}{} \drgeniusIndex{Texto}{colocar}{}{} Uno puede ventajosamente utilizar los scripts, de una manera ciertamente imprevista. Se selecciona la creación de un script --\link{Herramienta Script}[ Sección \Ref, página \Pageref]{script-tool} --, y se hace click sobre el fondo de la figura. De este modo un script sin parámetros de entrada es creado. Enseguida se editan las propiedades del script -- \link{Propiedades de un objeto}[ Sección \Ref, página \Pageref]{property-item}. En la zona de texto donde el código Scheme es normalmente escrito, colocamos un texto entre comillas precedido por una única apóstrofe, por ejemplo~: \begin{verbatim} '"Animación \n y \n observaciones ===================== Desplace los puntos de la figura para responder a las siguientes preguntas: \n 1.¿Dónde hay que colocar al punto A para que el punto A' se confunda con el punto A? 2. ¿Dónde hay que colocar al punto A para que el punto A' coincida con el punto B? 3. ¿Cómo hay que colocar al punto I para que los puntos B', C' e I estén alineados? 4. ¿Cuál es el simétrico del punto I? ¿Cuál es el simétrico del punto A'?" \end{verbatim} \drgeniusFigureSize{Ejemplo de párrafo de texto dentro de una figura}{fig58}{10} Como con todo script, es igualmente posible cambiar el color del texto. Observe que es posible usar algunos caracteres de control dentro del texto. % I ADDED THE FOLLOWING PARAGRAPH: Un script, que permite combinar cálculos con texto es el siguiente~: \begin{verbatim} (format #f "~s más ~s es casi siempre ~s" 3 4 (+ 3 4)) \end{verbatim} \W \chapter*{Índice} \W \htmlprintindex \W \begin{iftex} \appendix \listoffigures \printindex \W \end{iftex} \chapter{Histórico.} Redacciónes originales de la documentación~: Hilaire Fernandes (Inglés y Francés) y Andrea Centomo (Italiano). Traducción al Español~: Adrián Ulises Soto Bañuelos. \chapter{GNU Free Documentation License} \input{../fdl} \end{document} % LocalWords: Guile Homothétie homothétie macro-construction glisser-déposer % LocalWords: redessinée drgeo-doc-1.5/es/figures/0002777000175000017500000000000010117134567011051 5drgeo-doc-1.5/es/figures/blank.png0000644000175000017500000000012410117134567012555 ‰PNG  IHDR I´è·PLTE™ÌÿõÉj IDATxÚc`Ü Žû±´IEND®B`‚drgeo-doc-1.5/es/figures/dafig10.png0000644000175000017500000003502410117134567012710 ‰PNG  IHDRÐ#„mºýPLTE # 3" #"$!)2(( .-/' +**Ei"4(+-;21242)C2M*(E2!:;:˜v):OC#OC.GF@HFJ]>A¡'ð?PG„15VO“-)'[\jA4LMJJR7lG BTSKLlcOOPTw@Epa>'{zwc1admá01ffbfehMsb]lb•TR£Ak»@_è:foX Pc–h¥RQˆj.Us‰ykS]{XXvm&‰jKpqlkj¢imœtpnzodor}rru%–•m€læP$QŒŽ{}zèOH`vvx­f‡o†~|8†€dƒ~|ƒ|€Œ‚‚wÅiJ¦€0ÏQ™~eæZZ•…Q”}–~z„†ƒ™ˆIÂpbÆlmæe?X¡…rŽªƒ‘t‡’f¦…\Œ‹ƒ„…¼¢ˆfiœ›ŒŽ‹z”ž±~~‡—ÂLÑnƒÊrƒ‘Ž™Œ…ŠŒ–“Ÿ´“0š•w–”‰”–“»“?š••¼ž›š’®›[~ªÆ—6“¥ˆ£¦¬–“Ù™ ñ~[Ú“¦ž ˆ§¶i·¸¢Ÿ¤™¢²Ÿ¨‚¥ ž££š¾t£ ´¥©•«£«¶ž¨îx¬«¢®¬°²¦Æ¼¶Ù«CªŠÝ™ž¯¯¬Í°U¤´¹ë˜Ì«€ê•¥ª±Àã«H¦²ÉÝ·á¯=´³ªÎ±n¹¶´Ä±³é¾dz¨ÑÒ¼»²øµA¼¾»Á½¾Ý»ú¬˜ÄÄ»ÇÀ̺ÆÐó°¬ÂÉ­áÁžÈÆÊËÇŵ׿ÍÌÃæÊ°ÓÏͧãÞÔÓÊþÛ4îÉÄàÓµðÕ„Ó×ܨìèâÖÃÞØÖÙÛØÿé7æÛÎÿó ÝßÜïÛÝåàÞâãèëãÛðç½èèåíëðïðíÿîéõó÷öøôýûÿþÿüb6~ pHYs ‰ ‰7ÉË­tIMEÔ  ÞV IDATxÚí|å}ÿ¿7/xö²èG«¬xÃX«.‰G³`”…@›ÅµØ0)‰À1¿‚[²à?¿ŒmuÛ­œfÅ,;ÂmBÿ ÕAJÒ_í-© ™éPÕög,…X?EÓÕ¿êÖºòýl϶^¿çþHº“î¤ÓI:Ýž¯[:=÷<§{ßçù>ßçyî9lØ°iÙbg‘ 7þÒþÛØJjvJ™¹y@ýSÁ@”{ýÛ7a+©ývþ@#çÎ{!z«^,¦ eLû_K hu¼^5“Ü€H4ù—têܹà[[ Åbóû³$±Þ“““2¹¿ŒÕùSü¤ûgWWgjT¡IO$[BQæO Â974ìëõkJ¡1«utþ¦,IèÙŸL°*þp*ùþèâQ[ƒ=°M› ßc^ðG¸š•&Jóôúù@I÷“~÷9ÄUºZQ¨õ¦[ch-"ÉÜ?·ú*RÚý³«‹¬l™ VFplŠfc±øï«K.uB¡Ü>ÉLèÍûçn¼)vz‘‘úìQë7Ýtã†x”ÛìÚQh fŒÑ#mÑ«X¯/įrÇž"Cóç^ iJ¡ÛN/Òr²v.n»uv²q‰kö¥ ½ Œlg_e6ÜšLñj£ÕÊý¦?H¦N™Û'™ ½ùþÕ†[cÞm tŠU'N. 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Dr. Geo -- Contenido
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Contenido

¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

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drgeo-doc-1.5/es/default_behaviour.html0000644000175000017500000000661410117134567013704 Manual de Usuario de Dr. Geo -- Comportamiento Predeterminado
Otras PreferenciasPreferencias de UsuarioComportamiento Predeterminado

Comportamiento Predeterminado

El comportamiento predeterminado de DR. GEO puede ser modificado de varias maneras. Para ajustar las preferencias, el usuario va al elemento del menú Editar->Preferencias... para abrir el diálogo de preferencias.

Preferencias de las figuras geométricas

El diálogo se compone de dos partes ::
  1. La primera parte trata sobre propiedades de las figuras geométricas. Las distintas opciones permiten al usuario dar las reglas predeterminadas para cada tipo de objeto (geométrico o numérico). Estas reglas se refieren a la apariencia de los objetos.
  2. La segunda parte trata sobre preferencias globales :
    • El nivel para Deshacer/Rehacer;
    • El nombre de la figura predeterminado que se usará cuando una nueva figura es creada. El %d es remplazado por un valor entero que es manejado por DR. GEO, este valor es incrementado con cada nueva figura creada;
    • El navegador de internet predeterminado para visualisar la ayuda en línea ;
    • Los nombres predeterminadas para ser utilizados cuando se guarde una figura o una sesión ;
    • Los nombres predeterminados para exportar en los formatos LaTeX  y PostScript ;

 

¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Otras PreferenciasPreferencias de UsuarioComportamiento Predeterminado
drgeo-doc-1.5/es/drgenius_100.html0000644000175000017500000000722610117134567012414 Manual de Usuario de Dr. Geo -- Colocar un párrafo de texto en la figura
Libro de recetasImprimir una figuraColocar un párrafo de texto en la figura

Colocar un párrafo de texto en la figura

Uno puede ventajosamente utilizar los scripts, de una manera ciertamente imprevista. Se selecciona la creación de un script -Herramienta Script -, y se hace click sobre el fondo de la figura. De este modo un script sin parámetros de entrada es creado.

Enseguida se editan las propiedades del script - Propiedades de un objeto. En la zona de texto donde el código Scheme es normalmente escrito, colocamos un texto entre comillas precedido por una única apóstrofe, por ejemplo : 


'"Animación \n  y \n  observaciones
=====================
Desplace los puntos de la figura para responder a las siguientes preguntas:
\n
1.¿Dónde hay que colocar al punto A para que el punto A' se confunda con el punto A?
2. ¿Dónde hay que colocar al punto A para que el punto A' coincida con el punto B?
3. ¿Cómo hay que colocar al punto I para que los puntos B', C' e I estén alineados?
4. ¿Cuál es el simétrico del punto I? ¿Cuál es el simétrico del punto A'?"

Ejemplo de párrafo de texto dentro de una figura

Como con todo script, es igualmente posible cambiar el color del texto. Observe que es posible usar algunos caracteres de control dentro del texto. Un script, que permite combinar cálculos con texto es el siguiente : 
(format #f "~s   más   ~s es casi siempre ~s" 3 4 (+ 3 4))
¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Libro de recetasImprimir una figuraColocar un párrafo de texto en la figura
drgeo-doc-1.5/es/drgenius_101.html0000644000175000017500000003324610117134567012416 Manual de Usuario de Dr. Geo -- Índice
Histórico.TopLibro de recetasÍndice

Índice

Symbols A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Symbols
Ángulo - Geométrico -
Ángulo - Orientado -
A
Arco de círculo - -
Arco de círculo - Longitud -
Ayuda - Preferencias predeterminadas - Navegador
C
Colocar - Texto -
Círculo - -
Círculo - Perímetro -
E
Editar - Apariencia -
Editar - Estilo predeterminado (por default) -
Editar - Preferencias predeterminadas - Nombres
Editar - Preferencias predeterminadas (por default) - Deshacer/Hacer
Editar - Preferencias predeterminadas(default) -
Editar - Propiedades -
Editar - Punto -
Editar - Script -
Editar - Valor -
Enrejado - Activar -
F
Figura - Abrir -
Figura - Activar - Enrejado(rejilla)
Figura - Colocar - Texto
Figura - Exportar - Definir el área de exportación
Figura - Exportar - Fly Draw/WIMS
Figura - Exportar - PNG
Figura - Exportar - PostScript
Figura - Exportar - LaTeX
Figura - Guardar -
Figura - Imprimir -
Figura - Mover -
Figura Scheme de DR. GEO - Evaluar -
Figura Scheme de DR. GEO- Creación de objetos - Atributos(Apariencia) de los objetos
Figura Scheme de DR. GEO- Creación de objetos - Círculo
Figura Scheme de DR. GEO- Creación de objetos - Polígono
Figura Scheme de DR. GEO- Creación de objetos - Segmento
Figura Scheme de DR. GEO- Creación de objetos - Semirrecta
Figura Scheme de DR. GEO- Creación de objetos - Transformaciones geométricas
Figura Scheme de DR. GEO- Creación de objetos - Ángulo
Figura Scheme de DR. GEO- Creación de objetos -
Figura Scheme de DR. GEO- Creación de objetos - Arco
Figura Scheme de DR. GEO- Creación de objetos - Lugar Geométrico
Figura Scheme de DR. GEO- Creación de objetos - Número
Figura Scheme de DR. GEO- Creación de objetos - Punto
Figura Scheme de DR. GEO- Creación de objetos - Recta
Figura Scheme de DR. GEO- Creación de objetos - Vector
Figura Scheme de DR. GEO- Ejemplos -
Figura Scheme de DR. GEO- Ejemplos -
Figura Scheme de DR. GEO- Ejemplos - Cadena de Papus
Figura Scheme de DR. GEO- Ejemplos - Espiral de Baravelle
Figura Scheme de DR. GEO- Ejemplos - Espiral de Teodoro
Figura Scheme de DR. GEO- Ejemplos - Fractal
Figura Scheme de DR. GEO- Ejemplos - Polígono regular
Figura Scheme de DR. GEO- Introducción -
Figura Scheme de DR. GEO- Nueva figura -
Figura Scheme de DR. GEO- Sinónimos -
H
Herramientas - Bloquear -
Herramientas - Desbloqueo -
Histórico - Árbol lógico -
I
Imprimir - Figura -
L
Locus - -
Lugar Geométrico - -
Lugar geométrico - Script -
Línea - -
Línea - Distancia -
Línea - Paralela -
Línea - Pendiente -
Línea - Perpendicular -
M
Macro - -
Macro - Abrir -
Macro - Crear -
Macro - Ejecutar -
Macro - Ejecutar - Menu
Macro - Guardar -
Macro - Guardar -
Macro - Polígono -
Macro - Script -
N
Número - -
Número - Valor libre -
O
Objeto - Borrar -
Objeto - Enmascarar -
Objeto - Mover -
Objeto - Ocultar -
Objeto - Renombrar -
P
Polígono - -
Polígono - Macro -
Punto - Coordenadas -
Punto - Definido por sus coordenadas -
Punto - Intersección -
Punto - Libre -
Punto - Medio -
Punto - Renombrar -
R
Rayo - -
Recta - -
Recta - Distancia -
Recta - Ortogonal -
Recta - Paralela -
Recta - Pendiente -
Recta - Perpendicular -
Rejilla - Activar -
Rotación - De 180 grados -
S
Script - -
Script - Con parámetros de entrada -
Script - Ejemplos -
Script - Ejemplos - Diferencia en la longitud de dos segmentos
Script - Ejemplos - Perímetro
Script - Ejemplos - Raíz cuadrada
Script - Ejemplos - Tangente a una curva
Script - Ejemplos - Teorema de Pitágoras
Script - Ejemplos - Teorema de Ptolomeo
Script - Ejemplos - Área de un trapecio
Script - Intervalo -
Script - Introducción -
Script - getAbscissa -
Script - getAngle -
Script - getCenter -
Script - getCoordinates -
Script - getLength -
Script - getLength -
Script - getNormal -
Script - getNorm -
Script - getRadius -
Script - getSlope -
Script - getUnit -
Script - getValue -
Script - move -
Script - números aleatorios -
Script - setAbscissa -
Script - setCoordinates -
Script - setValue -
Segmento - -
Segmento - Longitud -
Semirrecta - -
Sesión - Abrir -
Sesión - Guardar -
T
Texto - colocar -
Transformación del plano - Escala -
Transformación del plano - Homotecia -
Transformación del plano - Reflexión -
Transformación del plano - Rotación - General
Transformación del plano - Simetría - Axial
Transformación del plano - Simetría - Central
Transformación del plano - Traslación -
V
Vector - -
Vector - Coordenadas -
Vector - Longitud -
Vector - Norma -
¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Histórico.TopLibro de recetasÍndice
drgeo-doc-1.5/es/drgenius_102.html0000644000175000017500000000431410117134567012411 Manual de Usuario de Dr. Geo -- Histórico.
GNU Free Documentation LicenseTopÍndiceHistórico.

Histórico.

Redacciónes originales de la documentación : Hilaire Fernandes (Inglés y Francés) y Andrea Centomo (Italiano).

Traducción al Español : Adrián Ulises Soto Bañuelos.

¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

GNU Free Documentation LicenseTopÍndiceHistórico.
drgeo-doc-1.5/es/drgenius_103.html0000644000175000017500000005656310117134567012427 Manual de Usuario de Dr. Geo -- GNU Free Documentation License
FootnotesTopHistórico.GNU Free Documentation License

GNU Free Documentation License


                GNU Free Documentation License
                  Version 1.2, November 2002


 Copyright (C) 2000,2001,2002  Free Software Foundation, Inc.
     59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 Everyone is permitted to copy and distribute verbatim copies
 of this license document, but changing it is not allowed.


0. PREAMBLE

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Translation is considered a kind of modification, so you may
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If a section in the Document is Entitled "Acknowledgements",
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9. TERMINATION

You may not copy, modify, sublicense, or distribute the Document except
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10. FUTURE REVISIONS OF THIS LICENSE

The Free Software Foundation may publish new, revised versions
of the GNU Free Documentation License from time to time.  Such new
versions will be similar in spirit to the present version, but may
differ in detail to address new problems or concerns.  See
http://www.gnu.org/copyleft/.

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If the Document specifies that a particular numbered version of this
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ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of
the License in the document and put the following copyright and
license notices just after the title page:

    Copyright (c)  YEAR  YOUR NAME.
    Permission is granted to copy, distribute and/or modify this document
    under the terms of the GNU Free Documentation License, Version 1.2
    or any later version published by the Free Software Foundation;
    with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
    A copy of the license is included in the section entitled "GNU
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If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
replace the "with...Texts." line with this:

    with the Invariant Sections being LIST THEIR TITLES, with the
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If you have Invariant Sections without Cover Texts, or some other
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If your document contains nontrivial examples of program code, we
recommend releasing these examples in parallel under your choice of
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to permit their use in free software.

¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

FootnotesTopHistórico.GNU Free Documentation License
drgeo-doc-1.5/es/drgenius_104.html0000644000175000017500000001277410117134567012424 Manual de Usuario de Dr. Geo -- Footnotes
TopGNU Free Documentation LicenseFootnotes

Footnotes

 (1)
Se trata de poder, a partir de un mismo comando, crear un tipo de objeto según se requiera. Por ejemplo, a partir del comando para la construcción de un círculo, el usuario puede crear un círculo a partir de su centro y de ya sea un punto, una longitud, un segmento, etc. Con todo, este comando es representado por un solo icono, y DR. GEO se anticipa para ofrecer al usuario la construcción deseada. El efecto inmediato es que existe una disminución en el tiempo de aprendizaje de la interfaz, al proponer un número importante de modos de construcción
 (2)
O procedimientos para los que se iniciaron en el lenguaje Pascal.
 (3)
Por ejemplo, permite la recursión.
 (4)
Esta restricción ha sido posteriormente flexibilizada, lo cual permite ir más allá con las macors. Ver Crear un polígono regular.
 (5)
Las macros constituyen el aspecto geométrico, en tanto que los DGS abarcan también el aspecto numérico; pero no sólo eso, pues nos permiten utilizarlos con un espíritu de programador ("hacker", en inglés, sería un término más apropiado)
 (6)
En particular, las funciones matemáticas
 (7)
Si por accidente hacemos click sobre un objeto, el seleccionar de nuevo la herramienta Script en el menú bastará para anular nuestro error
 (8)
En este punto x toma un valor entre 0 y 1 inclusive. La "abscisa curvilínea" del objeto es 0 en un extremo, y va creciendo hasta ser 1 en el otro extremo; es 0.5 en la mitad, 0.25 a un cuarto, etc.
 (9)
Ya que x estaba entre 0 y 1, 20 ×( x -0.5) estará entre -10 y 10.
 (10)
Desde el punto de vista del lenguaje Scheme, estas referencias son símbolos que apuntan hacia una estructura interna del objeto -un prototipo- mientras que los nombres son simplemente cadenas de caracteres.
 (11)
Archivos que contienen varios documentos de DR. GEO (i.e. figuras y/o texto)
 (12)
GhostView es un programa que permita visualizar documentos PostScript (.ps o .eps) así como documentosPDF
 (13)
Este formato es reconocido por TeXmacs, OpenOffice.org, Lyx, LaTeX Xfig, el Gimp y muchos más.
 (14)
OpenOffice.org permite integrar una imagen EPS pero no la puede mostrar. Únicamente en la impresión en papel aparecerá la imagen
 (15)
Cuando lo deseemos, el panel lateral que contiene el árbol lógico de la figura, puede ser desplegado reduciendo aún más la zona visible, y, en consecuencia, el área de exportación.
 (16)
Esto es una verificación numérica; no una prueba
 (17)
Si no, las macros no podrían ser llamadas. Por ejemplo,¿qué valor debemos dar a un objeto tipo valor libre que interviene dentro de la construcción de una figura?
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TopGNU Free Documentation LicenseFootnotes
drgeo-doc-1.5/es/drgenius_10.html0000644000175000017500000000436710117134567012337 Manual de Usuario de Dr. Geo -- Punto Medio
IntersecciónHerramientas de puntosPunto LibrePunto Medio

Punto Medio

 

Crear el punto medio de un par de puntos o la mitad de un segmento.

  1. En el primer caso, el usuario selecciona dos puntos.
  2. En el segundo caso, el usuario simplemente selecciona un segmento
.
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IntersecciónHerramientas de puntosPunto LibrePunto Medio
drgeo-doc-1.5/es/drgenius_11.html0000644000175000017500000000461010117134567012327 Manual de Usuario de Dr. Geo -- Intersección
Punto definido por sus coordenadasHerramientas de puntosPunto MedioIntersección

Intersección

 

Crear el(los) punto(s) de intersección de dos líneas (objetos unidimensionales, i.e. recta, semirrecta, segmento, arco de círculo, círculo o lugar geométrico). El usuario necesita seleccionar dos líneas (v.g arco de círculo y semirrecta).

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Punto definido por sus coordenadasHerramientas de puntosPunto MedioIntersección
drgeo-doc-1.5/es/drgenius_12.html0000644000175000017500000000530410117134567012331 Manual de Usuario de Dr. Geo -- Punto definido por sus coordenadas
Herramientas de puntosIntersecciónPunto definido por sus coordenadas

Punto definido por sus coordenadas

 

Crear un punto definido por sus coordenadas. El usuario necesita seleccionar dos números, el primer número seleccionado es la abscisa, el segundo la ordenada.

¿Cómo colocar un punto con restricciones a sus coordenadas?

Esta funcion es muy utilizada cuando deseamos, por ejemplo, construir el lugar geométrico de un punto. Esta construcción supone la existencia de dos valores - ver Sección Valores Numéricos - el punto es construidoluego de seleccionar esos dos valores. Los valores pueden ser independientes o uno depender del otro.

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Herramientas de puntosIntersecciónPunto definido por sus coordenadas
drgeo-doc-1.5/es/drgenius_13.html0000644000175000017500000000403210117134567012327 Manual de Usuario de Dr. Geo -- Segmento
VectorHerramientas de lineasSemirrectaSegmento

Segmento

 

Crea un segmento definido por dos puntos.

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VectorHerramientas de lineasSemirrectaSegmento
drgeo-doc-1.5/es/drgenius_14.html0000644000175000017500000000401310117134567012327 Manual de Usuario de Dr. Geo -- Recta
SemirrectaHerramientas de líneasRecta

Recta

 

Crear una línea recta definida por sus dos puntos. El usuario selecciona dos puntos.

¿Comentarios?/¿Sugerencias?
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SemirrectaHerramientas de líneasRecta
drgeo-doc-1.5/es/drgenius_15.html0000644000175000017500000000427010117134567012335 Manual de Usuario de Dr. Geo -- Semirrecta
SegmentoHerramientas de líneasRectaSemirrecta

Semirrecta

Crea una semirrecta (también llamada rayo) definida por dos puntos. El usuario selecciona dos puntos, el primero es el origen, el segundo pertenece a la semirrecta.

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SegmentoHerramientas de líneasRectaSemirrecta
drgeo-doc-1.5/es/drgenius_16.html0000644000175000017500000000407010117134567012334 Manual de Usuario de Dr. Geo -- Segmento
VectorHerramientas de líneasSemirrectaSegmento

Segmento

 

Crea un segmento definido por dos puntos.

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VectorHerramientas de líneasSemirrectaSegmento
drgeo-doc-1.5/es/drgenius_17.html0000644000175000017500000000466310117134567012345 Manual de Usuario de Dr. Geo -- Vector
CírculoHerramientas de líneasSegmentoVector

Vector

 

Crea un vector definido por dos puntos. El usuario selecciona dos puntos, el primer punto es el origen, el segundo es el extremo.

Una vez que el vector es creado, éste puede ser desplazado independientemente de los dos puntos que le dieron origen. Esto sigue siendo cierto para vectores construidos a través de una transformación. (Ver la sección de Transformaciones en este manual).

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CírculoHerramientas de líneasSegmentoVector
drgeo-doc-1.5/es/drgenius_18.html0000644000175000017500000000453610117134567012345 Manual de Usuario de Dr. Geo -- Círculo
Arco de CírculoHerramientas de líneasVectorCírculo

Círculo

 

Crea un círculo. El usuario puede crear un círculo a partir de varias opciones:

  1. el centro y un punto del círculo;
  2. el centro y un número (el radio del círculo);
  3. el centro y un segmento cuya longitud es el radio del círculo.
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Arco de CírculoHerramientas de líneasVectorCírculo
drgeo-doc-1.5/es/drgenius_19.html0000644000175000017500000000453510117134567012345 Manual de Usuario de Dr. Geo -- Arco de Círculo
Lugar geométricoHerramientas de líneasCírculoArco de Círculo

Arco de Círculo

 

Crea un arco de círculo definido por tres puntos. El primer punto seleccionado es el origen del arco, el tercero es su extremo, el segundo es un punto sobre el arco. Los tres puntos seleccionados formarán parte del arco.

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Lugar geométricoHerramientas de líneasCírculoArco de Círculo
drgeo-doc-1.5/es/drgenius_20.html0000644000175000017500000000465210117134567012335 Manual de Usuario de Dr. Geo -- Lugar geométrico
PolígonoHerramientas de líneasArco de CírculoLugar geométrico

Lugar geométrico

 

Crea un lugar geométrico (locus en latín) dados dos puntos. El usuario selecciona dos puntos; uno es un punto libre sobre una línea (linea o círculo); el otro es un punto que depende del primero (i.e. cuando uno mueve el primero, el segundo también tiene que moverse).

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PolígonoHerramientas de líneasArco de CírculoLugar geométrico
drgeo-doc-1.5/es/drgenius_21.html0000644000175000017500000000513610117134567012334 Manual de Usuario de Dr. Geo -- Polígono
Herramientas de líneasLugar geométricoPolígono

Polígono

 

Crea un polígono definido por n puntos. El usuario selecciona n+1 puntos delimitando el polígono. El primero y el último seleccionado deben ser los mismos, esto indica a DR. GEO que la selección esta terminada. El objeto polígono no es un objeto como los objetos unidimensionales, no es posible colocar un punto sobre él o calcular la intersección entre un polígono y otro objeto unidimensional. Por otro lado, es posible aplicar a un polígono una transformación geométrica (rotación, reflexión, homotecia, etc.)

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Herramientas de líneasLugar geométricoPolígono
drgeo-doc-1.5/es/drgenius_22.html0000644000175000017500000000513010117134567012327 Manual de Usuario de Dr. Geo -- Simetría Axial (Reflexión)
Simetría Central Herramientas de TransformaciónLínea PerpendicularSimetría Axial (Reflexión)

Simetría Axial (Reflexión)

 

Crea la imagen de un objeto a través de una simetría axial (reflexión en una recta). El usuario selecciona el objeto a transformar y el eje de simetría (que debe ser una recta). Cuando el usuario quiere construir la imagen de una línea recta, la primera linea recta seleccionada por el usuario será la recta a reflejar.

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Simetría Central Herramientas de TransformaciónLínea PerpendicularSimetría Axial (Reflexión)
drgeo-doc-1.5/es/drgenius_23.html0000644000175000017500000000442010117134567012331 Manual de Usuario de Dr. Geo -- Línea Paralela
Línea PerpendicularHerramientas de TransformaciónLínea Paralela

Línea Paralela

 

Crea una línea paralela a una dirección y que pase a través de un punto. El usuario selecciona un punto y una dirección (i.e. una línea recta, una semirrecta, un segmento o un vector).

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Línea PerpendicularHerramientas de TransformaciónLínea Paralela
drgeo-doc-1.5/es/drgenius_24.html0000644000175000017500000000476510117134567012346 Manual de Usuario de Dr. Geo -- Línea Perpendicular
Simetría Axial (Reflexión)Herramientas de TransformaciónLínea ParalelaLínea Perpendicular

Línea Perpendicular

 

Crea una línea perpendicular a una dirección y que pasa a través de un punto. El usuario selecciona un punto y una dirección (i.e. una línea recta, una semirrecta, un segmento o un vector). (Ortogonal es un sinónimo de Perpendicular)

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Simetría Axial (Reflexión)Herramientas de TransformaciónLínea ParalelaLínea Perpendicular
drgeo-doc-1.5/es/drgenius_25.html0000644000175000017500000000515610117134567012342 Manual de Usuario de Dr. Geo -- Simetría Axial (Reflexión)
Simetría Central Herramientas de TransformaciónLínea PerpendicularSimetría Axial (Reflexión)

Simetría Axial (Reflexión)

 

Crea la imagen de un objeto a través de una simetría axial (reflexión en una recta). El usuario selecciona el objeto a transformar y el eje de simetría (que debe ser una recta). Cuando el usuario quiere construir la imagen de una línea recta, la primera línea recta seleccionada por el usuario será la recta a reflejar.

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Simetría Central Herramientas de TransformaciónLínea PerpendicularSimetría Axial (Reflexión)
drgeo-doc-1.5/es/drgenius_26.html0000644000175000017500000000510510117134567012335 Manual de Usuario de Dr. Geo -- Simetría Central
TraslaciónHerramientas de TransformaciónSimetría Axial (Reflexión)Simetría Central

Simetría Central

 

Crea la imagen de un objeto a través de una simetría central. El usuario selecciona los objetos que serán transformados y el centro de simetría (un punto). Cuando el usuario quiere construir la imagen de un punto, el primer punto seleccionado es el punto a transformar.(La simetría central es equivalente a una rotación de 180 grados).

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TraslaciónHerramientas de TransformaciónSimetría Axial (Reflexión)Simetría Central
drgeo-doc-1.5/es/drgenius_27.html0000644000175000017500000000465510117134567012347 Manual de Usuario de Dr. Geo -- Traslación
RotaciónHerramientas de TransformaciónSimetría Central Traslación

Traslación

 

Crear la imagen de un objeto a través de una traslación. El usuario selecciona el objeto que será transformado y el vector de traslación. Cuando el usuario quiere construir la imagen de un vector, el primer vector seleccionado es el vector que será trasladado.

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RotaciónHerramientas de TransformaciónSimetría Central Traslación
drgeo-doc-1.5/es/drgenius_28.html0000644000175000017500000000613110117134567012337 Manual de Usuario de Dr. Geo -- Rotación
Escala (Homotecia)Herramientas de TransformaciónTraslaciónRotación

Rotación

 

Crea la imagen de un objeto a través de una rotación. El usuario selecciona el punto que será rotado, el centro y el ángulo de la rotación. Cuando el usuario quiere crear la imagen de un punto, el primer punto seleccionado es el punto a transformar.

El ángulo puede ser seleccionado a partir de varios tipos de valores :

  • valor numérico : el ángulo es expresado en radianes. Ejemplos de valores numéricos : valor libre, un valor devuelto por un script Guile de DR. GEO, etc. ;
  • la medida de un ángulo geométrico formado por tres puntos : su medida es entonces expresada en grados. Atención, pues en este caso la medida estará en el intervalo [0 ; 180] ;
  • la medida de un ángulo orientado entre dos vectores : esta medida es expresada en grados y cubre el intervalo ]-180 ; 180].
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Escala (Homotecia)Herramientas de TransformaciónTraslaciónRotación
drgeo-doc-1.5/es/drgenius_29.html0000644000175000017500000000500010117134567012332 Manual de Usuario de Dr. Geo -- Escala (Homotecia)
Herramientas de TransformaciónRotaciónEscala (Homotecia)

Escala (Homotecia)

 

Crea la imagen de un objeto a través de una transformación de escala (es decir, homotecia). El usuario selecciona el objeto a transformar, el centro de homotecia, y el factor (i.e. un número). Cuando el usuario quiera crear la imagen de un punto, el primer punto seleccionado es el punto a transformar. (Por ejemplo, si se desea hacer un polígono un tercio de grande, se selecciona un punto -centro de homotecia-, el polígono, y el valor 0.33333 )

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Herramientas de TransformaciónRotaciónEscala (Homotecia)
drgeo-doc-1.5/es/drgenius_2.html0000644000175000017500000000465510117134567012260 Manual de Usuario de Dr. Geo -- Copyright
IntroducciónTopContenidoCopyright

Copyright

Copyright (c) 2000-2004 OFSET.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".

Other copyright apply to the respective owners of the modified documentations. See the section history for the complet list.

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IntroducciónTopContenidoCopyright
drgeo-doc-1.5/es/drgenius_30.html0000644000175000017500000000450410117134567012332 Manual de Usuario de Dr. Geo -- Coordenadas
Script Guile de DR. GEOHerramientas NuméricasÁnguloCoordenadas

Coordenadas

 

Al selecciona un punto o un vector, nos da como resultado las coordenadas del punto o nos da las coordenadas del vector (coordenadas del punto final menos coordenadas del punto inicial). Esta herramienta crea tanto a la abscisa como a la ordenada.

¿Comentarios?/¿Sugerencias?
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Script Guile de DR. GEOHerramientas NuméricasÁnguloCoordenadas
drgeo-doc-1.5/es/drgenius_31.html0000644000175000017500000000640510117134567012335 Manual de Usuario de Dr. Geo -- Distancias, longitudes & Números
ÁnguloHerramientas NuméricasDistancias, longitudes & Números

Distancias, longitudes & Números

 

Crea un valor numérico. El valor numérico puede ser computado o editado por el usuario dependiendo de las selecciones que haga el usuario:

  1. dos puntos: la distancia entre dos puntos;
  2. un segmento: la longitud de este segmento;
  3. un vector; la magnitud de ese vector (también llamada norma del vector);
  4. un círculo: el perímetro del círculo;
  5. un arco de círculo; la longitud del arco;
  6. una línea recta: la pendiente de la recta;
  7. una línea recta y un punto: la distancia entre la línea y el punto
  8. un click sobre el fondo permite al usuario entrar un valor nuevo (i.e. un valor numérico libre)

Esta última posibilidad es muy intenresante en ciertas situaciones. Por ejemplo, ella permite fijar una longitud, el radio de un círculo, la medida de un ángulo (en radianes) o las coordenadas de un punto. Estos valores numéricos pueden ser enseguida utilizados por las herramientas de construcción de círculos, de rotación de objetos o para la creación de puntos dadas sus coordenadas.

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ÁnguloHerramientas NuméricasDistancias, longitudes & Números
drgeo-doc-1.5/es/drgenius_32.html0000644000175000017500000000473010117134567012335 Manual de Usuario de Dr. Geo -- Ángulo
CoordenadasHerramientas NuméricasDistancias, longitudes & NúmerosÁngulo

Ángulo

 

Calcula la magnitud de un ángulo definido por tres puntos o dos vectores. En el primer caso, el ángulo se considera no orientado (i.e. un ángulo geométrico con valores en el intervalo [0 ; 180°]. En el segundo caso, el ángulo se considera orientado y toma valores en el rango ]-180 ; 180].

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CoordenadasHerramientas NuméricasDistancias, longitudes & NúmerosÁngulo
drgeo-doc-1.5/es/drgenius_33.html0000644000175000017500000000452010117134567012333 Manual de Usuario de Dr. Geo -- Coordenadas
Script Guile de DR. GEOHerramientas NuméricasÁnguloCoordenadas

Coordenadas

 

Al selecciona un punto o un vector, nos da como resultado las coordenadas del punto o nos da las coordenadas del vector (coordenadas del punto final menos coordenadas del punto inicial). Esta herramienta crea tanto a la abscisa como a la ordenada.

¿Comentarios?/¿Sugerencias?
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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Script Guile de DR. GEOHerramientas NuméricasÁnguloCoordenadas
drgeo-doc-1.5/es/drgenius_34.html0000644000175000017500000000511510117134567012335 Manual de Usuario de Dr. Geo -- Script Guile de DR. GEO
Herramientas NuméricasCoordenadasScript Guile de DR. GEO

Script Guile de DR. GEO

 

Crea un script Scheme de DR. GEO(i.e. un script en el lenguaje Scheme). El script recibe una entrada de n objetos. Siempre dará como resultado un número, que será presentado en la figura. Un script puede ser usado para obtener efectos colaterales o por el valor que da como resultado. Los Scripts Scheme de DR. GEO están cubiertos en detalle en el Capítulo Construcciones Avanzadas y exactamente en la Sección Script.

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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Herramientas NuméricasCoordenadasScript Guile de DR. GEO
drgeo-doc-1.5/es/drgenius_36.html0000644000175000017500000000415510117134567012342 Manual de Usuario de Dr. Geo -- Crear una Macro
Ejecutar una MacroHerramientas para Macros de construccionesCrear una Macro

Crear una Macro

Extrae una secuencia de construcción dada en una figura y la convierte en la macro de una construcción.

¿Comentarios?/¿Sugerencias?
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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Ejecutar una MacroHerramientas para Macros de construccionesCrear una Macro
drgeo-doc-1.5/es/drgenius_37.html0000644000175000017500000000453410117134567012344 Manual de Usuario de Dr. Geo -- Ejecutar una Macro
Herramientas para Macros de construccionesCrear una MacroEjecutar una Macro

Ejecutar una Macro

Ejecuta (i.e. "lanza" o "corre") una macro previamente construida. La macro puede haber sido recién creada o puede ser cargada desde un archivo.

(!) Las construcciones de Macro están expuestas en laSección Construcción de Macros .
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Herramientas para Macros de construccionesCrear una MacroEjecutar una Macro
drgeo-doc-1.5/es/drgenius_38.html0000644000175000017500000000437310117134567012346 Manual de Usuario de Dr. Geo -- Mover un Objeto
Mover la figuraMover un Objeto

Mover un Objeto

 

Un objeto puede ser movido al jalarlo con el ratón. La figura es redibujada con respecto a las nuevas posiciones. Casi cualquier tipo de objeto geométrico puede ser movido. Cuando es necesario, DR. GEO mueve los puntos libres asociados con la figura. Por ejemplo, cuando el usuario mueve una linea definida por dos puntos libres, DR. GEO moverá los dos puntos simultáneamente..

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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Mover la figuraMover un Objeto
drgeo-doc-1.5/es/drgenius_39.html0000644000175000017500000000557310117134567012352 Manual de Usuario de Dr. Geo -- Árbol lógico de construcción
Mover la figuraOtras herramientasÁrbol lógico de construcción

Árbol lógico de construcción

Cada figura esta asociada a un árbol lógico de construcción. Este árbol es cronológico; es decir que recuerda, desde la parte alta hasta la parte baja, el orden de construcción de la figura. Ciertas entradas del árbol pueden ser desplegadas para que aparezcan los antecedentes -es decir, los objetos originadores (objetos padres)- utilizados en la definición del objeto.

Inicialmente el árbol esta oculto (enmascarado); de hecho está replegado en el borde izquierdo de la ventana. Para hacerlo aparecer hace falta desplegarlo con la ayuda del ratón. Mover el puntero del ratón hacia el borde izquierdo de la ventana de DR. GEO cuando éste se transforme en "<->", presionar el botón del ratón y manteniéndolo presionado mueva el ratón a la derecha.

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Mover la figuraOtras herramientasÁrbol lógico de construcción
drgeo-doc-1.5/es/drgenius_3.html0000644000175000017500000000453610117134567012257 Manual de Usuario de Dr. Geo -- Funciones Básicas
Características AvanzadasTopIntroducciónFunciones Básicas

Funciones Básicas

Este capítulo describe las herramientas usadas para construir figuras geométricas. Al final del capítulo, la configuración de las preferencias del usuario es también presentada.

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Características AvanzadasTopIntroducciónFunciones Básicas
drgeo-doc-1.5/es/drgenius_40.html0000644000175000017500000000442210117134567012332 Manual de Usuario de Dr. Geo -- Mover la figura
Borrar un objetoOtras herramientasÁrbol lógico de construcciónMover la figura

Mover la figura

La figura puede ser movida presionando al mismo tiempo la tecla Control y el botón izquierdo del ratón al moverlo hacia donde se desea mover la figura.

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Borrar un objetoOtras herramientasÁrbol lógico de construcciónMover la figura
drgeo-doc-1.5/es/drgenius_41.html0000644000175000017500000000442310117134567012334 Manual de Usuario de Dr. Geo -- Mover un Objeto
Mover la figuraMover un Objeto

Mover un Objeto

 

Un objeto puede ser movido al jalarlo con el ratón. La figura es redibujada con respecto a las nuevas posiciones. Casi cualquier tipo de objeto geométrico puede ser movido. Cuando es necesario, DR. GEO mueve los puntos libres asociados con la figura. Por ejemplo, cuando el usuario mueve una línea definida por dos puntos libres, DR. GEO moverá los dos puntos simultáneamente..

¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Mover la figuraMover un Objeto
drgeo-doc-1.5/es/drgenius_42.html0000644000175000017500000000504610117134567012337 Manual de Usuario de Dr. Geo -- Borrar un objeto
Editar la Apariencia de un ObjetoOtras herramientasMover la figuraBorrar un objeto

Borrar un objeto

 

Los objetos en la figura pueden ser borrados cuando se activa este menú. En cualquier momento posterior, el usuario puede anular el borrado usando la función "deshacer" de la bara de íconos o del menú editar->deshacer. Inicialmente el número de anulaciones posibles es de 10, pero el usuario puede ajustar este valor a través del diálogo de preferencias (Editar ->preferencias).

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Editar la Apariencia de un ObjetoOtras herramientasMover la figuraBorrar un objeto
drgeo-doc-1.5/es/drgenius_43.html0000644000175000017500000000410410117134567012332 Manual de Usuario de Dr. Geo -- Preferencias de Usuario
Funciones BásicasHerramientas de ConstrucciónPreferencias de Usuario

Preferencias de Usuario

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Funciones BásicasHerramientas de ConstrucciónPreferencias de Usuario
drgeo-doc-1.5/es/drgenius_44.html0000644000175000017500000000623010117134567012335 Manual de Usuario de Dr. Geo -- Editando Propiedades de Objetos
Activar un enrejadoOtras herramientasEditar la Apariencia de un ObjetoEditando Propiedades de Objetos

Editando Propiedades de Objetos

 

Ciertas propiedades de los objetos son ajustables por el usuario. Cuando el usuario hace click en tales objetos, un diálogo apropiado aparece. De hecho, los siguientes objetos poseen propiedades ajustables por el usuario:

  1. punto libre : la abscisa y la ordenada pueden ser editadas;

    Editar las coordenadas de un punto libre

  2. valor libre : su valor puede ser editado

    Editar valor libre

  3. script : su código puede ser editado (El código esta en el lenguaje Scheme, que es un dialecto del lenguaje Lisp)

    Editando un script

¿Comentarios?/¿Sugerencias?
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Activar un enrejadoOtras herramientasEditar la Apariencia de un ObjetoEditando Propiedades de Objetos
drgeo-doc-1.5/es/drgenius_45.html0000644000175000017500000000470410117134567012342 Manual de Usuario de Dr. Geo -- Activar un enrejado
Otras herramientasEditando Propiedades de ObjetosActivar un enrejado

Activar un enrejado

Es posible mostrar un enrejado unitario dentro de cualquier figura de DR. GEO. El comando es accesible desde el menú Editar->Mostrar u ocultar rejilla. Puede ser también activado con la tecla Ctrl-G. Si el comando es reactivado, el enrejado es ocultado. El enrejado es unitario: cada subdivisión representa una unidad. Por último, si el enrejado esta activado al momento de guardar la figura; éste también será guardado junto con ella.

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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Otras herramientasEditando Propiedades de ObjetosActivar un enrejado
drgeo-doc-1.5/es/drgenius_46.html0000644000175000017500000000406410117134567012342 Manual de Usuario de Dr. Geo -- Preferencias de Usuario
Funciones BásicasOtras herramientasPreferencias de Usuario

Preferencias de Usuario

¿Comentarios?/¿Sugerencias?
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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Funciones BásicasOtras herramientasPreferencias de Usuario
drgeo-doc-1.5/es/drgenius_48.html0000644000175000017500000000441410117134567012343 Manual de Usuario de Dr. Geo -- Otras Preferencias
Preferencias de UsuarioComportamiento PredeterminadoOtras Preferencias

Otras Preferencias

Además del comportamiento predeterminada de DR. GEO, el usuario puede cambiar el nombre de una figura desde el elemento menú Editar->Renombrar.

Renombrar la vista de una figura

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Preferencias de UsuarioComportamiento PredeterminadoOtras Preferencias
drgeo-doc-1.5/es/drgenius_49.html0000644000175000017500000001131710117134567012344 Manual de Usuario de Dr. Geo -- Características Avanzadas
Archivos y documentosTopFunciones BásicasCaracterísticas Avanzadas

Características Avanzadas

En este capítulo presentamos características usadas para extender las características de DR. GEO o adaptarlo a una situación pedagógica dada.

La primera es la macro de una construcción geométrica. Ella permite la extracción de la lógica de una construcción en un registro. Ya hecho esto, este registro se puede repetir o guardar en un archivo que lleve la extensión .mgeo, y puede ser abierto cuando sea necesario..

Los Scripts Scheme de DR. GEO - DR. GEO Script en inglés; abreviado DGS  -representan otra forma de extender DR. GEO. Estos scripts son en realidad elementos de figuras como cualquier otro elemento geométrico. Ellos reciben como entrada las referencias a los elementos de figura seleccionados por el usuario y dan como resultado un valor numérico, que se inserta en la figura . Son, en efecto, funciones 2 injertadas en una figura, y son evaluadas en cada actualización de la figura (i.e. cada vez que el programa requiere volver a dibujar la figura)

Los Scripts Guile de DR. GEO pueden ser útiles por el valor que dan como resultado o por sus efectos colaterales, dependiendo de lo que el usuario desee hacer.

Extendiendo la funcionalidad de los Scripts de DrGeo, DR. GEO puede ir todavía más allá, con la Figura Scheme de DR. GEO: Ésta consiste en un archivo de texto que contiene una figura geométrica completamente escrita en el lenguaje de programación Scheme. La potencia de este modo de crear una figura radica en permitir una construcción usando el tipo de programación llamado funcional 3, y no solamente declarativo, como es el caso de la interfaz gráfica. De este modo, DR. GEO se convierte en un programa que puede ser utilizado para la introducción a la programación.

Por último, la adaptación de la interfaz de usuario de DR. GEO permite al maestro preparar una sesión de trabajo con varios documentos en los que ciertas funciones han sido bloqueadas a través de una contraseña (password). El objetivo de esto es permitir el uso del programa en ciertas situaciones pedagógicas dadas.

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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Archivos y documentosTopFunciones BásicasCaracterísticas Avanzadas
drgeo-doc-1.5/es/drgenius_4.html0000644000175000017500000001445210117134567012256 Manual de Usuario de Dr. Geo -- Preliminares
DR. GEO en la redIntroducciónPreliminares

Preliminares

DR. GEO es un programa tanto de geometría interactiva como de programación en el lenguaje Scheme. Permite crear figuras geométricas, así como manipularlas interactivamente respetando sus restricciones geométricas. Ofrece igualmente la posibilidad de introducirse gradualmente en la programación. Es útil para la enseñanza a estudiantes de nivel básico o superior.

La interfaz de usuario de DR. GEO ha sido concebida para dar, dentro de un conjunto armónico, a la vez sencillez en su operación, ergonomía y funcionalidades avanzadas.

Así la interfaz de DR. GEO , con una gran sencillez, permite al neófito la familiarización con las funciones básicas del programa. Posteriormente, a medida que lo conozca más, el usuario conocerá los aspectos más avanzados de la interfaz y del funcionamiento de DR. GEO : múltiples modos para la construcción de objetos 1, macros de construcciones, sesiones, adaptabilidad de la interfaz, uso de scripts y de Figuras Scheme de DR. GEO(i.e. DR. GEO es programable en dos modos distintos). Estas funciones avanzadas generan muy poca sobrecarga a la interfaz, por lo que DR. GEO es utilizado con entusiasmo en la enseñanza primaria, lo que no resta su uso en el nivel medio.

En las secciones siguientes, expondremos las herramientas básicas. Posteriormente las funciones avanzadas serán presentadas en detalle.

Pantalla de Bienvenida de DR. GEO

La estructura de la interfaz es la siguiente :
  1. la barra de menú característica con Archivo, Editar, Macros, Ventanas, Ayuda ;
  2. la barra de acciones para crear una nueva figura o un texto explicativo; contiene también las herramientas de hacer/deshacer y la rejilla .

Para crear una figura geométrica nueva, el usuario debe hacer click en el primer botón de la barra de herramientas. De manera alternativa, una nueva figura puede ser creada usando el elemento de la barra del menú Archivo->Nuevo->Figura. Cuando una nueva figura es creada, una nueva barra de íconos formada por seis iconos aparece. Esta barra de íconos termina con un menú que permite ajustar la escala de la figura geométrica actual.

Además, una barra de íconos vertical, a la izquierda de la figura, ofrece un rápido acceso a las herramientas más utilizadas.

Una figura geométrica vacía

Los seis iconos de la barra de íconos son entradas de menú generales desde donde se llaman a funciones específicas. Estas funciones son descritas en el siguiente capítulo.

Una figura de DR. GEO y su descripción

Para cada figura, un árbol sinóptico está disponible. Inicialmente este panel está oculto en el extremo izquierdo de modo que sólo la representación de la figura es visible. En cualquier momento, el usuario puede empujar el panel hacia la derecha como sigue: Lleve el ratón a la parte izquierda de la figura, justo a la izquierda de donde está la regla; cuando el puntero del ratón cambie de forma, presione el botón y continúe presionando mientras mueve el ratón a la derecha. Con ello, será visible la descripción de la figura. La descripción de una figura es un árbol formado con todos los elementos de la figura. Los elementos que dependen de otros elementos pueden ser revelados al hacer click sobre el símbolo `+'. Con ello, se mostrarán los elementos que dieron origen (v.g. los que dieron origen a una línea pueden ser dos puntos; aunque pueden ser otros originadores. También se les llama elementos antecedentes o elementos padre).
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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

DR. GEO en la redIntroducciónPreliminares
drgeo-doc-1.5/es/drgenius_51.html0000644000175000017500000001172710117134567012342 Manual de Usuario de Dr. Geo -- Crear una Macro
Ejecutar una MacroMacros de ConstruccionesCrear una Macro

Crear una Macro

En esta etapa, la serie de pasos para la construcción ya está hecha. Ahora el usuario necesita ordenar a DR. GEO que quiere una macro a partir de esta serie de pasos. Puede llamar la función Construir una macro de la barra de íconos o del menú contextual que aparece al pulsar el botón derecho sobre el fondo de la figura..

Desde el menú de creación de la macro, el usuario selecciona los parámetros de entrada y de salida, el nombre y la descripción de la macro.

La primera parte del menú de creación de la macro

La segunda parte del diálogo sirve para seleccionar los parámetros de entrada. En nuestro ejemplo, estos son los tres puntos iniciales. El usuario sólo necesita llegar a este lugar y seleccionar los tres puntos en la figura. Los elementos seleccionados parpadearán.

Segunda parte, los tres puntos ya están seleccionados

En la tercera parte del diálogo, el usuario selecciona los parámetros de salida. En nuestro ejemplo, deseamos que el círculo y el centro sean los parámetros de salida para la macro. El usuario procede entonces como en el caso de los parámetros de entrada par seleccionarlos.

La tercera página, el círculo y su centro ya están seleccionados

En la cuarta parte del diálogo, el usuario escribe el nombre y la descripción de la macro. Estos datos son desplegados cuando el usuario ejecuta una macro, de modo que ayuda a distinguir una macro de otra.

La cuarta parte, el nombre y la descripción de la macro

En la última parte del diálogo (la quinta), el usuario crea la macro haciendo click sobre el botón Aplicar(finalizar la construcción). Alternativamente, el usuario puede regresar a las partes previas para ajustar los parámetros de la macro.

(!) Si los parámetros de entrada y de salida no coinciden (DR. GEO no puede extraer la lógica de la construcción), la macro no puede ser construida. En este caso, el usuario necesita reconsiderar la selección de los parámetros de entrada y de salida. Puede regresar a la segunda o a la tercera parte del menú de creación para ajustar sus elecciones.

En este momento la macro está construida y grabada en DR. GEO. En la siguiente sección, veremos cómo usarla.

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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Ejecutar una MacroMacros de ConstruccionesCrear una Macro
drgeo-doc-1.5/es/drgenius_52.html0000644000175000017500000000725010117134567012337 Manual de Usuario de Dr. Geo -- Ejecutar una Macro
Macros de ConstruccionesCrear una MacroEjecutar una Macro

Ejecutar una Macro

Para ejecutar la macro de una construcción, el usuario llama la función Ejecutar macro previamente construida de la barra de íconos o desde el menú contextual que se obtiene pulsando el boton derecho. Una ventana de diálogo que describe el procedimiento se inserta entonces.

Desde la ventana de diálogo, el usuario selecciona la macro. En la segunda parte, selecciona la macro de la lista en la parte más alta del diálogo. Una vez que la macro fue seleccionada, puede hacer click directamente en los parámetros de entrada en la figura. Tan pronto como todos los parámetros de entrada sean seleccionados, la macro es ejecutada y los elementos de salida aparecen.

El usuario selecciona los parámetros de entrada directamente en la figura

En nuestro ejemplo, la macro necesita tres parámetros de entrada (tres puntos) y crea a partir de ellos un círculo y un punto. Para ejecutar nuestra macro, necesitamos una figura con al menos tres puntos.

Una figura con tres puntos

Una vez que nuestra macro es ejecutada usando esos tres puntos, obtenemos el círculo deseado y también su centro.

La figura resultante con el círculo y su centro

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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Macros de ConstruccionesCrear una MacroEjecutar una Macro
drgeo-doc-1.5/es/drgenius_53.html0000644000175000017500000000525310117134567012341 Manual de Usuario de Dr. Geo -- Con la ayuda del menú Macros
Ejecutar una MacroCon la ayuda del menú Macros

Con la ayuda del menú Macros

Existe otro procedimiento -más rápido- para ejecutar una macro. La barra de menú principal de DR. GEO contiene un menú Macro-constructions. Este menú esta poblado con los nombres de las macros cargadas en la memoria del programa. Para ejecutar una macro, el usuario selecciona directamente la macro de su preferencia.

En outre un passage du pointeur souris au dessus de chaque item de menu fait apparaître une info-bulle de la description de la macro. L'utilisateur peut ainsi avoir rapidement une explication sur l'ensemble des macro-constructions.

Ejecutar una macro directamente desde el menú Macro-constructions

¿Comentarios?/¿Sugerencias?
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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Ejecutar una MacroCon la ayuda del menú Macros
drgeo-doc-1.5/es/drgenius_54.html0000644000175000017500000000575510117134567012351 Manuel utilisateur de Dr. Geo -- À l'aide du menu Macro-constructions
Exécution d'une macro-constructionÀ l'aide de la boîte de dialogueÀ l'aide du menu Macro-constructions

À l'aide du menu Macro-constructions

Il existe une autre procédure - plus rapide - pour exécuter une macro-construction. La barre de menu principale de DR. GEO comporte un menu Macro-constructions. Ce menu est peuplé par les noms des macro-constructions chargées en mémoire dans le programme. Pour exécuter une macro-construction, l'utilisateur sélectionne directement celle de son choix.

En outre un passage du pointeur souris au dessus de chaque item de menu fait apparaître une info-bulle de la description de la macro. L'utilisateur peut ainsi avoir rapidement une explication sur l'ensemble des macro-constructions.

Exécuter une macro-construction directement depuis le menu Macro-constructions

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Exécution d'une macro-constructionÀ l'aide de la boîte de dialogueÀ l'aide du menu Macro-constructions
drgeo-doc-1.5/es/drgenius_55.html0000644000175000017500000003416710117134567012351 Manual de Usuario de Dr. Geo -- DGS a través de ejemplos
Métodos de referencia para los scripts de DR. GEO Script Scheme de DR. GEODGS a través de ejemplos

DGS a través de ejemplos

La herramienta para crear un DGS esta disponibe al seleccionar la sección Valor Numérico dentro del menú contextual que se obtiene al hacer click con el botón derecho del ratón en el fondo de la figura. Un DGS puede recibir de 0 a n parámetros de entrada.

Después de haber escogido el DGS, basta hacer click en los objetos geométricos (o numéricos) que constituirán los parámetros de entrada. Al terminar de escoger los parámetros de entrada, se debe hacer click en un área libre del fondo de la figura; con ello, el script sera visible.

En lo que sigue nos proponemos trabajar con algunos ejemplos de DGS que permitirán comprender fácilmente su uso y su potencialidad.

Los DGS, como las macros, dan una dimensión particular a DR. GEO, Le permiten, junto con las macros5, llevar a cabo cosas que los autores del programa no incorporaron o no quisieron incorporar: "Ir hacia donde ellos no fueron o no quisieron ir".

Es también importante comprender que la mayor parte de las funciones del intérprete GNU Guile están disponibles a través del DGS. Esto es particularmente cierto para las librerías de funciones6 que utilizaremos ampliamente.

DGS sin parámetros de entrada

El procedimiento para crear un script sin parámetros de entrada es el siguiente :

  1. Después de haber escogido Script Guile de DR. GEO , hacer click en el lugar de la figura donde se desee colocar el script. Como deseamos que el script no tenga parámetros de entrada, debemos prestar atención y no hacer click erróneamente en algún objeto geométrico; no sea que DR. GEO considere ese objeto como un parámetro de entrada 7.
  2. Una vez que el DGS ha sido creado, aparece en la figura la cadena de caracteres "Dr. Genius". Todo script recién creado contiene un comando predeterminado que muestra ese mensaje. Usted puede editarlo seleccionando propiedades del objeto.
  3. Una vez que esta herramienta ha sido seleccionada, hacer click sobre el script -o para ser más precisos sobre su valor - de su elección. Una ventana se abrirá con el contenido del script y le permitirá editarlo. En lo que sigue, usaremos ese diálogo para escribir nuestros ejemplos.
Un generador de números aleatorios y otros ejemplos

Si usted desea un generador de números aleatorios, nada es más simple: simplemente su script contiene únicamente la siguiente línea (recuerde hacer click en aplicar y luego cerrar...): 

(random 10)

Así, cada vez que se dibuja la figura, este script devuelve un número entero aleatorio en el intervalo [0 ; 10[ (es decir, [0 ; 10) )

Si usted prefiere un número real en el intervalo [0 , 1), utilice el siguiente script: 

(random:uniform)

(!) Algunas precisiones :
  • El valor devuelto por el script es el valor calculado por la última línea del script. En nuestros ejemplos, se trata del valor devuelto por la función que usamos.
  • La última línea debe devolver un número real; de otro modo DR. GEO imprimirá "Resultado no imprimible".
  • Si lo que se desea es mostrar el valor de una variable, basta poner esa variable en la última línea.

Cálculo de algunas constantes comunes

Para calcular el valor aproximado de pi : 

(acos -1)

O de e : 

(exp 1)

Los valores devueltos por estos DGS pueden ser inmediatamente utilizados como todos los demás valores numéricos que DR. GEO genera. Por todo lo anterior, los DGS son verdaderamente nuestros aliados. Pero eso no es todo, los DGS pueden hacer muchas más cosas interesantes cuando reciben parámetros de entrada. Enseguida veremos cómo.

DGS con al menos un parámetro de entrada

El procedimiento para crear un DGS con un parámetro de entrada es esencialmente el mismo. Justo después de haber seleccionado la herramienta script, basta hacer click sobre el objeto que será el parámetro de entrada y enseguida hacer click sobre el fondo de la figura, en el lugar donde se desee tener al nuevo script.

Enseguida, dentro del script, el parametro de entrada será referido por la variable a1. En caso de tengamos dos o más parámetros de entrada, utilizaremos, respetando el orden en que fueron seleccionados, las variables a1, a2, a3, a4, etc. dependiendo del número de objetos seleccionados.

Dependiendo del objeto que seleccionemos, diversos métodos estarán disponibles para obtener valores, como pueden ser coordenadas, longitud, etc. Estos métodos son mostrados en la Sección Métodos de referencia para un DGS.

En lo que sigue, expondremos gradualmente un ejemplo no muy complicado en que construiremos la curva de una función así como la tangente en un punto de la curva que podremos mover.

La figura final es mostrada por DR. GEO. Esta se llama slope.fgeo

La figura que obtendremos

Definir un valor en un intervalo dado.

En una nueva figura, empezamos colocando dos puntos y el segmento que ellos determinan. Sobre este segmento colocamos un punto libre al que llamaremos "¡Muéveme!"("Move me!" en inglés). Este punto nos sirve para determinar un valor numérico que identifica la posición del punto dentro del segmento; esto lo lograremos dentro del script.

En seguida crearemos un script que tiene como único parámetro de entrada el punto "¡Muéveme!".

Ya que a1 es la variable en el script del punto "¡Muéveme!", el script siguiente (que llamaremos Xo) nos dará un valor decimal comprendido entre [-10 ; 10] . 

(define x (getAbscissa a1))
(* 20  (- x 0.5))

Cabe aclarar algunas cosas. En la primera línea, (getAbscissa a1) permite obtener la "abscisa curvilínea" del objeto al que se refiere a18 . En la segunda línea calibramos el valor. En este caso la expresión significa 20 ×( x -0.5). Dado que ésta es la última línea del script, el resultado de esta última operación será el valor que el script devuelva, y será un número decimal en el intervalo [-10;+10] como se deseaba9.

Finalmente, llamemos este script Xo. (Esto se puede hacer en el menú contextual: seleccione otros, luego apariencia, y haga click en el script para ponerle nombre).

Dibujar la gráfica de una función.

El valor obtenido por el script precedente nos servirá, a través de otro script, para calcular la imagen del punto bajo la función x -> cos(x). Este segundo script tiene como parámetro de entrada al script Xo. 

(define x (getValue a1))
(cos x)

Subrayemos que en (getValue a1) el objeto al que se refiere a1 no es el punto "¡Muéveme!", sino el script Xo, y que no estamos obteniendo la "abscisa curvilínea" de un punto, sino el valor de un número (en este caso del script Xo, que dentro del segundo script es llamado a1). Llamamos a este script Yo

Por ejemplo, si el punto "¡Muéveme!" estaba a la mitad entonces su "abscisa curvilínea" es 0.5, de modo que Xo toma el valor 20 ×( 0.5 -0.5)=0, y Yo toma el valor cos(0)=1.

Enseguida crearemos el punto Mo de coordenadas (Xo ; Yo). Es un punto de la curva de la función x -> cos(x). Para dibujar la porción de la gráfica con dominio [-10 ; 10], crearemos el lugar geométrico del punto Mo cuando el punto "¡Muéveme" describe el segmento. Con ello obtendremos la gráfica!(Recordar que para crear Mo, hay que seleccionar, en el menú contextual, punto, coordenadas y luego hacer click en los scripts que dan las coordenadas. Para lograr el lugar geométrico, recordar seleccionar en el menú contextual curva, lugar geométrico y luego seleccionar los puntos "¡Muéveme!" y Mo.)

Calcular y dibujar la tangente a la gráfica en un punto

Para dibujar la tangente en Mo=(Xo,Yo), hace falta tener la pendiente en ese punto. Usando Cálculo Diferencial, sabemos que la pendiente esta dada por la derivada, que en este caso es x -> -sin(x) evaluada en el punto Xo. De modo que crearemos un script que tiene como parámetro de entrada al script Xo : 

(- 0 (sin (getValue a1)))

La notación prefija (i.e "* 2 3" en vez de "2 * 3") utilizada por Scheme/Guile puede parecer poco intuitiva, pero es cuestión de simplemente acostumbrarse a ella; es simplemente decir "El producto de dos y tres" en lugar de "dos por tres".

Llamemos al script recién creado "Pendiente en el punto Mo".

Resta, pues dibujar la tangente. Para esto calcularemos, primero, las coordenadas de un segundo punto - M1 - de esa recta.

Comencemos por su abscisa (No confundir con la "abscisa geométrica"); por ejemplo: X1 = X0 + 2. Para hacer esto crearemos un script que tendrá como parámetro de entrada al script Xo , y al que llamaremos X1: 

(define x1 (getValue a1))
(+ x1 2)

Encontremos en este momento la ordenada del punto M1. Para ello necesitamos:

  • Mo (referencia a1) ;
  • la pendiente en Mo (a2) ;
  • la abscisa X1 (a3).(No confundir con "la abscisa geométrica")

Después de seleccionar como parámetros de entrada al punto Mo, a la pendiente en Mo(que llamamos "Pendiente en el punto Mo", "Slope at Mo" en inglés), y a X1, determinamos la ordenada de M1, que llamaremos Y1, a través del siguiente cálculo:

Yo + m ×(X1 - X0) : 

(define x0 (car (getCoordinates a1)))
(define y0 (cadr (getCoordinates a1)))
(define m (getValue a2))
(define x1 (getValue a3))
(+ (* m (- x1 x0)) y0)

En relación con la función (getCoordinates a1) en la que a1 debe ser una referencia a un objeto de tipo punto, el método devuelve una lista que contiene las coordenadas del punto, en este caso Mo. La instrucción car permite extraer el primer elemento de esta lista; la instrucción cadr, el segundo. El resto del script debe resultar claro.

Habiendo nombrado este último script Y1, construimos el punto M1=(X1 ; Y1), y, para terminar, construimos la tangente (MoM1). (Para esto ya no necesitamos scripts; podemos usar el menú, escogiendo punto dadas sus coordenadas y la recta dados dos puntos).

Por supuesto, habría sido posible utilizar unos dos o tres scripts en lugar de la gran cantidad que usamos. Sin embargo, esperamos que estos pequeños ejemplos logren en usted el deseo de experimentar por usted mismo los DGS.

¿Comentarios?/¿Sugerencias?
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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Métodos de referencia para los scripts de DR. GEO Script Scheme de DR. GEODGS a través de ejemplos
drgeo-doc-1.5/es/drgenius_56.html0000644000175000017500000000533110117134567012341 Manual de Usuario de Dr. Geo -- Métodos de referencia para los scripts de DR. GEO
Script Scheme de DR. GEODGS a través de ejemplosMétodos de referencia para los scripts de DR. GEO

Métodos de referencia para los scripts de DR. GEO

Las secciones siguientes contienen la descripción de los métodos disponibles para los DGS. Estos métodos están clasificados de acuerdo al tipo de objeto geométrico o numérico.

¿Comentarios?/¿Sugerencias?
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Script Scheme de DR. GEODGS a través de ejemplosMétodos de referencia para los scripts de DR. GEO
drgeo-doc-1.5/es/drgenius_57.html0000644000175000017500000000676310117134567012354 Manual de Usuario de Dr. Geo -- Punto
Recta, Semirrecta, Segmento, VectorMétodos de referencia para los scripts de DR. GEO Punto

Punto

valor (getAbscissa punto)
punto: Referencia a un punto sobre una curva
Devuelve: La "abscisa geométrica" del punto sobre la curva.El valor pertenece al intervalo [0 ; 1]
Ejemplo:
(define x (getAbscissa a1))
(* x 10)

  (setAbscissa punto x)
punto: Referencia a un punto libre sobre una línea
x: Valor decimal en el intervalo [0 ; 1] que representa a la nueva "abscisa geométrica"
Ejemplo:
(setAbscissa a1 0.5)

  lista (getCoordinates punto|vector)
Devuelve las coordenadas de un punto o de un vector.
punto|vector: Referencia a un punto o un vector
Devuelve: Lista que contiene las coordenadas del punto o del vector
Ejemplo:
(define c (getCoordinates a1))
(define x (car c))
(define y (cadr c))
(+ (* x x) (* y y))

  (setCoordinates punto coord)
Asigna coordenadas a un punto
punto: Referencia a un punto libre en el plano
coord: Lista de dos números decimales
Ejemplo:
(define l (list 1.4 (random 5)))
(setCoordinate a1 l)

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Recta, Semirrecta, Segmento, VectorMétodos de referencia para los scripts de DR. GEO Punto
drgeo-doc-1.5/es/drgenius_58.html0000644000175000017500000000750410117134567012347 Manual de Usuario de Dr. Geo -- Recta, Semirrecta, Segmento, Vector
Círculo, Arco de círculoMétodos de referencia para los scripts de DR. GEO PuntoRecta, Semirrecta, Segmento, Vector

Recta, Semirrecta, Segmento, Vector

valor (getSlope dirección)
dirección: Referencia a un objeto de tipo recta, semirrecta, segmento o vector
Devuelve: La pendiente en esa dirección
Ejemplo:
(define p (getSlope a1))

  valor (getUnit dirección)
dirección: Referencia a un objeto de tipo recta, semirrecta, segmento o vector
Devuelve: Una lista que contiene las coordenadas de un vector unitario en la dirección dada
Ejemplo:
(define v (getUnit a1))

  valor (getNormal dirección)
dirección: Referencia a un objeto de tipo recta, semirrecta segmento o vector
Devuelve: Una lista que contiene las coordenadas de un vector normal a la dirección dada
Ejemplo:
(define n (getNormal a1))

  valor (getNorm vector)
vector: Referencia a un vector
Devuelve: La norma (i.e., magnitud, longitud) de ese vector
Ejemplo:
(define n (getNorm a1))

  valor (getLength segmento)
segmento: Referencia a un segmento
Devuelve: La longitud de ese segmento
Ejemplo:
(define l (getLength a1))

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Círculo, Arco de círculoMétodos de referencia para los scripts de DR. GEO PuntoRecta, Semirrecta, Segmento, Vector
drgeo-doc-1.5/es/drgenius_59.html0000644000175000017500000000651610117134567012352 Manual de Usuario de Dr. Geo -- Círculo, Arco de círculo
Funciones NuméricasMétodos de referencia para los scripts de DR. GEO Recta, Semirrecta, Segmento, VectorCírculo, Arco de círculo

Círculo, Arco de círculo

lista (getCenter círculo|arco)
círculo|arco: Referencia a un círculo o un arco de círculo
Devuelve: Lista que contiene las coordenadas del centro de un círculo o de un arco de círculo
Ejemplo:
(define c (getCenter a1))
(car c)

  valor (getRadius círculo|arco)
círculo|arco: Referencia a un círculo o un arco de círculo
Devuelve: Radio del círculo o del arco de círculo
Ejemplo:
(define r (getRadius a1))

  valor (getLength círculo|arco)
círculo|arco: Referencia a un círculo o un arco de círculo
Devuelve: Perímetro del círculo o longitud del arco de círculo
Ejemplo:
(define l (getLength a1))

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Funciones NuméricasMétodos de referencia para los scripts de DR. GEO Recta, Semirrecta, Segmento, VectorCírculo, Arco de círculo
drgeo-doc-1.5/es/drgenius_5.html0000644000175000017500000000462210117134567012255 Manual de Usuario de Dr. Geo -- DR. GEO en la red
IntroducciónPreliminaresDR. GEO en la red

DR. GEO en la red

DR. GEO dispone de su propio espacio en la red en el sitio OFSET en la dirección : http://www.ofset.org/drgeo

En este espacio, el usuario encontrará la siguiente información :

  • la información para obtener DR. GEO ;
  • la documentación del programa;
  • algunas indicaciones para involucrarse en el proyecto DR. GEO ;
  • algunas referencias para el uso pedagógico del programa.
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IntroducciónPreliminaresDR. GEO en la red
drgeo-doc-1.5/es/drgenius_60.html0000644000175000017500000000536310117134567012341 Manual de Usuario de Dr. Geo -- Funciones Numéricas
ÁnguloMétodos de referencia para los scripts de DR. GEO Círculo, Arco de círculoFunciones Numéricas

Funciones Numéricas

valor (getValue número)
número: Referencia a un número
Devuelve: Valor de ese número
Ejemplo:
(define a (getValue a1))
(define b (getValue a2))
(+ a b)

  (setValue número v)
número: Referencia a un número
v: Valor decimal
Ejemplo:
(define v (getValue a1))
(setValue a2 v)

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ÁnguloMétodos de referencia para los scripts de DR. GEO Círculo, Arco de círculoFunciones Numéricas
drgeo-doc-1.5/es/drgenius_61.html0000644000175000017500000000505310117134567012336 Manual de Usuario de Dr. Geo -- Ángulo
OtrosMétodos de referencia para los scripts de DR. GEO Funciones NuméricasÁngulo

Ángulo

valor (getAngle ángulo)
ángulo: Referencia a un ángulo orientado o geométrico
Devuelve: La medida de ese ángulo en grados. Para obtener la medida en radianes, utilice la función getValue
Ejemplo:
(define angle1 (getAngle a1))
(define angle2 (getAngle2))
(define angle3 (getAngle a3))
(+ angle1 angle2 angle3)

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OtrosMétodos de referencia para los scripts de DR. GEO Funciones NuméricasÁngulo
drgeo-doc-1.5/es/drgenius_62.html0000644000175000017500000000427010117134567012337 Manual de Usuario de Dr. Geo -- Otros
Métodos de referencia para los scripts de DR. GEO ÁnguloOtros

Otros

(move item t)
item: Referencia a un objeto de la figura
t: vector de dos dimensiones
Ejemplo:
(define v (vector .1 0))
(move a1 v)

¿Comentarios?/¿Sugerencias?
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Métodos de referencia para los scripts de DR. GEO ÁnguloOtros
drgeo-doc-1.5/es/drgenius_63.html0000644000175000017500000000704010117134567012336 Manual de Usuario de Dr. Geo -- Figura Scheme de DR. GEO
Bloquear las herramientas de la interfazCaracterísticas AvanzadasScript Scheme de DR. GEOFigura Scheme de DR. GEO

Figura Scheme de DR. GEO

Las Figuras Scheme de DR. GEO - (FSD) - son figuras escritas en un lenguaje relativamente natural. No se trata entonces de construir una figura con la ayuda de la interfaz gráfica de DR. GEO sino más bien de describir una figura dentro del lenguaje Scheme(Una variante de Lisp). Hemos cuidado mucho que la sintaxis utilizada sea fácil y concisa. Además, el conjunto de palabras clave utilizadas en Scheme para para describir una figura simple son adaptables de modo que aparezcan en Español, Francés, Inglés, etc. . Una combinación de varios idiomas es también posible; pero no es deseable.(N. del T. es por ello que varias palabras clave en este manual aparecen en Español. Basta con traducir un archivo en el directorio scm donde DR. GEO está instalado; notar que en la traducción hecha del archivo, se incluyó una versión de los comandos con acentos y eñes, así como otra sin acentos y sin eñes. Las palabras clave no traducidas seran escritas en inglés.)

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Bloquear las herramientas de la interfazCaracterísticas AvanzadasScript Scheme de DR. GEOFigura Scheme de DR. GEO
drgeo-doc-1.5/es/drgenius_64.html0000644000175000017500000002220610117134567012340 Manual de Usuario de Dr. Geo -- Algunos Ejemplos
Métodos de referencia para las figuras Scheme de DR. GEOFigura Scheme de DR. GEOAlgunos Ejemplos

Algunos Ejemplos

(N.del T. En lo que sigue se usarán las palabras "referencia" y "nombre". "referencia" es una variable que apunta a un objeto. "nombre" es el rótulo que aparece en la figura. A veces se usará el termino variable; pero "referencia" es más preciso en otros casos.)

En sí, Scheme es un lenguaje de muy alto nivel. Cuando una figura es definida en este lenguaje, disponemos también de todo su poder para, por ejemplo, definir recursivamente alguna parte de la figura o bien para colocar aleatoriamente ciertos objetos de tal suerte que, cada vez que se cargue la figura, los objetos aparecerán ligeramente distintos. En pocas palabras, los FSD no están atados a las limitantes de la interfaz gráfica, y además poseen todo el poder del lenguaje Scheme. Un FSD es entonces un archivo con extension .scm creado con la ayuda de un editor de texto, el cual es abierto en DR. GEO con la ayuda del comando Archivo->Evaluar.

Comencemos por estudiar un ejemplo sencillo de FSD : 

(nueva-figura "Mi figura")

Este es el script más pequeño que podemos definir. Después de ser cargado en DR. GEO, simplemente crea una nueva figura vacía con el nombre "Mi figura". Podemos escribir comandos (nueva-figura "Mi figura") tantas veces como deseemos.

Veamos ahora un segundo ejemplo : 

(nueva-figura "Mi figura")
(sea Punto "A" libre 1.2 -2)

Este FSD define una figura con un punto libre A de coordenadas iniciales (1,2 ; -2). Como podemos ver la sintaxis de la definición de un objeto geométrico es relativamente cómoda, a tal grado que esa expresada en nuestra lengua madre. Esto es de interés especial para la enseñanza secundaria. De hecho, todos los comandos de definición de objeto tienen una sintaxis común. Tal sintaxis es como sigue:

  1. Se comienza siempre con la palabra clave sea, la cual indica que deseamos definir un nuevo objeto
  2. Inmediatamente le sigue la clase de objeto; en este caso Punto.
  3. El nombre del objeto va enseguida, A, debe siempre estar entre dos comillas ". Si no deseamos nombrar al objeto, de todos modos es necesario dar un nombre vacío como sigue: "".
  4. Para terminar, necesitamos precisar, dentro de la clase, qué tipo de objeto, en nuestro ejemplo, la clase es punto, y el tipo es libre. Esto significa que el punto A es libre.
  5. El tipo de objeto es seguido por una lista de argumentos que depende de la clase de objeto y de que tipo de objeto. En nuestro ejemplo, esta lista se compone de dos números, las coordenadas del punto libre A.

Prosigamos con un tercer ejemplo : 

(define (triángulo p1 p2 p3)
  (Segmento "" extremos p1 p2)
  (Segmento "" extremos p2 p3)
  (Segmento "" extremos p1 p3))

(define (azar)
  (- 8 (* 16 (random:uniform))))

(nueva-figura "Mi figura")

(sea Punto "A" libre (azar) 0)
(sea Punto "B" libre 5 0)
(sea Punto "C" libre (azar) 5)

(triángulo A B C)

(N. del T. En este ejemplo, dos palabras están en inglés: "random" que significa "azar", y "uniform" que significa "uniforme". Como se comentó antes es posible traducirlas modificando el archivo dentro del directorio scm donde DR. GEO esté instalado. El archivo para español es: /usr/share/drgeo/scm/drgeo_scm_interface_constant_es.scm).

Este ejemplo es particularmente interesante, nos muestra tres cosas importantes :

  1. La definición de una construcción de alto nivel no prevista por los autores de DR. GEO. En el programa que acabamos de ver hemos definido la función triángulo la cual, a partir de tres puntos construye el triángulo que pasa por esos tres puntos. Podemos comparar esto con las macros; pero con un grado de libertad mucho más amplio e importante.
  2. La definición de las funciones asociadas, en este caso definimos la función azar que devuelve un número decimal comprendido entre -8 y 8. Utilizamos esta función para añadir un elemento de azar en ciertos puntos en nuestra figura. De este modo cada vez que se cargue la figura, ésta será ligeramente distinta.
  3. En efecto, la utilización de la palabra clave sea no es obligatoria; nosotros la utilizamos para guardar una referencia al objeto creado. Por ejemplo, dentro de la función triángulo no guardamos referencias para los segmentos creados. Por otro lado, cuando definimos los puntos A, B y C necesitamos guardar una referencia para ellos, estas referencias se llamarán igual10; pero sin las comillas; así nuestras referencias son: A, B y C. En lo que sigue llamaremos símbolos a esas variables, esta es la terminología precisa del lenguaje Scheme. De este modo, al llamar a la función triángulo, pasamos como parámetros a los símbolos A, B y C que son utilizados para definir nuestros tres segmentos.

Notar que cuando definimos los segmentos, no les dimos ningún nombre; en ese caso DR. GEO les dará un nombre que está determinado a partir del nombre de sus extremos. Nuestros tres segmentos tendrán entonces los nombres [AB], [BC] y [AC].

Para concluir esta sección, veamos un último ejemplo : 

(sea Punto "A" libre 1 0)
(sea Punto "B" libre 5 0)
(sea Recta "d1" 2puntos A B)

(envía A color amarillo)
(envía A forma redonda)
(envía A tamaño grande)
(envía B oculto)
(envía d1 grosor punteado)

Los tres primeros comandos crean dos puntos y una recta. La parte que nos interesa particularmente es la serie de comandos envía. Estos comandos permiten la comunicación con un objeto cuyo símbolo hemos guardado; en este caso tenemos los símbolos A, B y d1. El comando consiste en enviar un mensaje a un objeto. Su primer parámetro de entrada es el objeto con el que deseamos comunicarnos, el segundo argumento es el mensaje, los restantes argumentos están determinados por tipo de mensaje que es enviado. Por ejemplo (envía A color amarillo) envía el mensaje color con parámetro de entrada amarillo. El punto A toma entonces el color amarillo. Es fácil comprender el sentido de los otros comandos envía. Estos serán explicadosen la sección siguiente.

Hemos terminado nuestra pequeña visita guiada a las Figuras Scheme de Dr. Geo, FSD. En las secciones siguientes expondremos el conjunto de comandos disponibles para definir las FSD.

¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Métodos de referencia para las figuras Scheme de DR. GEOFigura Scheme de DR. GEOAlgunos Ejemplos
drgeo-doc-1.5/es/drgenius_65.html0000644000175000017500000000550310117134567012342 Manual de Usuario de Dr. Geo -- Métodos de referencia para las figuras Scheme de DR. GEO
Sinónimos en DGSFigura Scheme de DR. GEOAlgunos EjemplosMétodos de referencia para las figuras Scheme de DR. GEO

Métodos de referencia para las figuras Scheme de DR. GEO

La definición de los objetos en un documento FSD se hace a través de prototipos. Los prototipos son en cierto sentido objetos a los que podemos interrogar y modificar como veremos en lo que sigue.

Empero, antes de la definición de objeto alguno en un FSD, el FSD debe ser creado con el comando nueva-figura en el principio del archivo.

¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Sinónimos en DGSFigura Scheme de DR. GEOAlgunos EjemplosMétodos de referencia para las figuras Scheme de DR. GEO
drgeo-doc-1.5/es/drgenius_66.html0000644000175000017500000000476510117134567012354 Manual de Usuario de Dr. Geo -- Comandos generales
Definición de objetos en una figuraMétodos de referencia para las figuras Scheme de DR. GEOComandos generales

Comandos generales

(nueva-figura nombre)
nombre: Cadena de caracteres
Devuelve: No devuelve ningún valor. Es llamada por el efecto que produce, no por el valor que devuelve. Este comando crea una figura nueva. Los objetos creados posteriormente se crean dentro de esta figura hasta que se vuelva a llamar este comando.
Ejemplo:
(nueva-figura "Mi 1er figura")

¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Definición de objetos en una figuraMétodos de referencia para las figuras Scheme de DR. GEOComandos generales
drgeo-doc-1.5/es/drgenius_67.html0000644000175000017500000005425710117134567012356 Manual de Usuario de Dr. Geo -- Definición de objetos en una figura
Modificación de los atributos(Apariencia) de los objetosMétodos de referencia para las figuras Scheme de DR. GEOComandos generalesDefinición de objetos en una figura

Definición de objetos en una figura

Un objeto puede ser definido a través de varias sintaxis :
  • (sea Punto "p1" tipo args) El punto es creado y su referencia guardada en la variable p1. Esta sintaxis utiliza una macro Scheme.
  • (Punto "Nombre" tipo args) El punto es creado pero ninguna referencia al punto es conservada.
  • (define p1 (Punto "Nombre" tipo args)) El punto es creado y su referencia guardada en la variable p1.
  • (set! p1 (Punto "Nombre" tipo args)) El punto es creado y su referencia es copiada en la variable, ya existente, p1.

Si unos objetos son creados después del cuerpo de una función, utilice ya sea la forma set! o la forma especial de Scheme let. Es importante subrayar que la llamada se hace a una función que devuelve una referencia al objeto creado.

Para saber más sobre la correspondencia entre los nombres de los comandos Scheme en Español y en Inglés, vea el archivo /usr/share/drgeo/scm/drgeo_scm_interface_constant_es.scm.

 

Punto
prototipo (Punto nombre libre x y)
nombre: Cadena de caracteres que designa al nombre del objeto
x: La abscisa del punto
y: La ordenada del punto
Devuelve: Referencia a un punto libre del plano con coordenadas iniciales x y y.
Ejemplo:
(define p1 (Punto "A" libre 1.2 (acos -1)))

prototipo (Punto nombre sobre-la-curva curva x)
nombre: Cadena de caracteres que designa al nombre del objeto
curva: Referencia a una curva (recta, semirrecta, segmento, arco, círculo, etc..)
x: Abscisa curvilínea (la "abscisa geométrica") del punto libre; el valor pertenece al intervalo [0 ; 1]
Devuelve: Referencia a un punto libre sobre la curva
Ejemplo:
(Punto "M" sobre-la-curva s1 0.5)

prototipo (Punto nombre mitad-2pts p1 p2)
nombre: Cadena de caracteres que designa al nombre del objeto
p1: Referencia a un punto
p2: Referencia a un punto
Devuelve: Referencia al punto medio de los dos puntos.
Ejemplo:
(sea Punto "A" libre 1 1)
(sea Punto "B" libre 4 4)
(Punto "I" mitad-2pts A B)

prototipo (Punto nombre mitad-segmento s)
nombre: Cadena de caracteres que designa al nombre del objeto
s: Referencia a un segmento
Devuelve: Referencia a la mitad de un segmento.
Ejemplo:
(Punto "L" mitad-segmento s)

prototipo (Punto nombre intersección l1 l2)
nombre: Cadena de caracteres que designa al nombre del objeto
l1: Referencia a una línea(recta o curva)
l2: Referencia a una línea(recta o curva)
Devuelve: Referencia al punto de intersección de las dos líneas
Ejemplo:
(Punto "I" intersección recta segmento)

prototipo (Punto nombre intersección2 l1 l2)
nombre: Cadena de caracteres que designa al nombre del objeto
l1: Referencia a una línea(recta o curva)
l2: Referencia a una línea(recta o curva)
Devuelve: Referencia al segundo punto de intersección de las dos líneas cuando una de las dos líneas es del tipo arco de círculo o del tipo círculo.
Ejemplo:
(Punto "I" intersección2 recta círculo)

 

Recta
prototipo (Recta nombre 2puntos p1 p2)
nombre: Cadena de caracteres que designa al nombre del objeto
l1: Referencia a un punto
l2: Referencia a un punto
Devuelve: Referencia a una recta que pasa por los dos puntos.
Ejemplo:
(sea Punto "A" libre 0 0)
(sea Punto "M" libre 1 2)
(Recta "" 2puntos A M)

prototipo (Recta nombre paralela p d)
nombre: Cadena de caracteres que designa al nombre del objeto
p: Referencia a un punto
d: Referencia a una dirección (recta, segmento, vector,...)
Devuelve: Referencia a una recta paralela a la dirección d y que pasa por el punto p.
Ejemplo:
(sea Punto "A" libre 1 5)
(sea Recta "d1" paralela A d)

prototipo (Recta nombre perpendicular p d)
nombre: Cadena de caracteres que designa al nombre del objeto
p: Referencia a un punto
d: Referencia a una dirección (recta, segmento, vector, ...)
Devuelve: Referencia a una recta perpendicular à la dirección de d y que pasa por por p.
Ejemplo:
(sea Punto "A" libre 1 5)
(sea Recta "d1" perpendicular A d)

 

Semirrecta
prototipo (Semirrecta nombre 2puntos o p)
nombre: Cadena de caracteres que designa al nombre del objeto
o: Referencia a un punto, origen de la semirrecta
p: Referencia a un punto, punto de la semirrecta
Devuelve: Referencia a una semirrecta definida por su origen y por un punto.
Ejemplo:
(sea Punto "A" libre 1 5)
(sea Punto "O" libre 0 0)
(sea Semirrecta "dd1" 2puntos A 0)

 

Segmento

prototipo (Segmento nombre extremos p1 p2)
nombre: Cadena de caracteres que designa al nombre del objeto
p1: Referencia a un punto
p2: Referencia a un punto
Devuelve: Referencia a un segmento definido por sus extremos
Ejemplo:
(sea Punto "A" libre 1 5)
(sea Punto "B" libre 10 4)
(sea Segmento "" extremos A B)

 

Círculo
prototipo (Círculo nombre 2puntos c p)
nombre: Cadena de caracteres que designa al nombre del objeto
c: Referencia a un punto, centro del círculo
p: Referencia a un punto sobre el círculo
Devuelve: Referencia a un círculo definido por su centro y por un punto.
Ejemplo:
(sea Punto "A" libre 1 5)
(sea Punto "B" libre 10 4)
(sea Círculo "C1" 2puntos A B)

prototipo (Círculo nombre centro-radio c r)
nombre: Cadena de caracteres que designa al nombre del objeto
c: Referencia a un punto, centro del círculo
r: Referencia a una valor numérico, radio del círculo
Devuelve: Referencia a un círculo definido por su centro y por su radio
Ejemplo:
(sea Punto "A" libre 1 5)
(sea Número "r" libre 10)
(sea Círculo "C1" centro-radio A r)

prototipo (Círculo nombre centro-segmento c s)
nombre: Cadena de caracteres que designa al nombre del objeto
c: Referencia a un punto, centro del círculo
s: Referencia a un segmento dada la donde la longitud del segmento será el radio del círculo
Devuelve: Referencia a un círculo definido por su centro y por un segmento cuya longitud es su radio.
Ejemplo:
(sea Punto "A" libre 1 5)
(sea Círculo "C1" centro-segmento A s)

 

Arco de círculo
prototipo (Arco nombre 3puntos p1 p2 p3)
nombre: Cadena de caracteres que designa al nombre del objeto
p1: Referencia a un punto, 1er extremo del arco de círculo
p2: Referencia a un punto del arco
p3: Referencia a un punto, 2o extremo del arco de círculo
Devuelve: Referencia a un arco de círculo definido por sus extremos y por un punto interno.
Ejemplo:
(sea Punto "A" libre 1 5)
(sea Punto "B" libre 0 5)
(sea Punto "C" libre -1 -2)
(sea Arco "arc" 3puntos A B C)

 

Polígono
prototipo (Polígono nombre npuntos args)
nombre: Cadena de caracteres que designa al nombre del objeto.
args: Una lista de referencias de puntos ; vértices del polígono.
Devuelve: Referencia a un polígono definido por sus vértices.
Ejemplo:
(sea Polígono "quad" npuntos A B C D)

 

Las transformaciones geométricas
Los prototipos de las transformaciones geométricas permiten la obtención de objetos rotados, reflejados, trasladados, a escala, etc.. Estos prototipos usan como referencia a los tipos punto, recta, semirrecta, vector, círculo, arco de círculo y polígono.

prototipo (TipoDeObjeto nombre rotación objeto centro ángulo)
TipoDeObjeto: Punto, Segmento, Recta, Semirrecta, Vector, Círculo, Arco, Polígono
nombre: Cadena de caracteres que designa al nombre del objeto
objeto: Referencia del objeto a transformar
centro: Referencia a un punto, centro de la rotación
ángulo: Referencia a un valor numérico, ángulo de la rotación
Devuelve: Referencia del objeto ya transformado.
Ejemplo:
(sea Punto "I1" rotación I C a)

prototipo (TipoDeObjeto nombre escala objeto centro k)
TipoDeObjeto: Punto, Segmento, Recta, Semirrecta, Vector, Círculo, Arco, Polígono
nombre: Cadena de caracteres que designa al nombre del objeto
objeto: Referencia del objeto a transformar
centro: Referencia a un punto, centro de la escala (centro de homotecia)
k: Referencia a un valor numérico, factor de la escala (homotecia)
Devuelve: Referencia del objeto transformado.
Ejemplo:
(sea Polígono "P1" escala P C k1)

prototipo (TipoDeObjeto nombre simetría objeto centro)
TipoDeObjeto: Punto, Segmento, Recta, Semirrecta, Vector, Círculo, Arco, Polígono
nombre: Cadena de caracteres que designa al nombre del objeto
objeto: Referencia del objeto a transformar
centro: Referencia a un punto, centro de la simetría (esto es, una rotación de 180 grados)
Devuelve: Referencia del objeto ya transformado.
Ejemplo:
(sea Segmento "S1" simetría S C)

prototipo (TipoDeObjeto nombre reflexión objeto eje)
TipoDeObjeto: Punto, Segmento, Recta, Semirrecta, Vector, Círculo, Arco, Polígono
nombre: Cadena de caracteres que designa al nombre del objeto
objeto: Referencia del objeto a transformar
eje: Referencia a una recta, eje de la reflexión
Devuelve: Referencia del objeto ya transformado
Ejemplo:
(sea Polígono "P1" reflexión P d1)

prototipo (TipoDeObjeto nombre traslación objeto vector)
TipoDeObjeto: Punto, Segmento, Recta, Semirrecta, Vector, Círculo, Arco, Polígono
nombre: Cadena de caracteres que designa al nombre del objeto
objeto: Referencia del objeto a transformar
vector: Referencia a un vector
Devuelve: Referencia del objeto ya transformado
Ejemplo:
(sea Círculo "C1" traslación C v)

 

Lugar geométrico
prototipo (Lugar-geométrico nombre 2puntos m c)
nombre: Cadena de caracteres que designa al nombre del objeto
m: Referencia a un punto móvil sobre una línea (recta, círculo, etc.)
c: Referencia a un punto fijo que depende del punto m
Devuelve: Referencia al lugar geométrico de c cuando m se mueve sobre la línea (recta, círculo, etc.)
Ejemplo:
(Lugar-geométrico "locus1" 2puntos M I)

 

Vector
prototipo (Vector nombre 2puntos o e)
nombre: Cadena de caracteres que designa al nombre del objeto
o: Referencia a un punto, origen del vector
e: Referencia a un punto, extremo del vector
Devuelve: Referencia a un vector.
Ejemplo:
(sea Punto "B" libre 0 5)
(sea Punto "C" libre -1 -2)
(Vector "" 2puntos C B)

 

Número
prototipo (Número nombre libre x y v)
nombre: Cadena de caracteres que designa al nombre del objeto
x,y: Las coordenadas del número
v: El valor inicial del número
Devuelve: Referencia a un número libre.
Ejemplo:
(sea Número "pi" libre 5 5 (acos -1))

prototipo (Número nombre longitud-segmento x y s)
nombre: Cadena de caracteres que designa al nombre del objeto
x,y: Las coordenadas del número
s: Referencia a un segmento
Devuelve: Referencia a un número, longitud de un segmento.
Ejemplo:
(sea Número "l" longitud-segmento 5 5 S)

prototipo (Número nombre norma-vector x y v)
nombre: Cadena de caracteres que designa al nombre del objeto
x,y: Las coordenadas del número
s: Referencia a un vector
Devuelve: Referencia a un número, norma(longitud) de un vector.
Ejemplo:
(sea Número "l" norma-vector 5 5 V)

prototipo (Número nombre punto-círculo x y p c)
nombre: Cadena de caracteres que designa al nombre del objeto
x,y: Las coordenadas del número
p: Referencia a un punto
c: Referencia a un círculo
Devuelve: Referencia a un número, distancia entre el punto y el círculo.
Ejemplo:
(sea Número "l" punto-círculo 5 5 P C)

prototipo (Número nombre punto-recta x y p d)
nombre: Cadena de caracteres que designa al nombre del objeto
x,y: Las coordenadas del número
p: Referencia a un punto
c: Referencia a una recta
Devuelve: Referencia a un número, distancia entre el punto y la recta.
Ejemplo:
(sea Número "d" punto-recta 5 5 M D1)

prototipo (Número nombre punto-punto x y p1 p2)
nombre: Cadena de caracteres que designa al nombre del objeto
x,y: Las coordenadas del número
p1: Referencia a un punto
p2: Referencia a un punto
Devuelve: Referencia a un número, distancia entre los dos puntos.
Ejemplo:
(sea Número "d" punto-punto 5 5 A B)

prototype (Número nombre longitud-círculo x y c)
nombre: Cadena de caracteres que designa al nombre del objeto.
x,y: Las coordenadas del número.
c: Referencia a un círculo.
Devuelve: Referencia a un número, perímetro del círculo.
Ejemplo:
(sea Número "p" longitud-círculo 5 5 C)

prototype (Número nombre pendiente-línea x y d)
nombre: Cadena de caracteres que designa al nombre del objeto.
x,y: Las coordenadas del número.
d: Referencia a una recta.
Devuelve: Referencia a un número, pendiente de la recta dada.
Ejemplo:
(sea Número "p" pendiente-línea 5 5 d1)

prototype (Número nombre longitud-arco x y arc)
nombre: Cadena de caracteres que designa al nombre del objeto.
x,y: Las coordenadas del número.
arc: Referencia a un arco de círculo.
Devuelve: Referencia a un número, longitud del arco de círculo dado.
Ejemplo:
(sea Número "l" longitud-arco 5 5 ABC)

 

Ángulo
prototipo (Ángulo nombre geométrico A B C)
nombre: Cadena de caracteres que designa al nombre del objeto
A: Referencia a un punto
B: Referencia a un punto, vértice del ángulo
C: Referencia a un punto
Devuelve: Referencia a un ángulo geométrico
Ejemplo:
(sea Ángulo "a" geométrico A B C)
¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Modificación de los atributos(Apariencia) de los objetosMétodos de referencia para las figuras Scheme de DR. GEOComandos generalesDefinición de objetos en una figura
drgeo-doc-1.5/es/drgenius_68.html0000644000175000017500000001064210117134567012345 Manual de Usuario de Dr. Geo -- Modificación de los atributos(Apariencia) de los objetos
Métodos de referencia para las figuras Scheme de DR. GEODefinición de objetos en una figuraModificación de los atributos(Apariencia) de los objetos

Modificación de los atributos(Apariencia) de los objetos

Para modificar los atributos de un objeto ya creado, utilizamos un sistema de envío de mensajes directamente al prototipo que representa al objeto en cuestión. La modificación de sus atributos(apariencia) es resultado de este proceso, y se hace ya que los objetos han sido creados.

(envía objeto color valor)
objeto: Referencia a un objeto
valor: El color; los valores posibles son: negro, gris-oscuro, gris, blanco, verde-oscuro, verde, azul-oscuro, azul, rojo, bordeaux, amarillo, naranja
Ejemplo:
(sea Punto "A" libre 1 2)
(envía A color verde)

(envía línea grosor valor)
línea: Referencia a una línea (recta, semirrecta, círculo, lugar geométrico, etc.)
valor: El grosor, los valores posibles son: punteado, pequeño, grande
Ejemplo:
(sea Punto "A" libre 1 2)
(sea Punto "O" libre 0 0)
(sea Recta "d" 2puntos A B)
(envía d grosor punteado)

(envía punto tamaño valor)
punto: Referencia a un punto
valor: El tamaño del punto, los valores posibles son: pequeño, normal, grande
Ejemplo:
(sea Punto "A" libre 1 2)
(envía A tamaño pequeño)

(envía punto forma valor)
punto: Referencia a un punto
valor: La forma del punto, los valores posibles son: redondo , cruz, redondo-vacío,rec, rec-vacío
Ejemplo:
(sea Punto "A" libre 1 2)
(envía A forma redondo)

(envía objeto oculto)
objeto: Referencia a un objeto que va a ser ocultado
Ejemplo:
(sea Punto "A" libre 1 2)
(envía A oculto)

¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Métodos de referencia para las figuras Scheme de DR. GEODefinición de objetos en una figuraModificación de los atributos(Apariencia) de los objetos
drgeo-doc-1.5/es/drgenius_69.html0000644000175000017500000001317410117134567012351 Manual de Usuario de Dr. Geo -- Sinónimos en DGS
Galería de EjemplosFigura Scheme de DR. GEOMétodos de referencia para las figuras Scheme de DR. GEOSinónimos en DGS

Sinónimos en DGS

Esta sección consta de una transcripción ligeramente modificada del archivo /usr/share/drgeo/scm/drgeo_scm_interface_constant_es.scm)

Modificando este archivo se pueden obtener sinónimos para escribir en el lenguaje Scheme como si fuera Español. Esta sección ayudara a comprender programas escritos en Inglés.

Aunque es posible combinar código en Inglés con codigo con sinónimos en Español, francés o lo que se desee, convendría hacer todo el código en Inglés para asegurar su lectura por usuarios de todo el mundo.

Por ejemplo, los siguientes comandos son sinónimos: 

(lets  Point "P" free 3 3)(send A 'color bordeaux)
(sea Punto ¨P¨ libre 3 3)(env~a A color rojo-oscuro)

Notar que se han traducido varias versiones, de modo que es posible evitar escribir eñes o acentos. 

COLORES:
negro black
gris-oscuro dark-grey
gris-obscuro dark-grey
gris grey
blanco white
verde-oscuro dark-green
verde-obscuro dark-green
verde green
azul-oscuro dark-blue
azul-obscuro dark-blue
azul blue
rojo red
rojo-oscuro bordeaux
rojo-obscuro bordeaux
amarillo yellow
anaranjado orange
naranja orange

  
GROSORES:
punteado dashed
pequeño small
pequeno small
grande large


PUNTOS
redondo round
redonda round
cruz cross
redondo-vacío round-empty
redondo-vacio round-empty
redonda-vacía round-empty
redonda-vacia round-empty
cuadrado-vacío rec-empty
cuadrado-vacio rec-empty
cuadrada-vacía rec-empty
cuadrada-vacia rec-empty
rec-vacía rec-empty
rec-vacia rec-empty

ESTILO
color 'color
grosor 'thickness
forma 'shape
tamaño 'size
tamano 'size
enmascarado 'masked
oculto 'masked
ocultar 'masked

PUNTOS
libre 'free
sobre-la-curva 'on-curve
sobre-curva 'on-curve
en-curva 'on-curve
mitad-2pts 'middle-2pts
mitad-segmento 'middle-segment
intersección 'intersection
intersección2 'intersection2

SEGMENTOS
extremos 'extremities
2puntos '2points

RECTAS
paralela 'parallel
ortogonal 'orthogonal
perpendicular 'orthogonal
2puntos '2points

CÍRCULOS
centro-radio 'center-radius
centro-segmento 'center-segment


ARCOS
3puntos '3points

POLÍGONOS
npuntos 'npoints

NÚMEROS
longitud-segmento 'segment-length
norma-vector 'vector-norm
longitud-vector 'vector-norm
punto-recta 'point-line
punto-círculo 'point-circle
punto-circulo 'point-circle
punto-punto 'point-point
perímetro-círculo 'circle-length
perimetro-circulo 'circle-length
longitud-círculo 'circle-length
longitud-circulo 'circle-length
pendiente-línea 'line-slope
pendiente-linea 'line-slope
longitud-arco 'arc-length

ÁNGULOS
geométrico 'geometric
geometrico 'geometric

TRANSFORMACIONES
rotación 'rotation
rotacion 'rotation
homotecia 'scale
escala 'scale
simetría 'symmetry
simetria 'symmetry
translación 'translation
translación 'translation
traslación 'translation
traslacion 'translation


GENERALES
sea lets
nueva-figura new-figure
figura-nueva new-figure
enviar send
envía send
envia send
Punto Point
Recta Line
Línea Line
Linea Line
Segmento Segment
Semirrecta Ray
Rayo Ray
Círculo Circle
Circulo Circle
Arco Arc
Arco Arc
Lugar-geométrico Locus
Lugar-geometrico Locus
Vector Vector
Numérico Numeric
Numerico Numeric
Número Numeric
Numero Numeric
Ángulo Angle
Angulo Angle
Polígono Polygon
Poligono Polygon
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Galería de EjemplosFigura Scheme de DR. GEOMétodos de referencia para las figuras Scheme de DR. GEOSinónimos en DGS
drgeo-doc-1.5/es/drgenius_6.html0000644000175000017500000000464410117134567012262 Manual de Usuario de Dr. Geo -- Funciones Básicas
Características AvanzadasTopIntroducciónFunciones Básicas

Funciones Básicas

Este capítulo describe las herramientas usadas para construir figuras geométricas. Al final del capítulo, la configuración de las preferencias del usuario es también presentada.

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Características AvanzadasTopIntroducciónFunciones Básicas
drgeo-doc-1.5/es/drgenius_70.html0000644000175000017500000000544110117134567012337 Manual de Usuario de Dr. Geo -- Galería de Ejemplos
Figura Scheme de DR. GEOSinónimos en DGSGalería de Ejemplos

Galería de Ejemplos

Para ilustrar la utilización de las Figuras Scheme de DR. GEO, proponemos una breve serie de ejemplos. En ellos mostraremos el potencial de las FSD y esperamos igualmente que le sean una fuente de inspiración. Para cada uno de estos ejemplos, damos el código fuente en Scheme de la figura, y en seguida el resultado. El código fuente puede ser copiado dentro de un archivo de texto con un editor, y luego guardado con la extensión .scm con lo que podrá ser evaluado después por DR. GEO.

El código siguiente se encuentra en inglés. Favor de ver la seccion Sinónimos para poder escribir la mayor parte del código en Español.

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Figura Scheme de DR. GEOSinónimos en DGSGalería de Ejemplos
drgeo-doc-1.5/es/drgenius_71.html0000644000175000017500000000563710117134567012347 Manual de Usuario de Dr. Geo -- Polígono regular
FractalGalería de EjemplosPolígono regular

Polígono regular

Para construir un polígono regular, con un número arbitrario de lados, podemos hacer uso de una función recursiva en Scheme. Construire un polygone régulier, avec un nombre de coté arbitraire, peut se faire par l'intermédiaire d'une fonction récursive Scheme. 

(define pi (acos -1))
(define n 15)
(define x0 0)
(define y0 0)
(define p1 0)

(define (polygon center p a n)
  (if (> n 0)
      (begin
        (set! p1 (Point "" rotation p center a))
        (send p1 masked)
        (Segment "" extremities p p1)
        (polygon center p1 a (- n 1)))))

(new-figure "Regular Polygon!")
(lets Point "C" free x0 y0)
(lets Numeric "a" free 0 0 (* 2 (/ pi n)))
(send a masked)

(set! p1 (Point "I" free 5 0))

(lets Segment "S" extremities C p1)
(Segment ""  rotation S C a)

(polygon C p1 a n)

Un polígono regular de 15 lados

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FractalGalería de EjemplosPolígono regular
drgeo-doc-1.5/es/drgenius_72.html0000644000175000017500000000632310117134567012341 Manual de Usuario de Dr. Geo -- Fractal
Galería de EjemplosPolígono regularFractal

Fractal

La construcción de una curva fractal con la forma de un árbol se logra fácilmente con una Figura Scheme. El código fuente de la figura es sorprendentemente breve, sobre todo cuando lo comparamos con la construcción "a mano" usando la interfaz gráfica. 

(new-figure "Baum")
(lets Numeric "A1" free 2 2 +3.4)
(lets Numeric "A2" free 2 3 -3.7)
(lets Numeric "S1" free 2 4 +0.5)
(lets Numeric "S2" free 2 5 +0.9)

(define (dec n)
  (- n 1))
(define (inc n)
  (+ n 1))
(define (invisible p)
  (send p masked)
  p)
(define (scalerot oP C a s)
  (let* ((sP (invisible (Point "" scale oP C s)))
         (rP (invisible (Point "" rotation sP C a))) )
    rP))
(define (Zweig p0 p1 n)
  (Segment "" extremities p0 p1)
  (let* ((left-scale (if (odd? n) S1 S2))
         (left-angle A1)
         (right-scale (if (odd? n) S2 S1))
         (right-angle A2) )
    (if (> n 0)
      (begin
        (Zweig p1 (scalerot p0 p1  left-angle  left-scale) (dec n))
        (Zweig p1 (scalerot p0 p1 right-angle right-scale) (dec n))))))
        
(lets Point "A" free -3 0)
(lets Point "B" free -3 2)
(Zweig A B 6)

Una curva fractal que simula la representación de un árbol

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Galería de EjemplosPolígono regularFractal
drgeo-doc-1.5/es/drgenius_73.html0000644000175000017500000000513310117134567012340 Manual de Usuario de Dr. Geo -- Bloquear las herramientas de la interfaz
Características AvanzadasFigura Scheme de DR. GEOBloquear las herramientas de la interfaz

Bloquear las herramientas de la interfaz

DR. GEO ofrece la posibilidad de preparar sesiones11 dentro de los cuales el maestro puede decidir, para ciertas figuras, impedir el acceso a ciertas herramientas, el bloqueo se realiza utilizando una contraseña distinta para cada figura. Esto da al maestro flexibilidad al preparar una actividad con distintas figuras, y diversas herramientas disponibles en cada figura.

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Características AvanzadasFigura Scheme de DR. GEOBloquear las herramientas de la interfaz
drgeo-doc-1.5/es/drgenius_74.html0000644000175000017500000000662310117134567012346 Manual de Usuario de Dr. Geo -- Bloqueo de las herramientas
Desbloqueo de las herramientasBloquear las herramientas de la interfazBloqueo de las herramientas

Bloqueo de las herramientas

Para impedir el acceso a las herramientas de construcción recurrimos al comando Editar->Interfaz personalizado. Después de haberlo seleccionado se abre una gran ventana de diálogo con todos los iconos de los instrumentos de DR. GEO. Allí, podemos hacer click sobre los iconos para activarlos o desactivarlos. Cuando una herramienta está desactivada, el icono que la representa aparece ligeramente desvanecido. Es igualmente posible desactivar todas las herramientas en una misma columna haciendo click en el icono principal del menú (que se reconoce por tener un pequeño triángulo verde en la parte inferior derecha).

Ventana de diálogo para bloquear algunas herramientas de la interfaz

Cuando el usuario ha terminado de seleccionar los iconos que han de ser bloqueados, se procede al bloqueo propiamente dicho haciendo click sobre el botón bloqueo en la ventana de diálogo. En este momento, DR. GEO pedirá una contraseña.

(!) Cuando se guarda una figura o una sesión en que se impide el acceso a ciertas herramientas, las contraseñas son igualmente guardadas, de forma encriptada, en el archivo
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Desbloqueo de las herramientasBloquear las herramientas de la interfazBloqueo de las herramientas
drgeo-doc-1.5/es/drgenius_75.html0000644000175000017500000000513310117134567012342 Manual de Usuario de Dr. Geo -- Desbloqueo de las herramientas
Bloquear las herramientas de la interfazBloqueo de las herramientasDesbloqueo de las herramientas

Desbloqueo de las herramientas

Es por supuesto posible desbloquear la interfaz, ya sea para dar acceso progresivo a las herramientas - estando en la clase con los estudiantes- o para volver a diseñar la figura. Para ello, se necesita escoger dentro de la ventana de diálogo el botón Desbloquear. DR. GEO pide entonces la contraseña que se ingresó previamente.

La ventana de diálogo para desbloquear la interfaz de una figura.

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Bloquear las herramientas de la interfazBloqueo de las herramientasDesbloqueo de las herramientas
drgeo-doc-1.5/es/drgenius_76.html0000644000175000017500000000600010117134567012335 Manual de Usuario de Dr. Geo -- Archivos y documentos
Aplicaciones DidácticasTopCaracterísticas AvanzadasArchivos y documentos

Archivos y documentos

Las construcciones pueden ser guardadas de dos maneras. Una construcción por archivo o un conjunto de construcciones por archivo (i.e. una sesión de DR. GEO). Le recordamos que los documentos que con tienen las figuras debes ser guardados con una extensión .fgeo y que aquellos que contengan sólo macros que sean guardados con la extensión .mgeo. Para los documentos que contienen varias figuras, construcciones de macros y textos explicativos, utilizar la extensión .fgeo

Lo anterior es sólo indicativo, pero seguir estas reglas permitirá identificar y volver a cargar los archivos más fácilmente.

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Aplicaciones DidácticasTopCaracterísticas AvanzadasArchivos y documentos
drgeo-doc-1.5/es/drgenius_77.html0000644000175000017500000000542310117134567012346 Manual de Usuario de Dr. Geo -- Guardar una construcción
Guardar una sesiónArchivos y documentosGuardar una construcción

Guardar una construcción

A partir del menú Archivo->Guardar o del menú Archivo->Guardar como..., un archivo que contiene la figura de la vista activa puede ser guardada.

(!) DR. GEO puede trabajar con varias figuras al mismo tiempo. El usuario puede pasar de una figura a otra haciendo click sobre el nombre de la figura (ubicado en la parte baja de la figura).
.

Con el segundo menú, el usuario puede cambiar el nombre del documento a guardar.

(!) El nombre del archivo inicialmente propuesto puede ser cambiado con el menúEditar->Preferencias.... Para más información ver la sección comportamiento predeterminado.
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Guardar una sesiónArchivos y documentosGuardar una construcción
drgeo-doc-1.5/es/drgenius_78.html0000644000175000017500000000700510117134567012345 Manual de Usuario de Dr. Geo -- Guardar una sesión
Guardar una MacroArchivos y documentosGuardar una construcciónGuardar una sesión

Guardar una sesión

Una sesión es un conjunto de objetos de DR. GEO que el usuario desea guardar de un solo golpe en un archivo. Esto permite al maestro organizar un conjunto de objetos (figuras, macros y notas de clase) en un solo archivo con el fin de facilitar su uso.

A partir del menú ->Guardar múltiple, el usuario puede abrir la ventana de diálogo de la sesión.

La ventana de diálogo de la sesión DR. GEO

En esta ventana de diálogo, la lista de todos los objetos activos está presente en una tabla. La primera columna muestra los tipos de objetos contenidos en la sesión de DR. GEO, la segunda muestra los nombres de los objetos.

(!) De hecho, una sesión puede contener tres tipos de objetos : figuras interactivas en dos dimensiones, macros y textos.

El usuario puede seleccionar uno por uno los objetos a guardar y después hacer click en el botónGuardar selección. Alternativamente, puede guardar todos los objetos haciendo click sobre el botón Guardar todo.

(!) El menú Archivo->Guardar múltiple es el único medio de guardar una macro en un archivo.
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Guardar una MacroArchivos y documentosGuardar una construcciónGuardar una sesión
drgeo-doc-1.5/es/drgenius_79.html0000644000175000017500000000477110117134567012355 Manual de Usuario de Dr. Geo -- Guardar una Macro
Abrir un archivoArchivos y documentosGuardar una sesiónGuardar una Macro

Guardar una Macro

Para guardar una o varias macros en un archivo. es necesario proceder como cuando uno desea guardar una sesión -guardar múltiple-. Posteriormente , en la ventana para guardar una sesión, seleccionar la o las macros que se desea guardar. En seguida guárdelas en un archivo que contenga la extensión .mgeo. ¡Eso es todo!

Es de este modo posible crear bibliotecas de macros, una por archivo, o varias agrupadas por temas en un sólo archivo.

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Abrir un archivoArchivos y documentosGuardar una sesiónGuardar una Macro
drgeo-doc-1.5/es/drgenius_7.html0000644000175000017500000000653010117134567012257 Manual de Usuario de Dr. Geo -- Herramientas de Construcción
Otras herramientasFunciones BásicasHerramientas de Construcción

Herramientas de Construcción

Estas herramientas están separadas en seis grupos disponibles desde la segunda barra de herramientas de DR. GEO .

Categorías de herramientas de DR. GEO y sus descripciones

Cuando el usuario hace click sobre uno de los iconos decorados con un triangulito verde, una nueva barra vertical de iconos aparece inmediatamente. En ella se agrupan funciones de una misma familia.

De izquierda a derecha, tenemos acceso a las barras de herramientas verticales para: construir puntos, construir líneas, realizar transformaciones geométricas, calcular valores numéricos, generar macros de construcciones, y utilizar las herramientas de edición - Otras herramientas

Estas funciones también aparecen dentro del menú contextual de una figura, que es llamado haciendo click con el botón derecho en el fondo de la figura.

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Otras herramientasFunciones BásicasHerramientas de Construcción
drgeo-doc-1.5/es/drgenius_80.html0000644000175000017500000000500410117134567012333 Manual de Usuario de Dr. Geo -- Abrir un archivo
Exportar una figuraArchivos y documentosGuardar una MacroAbrir un archivo

Abrir un archivo

Ya sea que el usuario haya guardado una sola figura o una sesión con los distintos objetos, el procedimiento para la apertura de cualquier tipo de archivo es siempre a través del menú Archivo->Abrir. Si la sesión recién abierta contiene macros, estas están directamente disponibles a partir de que la herramienta para ejecutar macros esté disponible para la ejecución. Las macros están disponibles para todas las figuras abiertas.

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Exportar una figuraArchivos y documentosGuardar una MacroAbrir un archivo
drgeo-doc-1.5/es/drgenius_81.html0000644000175000017500000000513510117134567012341 Manual de Usuario de Dr. Geo -- Exportar una figura
Archivos y documentosAbrir un archivoExportar una figura

Exportar una figura

DR. GEO ofrece la posibilidad de exportar una figura geométrica a un documento LaTeXo PostScript. Estos dos formatos de exportación son de tipo vectorial, a diferencia de las imágenes de mapas de bits que son de menor calidad para una impresión. Los comandos de exportación son accesibles a través del menú Archivo->Exportar como...

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Archivos y documentosAbrir un archivoExportar una figura
drgeo-doc-1.5/es/drgenius_82.html0000644000175000017500000000470410117134567012343 Manual de Usuario de Dr. Geo -- Exportar a LaTeX
Exportar a PostScriptExportar una figuraExportar a LaTeX

Exportar a LaTeX

En el caso de una exportación al formato LaTeX, el documento exportado necesita el paquete pstricks. Éste es en general distribuido con LaTeX. Típicamente un documento exportado en LaTeX podrá ser integrado dentro de otro documento LaTeX o bien directamente compilado con los comandos: 

latex figure.tex
dvips figure.dvi

Esta serie de comandos permite obtener el documento figure.ps, el cual puede ser abierto por el programa GhostView12 gv.

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Exportar a PostScriptExportar una figuraExportar a LaTeX
drgeo-doc-1.5/es/drgenius_83.html0000644000175000017500000000476010117134567012346 Manual de Usuario de Dr. Geo -- Exportar a PostScript
Exportar a PNGExportar una figuraExportar a LaTeXExportar a PostScript

Exportar a PostScript

La exportación al formato PostScript - extensión eps - ofrece la ventaja de ser fácilmente utilizable por diversos programas 13. En efecto, el formato EPS es cercano a ser un estandard en lo que se refiere a imágenes vectoriales. Para visualizar rápidamente este tipo de imágenes,utilizamos, como ya antes mencionamos, el programa GhostView; en una terminal se invoca escribiendo gv.

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Exportar a PNGExportar una figuraExportar a LaTeXExportar a PostScript
drgeo-doc-1.5/es/drgenius_84.html0000644000175000017500000000453610117134567012350 Manual de Usuario de Dr. Geo -- Exportar a PNG
Exportar Fly DrawExportar una figuraExportar a PostScriptExportar a PNG

Exportar a PNG

Ciertos programas como OpenOffice.org sólo explotan parcialmente el formato EPS14.

Es posible, afortunadamente, exportar al formato PNG. La imagen exportada bajo este formato tiene una alta definición y posee un fondo transparente. Esto puede permitir escribir un texto a lo largo de la figura.

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Exportar Fly DrawExportar una figuraExportar a PostScriptExportar a PNG
drgeo-doc-1.5/es/drgenius_85.html0000644000175000017500000000437710117134567012354 Manual de Usuario de Dr. Geo -- Exportar Fly Draw
Definir el área de exportaciónExportar una figuraExportar a PNGExportar Fly Draw

Exportar Fly Draw

El servidor de ejercicios WIMS desarrollado por el Dr. Xiao Gang en la universidad de Nice dispone de un formato de descripción de figuras llamado Fly Draw. DR. GEO puede exportar hacia ese formato.

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Definir el área de exportaciónExportar una figuraExportar a PNGExportar Fly Draw
drgeo-doc-1.5/es/drgenius_86.html0000644000175000017500000000736210117134567012352 Manual de Usuario de Dr. Geo -- Definir el área de exportación
Exportar una figuraExportar Fly DrawDefinir el área de exportación

Definir el área de exportación

Inicialmente, DR. GEO exporta la zona visible de la figura. Por lo anterior, si deseamos exportar una zona precisa de la figura, una manera de hacerlo es redimensionar la ventana de DR. GEO hasta obtener la zona deseada 15.

Esta solución, empero, aunque rápida y simple, no es lo suficientemente flexible. Además, el área de exportación no queda guardada junto con la figura. Afortunadamente, existe otro modo de definirla usando el comando Definir el área de exportación el cual es accesible desde el menú Archivo->Preferencias de Exportación

Habiendo seleccionado el comando, podemos seleccionar un rectángulo en la figura que corresponderá con el área de exportación. Esta área puede ser redefinida tantas veces como sea necesario. En la figura estará representada por un rectángulo gris claro. Cuando la figura sea guardada, esta zona lo será también.

Para suprimir el área de exportación y regresar al comportamiento inicial de DR. GEO use el comando Eliminar área de exportación, el cual, por supuesto, no borra ningún objeto de la figura.

Una figura con un área de exportación definida

El área de exportación ha sido exportada a un documento PostScript; es visible con el programa GhostView

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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Exportar una figuraExportar Fly DrawDefinir el área de exportación
drgeo-doc-1.5/es/drgenius_87.html0000644000175000017500000000527210117134567012351 Manual de Usuario de Dr. Geo -- Aplicaciones Didácticas
Libro de recetasTopArchivos y documentosAplicaciones Didácticas

Aplicaciones Didácticas

Este capítulo constituye una ayuda para el usuario que desea familiarisarse con DR. GEO a través de ejemplos. A diferencia de los capítulos precedentes, el enfoque es más concreto, y es orientado a situaciones precisas. El capítulo consiste en diversas aplicaciones pedagógicas.

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Libro de recetasTopArchivos y documentosAplicaciones Didácticas
drgeo-doc-1.5/es/drgenius_88.html0000644000175000017500000001131210117134567012342 Manual de Usuario de Dr. Geo -- Pitágoras y scripts
Teoremas y conjeturasAplicaciones DidácticasPitágoras y scripts

Pitágoras y scripts

Una de las aplicaciones didácticas en DR. GEO consiste en la utilización de los scripts Scheme para resolver ejercicios de Geometría.

Como ejemplo, vamos a mostrar la solución a un problema clásico en cuya solución se usa el teorema de Pitágoras. El texto es el siguiente :

Sea un trapecio rectángulo ABCD del que son conocidas las bases y la altura. Calcular el perímetro y el área del trapecio.

No es difícil, siguiendo el mismo modelo, desarrollar otros ejemplos semejantes.

Solución :

Comencemos por construir la figura en DR. GEO, la cual debe ser como sigue :

Trapecio Rectángulo

La figura contiene los datos a partir de los cuales podemos resolver el problema. Podemos contestar enseguida la pregunta relacionada con el área, para ello podemos escribir el script Scheme sigueinte que tiene como entradas las dos bases y la altura del trapecio :

  

define AB (getLength a1))
(define DC (getLength a2))
(define AD (getLength a3))
(/ ( * AD (+ AB DC )) 2 )

Calculamos la longitud del segmento BH escribiendo un script Scheme que tiene por parámetros de entrada a los segmentos AB y CD. El texto del script es el siguiente : 

(define AB (getLength a1))
(define CD (getLength a2))
(- AB CD)

En este momento, podemos aplicar el Teorema de Pitágoras al triángulo rectángulo CHB. Aquí también utilizamos un script Scheme que tiene por parámetros de entrada al segmento CH y al script BH : 

(define CH (getLength a1))
(define BH (getValue a2))
(+ (* CH CH) (* BH BH))

Finalmente, podemos obtener el valor del segmento BC calculando la raiz cuadrada del valor devuelto por el script anterior : 

(define q (getValue a1))
( sqrt q )

Los dos scripts anteriores pueden ser combinados en un solo script un poco más elaborado.

Ahora podemos concluir el ejercicio calculando el perímetro con un script Scheme : 

(define AB (getLength a1))
(define CB (getValue  a2))
(define DC (getLength a3))
(define AD (getLength a4))
(+ (+ AB CB )(+ DC AD ))

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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Teoremas y conjeturasAplicaciones DidácticasPitágoras y scripts
drgeo-doc-1.5/es/drgenius_89.html0000644000175000017500000001204410117134567012346 Manual de Usuario de Dr. Geo -- Teoremas y conjeturas
Números irracionalesAplicaciones DidácticasPitágoras y scriptsTeoremas y conjeturas

Teoremas y conjeturas

Los scripts Scheme permiten no sólo resolver ejercicios, sino también comprender mejor el enunciado de los teoremas (y las hipótesis de los mismos) asi como corroborar o descartar conjeturas.

En esta sección comenzaremos analizando el enunciado del Teorema de Ptolomeo :

Dado un cuadrilátero inscrito en una circunferencia, la suma de los productos de los lados opuestos es igual al producto de las diagonales.

Podemos construir la figura con DR. GEO como abajo :

Teorema de Ptolomeo: cuadrilátero convexo

En la figura, hemos implementado dos scripts que calculan, respectivamente, la suma del producto de los lados opuestos, y el producto de las diagonales.  

El primer script es el siguiente : 

(define AB (getLength a1))
(define DC (getLength a2))
(define BC (getLength a3))
(define AD (getLength a4))
(+ (* AB DC )(* BC AD ))

El segundo script es . 

(define DB (getLength a1))
(define AC (getLength a2))
(* DB AC )

Como podemos ver, los valores devueltos por los dos scripts, en conformidad con el Teorema de Ptolomeo, son iguales 16. Cuando modificamos dinámicamente la figura, los valores de los scripts son idénticos, salvo en el caso siguiente :

Teorema de Ptolomeo: cuadrilátero no convexo

Vemos en la figura que el cuadrilátero ya no es convexo.

En este caso el enunciado del Teorema es falso. Por lo tanto, para contemplar ese caso, debemos reformular el enunciado como sigue :

Dado un cuadrilátero CONVEXO inscrito en una circunferencia, la suma del producto de lados opuestos es igual al producto de las diagonales..

En este momento las conjeturas aparecen de modo natural : ¿es acaso valida la conclusión del teorema de Ptolomeo también valida para un cuadrilátero convexo no inscrito en un círculo ?(i.e. ¿es cierto el recíproco?)

Con DR. GEO podemos ver que dicha conjetura es falsa como muestra la figura siguiente :

Refutación de la conjetura

El lector no tendrá problemas en utilizar DR. GEO para la construcción de ejemplos didácticos, relacionados probablemente con teoremas más conocidos, como el Teorema de Pitágoras o alguno de los teoremas de Euclides.
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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Números irracionalesAplicaciones DidácticasPitágoras y scriptsTeoremas y conjeturas
drgeo-doc-1.5/es/drgenius_8.html0000644000175000017500000000441310117134567012256 Manual de Usuario de Dr. Geo -- Intersección
Punto definido por sus coordenadasHerramientas de puntosPunto MedioIntersección

Intersección

 

Crear el(los) punto(s) de intersección de dos objetos unidimensionales. El usuario necesita seleccionar dos objetos unidimensionales (v.g arco de círculo y semirrecta).

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Punto definido por sus coordenadasHerramientas de puntosPunto MedioIntersección
drgeo-doc-1.5/es/drgenius_90.html0000644000175000017500000001120310117134567012332 Manual de Usuario de Dr. Geo -- Números irracionales
Espiral de BaravelleAplicaciones DidácticasTeoremas y conjeturasNúmeros irracionales

Números irracionales

Una construcción clásica, relacionada con los números irracionales, conocida bajo el nombre de "Espiral de Teodoro" permite construir geométricamente la raíz cuadrada de números enteros a partir de un triángulo isósceles.

Consideremos el triángulo OAB donde OA=1 :

Construción de la raíz cuadrada de 2

Por el teorema de Pitágoras, tenemos que OB es igual a la raíz cuadrada de 2. Si, ahora, con la figura, construímos un nuevo triángulo rectángulo en B, con lados OB y BC tal que BC=1.

Construcción de la raíz de 3

Nuevamente, por el teorema de Pitágoras, es claro que la hipotenusa OC del triángulo OBC tiene por longitud la raíz cuadrada de 3. Repitiendo este proceso obtenemos todas las raíces cuadradas de los números naturales.

La naturaleza repetitiva de la construcción se presta perfectamente para la utilización de un FSD. Consideremos el código siguiente : 

(new-figure "Triangle")

(define (triangle p1 p2 p3 n)
  (let* ((s1 (Segment "" extremities    p1 p2))
         (s2 (Segment "" extremities    p2 p3))
         (s3 (Segment "" extremities    p3 p1))
         (pe (Line    "" orthogonal     p3 s3))
         (ci (Circle  "" center-segment p3 s2))
         (p4 (Point   "" intersection2  pe ci)))
    (send pe masked)
    (send ci masked)
    (send p4 masked)
    (if (> n 0)
       (triangle p1 p3 p4 (- n 1)))))


(lets Point "O" free  0  0)
(lets Point "A" free -1  0)
(lets Point "B" free -1  1)
(triangle O A B 15)

El triángulo inicial está definido a través de coordenadas por comodidad unicamente. El código es la transcripción literal del procedimiento repetitivo previamente descrito. Una vez evaluado por DR. GEO, el código nos da la siguiente figura :

Espiral de Teodoro

Las hipotenusas de cada triángulo tienen por longitud las raíces cuadradas de los números enteros naturales entre 2 y 17.
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Espiral de BaravelleAplicaciones DidácticasTeoremas y conjeturasNúmeros irracionales
drgeo-doc-1.5/es/drgenius_91.html0000644000175000017500000001165410117134567012345 Manual de Usuario de Dr. Geo -- Espiral de Baravelle
Cadena de PapusAplicaciones DidácticasNúmeros irracionalesEspiral de Baravelle

Espiral de Baravelle

Como vimos anteriormente, con la ayuda de una FSD es posible construir de manera intuitiva y simple figuras que permiten visualizar situaciones que en un programa son ya sea iterativas o recursivas.

Profundicemos un poco más en este aspecto. Modificando el código Scheme utilizado para la construcción de los números irracionales, podemos obtener una figura famosa en la literatura matemática: la espiral de Baravelle.

El código Scheme que define la espiral es el siguiente : 

 
(new-figure "Baravelle")
 
(define (triangle p1 p2 p3 n)   
  (let* ((s1  (Segment "" extremities    p1 p2))
         (s2  (Segment "" extremities    p2 p3))
         (s3  (Segment "" extremities    p3 p1))
         (m   (Point   "" middle-2pts    p1 p3))
         (r   (Segment "" extremities    m  p3))
         (pe  (Line    "" orthogonal     p3 s3))
         (ci  (Circle  "" center-segment p3 r ))
         (p4  (Point   "" intersection2  pe ci)))
    (send pe  masked)
    (send ci  masked)
    (send p4  masked)
    (send m   masked)
    (if (> n 0)
      (triangle  m  p3  p4 (- n 1)))))
   
 
(lets Point "A" free  0  5)
(lets Point "B" free  5  5)
(lets Point "C" free  5  0)
(triangle A B C 9)
 
(lets Point "D" free  0 -5)
(lets Point "E" free -5 -5)
(lets Point "F" free -5  0)
(triangle D E F 9)

La espiral de Baravelle obtenida al evaluar el código Scheme

Con base en la figura y en el código Scheme correspondiente, vemos claramente la naturaleza iterativa del mecanismo de construcción de la figura. Un problema interesante, que dejamos al lector, consiste en establecer cuándo las dos ramas de la espiral convergen.

Una pequeña variación al codigo precedente : 

(new-figure "Spirale")

(define (square p1 p2 p3 p4 n)
  (let* ((s1 (Segment "" extremities p1 p2))
         (s2 (Segment "" extremities p2 p3))
         (s3 (Segment "" extremities p3 p4))
         (s4 (Segment "" extremities p4 p1))
         (A (Point "" on-curve s1 1/10))
         (B (Point "" on-curve s2 1/10))
         (C (Point "" on-curve s3 1/10))
         (D (Point "" on-curve s4 1/10)))
     (send A masked)
     (send B masked)
     (send C masked)
     (send D masked)
     (if (> n 0)
       (square A B C D (- n 1)))))

(lets Point "M" free 5 5)
(lets Point "N" free -5 5)
(lets Point "O" free -5 -5)
(lets Point "P" free 5 -5)

(square M N O P 30)

Obtenemos, pues, una espiral simplificada.

Espiral simplificada

El lector está invitado a divertirse creando nuevas variaciones.
¿Comentarios?/¿Sugerencias?
O si usted es voluntario para escribir parte del manual.
-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Cadena de PapusAplicaciones DidácticasNúmeros irracionalesEspiral de Baravelle
drgeo-doc-1.5/es/drgenius_92.html0000644000175000017500000000677410117134567012355 Manual de Usuario de Dr. Geo -- Cadena de Papus
Cálculo de piAplicaciones DidácticasEspiral de BaravelleCadena de Papus

Cadena de Papus

Una aplicación de las Figuras Scheme de DR. GEO consiste en la reproducción de una figura cuando sólo conocemos sus características analíticas.

Nos proponemos desarrollar un ejemplo famoso: "La Cadena de Papus".

Cadena de Papus

Los centros y los radios de los círculos que la constituyen tienen una expresión analitica conocida, y es sencillo implementar la expresión analítica en una FSD que reproducirá la figura. 

(new-figure "Pappo")

(define (circle n)
(let*(
  (r (Numeric "" free 0 0 (/ 15 ( + 6 (* n n )))))
  (c (Point   "" free (* 5 (/ 15 ( + 6 (* n n )))) 
                      (* 2 (* n (/ 15 ( + 6 (* n n )))))))
  (p (Circle "" center-radius c r )))
 (send r masked)
 (if (> n 0)
    (circle (- n 1)))))

(circle 8)

(lets Point "A" free 5 0)
(lets Point "O" free 0   0)
(lets Point "B" free 15 0)
(lets Point "M" middle-2pts B O)
(lets Circle "" 2points M O)
(lets Circle "" 2points A O)
(lets Line   "" 2points A O)

El código de la figura es relativamente intuitivo y no necesita mayor comentario.

Un ejercicio no trivial, que dejamos al lector, consiste en determinar una construcción con regla y compás que conduzca a una implementación iterativa. (la implementación dada es recursiva).

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Cálculo de piAplicaciones DidácticasEspiral de BaravelleCadena de Papus
drgeo-doc-1.5/es/drgenius_93.html0000644000175000017500000000766410117134567012355 Manual de Usuario de Dr. Geo -- Cálculo de pi
Aplicaciones DidácticasCadena de PapusCálculo de pi

Cálculo de pi

El cálculo aproximado de pi ha tenido un papel importante en la historia de las Matemáticas. Los métodos para su cálculo son diversos, teniendo mejoras de uno a otro método. Nos proponemos atacar el problema con un método que llamaremos, aunque no sea del todo apropiado, Método de Exhaución. Éste método tiene la ventaja de mostrar la esencia misma del problema. (El método siguiente fue desarrollado por Arquímides usando el método de Exhaución desarrollado por Eudoxo, el cual fue precursor de la teoría de límites).

Comenzaremos con la construcción de un hexágono regular inscrito en una circunferencia a partir de su lado BC. Notemos de paso que es posible a partir de esta construcción crear y memorizar una macro que llamaremos Hexágono

Hexágono regular inscrito

La idea del método de exhaución consiste en primero aproximar la longitud del círculo con el perímetro P(0) del hexágono y de calcular una aproximación de pi dividiendo P(0) por el diámetro del círculo. Claramente, la aproximación obtenida sera de 3.

En una segunda etapa podemos, utilizando DR. GEO, construir dentro de la misma circunferencia, un dodecágono regular. Calculemos su perímetro,P(1), y dividamos por el diámetro de la circunferencia. Esto nos dará una mejor aproximación.

Aproximación de pi

Duplicando en cada paso el número de lados del polígono regular inscrito obtenemos mejores aproximaciones.
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Aplicaciones DidácticasCadena de PapusCálculo de pi
drgeo-doc-1.5/es/drgenius_94.html0000644000175000017500000000504210117134567012342 Manual de Usuario de Dr. Geo -- Libro de recetas
ÍndiceTopAplicaciones DidácticasLibro de recetas

Libro de recetas

Este capítulo constituye una ayuda para el usuario que desea realizar construcciones geométricas con DR. GEO. Contrariamente a los capítulos precedentes, el enfoque es hacia problemas precisos. El contenido de este capítulo es fruto del uso que los usuarios han hecho del programa, y responde a algunas peticiones de los mismos.

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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

ÍndiceTopAplicaciones DidácticasLibro de recetas
drgeo-doc-1.5/es/drgenius_95.html0000644000175000017500000000602110117134567012341 Manual de Usuario de Dr. Geo -- Crear un polígono regular
Imprimir una figuraLibro de recetasCrear un polígono regular

Crear un polígono regular

DR. GEO puede crear varias macros con elementos independientes (i.e. varios puntos libres, valores libres o scripts independientes). Para hacer esto drgeo dota de valores a los parámetros libres de esos objetos 17. DR. GEO puede crear varias macros. El o los valores escogidos son, en efecto, los valores del objeto que sirvió de modelo durante la creación de la macro.

En lo que sigue, un pequeño ejemplo que permite crear polígonos regulares de cualquier número de lados es presentado. En varias de las macros, un script Scheme interviene en el proceso.

El ejemplo es mostrado paso a paso, aunque el lector no familiarizado con las macros, los scripts o más generalmente el funcionamiento de DR. GEO está invitado a leer las secciones anteriores.

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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Imprimir una figuraLibro de recetasCrear un polígono regular
drgeo-doc-1.5/es/drgenius_96.html0000644000175000017500000000646310117134567012354 Manual de Usuario de Dr. Geo -- El modelo del polígono
La macro del polígonoCrear un polígono regularEl modelo del polígono

El modelo del polígono

Para comenzar, crearemos un punto libro, en seguida un Script que no toma parámetros de entrada (para crear el script, seleccionar la herramienta script y hacer enseguida click sobre el fondo de la figura). Editar el script y escribir lo siguiente : 

(/ (* 2 (acos -1)) 7)

El resultado de este script es el valor del script y servirá para construir, a través de una rotación un polígono regular de 7 lados. Colocar enseguida un valor libre con valor 2. Éste será el radio de nuestro polígono.

Construir un círculo de centro el punto y de radio el valor recién creado. Sobre este círculo colocar un punto. Llamemos a este punto O.

Ahora utilicemos la herramienta rotación para crear la imágen del punto O bajo la rotación con centro de rotación en el centro del círculo, y con un ángulo de rotación cuyo valor es el valor del script. Continuar sucesivamente hasta obtener los siete vértices del polígono. Unir los vertices con los segmentos hasta obtener el polígono.

Resultado de construir un polígono regular de 7 lados.

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La macro del polígonoCrear un polígono regularEl modelo del polígono
drgeo-doc-1.5/es/drgenius_97.html0000644000175000017500000000516710117134567012355 Manual de Usuario de Dr. Geo -- La macro del polígono
Algunas consideracionesCrear un polígono regularEl modelo del polígonoLa macro del polígono

La macro del polígono

Abrir el diálogo para la creación de la macro y crearla como se indica a continuación :

  1. parámetro de entrada : el centro del círculoe ;
  2. paramètres de sortie : el punto O y los 7 lados del polígono.

Listo, la macro ha sido creada.

Para crear un polígono regulara de 7 lados, abrir la ventana de diálogo para ejecutar una macro. Basta seleccionar un punto de la figura para crear un polígono de 7 lados.

¿Comentarios?/¿Sugerencias?
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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Algunas consideracionesCrear un polígono regularEl modelo del polígonoLa macro del polígono
drgeo-doc-1.5/es/drgenius_98.html0000644000175000017500000000555410117134567012356 Manual de Usuario de Dr. Geo -- Algunas consideraciones
Crear un polígono regularLa macro del polígonoAlgunas consideraciones

Algunas consideraciones

Cuando DR. GEO encuentra los elementos libres en una macro, fija sus valores toamndo a la figura como modelo. En nuestro ejemplo, el script, el valor del radio y el punto O son los elementos libres de los que hablamos. Cuando la macro es ejecutada, sus valores se fijan como sigue :

  • El valor se fija 2 ;
  • el script se fija en (/ (* 2 (acos -1)) 7) ;
  • el punto sobre el círculo se fija con la misma abscisa curvilínea que la que tenía el punto O..

Es esto último lo que da sentido a la utilización conjunta de macros con scripts u otros elementos libres.

En otras palabras, por ejemplo, si para construir una figura necesitamos 7 elementos libres al empezar, y al crear la macro sólo damos 1, el resto de los elementos libres necesarios para la figura se toman de la figura que sirvió de modelo.

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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Crear un polígono regularLa macro del polígonoAlgunas consideraciones
drgeo-doc-1.5/es/drgenius_99.html0000644000175000017500000000471610117134567012356 Manual de Usuario de Dr. Geo -- Imprimir una figura
Colocar un párrafo de texto en la figuraLibro de recetasCrear un polígono regularImprimir una figura

Imprimir una figura

Lo más sencillo es exportar la figura al formato PostScript - Exportar a PostScript. En seguida es posible usar un programa que permita visualizar los documentos e imprimirlos. El documento, de calidad vectorial, puede ser abierto e impreso por programas como GhostView, Gnome GhostView o incluso K GhostView, por citar algunos.

¿Comentarios?/¿Sugerencias?
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-> Contacte a Hilaire Fernandes en OFSET (hilaire@ofset.org) o únase a la lista de correo de DR. GEO.

Colocar un párrafo de texto en la figuraLibro de recetasCrear un polígono regularImprimir una figura
drgeo-doc-1.5/es/drgenius_9.html0000644000175000017500000000701610117134567012261 Manual de Usuario de Dr. Geo -- Punto Libre
Punto MedioHerramientas de puntosPunto Libre

Punto Libre

 

Crear un punto libre en el área o un punto libre en un objeto unidimensional(segmento, semirrecta,recta, arco de círculo, círculo, lugar geométrico).

  1. En el primer caso, el punto creado puede moverse a cualquier lugar del fondo de la figura; para construirlo, el usuario simplemente hace click en cualquier parte del fondo.
  2. En el segundo caso, el punto está limitado a moverse en el objeto unidimensional (línea o círculo); esta pegado al objeto. Para construir este tipo de punto el usuario hace click sobre una línea (i.e. una línea recta, una semirrecta, un segmento, un círculo, un arco de círculo, etc.).
¿Cómo ubicar un punto dadas sus coordenadas ?

La solución más simple consiste en colocar un punto libre y luego editar sus propiedades - herramienta Propiedades - ajustando sus coordenadas a voluntad..

Otra posibilidad - menos flexible para este tipo de figura - consiste en colocar dos valores libres en la figura - herramienta Valor Numérico - y luego construir el punto con coordenadas dadas por esos dos valores - herramienta Punto definido por sus coordenadas Cette possibilité a un avantage sur la Este procedimiento tiene una ventaja sobre el precedente: el punto construido no puede ser ya movido con el ratón; el punto está inexorablemente atado a su posición.

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Punto MedioHerramientas de puntosPunto Libre
drgeo-doc-1.5/es/drgenius_guile_script.html0000644000175000017500000001024310117134567014576 Manual de Usuario de Dr. Geo -- Script Scheme de DR. GEO
Figura Scheme de DR. GEOCaracterísticas AvanzadasMacros de ConstruccionesScript Scheme de DR. GEO

Script Scheme de DR. GEO

DR. GEO es compatible con Guile. Esto quiere decir que es posible ejecutar un script del lenguaje Scheme en DR. GEO. Pero ¿qué es Guile? Leemos en el manual de Guile :

Guile es un intérprete del lenguaje de programación Scheme, concebida para su uso en una gran variedad de ambientes

Las siguientes citas describen de modo preciso como es Guile usado dentro de DR. GEO:

Como un shell, Guile puede correr interactivamente, leyendo expresiones del usuario, evaluándolas, y mostrando los resultados, o como un intérprete para un script, leyendo y ejecutando código de Scheme a partir de un archivo. Por otro lado, Guile también está disponible como una biblioteca (library) de objetos, lo que permite a otras aplicaciones fácilmente incorporar un intérprete de Scheme completo. Un programa puede usar Guile como un lenguaje de extensión, un lenguaje de configuración simple y poderoso, o como un "pegamento" multipropósito que conecta primitivas elaboradas dentro del programa.

En DR. GEO, una API (Interfaz de programa para una aplicación, -Application Program Interface- en Inglés) está disponible a partir del intérprete Guile. Esta API es un conjunto de "enlaces" en la maquinaria geométrica. Por lo tanto el usuario puede escribir un script para manipular elementos de figuras (geométricas y numéricas). Asimismo, ya que los scripts son figuras como cualquier otra, los scripts no necesitan ser guardados en un archivo separado; son guardados en el archivo de la figura. En lo que sigue usaremos el acrónimo DGS para referirnos a un Script Scheme de DR. GEO ("DR. GEO Script").

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Figura Scheme de DR. GEOCaracterísticas AvanzadasMacros de ConstruccionesScript Scheme de DR. GEO
drgeo-doc-1.5/es/drgenius.html0000644000175000017500000000363010117134567012027 Manual de Usuario de Dr. Geo

Manual de Usuario de DR. GEO

Hilaire Fernandes, Andrea Centomo
Adrian Soto
OFSET
http://www.ofset.org

29 de agosto de 2004

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drgeo-doc-1.5/es/editing_object_styles.html0000644000175000017500000001053310117134567014563 Manual de Usuario de Dr. Geo -- Editar la Apariencia de un Objeto
Editando Propiedades de ObjetosOtras herramientasBorrar un objetoEditar la Apariencia de un Objeto

Editar la Apariencia de un Objeto

 

Cada objeto geométrico posee atributos de apariencia como son el color, el grosor, el nombre, el tamaño o la forma. Además, es posible ocultar temporalmente un objeto sin borrarlo. Por ejemplo, puede ser útil ocultar construcciones intermedias sin borrarlas. Todos estos atributos puedes ser ajustados desde un diálogo activado cuando el usuario selecciona un objeto en la figura.

 

El diálogo de apariencia para puntos se relaciona con cualquier tipo de objeto de punto. Desde él es posible ajustar el color, la forma, el tamaño, nombre y visibilidad.

El diálogo de estilo para un objeto tipo punto

El diálogo de apariencia para líneas se refiere a líneas rectas, semirrectas (rayos), segmentos, vectores, círculos, arcos de círculos, lugares geométricos. Desde él, es posible ajustar el color, el grosor, el nombre y su visibilidad. Cuando una recta, una semirrecta, un vector o un segmento son definidos por dos puntos que tienen nombres no vacíos, entonces el nombre de la recta es automáticamente deducido a partir de los nombres de los puntos que la originan. En este caso el usuario no puede renombrar a la recta.

El diálogo de apariencia para objetos tipo línea

El diálogo de estilo para los objetos tipo numérico y tipo polígono se refiere a todo tipo de valores (editados por el usuario, calculados por un Script Scheme de DR. GEO o valores que representan una medida de un objeto geométrico) y de formas de polígono. (Notar que dos polígonos pueden tener colores distintos; podemos cambiarles el color)

El diálogo de estilo para objetos numéricos y tipo polígono.

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Editando Propiedades de ObjetosOtras herramientasBorrar un objetoEditar la Apariencia de un Objeto
drgeo-doc-1.5/es/introduction.html0000644000175000017500000000410210117134567012723 Manual de Usuario de Dr. Geo -- Introducción
Funciones BásicasTopCopyrightIntroducción

Introducción

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Funciones BásicasTopCopyrightIntroducción
drgeo-doc-1.5/es/line_tools.html0000644000175000017500000000502310117134567012354 Manual de Usuario de Dr. Geo -- Herramientas de líneas
Herramientas de TransformaciónHerramientas de ConstrucciónHerramientas de puntosHerramientas de líneas

Herramientas de líneas

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Herramientas de TransformaciónHerramientas de ConstrucciónHerramientas de puntosHerramientas de líneas
drgeo-doc-1.5/es/macroconstruction_tools.html0000644000175000017500000000424110117134567015202 Manual de Usuario de Dr. Geo -- Herramientas para Macros de construcciones
Herramientas de ConstrucciónHerramientas NuméricasHerramientas para Macros de construcciones

Herramientas para Macros de construcciones

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Herramientas de ConstrucciónHerramientas NuméricasHerramientas para Macros de construcciones
drgeo-doc-1.5/es/numeric_tools.html0000644000175000017500000000467310117134567013101 Manual de Usuario de Dr. Geo -- Herramientas Numéricas
Herramientas para Macros de construccionesHerramientas de ConstrucciónHerramientas de TransformaciónHerramientas Numéricas

Herramientas Numéricas

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Herramientas para Macros de construccionesHerramientas de ConstrucciónHerramientas de TransformaciónHerramientas Numéricas
drgeo-doc-1.5/es/other_tools.html0000644000175000017500000000467210117134567012557 Manual de Usuario de Dr. Geo -- Otras herramientas
Preferencias de UsuarioFunciones BásicasHerramientas de ConstrucciónOtras herramientas

Otras herramientas

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Preferencias de UsuarioFunciones BásicasHerramientas de ConstrucciónOtras herramientas
drgeo-doc-1.5/es/point_tools.html0000644000175000017500000000425610117134567012565 Manual de Usuario de Dr. Geo -- Herramientas de puntos
Herramientas de líneasHerramientas de ConstrucciónHerramientas de puntos

Herramientas de puntos

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Herramientas de líneasHerramientas de ConstrucciónHerramientas de puntos
drgeo-doc-1.5/es/transformation_tools.html0000644000175000017500000000506710117134567014503 Manual de Usuario de Dr. Geo -- Herramientas de Transformación
Herramientas NuméricasHerramientas de ConstrucciónHerramientas de líneasHerramientas de Transformación

Herramientas de Transformación

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Herramientas NuméricasHerramientas de ConstrucciónHerramientas de líneasHerramientas de Transformación
drgeo-doc-1.5/es/using_macro.html0000644000175000017500000001073610117134567012522 Manual de Usuario de Dr. Geo -- Macros de Construcciones
Script Scheme de DR. GEOCaracterísticas AvanzadasMacros de Construcciones

Macros de Construcciones

Una Macro para una una construcción es una especie de procedimiento que recibe como entrada a elementos de figuras y devuelve uno o más elementos de figuras, construidas por la macro. Ellas son construidas en un modelo definido por el usuario. Esto significa que ella (o él) tiene que elaborar la serie de pasos para la construcción sólo una vez, a partir de entonces ordena a DR. GEO grabar esta serie de pasos en una macro (macro-construction). Esta macro puede ser entonces guardada en un archivo con extensión .mgeo.

Para grabar una serie de pasos para la construcción, DR. GEO necesita saber cuáles son los elementos iniciales de la serie y los elementos que se van a dar como resultado. Desde luego que los elementos que se den como resultado deben depender solamente de los elementos iniciales, 4, de otro modo DR. GEO no podría deducir los elementos producidos a partir de los dados.

De este modo, DR. GEO deduce la lógica de la serie de pasos de la construcción y la guarde en una macro. El usuario puede ejecutar esta macro con sólo especificar los elementos de entrada (que deben coincidir con los parámetros que necesita la macro) en la figura. Entonces la macro crealos elementos especificados como resultado.

(!) Los elementos invisibles de las figuras intermedias también son construidos por la macro. Estos elementos son necesarios para crear los elementos resultantes

Para ilustrar la característica de macros para construcciones, supondremos que el usuario desea grabar la construcción de un círculo que pasa por tres puntos. Supondremos, además, que se desea obtener el centro del círculo.

Nuestra figura inicial

 

Antes de la creación de la macro, el usuario necesita construir la figura final, ésta es usada como un molde con el cual se crea la macro.

Nuestra figura con la construcción resultante

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Script Scheme de DR. GEOCaracterísticas AvanzadasMacros de Construcciones
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do \ basename = `basename $$file`; \ $(INSTALL_DATA) $(srcdir)/$$file $(DESTDIR)$(drgenius_helpdir)/$$basefile; \ done -for file in $(srcdir)/figures/*.png; do \ basename = `basename $$file`; \ $(INSTALL_DATA) $(srcdir)/$$file $(DESTDIR)$(drgenius_helpdir)/figures/$$basefile; \ done # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. .NOEXPORT: drgeo-doc-1.5/fr/ChangeLog0000644000175000017500000000625410113164056011070 2004-08-15 Hilaire Fernandes * drgenius.tex: More didactic examples added, from the Italian version. A new section in 'Astuces diverses' concerning some new development in the macro stuff. Some other changes around. 2004-04-29 Hilaire Fernandes * drgenius.tex: Minor type fixes. 2003-11-22 Hilaire Fernandes * drgenius.tex (subsection{Changer l'aspect d'un objet}): updated explanation. 2003-11-19 Hilaire Fernandes * drgenius.tex (chapter{Figure Scheme de \drgeo}): Fix the \drgeniusIndex in this section, use \drgeo{} in the macro, instead of \drgeo. Add an index on Evaluate menu command. 2003-10-29 Hilaire Fernandes * drgenius.tex (paragraph{DGS avec au moins un paramètre d'entrée}): Give the full path for slope.fgeo. 2003-10-06 Hilaire Fernandes * drgenius.tex (chapter{GNU Free Documentation License}): Add a licence section. 2003-09-28 Hilaire Fernandes * drgenius.tex (section{Galerie d'exemples}): Examples section to hold examples of DrGeo Scheme Figure. 2003-09-20 Hilaire Fernandes * drgenius.tex (subsection{Modification d'attributs d'objets}): Write this section. 2003-09-19 Hilaire Fernandes * drgenius.tex (subsubsection{Nombre}): Complete the API. 2003-09-16 Hilaire Fernandes * drgenius.tex (subsubsection{Point}): Start writing the API description of the DrGeo Scheme Figure system. 2003-08-22 Hilaire Fernandes * drgenius.tex (subsection{Quelques exemples}): More examples about DSF. 2003-08-10 Hilaire Fernandes * drgenius.tex (chapter{Introduction}): Fix a typo. In the image 56, I removed the square bracket around AC. I added the description of the new getAngle method. 2003-08-05 Hilaire Fernandes * drgenius.tex (subsection{Afficher une grille}): Add the section. 2003-01-31 Hilaire Fernandes * drgenius.tex: Fix various typo. 2003-01-29 Hilaire Fernandes * drgenius.tex: API Doc. 2002-11-19 Hilaire Fernandes * drgenius.tex: Correct various errors. 2003-01-29 Hilaire Fernandes * drgenius.tex: Relecture 2003-01-28 Hilaire Fernandes * drgenius.tex: Relecture 2003-01-27 Hilaire Fernandes * drgenius.tex: Ouvrir un fichier 2003-01-26 Hilaire Fernandes * drgenius.tex: Construction d'un index. 2003-01-25 Hilaire Fernandes * drgenius.tex (section{Masquer des outils dans l'interface}): Section sur l'adaptation de l'interface. 2002-11-18 Hilaire Fernandes * Makefile.am (install-data-local): Add DESTDIR variable (CLEANFILES): Remove the .html fles from this list. 2002-11-17 Hilaire Fernandes * drgenius.tex: Update according to Jean Philippe Georget remarks. 2002-11-10 Hilaire Fernandes * drgenius.tex: Initial release of a French localisation of the Dr.Genius manual by Jean-Philippe Georget drgeo-doc-1.5/fr/Makefile.am0000644000175000017500000000173407731637044011366 CLEANFILES = *.dvi *.aux *.idx *.log *.toc core *~ *.lof *.pdf *.ps *.html *.ilg *.ind SUBDIRS = drgenius_helpdir = $(datadir)/drgeo/help/fr drgenius_help_DATA = \ drgenius.html LATEX_FILES = \ drgenius.tex EXTRA_DIST = \ drgenius.tex all: drgenius.html drgenius.pdf drgenius.html: drgenius.tex ../drgeniusCommon.tex -hyperlatex $< drgenius.pdf: drgenius.tex ../drgeniusCommon.tex -pdflatex $< true -makeindex drgenius true -pdflatex $< true dist-hook: mkdir $(distdir)/figures -cp *.html $(distdir) -cp figures/*.png $(distdir)/figures/ install-data-local: drgenius.html $(mkinstalldirs) $(DESTDIR)$(drgenius_helpdir)/figures -for file in $(srcdir)/*.html; do \ basename = `basename $$file`; \ $(INSTALL_DATA) $(srcdir)/$$file $(DESTDIR)$(drgenius_helpdir)/$$basefile; \ done -for file in $(srcdir)/figures/*.png; do \ basename = `basename $$file`; \ $(INSTALL_DATA) $(srcdir)/$$file $(DESTDIR)$(drgenius_helpdir)/figures/$$basefile; \ done drgeo-doc-1.5/fr/drgenius.tex0000644000175000017500000033111210114446641011656 % This is the documentation of DrGeo % Le manuel Dr. Geo % Copyright 2002-2004 OFSET % Licensed under the terms of the FDL % French version \documentclass[a4paper]{book} \usepackage{hyperlatex} \T \usepackage[pdftex]{color,graphicx} \usepackage{makeidx} \usepackage[latin1]{inputenc} \usepackage[french]{babel} % \W\usepackage{frames} \usepackage{hyperref} \captionsfrench \datefrench \extrasfrench \W \htmlpanelfrench % Prepare macro \newcommand{\drgeniusImagePath}{./figures} \newcommand{\drgeoApiOutLocale}{Retourne} \newcommand{\drgeoApiExampleLocale}{Exemple} % Include common definitions \input{../drgeniusCommon.tex} % FIXME experimental, to get nicer book \W\begin{iftex} \usepackage{fancybox} \usepackage{fancyhdr} \fancyhead{} \renewcommand{\headrulewidth}{0.4pt} \fancyhead[RO]{\slshape \rightmark} \fancyhead[LE]{\slshape \leftmark} \fancyfoot[RO]{\colorbox{white}{\ovalbox{\drgeniusIcon{fig0}}}} \fancyfoot[LE]{\colorbox{white}{\ovalbox{\drgeniusIcon{fig0-bis}}}} \pagestyle{fancy} \W\end{iftex} \makeindex \htmltitle{Manuel utilisateur de Dr. Geo} \htmladdress{\small Des commentaires, des remarques~? \\ Vous êtes volontaire pour écrire des parties du manuel~?\\ -> Contactez Hilaire Fernandes at OFSET \drgeniusImage{hilaire-email} ou rejoignez la liste de diffusion de \drgeo.} \title{Manuel utilisateur de \drgeo \\ \drgeniusImage{fig0}} \author{Hilaire Fernandes, Andrea Centomo, \\ Jean-Philippe Georget, \\ \textit{OFSET}\\ \texttt{http://www.ofset.org}} \begin{document} \W \begin{center} \maketitle \W \end{center} \xname{contents} \tableofcontents \chapter*{Copyright} Copyright (c) 2000-2004 OFSET. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Other copyright apply to the respective owners of the modified documentations. See the section history for the complet list. \xname{introduction} \chapter{Introduction} \T \fancyput(3.25in,-5in){\setlength{\unitlength}{1in}\fancyoval(7,10.5)} \section{Avant propos} \drgeo\ est un logiciel libre de géométrie interactive et de programmation en Scheme. Il permet de créer des figures géométriques et de les manipuler interactivement en respectant leurs contraintes géométriques. Il offre également la possibilité d'introduire graduellement la programmation. Il est ainsi utilisable dans des situations d'enseignement du niveau primaire au niveau supérieur. L'interface utilisateur de \drgeo\ a été conçue pour allier dans un ensemble harmonieux à la fois simplicité d'utilisation, ergonomie et fonctionnalités avancées. Ainsi l'interface de \drgeo, sous une très grande apparence de simplicité, permet au néophyte de se familiariser très rapidement avec les fonctions de base du logiciel. Puis, au fur et à mesure de sa découverte du logiciel, l'utilisateur découvrira des aspects plus avancés de l'interface et du fonctionnement de \drgeo\ : multiplicité des modalités de construction d'objet\footnote{Il s'agit de pouvoir, à partir d'une même commande, créer un type d'objet selon des modalités différentes. Par exemple à partir de la commande construction de cercle, l'utilisateur peut créer un cercle à partir de son centre et un point, ou bien une longueur, ou bien un segment, etc. Bien sûr cette commande n'est représentée que par une seule icône, à charge de \drgeo\ d'anticiper sur la construction de l'utilisateur. L'effet immédiat est donc une diminution de la charge cognitive de l'interface sur l'utilisateur, tout en proposant un nombre important de modes de construction.}, macro-construction, sessions, adaptabilité de l'interface, scriptabilité, Figure Scheme de \drgeo. Ces fonctionnalités avancées génèrent peu de surcharge sur l'interface, c'est pour cela que \drgeo\ est très agréablement utilisé en enseignement primaire, cependant il est également très intéressant pour le lycée. Dans les sections suivantes, les outils de base seront exposés. Ensuite les fonctionnalités avancées seront présentées en détail. \drgeniusFigureSize{Écran de bienvenue de \drgenius}{fig1}{8} L'agencement de l'interface est~: \begin{enumerate} \item la \textit{barre de menu} caractéristique avec \drgeoMenu{Fichier}, \drgeoMenu{Édition}, \drgeoMenu{Macro-constructions}, \drgeoMenu{Fenêtres}, \drgeoMenu{Aide}~; \item la \textit{barre d'action} pour créer une nouvelle figure, un texte d'explication, les outils faire/defaire, etc. \end{enumerate} Pour créer une nouvelle figure géométrique, l'utilisateur clique sur le premier bouton de la barre d'action. Alternativement, une nouvelle figure peut être créée en utilisant le menu \drgeniusMenu{Fichier->Nouveau->Figure}. Lorsqu'une nouvelle figure est créée, une nouvelle \textit{barre d'icônes} avec un ensemble de six icônes apparaît. Cette barre d'icônes se termine par un menu permettant d'ajuster l'échelle de la figure géométrique courante. En outre, une barre d'icônes verticale de raccourcis, à gauche de la figure, offre un accès rapide aux outils les plus utilisés. \drgeniusFigureSize{Une figure géométrique vide}{fig2}{8} Les six icônes de la barre d'icônes sont des entrées de menu pour des fonctions spécifiques. Ces fonctions sont décrites dans le prochain chapitre. \drgeniusFigureSize{Une figure \drgeo\ et sa description}{fig50}{8} Pour chaque figure, un \textit{panneau synoptique} décrivant sa séquence de construction est disponible. Par défaut ce panneau est poussé à l'extrême gauche et seule la représentation de la figure est visible. À tout moment, l'utilisateur peut pousser le panneau vers la droite pour rendre visible sa description. Une description de figure est un arbre composé de tous les éléments de la figure. Les éléments relatifs à d'autres éléments peuvent être développés en cliquant sur le signe `+', de manière à visualiser les parents de ces éléments. \section{\drgeo\ sur le web} \drgeo\ dispose de son propre espace web sur le site d'\textsc{ofset} à l'adresse~: \xlink{http://www.ofset.org/drgeo}. Sur cet espace, l'utilisateur trouvera les informations suivantes~: \begin{itemize} \item les informations pour obtenir \drgeo{}~; \item la documentation sur le logiciel~; \item des indications pour s'impliquer dans le projet \drgeo{}~; \item des références sur des exploitations pédagogiques du logiciel. \end{itemize} \chapter{Fonctions de base} Ce chapitre décrit les outils utilisés pour construire une figure géométrique. Il se termine par la présentation de la configuration des préférences par l'utilisateur. \section{Outils de construction} Ces outils sont partagés en six groupes accessibles à partir de la seconde barre d'icônes de \drgeo. \drgeniusFigureSize{Catégories d'outils de \drgeo\ et leur description}{fig3}{12} Lorsque l'utilisateur clique sur une des icônes décorées d'un petit triangle vert, une nouvelle barre verticale d'icônes s'affiche immédiatement. Celle-ci regroupe des fonctions d'une même famille. De la gauche vers la droite, nous avons accès aux barres d'icônes verticales pour construire des points et des lignes, utiliser des transformations, calculer des valeurs, gérer des macro-constructions, et utiliser les outils d'édition -- \emph{Divers outils} dans la figure. Ces fonctions se retrouvent à l'identique dans le menu contextuel d'une figure appelée par un clic droit dans le fond de celle-ci. \xname{point_tools} \subsection{Outils de point} \subsubsection{Point libre} \drgeniusIcon{fig4} \label{free_point} \drgeniusIndex{Point}{Libre}{}{} Crée un point libre dans le plan ou sur un objet unidimensionnel (segment, demi-droite, droite, arc de cercle, cercle, lieu)~: \begin{enumerate} \item Dans le premier cas, le point créé peut être déplacé n'importe où dans le plan de la figure. Pour le construire l'utilisateur clique simplement sur le fond. \item Dans le deuxième cas, le point n'est libre que dans l'objet unidimensionnel (ligne) où il a été crée~; il est collé sur l'objet. Pour construire ce type de point, l'utilisateur clique sur une ligne (i.e. droite, demi-droite, segment, cercle, arc de cercle, etc.). \end{enumerate} \paragraph{Comment placer un point avec des coordonnées données~?} Le plus simple est de placer un point libre puis d'éditer ses propriétés --~outil \link{Propriété}[ Section \Ref, page \Pageref]{property-item}~-- afin d'ajuster ses coordonnées comme souhaité. Une autre possibilité --~moins souple pour ce cas de figure~-- est de placer deux valeurs libres dans la figure --~outils \link{Numériques}[ Section \Ref, page \Pageref]{numeric_tool}~-- puis de construire le point ayant pour coordonnées ces deux valeurs --~outil \link{Point défini par ses coordonnées}[ Section \Ref, page \Pageref]{coordinate_point}. Cette possibilité a un avantage sur la précédente, le point ainsi construit ne peut pas être déplacé directement à la souris, le point est en quelque sorte bloqué dans sa position. \subsubsection{Milieu} \drgeniusIcon{fig5} \drgeniusIndex{Point}{Milieu}{}{} Crée le milieu de deux points ou d'un segment~: \begin{enumerate} \item Dans le premier cas, l'utilisateur sélectionne deux points. \item Dans le deuxième cas, l'utilisateur sélectionne simplement un segment. \end{enumerate} \subsubsection{Intersection} \drgeniusIcon{fig6} \drgeniusIndex{Point}{Intersection}{}{} Crée le ou les points d'intersection de deux lignes (i.e. droite, demi-droite, segment, arc de cercle, cercle). L'utilisateur doit sélectionner deux lignes. \subsubsection{Point défini par ses coordonnées} \drgeniusIcon{fig7} \label{coordinate_point} \drgeniusIndex{Point}{Défini par coordonnées}{}{} Crée un point défini par ses coordonnées. L'utilisateur doit sélectionner deux nombres, le premier correspond à l'abscisse, le second à l'ordonnée. \paragraph{Comment placer un point contraint par ses coordonnées~?} Cette fonction est largement utilisée lorsque nous souhaitons par exemple construire le lieu d'un point. Cette construction suppose au préalable l'existence de deux valeurs --~voir \link{Section numérique}[ Section \Ref, page \Pageref]{numeric_tool} -- le point est ensuite construit en sélectionnant ces deux valeurs. \xname{line_tools} \subsection{Outils de ligne} \subsubsection{Droite} \drgeniusIcon{fig8} \drgeniusIndex{Droite}{}{}{} Crée une droite définie par deux points. L'utilisateur sélectionne deux points. \subsubsection{Demi-droite} \drgeniusIcon{fig9} \drgeniusIndex{Demi-droite}{}{}{} Crée une demi-droite définie par deux points. L'utilisateur sélectionne deux points, le premier est l'origine, le second appartient à la demi-droite. \subsubsection{Segment} \drgeniusIcon{fig10} \drgeniusIndex{Segment}{}{}{} Crée un segment donné par deux points. \subsubsection{Vecteur} \drgeniusIcon{fig11} \drgeniusIndex{Vecteur}{}{}{} Crée un vecteur donné par deux points. L'utilisateur sélectionne deux points, le premier est l'origine, le second est l'extrémité. Une fois que le vecteur est créé, celui-ci peut être déplacé indépendamment des deux points. Ceci reste vrai pour un vecteur construit par une transformation (Cf. la section Transformations de ce manuel) \subsubsection{Cercle} \drgeniusIcon{fig12} \drgeniusIndex{Cercle}{}{}{} Crée un cercle. L'utilisateur peut créer un cercle à partir de différentes sélections~: \begin{enumerate} \item le centre et un point du cercle~; \item le centre et un nombre (le rayon du cercle)~; \item le cercle et un segment dont la longueur est le rayon du cercle. \end{enumerate} \subsubsection{Arc de cercle} \drgeniusIcon{fig13} \drgeniusIndex{Arc de cercle}{}{}{} Crée un arc de cercle défini par trois points. Le premier est l'origine de l'arc, le troisième est l'extrémité, le second est un point de l'arc. \subsubsection{Lieu} \drgeniusIcon{fig14} \drgeniusIndex{Lieu géométrique}{}{}{} Crée un lieu défini par deux points. L'utilisateur sélectionne deux points, l'un des deux est un point sur une ligne, l'autre est un point sous contraintes du premier (i.e. quand l'un bouge, l'autre fait de même). \subsubsection{Polygone} \drgeniusIcon{fig15} \drgeniusIndex{Polygone}{}{}{} Crée un polygone défini par n points. L'utilisateur sélectionne n+1 points limitant le polygone. Le premier et le dernier sont un seul et même point ce qui indique à \drgeo\ que la sélection est terminée. L'objet polygone n'est pas un objet comme les autres lignes, il n'est pas possible de placer un point dessus ou de construire une intersection entre un polygone et une autre ligne. En revanche il est possible de construire l'image d'un polygone par une transformation géométrique. \xname{transformation_tools} \subsection{Outils de transformation} \subsubsection{Droite parallèle} \drgeniusIcon{fig16} \drgeniusIndex{Droite}{Parallèle}{}{} Crée une ligne parallèle à une direction et passant par un point. L'utilisateur sélectionne un point et une direction (i.e. une droite, une demi-droite, un segment ou un vecteur). \subsubsection{Droite perpendiculaire} \drgeniusIcon{fig17} \drgeniusIndex{Droite}{Perpendiculaire}{}{} Crée une droite perpendiculaire à une direction et passant par un point. L'utilisateur sélectionne un point et une direction (i.e. une droite, une demi-droite, un segment ou un vecteur). \subsubsection{Symétrie axiale} \drgeniusIcon{fig18} \drgeniusIndex{Transformation}{Symétrie}{Axiale}{} Crée l'image d'un objet par une symétrie axiale. L'utilisateur sélectionne l'objet à transformer et l'axe de symétrie (une droite). Quand l'utilisateur veut construire l'image d'une droite, la première droite sélectionnée est la droite à transformer. \subsubsection{Symétrie centrale} \drgeniusIcon{fig19} \drgeniusIndex{Transformation}{Symétrie}{Centrale}{} Crée l'image d'un objet par une symétrie centrale. L'utilisateur sélectionne l'objet à transformer et le centre de symétrie (un point). Quand l'utilisateur veut construire l'image d'un point, le premier point sélectionné est le point à transformer. \subsubsection{Translation} \drgeniusIcon{fig20} \drgeniusIndex{Transformation}{Translation}{}{} Crée l'image d'un objet par une translation. Quand l'utilisateur veut construire l'image d'un vecteur, le premier vecteur sélectionné est le vecteur à translater. \subsubsection{Rotation} \drgeniusIcon{fig21} \drgeniusIndex{Transformation}{Rotation}{}{} Crée l'image d'un objet par une rotation. L'utilisateur sélectionne l'objet à transformer, le centre et l'angle de la rotation. Quand l'utilisateur veut créer l'image d'un point, le premier point sélectionné est le point à transformer. L'angle peut être sélectionné à partir de différents types de valeurs~: \begin{itemize} \item \textbf{valeur numérique}~: l'angle est alors exprimé en radians. Exemples de valeurs numériques~: valeur libre, distance entre deux points, longueur d'un segment, une coordonnée, une valeur retournée par un script Scheme \drgeo, etc.~; \item \textbf{la mesure d'un angle géométrique formé par trois points}~: sa mesure est alors exprimée en degrés. Attention, dans ce cas la mesure appartient seulement à l'intervalle [0~;~180]~; \item \textbf{la mesure d'un angle orienté de deux vecteurs}~: sa mesure est exprimée en degrés et couvre l'intervalle ]-180~;~180]. \end{itemize} \subsubsection{Homothétie} \drgeniusIcon{fig22} \drgeniusIndex{Transformation}{Homothétie}{}{} Crée l'image d'un objet par une homothétie. L'utilisateur sélectionne l'objet à transformer, le centre et le facteur (i.e. un nombre). Quand l'utilisateur veut créer l'image d'un point, le premier point sélectionné est le point à transformer. \xname{numeric_tools} \subsection{Outils numériques} \subsubsection{Distance, longueur \& nombre} \drgeniusIcon{fig23} \label{numeric_tool} \drgeniusIndex{Nombre}{}{}{} \drgeniusIndex{Droite}{Pente}{}{} \drgeniusIndex{Droite}{Distance}{}{} \drgeniusIndex{Cercle}{Périmètre}{}{} \drgeniusIndex{Segment}{Longueur}{}{} \drgeniusIndex{Vecteur}{Norme}{}{} \drgeniusIndex{Arc de cercle}{Longueur}{}{} \drgeniusIndex{Nombre}{Valeur libre}{}{} Crée une valeur numérique. La valeur numérique, selon la sélection de l'utilisateur, peut être calculée ou bien saisie~: \begin{enumerate} \item deux points~: distance entre ces deux points~; \item un segment~: la longueur de ce segment~; \item un vecteur~: la norme de ce vecteur~; \item un cercle~: le périmètre de ce cercle~; \item un arc de cercle~: la longueur de cet arc~; \item une droite~: la pente de cette droite~; \item une droite et un point~: la distance entre ce point et la droite~; \item un \textbf{clic souris directement sur le fond de la figure} permet à l'utilisateur d'entrer une nouvelle valeur (i.e. une valeur libre). \end{enumerate} Cette dernière possibilité est très intéressante dans certaines situations. Elle permet de fixer une longueur, le rayon d'un cercle, la mesure d'angle (en radian) ou les coordonnées d'un point. La valeur est ensuite utilisée à partir des outils spécifiques de construction de cercle, de rotation et de point défini par ses coordonnées. \subsubsection{Angle} \drgeniusIcon{fig24} \drgeniusIndex{Angle}{Géométrique}{}{}{} \drgeniusIndex{Angle}{Orienté}{}{}{} Calcule la mesure d'un angle défini par trois points ou deux vecteurs. Dans le premier cas, l'angle est considéré comme non orienté (i.e. angle géométrique dont la mesure est dans l'intervalle [0~;~180]). Dans le second cas, l'angle est orienté et sa mesure est dans l'intervalle ]-180~;~180]. \subsubsection{Coordonnées} \drgeniusIcon{fig25} \drgeniusIndex{Point}{Coordonnées}{}{} \drgeniusIndex{Vecteur}{Coordonnées}{}{} Crée les coordonnées (abscisse et ordonnée) d'un point ou d'un vecteur. \subsubsection{Script Scheme \drgenius} \label{script-tool} \drgeniusIcon{fig49} \drgeniusIndex{Script}{}{}{} Crée un script Scheme \drgeo. Le script reçoit \emph{n} objets en entrée. Il retourne éventuellement un nombre, affiché dans la figure. Un script peut être utilisé pour ses effets de bord ou pour sa valeur de retour. Les scripts Scheme \drgeo\ sont couverts en détails dans le \link{chapitre des fonctionnalités avancées}[ Chapitre \Ref]{advancedFeatures} et exactement à la \link{section script}[ Section \Ref, page \Pageref]{script}. \xname{macroconstruction_tools} \subsection{Outil macro-construction} \drgeniusIndex{Macro-construction}{}{}{} \subsubsection{Créer une macro-construction} \drgeniusIcon{fig26} Extrait une séquence de construction d'une figure et la transforme en macro-construction. \subsubsection{Exécuter une macro-construction} \drgeniusIcon{fig27} Exécute (i.e. ``lance'' ou ``joue'') une macro-construction pré-construite. La macro-construction peut être nouvelle ou chargée depuis un fichier. \drgeniusNote{Les macro-constructions sont présentées dans la \link{Section macro-construction}[ \Ref, page \Pageref]{macroConstruction}.} \xname{other_tools} \section{Autres fonctions} \subsection{Arbre logique de construction} \drgeniusIndex{Historique}{Arbre logique}{}{} Chaque figure est associée à un arbre logique de construction. Cet arbre est chronologique, c'est-à-dire qu'il reprend, du haut vers le bas, l'ordre de construction de la figure. Certaines entrées de l'arbre peuvent \^etre dépliées afin de faire apparaître les antécédents -- c'est à dire les objets parents -- utilisés lors de la définition de l'objet. Par défaut l'arbre est masqué, il est en fait replié sur le bord gauche de la fenêtre, pour le faire apparaître il faut le déplier à l'aide de la souris. Déplacer le pointeur souris vers le bord gauche de la fenêtre de \drgeo\, lorsque celui-ci se transforme en ``<->'', presser le bouton souris et tirer vers la droite. \subsection{Déplacer la figure} \drgeniusIndex{Figure}{Déplacer}{}{} La figure peut être déplacée en appuyant sur la touche contrôle et le premier bouton de la souris. \subsection{Déplacer un objet} \drgeniusIcon{fig28} \drgeniusIndex{Objet}{Déplacer}{}{} Un objet peut être déplacé par glisser-déposer. La figure est alors redessinée en respectant ses propriétés. Quasiment tous les objets géométriques peuvent être déplacés. Si nécessaire, \drgeo\ déplace les points libres associés. Par exemple, quand l'utilisateur déplace une droite définie par deux points, \drgeo\ déplace les deux points simultanément. \subsection{Supprimer un objet} \drgeniusIcon{fig30} \drgeniusIndex{Objet}{Supprimer}{}{} Un objet d'une figure peut être supprimé en activant ce menu. Éventuellement, l'utilisateur peut annuler la suppression à l'aide de la fonction d'annulation à partir de la barre d'icônes ou du menu de l'application. Par défaut le nombre d'annulations possibles est de 10 mais l'utilisateur peut ajuster cette valeur depuis la boîte de dialogue des préférences. \xname{editing_object_styles} \subsection{Changer l'aspect d'un objet} \drgeniusIcon{fig29} \drgeniusIndex{Editer}{Style}{}{} \drgeniusIndex{Objet}{Renommer}{}{} \drgeniusIndex{Renommer}{Objet}{}{} \drgeniusIndex{Objet}{Masquer}{}{} Chaque objet géométrique a ses propres attributs de style comme la couleur, l'épaisseur, l'étiquette, la taille et la forme. De plus, il est possible de cacher temporairement un objet sans le supprimer. Par exemple, il peut être utile de cacher des constructions intermédiaires sans les supprimer. Tous ces attributs sont ajustables depuis la boîte de dialogue qui s'affiche lorsque l'utilisateur clique sur un objet de la figure. Pour cela il faut d'abord se mettre dans le mode d'édition de style en sélectionnant \drgeniusMenu{Autres->Aspect} du menu contextuel de la figure, ou bien en cliquant sur l'icône ci-dessus, du 6ème tiroir d'icônes. \drgeniusIndex{Point}{Renommer}{}{} La boîte de dialogue du style d'un point concerne tous les types de point. Il est possible d'ajuster la couleur, la forme, la taille, le nom et la visibilité. \drgeniusFigure{Boîte de dialogue pour le style d'un objet point}{fig31} La boîte de dialogue du style d'une ligne concerne les droites, les demi-droites, les segments, les vecteurs, les cercles, les arcs de cercle, les lieux de points. Il est possible d'ajuster la couleur, le style, le nom et la visibilité. Lorsqu'une droite, une demi-droite, un vecteur ou un segment sont définis par deux points ayant des noms non vides, leur nom est automatiquement déduit à partir de celui des deux points. Dans ce cas, l'utilisateur ne peut pas les renommer. \drgeniusFigure{Boîte de dialogue pour le style d'un objet ligne}{fig32} La boîte de dialogue du style d'un nombre ou d'un polygone concerne toutes les sortes de valeur (saisie par l'utilisateur, calculée par un script Scheme \drgeo\ ou représentant une mesure géométrique) et les formes polygonales. \drgeniusFigure{Boîte de dialogue pour les nombres \& les objets polygones}{fig33} \T \clearpage \subsection{Changer les propriétés d'un objet} \label{property-item} \drgeniusIcon{fig52} \drgeniusIndex{Editer}{Propriétés}{}{} \drgeniusIndex{Editer}{Point}{}{} \drgeniusIndex{Editer}{Script}{}{} \drgeniusIndex{Editer}{Valeur}{}{} Certaines propriétés d'objets sont paramétrables par l'utilisateur. Quand l'utilisateur clique sur ces objets, une boîte de dialogue appropriée apparaît. Actuellement, les objets suivants sont concernés~: \begin{enumerate} \item point libre~: abscisse et ordonnée peuvent être éditées~;\\ \drgeniusFigure{Changement des coordonnées d'un point libre}{fig34} \item valeur libre~: sa valeur peut être modifiée~;\\ \drgeniusFigure{Modification d'une valeur libre}{fig36} \item script~: son code peut être modifié.\\ \drgeniusFigure{Modification d'un script}{fig35} \end{enumerate} \T \clearpage \subsection{Afficher une grille} \drgeniusIndex{Figure}{Afficher}{Grille}{} \drgeniusIndex{Grille}{Afficher}{}{} Il est possible d'afficher une grille unitaire dans toute figure de \drgeo, la commande est accessible depuis le menu \drgeniusMenu{Édition->Montrer ou cacher la grille}. Elle peut également être activée par le raccourci clavier \drgeniusMenu{Ctrl-G}. Si la commande est réactivée, la grille est cachée. La grille est unitaire, chaque subdivision représente une unité. Enfin, si la grille est affichée lors de la sauvegarde, celle-ci l'est aussi. \section{Préférences utilisateurs} \xname{default_behaviour} \subsection{Comportement par défaut} \label{default_behaviour} \drgeniusIndex{Editer}{Préférences par défaut}{}{} Le comportement par défaut de \drgeo\ peut être configuré de plusieurs manières. Pour paramétrer les préférences, l'utilisateur accède au menu \drgeniusMenu{Édition->Préférences...} pour ouvrir la boîte de dialogue des préférences. \drgeniusFigureSize{Préférences des figures géométriques}{fig38}{8} La boîte de dialogue est composée en deux parties~: \begin{enumerate} \item La première partie concerne les préférences des figures géométriques. Des onglets permettent à l'utilisateur de paramétrer le réglage par défaut de chaque type d'objet (géométrique ou numérique). Les réglages concernent l'aspect des objets. \item La deuxième partie concerne les préférences globales~: \begin{itemize} \item Le nombre de niveaux pour Annuler/Refaire~; \item Le nom par défaut lorsqu'une nouvelle figure est créée. Le \%d est remplacé par un entier géré par \drgeo, cette valeur est incrémentée à chaque nouvelle figure~; \item Le navigateur Internet -- visionneuse -- par défaut pour visualiser l'aide en ligne~; \item Les noms par défaut utilisés lors de la sauvegarde d'une figure et d'une session~; \item Les noms par défaut utilisés lors d'exportations aux formats \LaTeX~ et PostScript~; \end{itemize} \end{enumerate} \drgeniusIndex{Editer}{Style par défaut}{}{} \drgeniusIndex{Editer}{Préférences par défaut}{Annuler/Refaire}{} \drgeniusIndex{Editer}{Préférences par défaut}{Noms}{} \drgeniusIndex{Aide}{Préférences par défaut}{Visionneuse}{} \subsection{Autres préférences} \drgeniusIndex{Figure}{Renommer}{}{} En plus du comportement par défaut de \drgeo, l'utilisateur peut modifier le nom d'une figure à partir du menu \drgeniusMenu{Édition->Renommer}. \drgeniusFigure{Changement du nom d'une figure}{fig39} \chapter{Fonctionnalités avancées} \label{advancedFeatures} Dans ce chapitre, nous présentons les fonctionnalités qui permettent d'étendre les possibilités de \drgeo\ ou de l'adapter à une situation pédagogique donnée. La première est la \textit{macro-construction}. Elle permet l'extraction d'une construction logique dans un enregistrement. Cet enregistrement peut ensuite être répété ou sauvegardé dans un fichier portant l'extension \textbf{.mgeo} et ouvert lorsque nécessaire. Les scripts Scheme \drgeo\ --~\drgeo\ Script aka DGS~-- représentent une autre fonctionnalité pour étendre \drgeo. Ces scripts sont de véritables items de figure, comme les items géométriques. En entrée, ils reçoivent une ou plusieurs références d'items géométriques et ils retournent une valeur placée dans la figure. Ce sont en fait des fonctions\footnote{Ou procédures pour les amateurs de Pascal.} greffées dans une figure, elle sont évaluées à chaque mise à jour de la figure (i.e. lorsque la figure a besoin d'être redessinée). Les scripts Scheme \drgeo\ sont utiles pour la valeur qu'ils retournent ou leur effet de bord, cela dépend de ce que l'utilisateur souhaite réaliser. En extension des scripts Scheme, \drgeo\ propose d'aller encore plus loin avec les figures Scheme de \drgeo. Cette fois il s'agit de décrire une figure géométrique complètement sous la forme d'un code source écrit dans le langage Scheme. La force de cette approche est de permettre une construction fonctionnelle\footnote{Par exemple sous forme récursive} des figures et non plus simplement déclarative comme c'est le cas avec l'interface graphique. Enfin, l'adaptation de l'interface utilisateur de \drgeo\ permet à un enseignant de préparer une session de travail avec des documents dans lesquels certaines fonctions ont été bloquées par un mot de passe. L'intérêt est de contrainte à l'utilisation de certains outils pour des situations pédagogiques données. \xname{using_macro} \section{Macro-construction} \label{macroConstruction} \drgeniusIndex{Macro-construction}{Introduction}{}{} Une macro-construction ressemble un peu à une procédure qui reçoit des items d'une figure en entrée et qui retourne un ou plusieurs items de figure, construits par la macro-construction. Une macro est construite à partir d'un modèle défini par l'utilisateur. Cela signifie que l'utilisateur doit réaliser la séquence de construction une première fois dans une figure puis demander à \drgeo\ de l'enregistrer dans une macro-construction. La macro-construction peut ensuite être sauvegardée dans un fichier d'extension \textbf{.mgeo}. Pour enregistrer une séquence de construction, \drgeo\ doit connaître les items initiaux de la séquence ainsi que les items finaux. Évidemment, les items finaux ne doivent dépendre \textit{que} des items initiaux\footnote{Cette contrainte a depuis été assouplie et permet d'aller encore plus loin avec les macro-constructions. Voir \link{Créer un polygone régulier}[ Section \Ref, page \Pageref]{polygon_macro}.}, sinon \drgeo\ ne sera pas capable de déduire les items finaux à partir des items initiaux. Ainsi, \drgeo\ déduit la logique de la séquence de construction et l'enregistre dans une macro-construction. L'utilisateur peut exécuter cette macro-construction, elle demande seulement les items initiaux (du bon type) de la figure et construit les items résultants. \drgeniusNote{Les items de figure intermédiaires et invisibles sont aussi construits par la macro-construction. Ils sont nécessaires pour construire les items résultants.} Pour illustrer la fonctionnalité macro-construction, nous utiliserons l'exemple de l'utilisateur qui souhaite enregistrer la construction du cercle passant par trois points ainsi que son centre. \drgeniusFigureSize{La figure initiale}{fig40}{4} \drgeniusIndex{Macro-construction}{Créer}{}{} Avant la création de la macro-construction, l'utilisateur doit construire la figure finale, elle est considérée comme modèle par la macro-construction. \drgeniusFigureSize{La figure avec la construction finale}{fig41}{4} \subsection{Création d'une macro-construction} À cette étape, la séquence de construction est faite. L'utilisateur doit maintenant avertir \drgeo\ qu'il veut une macro-construction à partir de cette séquence. Il doit appeler la fonction \drgeniusMenu{Construire une macro} à partir de la barre d'icônes \drgeniusIcon{fig26} ou depuis le menu contextuel de la vue de la figure. Depuis la boîte de dialogue de l'assistant, l'utilisateur sélectionne les paramètres d'entrée et de sortie, le nom et la description de la macro-construction. \drgeniusFigureSize{Première page de la boîte de dialogue de l'assistant pour construire une macro-construction}{fig42}{6} La seconde page de la boîte de dialogue sert à sélectionner les paramètres d'entrée. Dans notre exemple, ce sont les trois points initiaux. L'utilisateur a juste besoin d'aller jusqu'à cette seconde page et il peut sélectionner les trois points de la figure. Les items sélectionnés clignotent. \drgeniusFigureSize{La seconde page, les trois points sont sélectionnés}{fig43}{6} À partir de la troisième page, l'utilisateur sélectionne les paramètres de sortie. Dans notre exemple, nous voulons le cercle et son centre comme résultat de la macro-construction. Il procède comme dans le cas des paramètres d'entrée pour les sélectionner. \drgeniusFigureSize{La troisième page, le cercle et son centre sont sélectionnés}{fig44}{6} À partir de la quatrième page, l'utilisateur entre le nom et la description de la macro-construction. Ces informations sont affichées lorsque l'utilisateur exécute une macro-construction. Ceci permet de distinguer les macro-constructions entre elles. \drgeniusFigureSize{La quatrième page, le nom et la description de la macro-construction}{fig45}{6} À partir de la dernière boîte de dialogue de l'assistant (la cinquième), l'utilisateur termine la création en appuyant sur le bouton \texttt{Terminer}. Il peut aussi revenir aux étapes précédentes pour ajuster les paramètres de la macro-construction. \drgeniusNote{Si la sélection des paramètres d'entrée et de sortie ne correspond pas (\drgeo\ ne peut pas extraire la logique de la construction), la macro-construction ne peut pas être créée. Dans ce cas, l'utilisateur doit reconsidérer la sélection des paramètres d'entrée et de sortie. Il peut revenir à la seconde ou la troisième page de la boîte de dialogue de l'assistant pour ajuster ses choix.} À cette étape, la macro-construction est créée et enregistrée dans \drgeo. Dans la prochaine section, nous verrons comme l'utiliser. \subsection{Exécution d'une macro-construction} \drgeniusIndex{Macro-construction}{Exécuter}{}{} \subsubsection{À l'aide de la boîte de dialogue} \drgeniusIndex{Macro-construction}{Exécuter}{Boîte de dialogue}{} Pour exécuter une macro-construction, l'utilisateur peut appeler la fonction \drgeniusMenu{Exécuter une macro pré-préconstruite} à partir de la barre d'icônes \drgeniusIcon{fig27} ou depuis le menu contextuel de la vue de la figure. Une boîte de dialogue décrivant la procédure s'affiche alors. À partir de cette boîte de dialogue, l'utilisateur sélectionne la macro-construction. Dans la seconde page, il sélectionne la macro-construction dans la liste en haut de la boîte de dialogue. Une fois la macro sélectionnée, il peut directement cliquer sur les paramètres d'entrée dans la figure. Dès que tous les paramètres d'entrée sont sélectionnés, la macro-construction est exécutée et les paramètres finaux sont affichés. \drgeniusFigureSize{L'utilisateur sélectionne les paramètres d'entrée dans la figure}{fig46}{6} Dans notre exemple, la macro-construction nécessite trois paramètres d'entrée (trois points) et elle construit un point et un cercle. Pour exécuter notre macro-construction, il faut une figure avec au moins trois points. \drgeniusFigureSize{Une figure avec trois points}{fig47}{3} Une fois que notre macro-construction est appliquée à ces trois points, nous avons le cercle souhaité et son centre. \drgeniusFigureSize{La figure finale avec le cercle et son centre}{fig48}{3} \subsubsection{À l'aide du menu Macro-constructions} \drgeniusIndex{Macro-construction}{Exécuter}{Menu}{} Il existe une autre procédure -- plus rapide -- pour exécuter une macro-construction. La barre de menu principale de \drgeo\ comporte un menu \drgeoMenu{Macro-constructions}. Ce menu est peuplé par les noms des macro-constructions chargées en mémoire dans le programme. Pour exécuter une macro-construction, l'utilisateur sélectionne directement celle de son choix. En outre un passage du pointeur souris au dessus de chaque item de menu fait apparaître une info-bulle de la description de la macro. L'utilisateur peut ainsi avoir rapidement une explication sur l'ensemble des macro-constructions. \drgeniusFigureSize{Exécuter une macro-construction directement depuis le menu \drgeoMenu{Macro-constructions}}{fig62}{6} \T \clearpage \xname{drgenius_guile_script} \section{Script Scheme \drgenius} \label{script} \drgeniusIndex{Script}{Introduction}{}{} \drgeo\ est compatible Guile. Cela signifie qu'il est possible d'exécuter des scripts Scheme avec \drgeo. Mais qu'est-ce que Guile~? Extrait du manuel de Guile~: \begin{quote}{\em Guile est un interpréteur pour le langage de programmation Scheme, prévu pour être utilisé dans une grande variété d'environnements. } \end{quote} Les citations suivantes décrivent précisément comment Guile est utilisé dans \drgenius~: \begin{quote}{\em Comme un shell, Guile peut être lancé de manière interactive, recevoir des expressions de l'utilisateur, les évaluer et afficher les résultats, ou comme un interpréteur de scripts, lire et exécuter du code Scheme à partir d'un fichier. Cependant, Guile est disponible sous forme de bibliothèque permettant à d'autres applications d'incorporer facilement un interpréteur Scheme complet. Une application peut utiliser Guile comme un langage d'extension, un langage de configuration propre et puissant, ou comme une ``colle'' multi-usages, liant des primitives fournies par l'application. } \end{quote} Dans \drgeo, une API est disponible à partir de l'interpréteur Guile. C'est un ensemble de ``crochets'' dans le moteur géométrique. C'est pourquoi l'utilisateur peut écrire des scripts pour manipuler les items (géométriques ou numériques) des figures. Aussi, puisque les scripts sont des items de figure au même titre que d'autres, ils n'ont pas besoin d'être dans un fichier séparé, ils sont enregistrés dans le fichier de la figure. Dans ce qui suit, nous allons utiliser l'acronyme DGS pour désigner un script Guile \drgeo\ (``\drgeo\ Script''). \subsection{DGS par l'exemple} \drgeniusIndex{Script}{Exemples}{}{} L'outil pour créer un DGS est disponible depuis la section numérique du menu contextuel ou de la barre d'icônes. Un DGS peut recevoir de 0 à \textit{n} paramètres d'entrée. Après avoir choisi l'outil, il suffit de cliquer sur les objets souhaités en entrée puis quelque part sur le fond de la figure, le script sera placé à ce dernier endroit. Dans la suite nous vous proposons de travailler sur quelques exemples de DGS, leurs fonctionnalités et leur puissance seront plus facilement analysées. Les DGS comme les macro-constructions donnent une dimension particulière à \drgeo, ils permettent --~chacun avec un positionnement différent\footnote{Les macro-constructions ont une approche géométrique tandis que les DGS ont une approche numérique mais aussi et surtout nous pouvons les utiliser dans un esprit de bidouillage (``hacking'' en anglais).}~-- d'aller là où les auteurs du logiciel ne sont pas allés ou ne souhaitent par aller. Il est aussi important de comprendre que la plupart des fonctionnalités de l'interpréteur GNU Guile sont disponibles depuis les DGS. C'est particulièrement vrai pour ses bibliothèques de fonctions\footnote{En particulier, les fonctions mathématiques}, nous allons bien sûr les utiliser intensément. \paragraph{DGS sans paramètre d'entrée} La procédure pour créer un script sans paramètre d'entrée est la suivante~: \begin{enumerate} \item Après avoir choisi \link{l'outil de script}[ Section \Ref, page \Pageref]{script-tool}, cliquer \emph{directement} dans le fond écran, à l'emplacement où vous souhaitez placer le script. \textbf{Surtout ne cliquez sur aucun objet} de la figure, sinon \drgeo\ comprendra que vous souhaitez cet objet comme paramètre d'entrée du script\footnote{Si par accident vous cliquiez sur un objet, sélectionnez de nouveau l'outil de script. Cela annulera votre sélection.}. \item Une fois le script placé, vous voyez la chaîne de caractères ``Dr.~Genius'' s'afficher. Tout script nouvellement créé contient une commande par défaut pour afficher cette chaîne de caractères, vous pouvez l'éditer en allant à \link{l'outil propriétés d'objet}[ Section \Ref, page \Pageref]{property-item}. \item Une fois cet outil choisi, cliquer sur le script --~ou pour être plus précis sur sa valeur~-- de votre choix dans la figure. Une boîte de dialogue contenant le script s'affichera. Dans la suite de cette section, c'est dans ce dialogue que nous saisissons les scripts. \end{enumerate} \subparagraph{Un générateur de nombres aléatoires et autres~:} \drgeniusIndex{Script}{\texttt{random}}{}{} Si vous souhaitez un générateur de nombres aléatoires, rien de plus simple, saisissez pour tout script le code suivant~: \begin{verbatim} (random 10) \end{verbatim} À chaque mise à jour de la figure, il génère un nombre aléatoire entier dans l'intervalle [0~;~10[. Si vous préférez un nombre flottant dans l'intervalle [0~;~1[, utilisez ce script~: \begin{verbatim} (random:uniform) \end{verbatim} \drgeniusNote{Quelques précisions~: \begin{itemize} \item La valeur retournée par le script est la valeur calculée par la dernière ligne. Ici en l'occurrence, il s'agit de la valeur retournée par l'appel d'une fonction~; \item La dernière ligne d'un script doit retourner un nombre réel. Sinon \drgeo\ affiche ``Résultat non imprimable''~; \item Si l'on souhaite retourner la valeur d'une variable, il suffit de mettre son nom en dernière ligne. \end{itemize} } \subparagraph{Calculer des valeurs usuelles~:} Pour calculer une valeur approchée de $\pi$~: \begin{verbatim} (acos -1) \end{verbatim} ou de $e$~: \begin{verbatim} (exp 1) \end{verbatim} Les valeurs retournées par ces DGS sont ensuite utilisables comme toutes les autres valeurs numériques que peut générer \drgeo. Pour toutes ces petites choses les DGS sont donc vos amis. Mais ils peuvent faire bien plus de choses intéressantes lorsqu'ils reçoivent des paramètres en entrée. \paragraph{DGS avec au moins un paramètre d'entrée} \drgeniusIndex{Script}{Paramètres}{}{} La procédure pour créer un DGS avec un paramètre d'entrée est sensiblement la même. Juste après avoir sélectionné l'outil script, il suffit de cliquer sur l'objet qui sera passé en paramètre d'entrée, puis de cliquer sur le fond de l'écran, à l'endroit où le script doit être placé. Ensuite, dans le script, la référence du paramètre d'entrée est placée dans la variable $a1$. Si nous avions défini deux paramètres d'entrée, leurs références auraient été placées suivant l'ordre de sélection dans les variables $a1$ et $a2$. De même pour un nombre de 3, 4, etc. de paramètres d'entrée. Selon le type d'objet en référence, diverses méthodes sont disponibles qui pour obtenir sa valeur, qui pour obtenir ses coordonnées, etc. Le répertoire des méthodes est disponible depuis la Section \link{Méthodes de référence des DGS}[ \Ref, page \Pageref]{api-dgs}. Dans la suite, nous exposerons graduellement la construction d'une portion de courbe représentative d'une fonction et la tangente en un point mobile à cette portion de courbe. La figure finale est fournie dans \drgeo. Elle s'appelle \xlink{slope.fgeo}[(/usr/share/drgeo/examples/figures/slope.fgeo)]{/usr/share/drgeo/examples/figures/slope.fgeo}. \drgeniusFigureSize{La figure que nous obtiendrons}{fig55}{8} \subparagraph{Définir une valeur dans un intervalle donné~:} \drgeniusIndex{Script}{Intervalle}{}{} Dans une nouvelle figure, nous commençons par placer deux points et le segment dont les extrémités sont ces deux points. Sur ce segment nous plaçons un point libre appelé ``Move me!''. Ce point servira de jauge, à nous de la calibrer avec un script. Ensuite nous créons un script ayant pour unique paramètre d'entrée ce point là. Lorsque $a1$ est une référence vers le point ``Move me!'', le script suivant nous retourne une valeur décimale comprise entre [-10~;~10]~: \begin{verbatim} (define x (getAbscissa a1)) (* 20 (- x 0.5)) \end{verbatim} Quelques explications s'imposent. Dans la première ligne, l'appel \texttt{(getAbscissa a1)} permet d'obtenir l'abscisse curviligne de l'objet référencé par $a1$\footnote{Cette abscisse est dans l'intervalle [0~;~1], quelque soit le type de ligne} --~c'est-à-dire le point ``Move me!''. Cette abscisse est placée dans une nouvelle variable $x$. Ensuite à la deuxième ligne nous calibrons, ici l'expression est équivalente en notation algébrique à $20 \times ( x - 0.5)$. Comme c'est la dernière ligne du script le résultat de ce calcul est la valeur retournée et affichée dans la figure. Enfin, nommons ce script Xo. \subparagraph{Afficher une portion de courbe représentative d'une fonction~:} \drgeniusIndex{Lieu géométrique}{Script}{}{} La valeur obtenue par le script précédant nous servira d'abscisse, nous allons nous servir de cette valeur pour calculer avec un deuxième script l'ordonnée en ce point par la fonction $x \rightarrow cos(x)$~: \begin{verbatim} (define x (getValue a1)) (cos x) \end{verbatim} L'appel \texttt{(getValue a1)} permet d'obtenir la valeur numérique de l'objet de référence $a1$. Ici il s'agit d'obtenir la valeur retournée par le script précédent. Nous nommons ce script Yo. Ensuite nous créons le point Mo de coordonnées (Xo~;~Yo). C'est un point de la courbe représentative de $x \rightarrow cos(x)$. Pour afficher sa portion de courbe représentative sur l'intervalle [-10~;~10], nous créons le lieu du point Mo lorsque le point ``Move Me!'' décrit le segment. Ça y est nous avons une courbe~! \subparagraph{Calculer et afficher la tangente à une courbe~:} \drgeniusIndex{Script}{Exemples}{Tangente à une courbe}{} Pour afficher la tangente en Mo, il nous faut d'abord la pente en ce point. Nous avons donc besoin de la fonction dérivée $x \rightarrow -sin(x)$ et de Xo. Nous créons un script avec comme paramètre d'entrée le script Xo~: \begin{verbatim} (- 0 (sin (getValue a1))) \end{verbatim} La notation préfixée utilisée par Scheme/Guile peut dérouter, c'est simplement une question d'habitude. Nommons ce script ``pente en Mo''. Ainsi lorsque Mo se déplace sur la courbe, la pente est recalculée. Il nous reste maintenant à afficher la tangente. Pour ce faire nous allons d'abord calculer les coordonnées d'un deuxième point --~M1~-- de cette droite. Commençons par son abscisse, par exemple $X1 = Xo + 2$, pour ce faire créons un script avec comme paramètre d'entrée le script Xo~: \begin{verbatim} (define x1 (getValue a1)) (+ x1 2) \end{verbatim} Nommons ce script X1. Attaquons-nous maintenant à l'ordonnée de M1. Là nous avons besoin de~: \begin{itemize} \item Mo (référence $a1$)~; \item la pente en Mo ($a2$)~; \item l'abscisse X1 ($a3$). \end{itemize} Dans le script suivant, nous calculons l'ordonnée de M1 par le calcul $Yo + m \times (X1 - X0)$~: \begin{verbatim} (define x0 (car (getCoordinates a1))) (define y0 (cadr (getCoordinates a1))) (define m (getValue a2)) (define x1 (getValue a3)) (+ (* m (- x1 x0)) y0) \end{verbatim} Quelques mots sur l'appel \texttt{(getCoordinates a1)}, dans cet appel $a1$ doit être une référence vers un objet de type point, la méthode retourne une liste contenant les coordonnées du point --~ici Mo. \texttt{car} permet d'extraire le premier élément de cette liste, \texttt{cadr} le deuxième. Le reste du script ne devrait pas poser de problème. Nommons ce script Y1 puis construisons le point M1 de coordonnées (X1~;~Y1) et enfin la tangente (MoM1). Bien sûr, il aurait été possible de n'utiliser que deux ou trois gros scripts à la place de cette myriade de scripts. Mais nous espérons que ces petits exemples vous ont donné envie d'essayer par vous même les DGS. \subsection{Méthodes de référence pour les scripts \drgeo} \label{api-dgs} % DGS API is exposed here Les sections suivantes contiennent la description des méthodes disponibles pour les DGS. Elles sont classées par type d'objet géométrique ou numérique. \subsubsection{Point} \drgeniusIndex{Script}{\texttt{getAbscissa}}{}{}{} \begin{drgeoApi}{valeur (getAbscissa point)} \drgeoApiIn{point}{Référence d'un point libre sur une ligne} \drgeoApiOut{L'abscisse de ce point sur la ligne. La valeur appartient à l'intervalle [0~;~1]} \drgeoApiExample{(define x (getAbscissa a1))\\ (* x 10)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{setAbscissa}}{}{}{} \begin{drgeoApi}{(setAbscissa point x)} \drgeoApiIn{point}{Référence d'un point libre sur une ligne} \drgeoApiIn{x}{Valeur décimale de l'intervalle [0~;~1] représentant la nouvelle abscisse} \drgeoApiExample{(setAbscissa a1 0.5)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getCoordinates}}{}{} \begin{drgeoApi}{liste (getCoordinates point|vecteur)} Retourne les coordonnées d'un point ou d'un vecteur.\\ \drgeoApiIn{point|vecteur}{Référence vers un point ou un vecteur} \drgeoApiOut{Liste contenant les coordonnées du point ou du vecteur} \drgeoApiExample{(define c (getCoordinates a1))\\ (define x (car c))\\ (define y (cadr c))\\ (+ (* x x) (* y y))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{setCoordinates}}{}{} \begin{drgeoApi}{(setCoordinates point coord)} Positionne les coordonnées d'un point\\ \drgeoApiIn{point}{Référence d'un point libre dans le plan} \drgeoApiIn{coord}{Liste de deux nombres décimaux} \drgeoApiExample{(define l (list 1.4 (random 5)))\\ (setCoordinate a1 l)} \end{drgeoApi} \subsubsection{Droite, Demi-droite, Segment, Vecteur} \drgeniusIndex{Script}{\texttt{getSlope}}{}{}{} \begin{drgeoApi}{valeur (getSlope direction)} \drgeoApiIn{direction}{Référence vers un objet de type droite, demi-droite, segment ou vecteur} \drgeoApiOut{La pente de cette direction} \drgeoApiExample{(define p (getSlope a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getUnit}}{}{}{} \begin{drgeoApi}{valeur (getUnit direction)} \drgeoApiIn{direction}{Référence vers un objet de type droite, demi-droite, segment ou vecteur} \drgeoApiOut{Une liste contenant les coordonnées d'un vecteur unitaire} \drgeoApiExample{(define v (getUnit a1))} \end{drgeoApi} \begin{drgeoApi}{valeur (getNormal direction)} \drgeoApiIn{direction}{Référence vers un objet de type droite, demi-droite, segment ou vecteur} \drgeoApiOut{Une liste contenant les coordonnées d'un vecteur normal à la direction} \drgeoApiExample{(define n (getNormal a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getNorm}}{}{} \begin{drgeoApi}{valeur (getNorm vecteur)} \drgeoApiIn{vecteur}{Référence vers un vecteur} \drgeoApiOut{La norme de ce vecteur} \drgeoApiExample{(define n (getNorm a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getLength}}{}{} \begin{drgeoApi}{valeur (getLength segment)} \drgeoApiIn{segment}{Référence vers un segment} \drgeoApiOut{La longueur de ce segment} \drgeoApiExample{(define l (getLength a1))} \end{drgeoApi} \subsubsection{Cercle, Arc de cercle} \drgeniusIndex{Script}{\texttt{getCenter}}{}{} \begin{drgeoApi}{liste (getCenter cercle|arc-cercle)} \drgeoApiIn{cercle|arc-cercle}{Référence vers un cercle ou un arc de cercle} \drgeoApiOut{Liste contenant les coordonnées du centre du cercle ou de l'arc de cercle} \drgeoApiExample{(define c (getCenter a1))\\ (car c)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getRadius}}{}{} \begin{drgeoApi}{valeur (getRadius cercle|arc-cercle)} \drgeoApiIn{cercle|arc-cercle}{Référence vers un cercle ou un arc de cercle} \drgeoApiOut{Rayon du cercle ou de l'arc de cercle} \drgeoApiExample{(define r (getRadius a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getLength}}{}{} \begin{drgeoApi}{valeur (getLength cercle|arc-cercle)} \drgeoApiIn{cercle|arc-cercle}{Référence vers un cercle ou un arc de cercle} \drgeoApiOut{Périmètre du cercle ou longueur de l'arc de cercle} \drgeoApiExample{(define l (getLength a1))} \end{drgeoApi} \subsubsection{Nombre} \drgeniusIndex{Script}{\texttt{getValue}}{}{} \begin{drgeoApi}{valeur (getValue nombre)} \drgeoApiIn{nombre}{Référence vers un nombre} \drgeoApiOut{Valeur de ce nombre} \drgeoApiExample{(define a (getValue a1))\\ (define b (getValue a2))\\ (+ a b)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{setValue}}{}{} \begin{drgeoApi}{(setValue nombre v)} \drgeoApiIn{nombre}{Référence vers un nombre} \drgeoApiIn{v}{Valeur décimale} \drgeoApiExample{(define v (getValue a1))\\ (setValue a2 v)} \end{drgeoApi} \subsubsection{Angle} \drgeniusIndex{Script}{\texttt{getAngle}}{}{} \begin{drgeoApi}{valeur (getAngle angle)} \drgeoApiIn{angle}{Référence vers un angle, orienté ou géométrique} \drgeoApiOut{Une mesure de cet angle en degré. Pour obtenir une mesure en radian, utiliser la méthode \texttt{getValue}} \drgeoApiExample{(define angle1 (getAngle a1))\\ (define angle2 (getAngle2))\\ (define angle3 (getAngle a3))\\ (+ angle1 angle2 angle3)} \end{drgeoApi} \subsubsection{Autres} \drgeniusIndex{Script}{\texttt{move}}{}{} \begin{drgeoApi}{(move item t)} \drgeoApiIn{item}{Référence vers un objet de la figure} \drgeoApiIn{t}{Vecteur à deux dimensions} \drgeoApiExample{(define v (vector .1 0))\\ (move a1 v)} \end{drgeoApi} \section{Figure Scheme de \drgeo} \drgeniusIndex{Figure Scheme de \drgeo{}}{Introduction}{}{} Les \emph{Figures Scheme de \drgeo} -- (FSD) -- sont des figures écrites dans un langage relativement naturel. Il ne s'agit donc plus de construire une figure à l'aide de l'interface graphique de \drgeo\ mais plutôt de décrire une figure dans le langage Scheme. Nous avons apporté le plus grand soin afin que la syntaxe utilsée soit facile et légère. Aussi l'ensemble des mots clés utilisés pour décrire une figure simple sont adaptables dans différentes langues. Ainsi une figure pourra être décrite en Français, en Anglais, en Espagnol, etc. (Un mélange de langues est même possible mais ce n'est pas souhaitable). \subsection{Quelques exemples} \drgeniusIndex{Figure Scheme de \drgeo{}}{Exemples}{}{} En lui même Scheme est un langage de très haut niveau, lorsqu'une figure est définie dans ce langage, nous disposons également de toute sa puissance pour par exemple définir récursivement telle partie de la figure, ou bien pour placer aléatoirement certains objets de telle sorte qu'à chaque ouverture de la figure, celle-ci est légèrement différente. Bref, les FSD sont libérées du carcan de l'interface graphique tout en étant renforcées du langage Scheme. \drgeniusIndex{Figure Scheme de \drgeo{}}{Evaluer}{}{} Un FSD est donc un fichier d'extension \textbf{.scm} créé à l'aide d'un éditeur de texte, il est ensuite ouvert dans \drgeo\ à l'aide de la commande \drgeniusMenu{Fichier->Évaluer}. \drgeniusIndex{Figure Scheme de \drgeo{}}{Nouvelle figure}{}{} Commençons par étudier un exemple simple de FSD~: % Note to the translator, most of the DSF commands can be translated % in various languages, this is why you can see the command % written in French, feel free to translate in your language, however % you will also have to maintain the corresponding % scm/drgeo_scm_interface_constant_xx.scm file \begin{verbatim} (nouvelle-figure "Ma figure") \end{verbatim} C'est la plus petite FSD que nous puissions définir. Lors de son chargement dans \drgeo, celle-ci va simplement créer une nouvelle figure vide nommée ``Ma figure''. Nous pourrions multiplier les commandes \texttt{(nouvelle-figure "Ma figure")} autant de fois que nous le souhaitons, autant de figures seraient créées. Abordons un deuxième exemple~: \begin{verbatim} (nouvelle-figure "Ma figure") (soit Point "A" libre 1.2 -2) \end{verbatim} Cette FSD définie une figure avec un point libre $A$ de coordonnées initiales $(1,2~;~-2)$. Comme nous pouvons le voir la syntaxe de définition d'un objet géométrique est relativement agréable, d'autant plus qu'elle est exprimée dans une langue maternelle. Intéressons nous de plus près à la deuxième instruction, en effet celle-ci suit une syntaxe qui est commune à toutes les commandes de définition d'objet. Ce type de commande se décompose comme suit~: \begin{enumerate} \item Elle commence toujours par le mot-clé \texttt{soit}, il indique que nous souhaitons définir un nouvel objet. \item Il est immédiatement suivi de la catégorie de l'objet, ici \texttt{Point}. \item Le nom de l'objet vient ensuite, $A$, il doit toujours être entouré de ". Si nous ne souhaitons pas nommer l'objet, il faut tout de même donner un nom vide comme suit: "". \item Enfin, nous précisons le type de l'objet -- le type de point dans notre exemple -- ici \texttt{libre}. Cela signifie que le point $A$ est libre. \item Le type de l'objet est suivi d'une liste d'arguments spécifiques. Dans notre exemple cette liste est composée de deux nombres, les coordonnées du point libre $A$. \end{enumerate} Poursuivons avec un troisième exemple~: \begin{verbatim} (define (triangle p1 p2 p3) (Segment "" extrémités p1 p2) (Segment "" extrémités p2 p3) (Segment "" extrémités p1 p3)) (define (hasard) (- 8 (* 16 (random:uniform)))) (nouvelle-figure "Ma figure") (soit Point "A" libre (hasard) 0) (soit Point "B" libre 5 0) (soit Point "C" libre (hasard) 5) (triangle A B C) \end{verbatim} Cet exemple est particulièrement intéressant, il nous montre trois choses importantes~: \begin{enumerate} \item L'introduction de construction de plus haut niveau, non prévue au départ par \drgeo. Ici nous avons défini la fonction \texttt{triangle} qui, à partir de trois points, construit le triangle passant par ces trois points. Nous pouvons comparer ceci avec les macro-constructions mais avec un degré de liberté beaucoup plus important. \item La définition de fonctions associées, ici nous avons défini la fonction \texttt{hasard} qui retourne un nombre décimal compris entre -8 et 8. Nous utilisons cette fonction pour placer au hasard certains points de notre figure, ainsi à chaque ouverture la figure est légèrement différente. \item En fait l'utilisation du mot clé \texttt{soit} n'est pas obligatoire, nous l'utilisons lorsque nous souhaitons garder une référence de l'objet créé. Par exemple dans la fonction \texttt{triangle}, nous ne gardons pas de références des segments créés, en revanche lorsque nous définissons nos points $A$, $B$ et $C$ nous avons besoin de garder une référence, ces références ont le même nom\footnote{D'un point de vue interne au langage Scheme, ces références sont des symboles pointant vers une structure interne à l'objet -- un prototype -- alors que les noms sont des chaînes de caractères.} sans guillemet~: \texttt{A}, \texttt{B} et \texttt{C}. Dans la suite nous appellerons \textbf{symbole} ces références, c'est la terminologie exacte du langage Scheme. Ainsi, lors de l'appel de la fonction \texttt{triangle}, nous passons en paramètre les symboles \texttt{A}, \texttt{B} et \texttt{C} qui sont utilisés pour définir nos trois segments. \end{enumerate} Noter que lors de la définition des segments, nous ne donnons pas de nom, dans ce cas \drgeo\ va attribuer un nom par défaut défini à partir du nom des extrémités. Nos trois segments auront donc comme nom $[AB]$, $[BC]$ et $[AC]$. Pour clore cette section, voici un dernier exemple~: \begin{verbatim} (soit Point "A" libre 1 0) (soit Point "B" libre 5 0) (soit Droite "d1" 2points A B) (envoi A couleur jaune) (envoi A forme rond) (envoi A taille large) (envoi B masquer) (envoi d1 épaisseur tiret) \end{verbatim} Les trois premières commandes créent deux points et une droite. La partie qui nous intéresse plus particulièrement est la série de commande \texttt{envoi}. Cette commande permet de communiquer avec un objet dont nous avons gardé un symbole, ici nous avons les symboles \texttt{A}, \texttt{B} et \texttt{d1}. Elle consiste à envoyer un message à un objet, son premier argument est l'objet avec lequel nous communiquons, le deuxième argument le message, le troisième et les suivants sont déterminés par la nature du message. Par exemple \texttt{(envoi A couleur jaune)} envoie le message \texttt{couleur} avec comme paramètre \texttt{jaune}, le point A est peint en jaune. Il est assez facile de comprendre le sens des autres commandes \texttt{envoi}. Elles seront expliquées dans la section suivante. Nous avons terminé notre petite visite guidée des \emph{Figure Scheme Dr. Geo}. Dans les sections suivantes nous exposons l'ensemble des commandes disponibles pour définir des FSD. \subsection{Méthodes de référence pour les Figures Scheme \drgeo} La définition d'objets dans un document FSD se fait par l'intermédiare de prototypes. Les prototypes sont en quelque sorte des objets qu'il est possible d'interroger et de modifier comme nous le verrons par la suite. Cependant, avant toute définition d'objets d'une figure, cette dernière doit être créée avec la commande \texttt{nouvelle-figure}. \subsubsection{Commandes générales} \begin{drgeoApi}{(nouvelle-figure nom)} \drgeoApiIn{nom}{Chaîne de caractère} \drgeoApiOut{Ne retourne pas de valeur. L'appel ne produit qu'un effet de bord, à savoir la création d'une nouvelle figure, les objets suivants sont créés dans cette figure, jusqu'au prochain appel de ce type.} \drgeoApiExample{(nouvelle-figure "Ma 1er figure")} \end{drgeoApi} \subsubsection{Définition d'objets d'une figure} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{}{} Un objet peut être défini par l'intermédiaire de différentes syntaxes~: \begin{itemize} \item \texttt{(soit Point "p1" type args)} Le point est créé et sa référence est sauvée dans la variable \texttt{p1}. Cette syntaxe utilise une macro Scheme. \item \texttt{(Point "Nom" type args)} Le point est créé mais aucune référence du point n'est conservée. \item \texttt{(define p1 (Point "Nom" type args))} Le point est créé et sa référence est sauvée dans la variable \texttt{p1}. \item \texttt{(set! p1 (Point "Nom" type args))} Le point est créé et sa référence est copiée dans la variable préexistante \texttt{p1}. \end{itemize} Si des objets sont créés depuis le corps d'une fonction, utiliser soit la forme \texttt{set!} ou la forme spéciale Scheme \texttt{let}. Il est important de remarquer que l'appel de base est celui d'une fonction retournant une référence de l'objet créé. Pour en savoir plus sur la correspondance entre les noms de commande Scheme en français et en anglais, voir le fichier \texttt{/usr/share/drgeo/scm/drgeo\_scm\_interface\_constant\_fr.scm}. \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Point}{} \paragraph{Point} \T ~\\ \begin{drgeoApi}{prototype (Point nom libre x y)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{x}{L'abscisse du point} \drgeoApiIn{y}{L'ordonnée du point} \drgeoApiOut{Référence d'un point libre du plan de coordonnées initiales \texttt{x} et \texttt{y}.} \drgeoApiExample{(define p1 (Point "A" libre 1.2 (acos -1)))} \end{drgeoApi} \begin{drgeoApi}{prototype (Point nom sur-courbe ligne x)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{ligne}{Référence d'une ligne (droite, demi-droite, segment, etc.)} \drgeoApiIn{x}{Abscisse curviligne du point libre, la valeur appartient à l'intervalle [0~;~1]} \drgeoApiOut{Référence d'un point libre sur une ligne.} \drgeoApiExample{(Point "M" sur-courbe s1 0.5)} \end{drgeoApi} \begin{drgeoApi}{prototype (Point nom milieu-2pts p1 p2)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{p1}{Référence d'un point} \drgeoApiIn{p2}{Référence d'un point} \drgeoApiOut{Référence du milieu des deux points.} \drgeoApiExample{(soit Point "A" libre 1 1)\\ (soit Point "B" libre 4 4)\\ (Point "I" milieu-2pts A B)} \end{drgeoApi} \begin{drgeoApi}{prototype (Point nom milieu-segment s)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{s}{Référence d'un segment} \drgeoApiOut{Référence du milieu du segment.} \drgeoApiExample{(Point "L" milieu-segment s)} \end{drgeoApi} \begin{drgeoApi}{prototype (Point nom intersection l1 l2)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{l1}{Référence d'une ligne} \drgeoApiIn{l2}{Référence d'une ligne} \drgeoApiOut{Référence du point d'intersection des deux lignes.} \drgeoApiExample{(Point "I" intersection droite segment)} \end{drgeoApi} \begin{drgeoApi}{prototype (Point nom intersection2 l1 l2)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{l1}{Référence d'une ligne} \drgeoApiIn{l2}{Référence d'une ligne} \drgeoApiOut{Référence du 2ème point d'intersection des deux lignes lorsqu'une des deux est du type arc de cercle ou cercle.} \drgeoApiExample{(Point "I" intersection2 droite cercle)} \end{drgeoApi} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Droite}{} \paragraph{Droite} \T ~\\ \begin{drgeoApi}{prototype (Droite nom 2points p1 p2)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{l1}{Référence d'un point} \drgeoApiIn{l2}{Référence d'un point} \drgeoApiOut{Référence d'une droite passant par deux points.} \drgeoApiExample{(soit Point "A" libre 0 0)\\ (soit Point "M" libre 1 2)\\ (Droite "" 2points A M)} \end{drgeoApi} \begin{drgeoApi}{prototype (Droite nom parallèle p d)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{p}{Référence d'un point} \drgeoApiIn{d}{Référence d'une direction (droite, segment, vecteur, ...)} \drgeoApiOut{Référence d'une droite parallèle à la direction de \texttt{d} et passant par \texttt{p}.} \drgeoApiExample{(soit Point "A" libre 1 5)\\ (soit Droite "d1" parallèle A d)} \end{drgeoApi} \begin{drgeoApi}{prototype (Droite nom perpendiculaire p d)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{p}{Référence d'un point} \drgeoApiIn{d}{Référence d'une direction (droite, segment, vecteur, ...)} \drgeoApiOut{Référence d'une droite perpendiculaire à la direction de \texttt{d} et passant par \texttt{p}.} \drgeoApiExample{(soit Point "A" libre 1 5)\\ (soit Droite "d1" perpendiculaire A d)} \end{drgeoApi} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Demi-droite}{}\paragraph{Demi-droite} \T ~\\ \begin{drgeoApi}{prototype (Demi-droite nom 2points o p)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{o}{Référence d'un point, origine de la demi-droite} \drgeoApiIn{p}{Référence d'un point, point de la demi-droite} \drgeoApiOut{Référence d'une demi-droite définie par son origine et un point.} \drgeoApiExample{(soit Point "A" libre 1 5)\\ (soit Point "O" libre 0 0)\\ (soit Demi-droite "dd1" 2points A 0)} \end{drgeoApi} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Segment}{} \paragraph{Segment} \T ~\\ \begin{drgeoApi}{prototype (Segment nom extrémités p1 p2)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{p1}{Référence d'un point} \drgeoApiIn{p2}{Référence d'un point} \drgeoApiOut{Référence d'un segment défini par ses extrémités.} \drgeoApiExample{(soit Point "A" libre 1 5)\\ (soit Point "B" libre 10 4)\\ (soit Segment "" extrémités A B)} \end{drgeoApi} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Cercle}{} \paragraph{Cercle} \T ~\\ \begin{drgeoApi}{prototype (Cercle nom 2points c p)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{c}{Référence d'un point, centre du cercle} \drgeoApiIn{p}{Référence d'un point sur le cercle} \drgeoApiOut{Référence d'un cercle défini par son centre et un point.} \drgeoApiExample{(soit Point "A" libre 1 5)\\ (soit Point "B" libre 10 4)\\ (soit Cercle "C1" 2points A B)} \end{drgeoApi} \begin{drgeoApi}{prototype (Cercle nom centre-rayon c r)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{c}{Référence d'un point, centre du cercle} \drgeoApiIn{r}{Référence d'une valeur numérique, rayon du cercle} \drgeoApiOut{Référence d'un cercle défini par son centre et son rayon.} \drgeoApiExample{(soit Point "A" libre 1 5)\\ (soit Nombre "r" libre 10)\\ (soit Cercle "C1" centre-rayon A r)} \end{drgeoApi} \begin{drgeoApi}{prototype (Cercle nom centre-segment c s)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{c}{Référence d'un point, centre du cercle} \drgeoApiIn{s}{Référence d'un segment dont la longueur est le rayon du cercle} \drgeoApiOut{Référence d'un cercle défini par son centre et son rayon.} \drgeoApiExample{(soit Point "A" libre 1 5)\\ (soit Cercle "C1" centre-rayon A s)} \end{drgeoApi} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Arc de cercle}{} \paragraph{Arc de cercle} \T ~\\ \begin{drgeoApi}{prototype (Arc-cercle nom 3points p1 p2 p3)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{p1}{Référence d'un point, 1$^{ere}$ extrémité de l'arc} \drgeoApiIn{p2}{Référence d'un point de l'arc} \drgeoApiIn{p3}{Référence d'un point, 2$^{eme}$ extrémité de l'arc} \drgeoApiOut{Référence d'un arc de cercle défini par ses extrémités et un point.} \drgeoApiExample{(soit Point "A" libre 1 5)\\ (soit Point "B" libre 0 5)\\ (soit Point "C" libre -1 -2)\\ (soit Arc-cercle "arc" 3points A B C)} \end{drgeoApi} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Polygone}{} \paragraph{Polygone} \T ~\\ \begin{drgeoApi}{prototype (Polygone nom npoints args)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{args}{Une liste de références de points~; sommets du polygone} \drgeoApiOut{Référence d'un polygone défini pas ses sommets.} \drgeoApiExample{(soit Polygone "quad" npoints A B C D)} \end{drgeoApi} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Transformations géométriques}{} \drgeniusIndex{Transformation}{Figure Scheme de \drgeo{}}{}{} \paragraph{Les transformations géométriques} \T ~\\ Les prototypes des transformations géométriques permettent la construction des tranformés d'objets. Elles s'appliquent à des références d'objets de type point, segment, droite, demi-droite, vecteur, cercle, arc de cercle et polygone. \begin{drgeoApi}{prototype (TypeObjet nom rotation objet centre angle)} \drgeoApiIn{TypeObjet}{Point, Segment, Droite, Demi-droite, Vecteur, Cercle, Arc-cercle, Polygone} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{objet}{Référence de l'objet à transformer} \drgeoApiIn{centre}{Référence d'un point, centre de la rotation} \drgeoApiIn{angle}{Référence d'une valeur, angle de la rotation} \drgeoApiOut{Référence de l'objet transformé.} \drgeoApiExample{(soit Point "I1" rotation I C a)} \end{drgeoApi} \begin{drgeoApi}{prototype (TypeObjet nom homothétie objet centre k)} \drgeoApiIn{TypeObjet}{Point, Segment, Droite, Demi-droite, Vecteur, Cercle, Arc-cercle, Polygone} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{objet}{Référence de l'objet à transformer} \drgeoApiIn{centre}{Référence d'un point, centre de l'homothétie} \drgeoApiIn{k}{Référence d'une valeur, facteur de l'homothétie} \drgeoApiOut{Référence de l'objet transformé.} \drgeoApiExample{(soit Polygone "P1" homothétie P C k1)} \end{drgeoApi} \begin{drgeoApi}{prototype (TypeObjet nom symétrie objet centre)} \drgeoApiIn{TypeObjet}{Point, Segment, Droite, Demi-droite, Vecteur, Cercle, Arc-cercle, Polygone} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{objet}{Référence de l'objet à transformer} \drgeoApiIn{centre}{Référence d'un point, centre de la symétrie} \drgeoApiOut{Référence de l'objet transformé.} \drgeoApiExample{(soit Segment "S1" symétrie S C)} \end{drgeoApi} \begin{drgeoApi}{prototype (TypeObjet nom reflexion objet axe)} \drgeoApiIn{TypeObjet}{Point, Segment, Droite, Demi-droite, Vecteur, Cercle, Arc-cercle, Polygone} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{objet}{Référence de l'objet à transformer} \drgeoApiIn{axe}{Référence d'une droite, axe de la réflexion} \drgeoApiOut{Référence de l'objet transformé.} \drgeoApiExample{(soit Polygone "P1" reflexion P d1)} \end{drgeoApi} \begin{drgeoApi}{prototype (TypeObjet nom translation objet vecteur)} \drgeoApiIn{TypeObjet}{Point, Segment, Droite, Demi-droite, Vecteur, Cercle, Arc-cercle, Polygone} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{objet}{Référence de l'objet à transformer} \drgeoApiIn{vecteur}{Référence d'un vecteur} \drgeoApiOut{Référence de l'objet transformé.} \drgeoApiExample{(soit Cercle "C1" translation C v)} \end{drgeoApi} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Lieu}{} \paragraph{Lieu géométrique} \T ~\\ \begin{drgeoApi}{prototype (Lieu nom 2points m c)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{m}{Référence d'un point mobile sur une ligne} \drgeoApiIn{c}{Référence d'un point fixe dépendant du point \texttt{m}} \drgeoApiOut{Référence d'un lieu.} \drgeoApiExample{(Lieu "lieu1" 2points M I)} \end{drgeoApi} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Vecteur}{} \paragraph{Vecteur} \T ~\\ \begin{drgeoApi}{prototype (Vecteur nom 2points o e)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{o}{Référence d'un point, origine du vecteur} \drgeoApiIn{e}{Référence d'un point, extrémité du vecteur} \drgeoApiOut{Référence d'un vecteur.} \drgeoApiExample{(soit Point "B" libre 0 5)\\ (soit Point "C" libre -1 -2)\\ (Vecteur "" 2points C B)} \end{drgeoApi} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Nombre}{} \paragraph{Nombre} \T ~\\ \begin{drgeoApi}{prototype (Nombre nom libre x y v)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{x,y}{Les coordonnées de l'emplacement du nombre} \drgeoApiIn{v}{La valeur initiale du nombre} \drgeoApiOut{Référence d'un nombre libre.} \drgeoApiExample{(soit Nombre "pi" libre 5 5 (acos -1))} \end{drgeoApi} \begin{drgeoApi}{prototype (Nombre nom longueur-segment x y s)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{x,y}{Les coordonnées de l'emplacement du nombre} \drgeoApiIn{s}{Référence d'un segment} \drgeoApiOut{Référence d'un nombre, longueur d'un segment.} \drgeoApiExample{(soit Nombre "l" longueur-segment 5 5 S)} \end{drgeoApi} \begin{drgeoApi}{prototype (Nombre nom norme-vecteur x y v)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{x,y}{Les coordonnées de l'emplacement du nombre} \drgeoApiIn{s}{Référence d'un vecteur} \drgeoApiOut{Référence d'un nombre, norme d'un vecteur.} \drgeoApiExample{(soit Nombre "l" norme-vecteur 5 5 V)} \end{drgeoApi} \begin{drgeoApi}{prototype (Nombre nom point-cercle x y p c)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{x,y}{Les coordonnées de l'emplacement du nombre} \drgeoApiIn{p}{Référence d'un point} \drgeoApiIn{c}{Référence d'un cercle} \drgeoApiOut{Référence d'un nombre, distance entre le point et le cercle.} \drgeoApiExample{(soit Nombre "l" point-cercle 5 5 P C)} \end{drgeoApi} \begin{drgeoApi}{prototype (Nombre nom point-droite x y p d)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{x,y}{Les coordonnées de l'emplacement du nombre} \drgeoApiIn{p}{Référence d'un point} \drgeoApiIn{c}{Référence d'une droite} \drgeoApiOut{Référence d'un nombre, distance entre le point et la droite.} \drgeoApiExample{(soit Nombre "d" point-droite 5 5 M D1)} \end{drgeoApi} \begin{drgeoApi}{prototype (Nombre nom point-point x y p1 p2)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{x,y}{Les coordonnées de l'emplacement du nombre} \drgeoApiIn{p1}{Référence d'un point} \drgeoApiIn{p2}{Référence d'un point} \drgeoApiOut{Référence d'un nombre, distance entre les deux points.} \drgeoApiExample{(soit Nombre "d" point-point 5 5 A B)} \end{drgeoApi} \begin{drgeoApi}{prototype (Nombre nom longueur-cercle x y c)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{x,y}{Les coordonnées du nombre} \drgeoApiIn{c}{Référence d'un cercle} \drgeoApiOut{Référence d'un nombre, longueur d'un cercle.} \drgeoApiExample{(soit Nombre "p" longueur-cercle 5 5 C)} \end{drgeoApi} \begin{drgeoApi}{prototype (Nombre nom pente-droite x y d)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{x,y}{Les coordonnées du nombre} \drgeoApiIn{d}{Référence d'une droite} \drgeoApiOut{Référence d'un nombre, pente d'une droite.} \drgeoApiExample{(soit Nombre "p" pente-droite 5 5 d1)} \end{drgeoApi} \begin{drgeoApi}{prototype (Nombre nom longueur-arc x y arc)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{x,y}{Les coordonnées du nombre} \drgeoApiIn{arc}{Référence d'un arc de cercle} \drgeoApiOut{Référence d'un nombre, longueur d'un arc de cercle.} \drgeoApiExample{(soit Nombre "l" longueur-arc 5 5 ABC)} \end{drgeoApi} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Angle}{} \paragraph{Angle} \T ~\\ \begin{drgeoApi}{prototype (Angle nom géométrique A B C)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{A}{Référence d'un point} \drgeoApiIn{B}{Référence d'un point, sommet de l'angle} \drgeoApiIn{C}{Référence d'un point} \drgeoApiOut{Référence d'un angle géométrique.} \drgeoApiExample{(soit Angle "a" géométrique A B C)} \end{drgeoApi} \begin{drgeoApi}{prototype (Angle nom orienté x y v1 v2)} \drgeoApiIn{nom}{Chaîne de caractère désignant le nom de l'objet} \drgeoApiIn{x,y}{Les coordonnées de l'emplacement de l'angle} \drgeoApiIn{v1}{Référence d'un vecteur} \drgeoApiIn{v2}{Référence d'un vecteur} \drgeoApiOut{Référence d'un angle orienté formé par les deux vecteurs.} \drgeoApiExample{(define v1 (Vecteur "" 2points A B))\\ (define v2 (Vecteur "" 2points A C))\\ (Angle "a" orienté 1 1 v1 v2)} \end{drgeoApi} \subsubsection{Modification d'attributs d'objets} \drgeniusIndex{Figure Scheme de \drgeo{}}{Création d'objets}{Attributs des objets}{} Pour modifier les attributs d'un objet déjà créé, nous utilisons un système de messages envoyés directement au prototype représentant l'objet en question. La modification des attributs se fait donc toujours à posteriori. \begin{drgeoApi}{(envoi objet couleur valeur)} \drgeoApiIn{objet}{Référence d'un objet} \drgeoApiIn{valeur}{La couleur, les valeurs possibles sont \texttt{noir, gris-noir, gris, blanc, vert-noir, vert, bleu-noir, bleu, rouge, bordeaux, jaune, orange}} \drgeoApiExample{(soit Point "A" libre 1 2)\\ (envoi A couleur vert)} \end{drgeoApi} \begin{drgeoApi}{(envoi ligne épaisseur valeur)} \drgeoApiIn{ligne}{Référence d'une ligne (droite, demi-droite, cercle, lieu, etc.)} \drgeoApiIn{valeur}{L'épaisseur, les valeurs possibles sont \texttt{tiret, normal, large}} \drgeoApiExample{(soit Point "A" libre 1 2)\\ (soit Point "O" libre 0 0)\\ (soit Droite "d" 2points A B)\\ (envoi d épaisseur tiret)} \end{drgeoApi} \begin{drgeoApi}{(envoi point taille valeur)} \drgeoApiIn{point}{Référence d'un point} \drgeoApiIn{valeur}{La taille du point, les valeurs possibles sont \texttt{petit, normal, large}} \drgeoApiExample{(soit Point "A" libre 1 2)\\ (envoi A taille petit)} \end{drgeoApi} \begin{drgeoApi}{(envoi point forme valeur)} \drgeoApiIn{point}{Référence d'un point} \drgeoApiIn{valeur}{La forme du point, les valeurs possibles sont \texttt{rond, croix, rond-vide, rec, rec-vide}} \drgeoApiExample{(soit Point "A" libre 1 2)\\ (envoi A forme rond)} \end{drgeoApi} \begin{drgeoApi}{(envoi objet masquer)} \drgeoApiIn{objet}{Référence d'un objet à masquer} \drgeoApiExample{(soit Point "A" libre 1 2)\\ (envoi A masquer)} \end{drgeoApi} \subsection{Galerie d'exemples} \drgeniusIndex{Figure Scheme de \drgeo{}}{Exemples}{}{} Pour illustrer l'utilisation des Figures Scheme \drgeo, nous vous proposons une petite série d'exemples. Ceux-ci vous montrent leurs importantes possibilités et nous espérons qu'ils seront également une source d'inspiration. Pour chacun de ces exemples, nous donnons le code source Scheme de la figure puis son résultat. Le code source peut être copié dans un éditeur de texte puis sauvegardé dans un fichier d'extension \textbf{.scm} pour l'évaluer avec \drgeo. \subsubsection{Polygone régulier} \drgeniusIndex{Figure Scheme de \drgeo{}}{Exemples}{Polygone régulier}{} Construire un polygone régulier, avec un nombre de cotés arbitraire, peut se faire par l'intermédiaire d'une fonction récursive Scheme. \begin{verbatim} (define pi (acos -1)) (define n 15) (define x0 0) (define y0 0) (define p1 0) (define (polygon center p a n) (if (> n 0) (begin (set! p1 (Point "" rotation p center a)) (send p1 masked) (Segment "" extremities p p1) (polygon center p1 a (- n 1))))) (new-figure "Regular Polygon!") (lets Point "C" free x0 y0) (lets Numeric "a" free 0 0 (* 2 (/ pi n))) (send a masked) (set! p1 (Point "I" free 5 0)) (lets Segment "S" extremities C p1) (Segment "" rotation S C a) (polygon C p1 a n) \end{verbatim} \drgeniusFigureSize{Un polygone régulier à 15 côtés}{fig59}{6} \subsubsection{Fractal} \drgeniusIndex{Figure Scheme de \drgeo{}}{Exemples}{Fractal}{} La construction d'une courbe fractale de la forme d'un arbre se fait très aisément avec une figure Scheme. Le code source de la figure est étonnement compact, surtout comparé à une construction ``à la main'' depuis l'interface graphique. \begin{verbatim} (new-figure "Baum") (lets Numeric "A1" free 2 2 +3.4) (lets Numeric "A2" free 2 3 -3.7) (lets Numeric "S1" free 2 4 +0.5) (lets Numeric "S2" free 2 5 +0.9) (define (dec n) (- n 1)) (define (inc n) (+ n 1)) (define (invisible p) (send p masked) p) (define (scalerot oP C a s) (let* ((sP (invisible (Point "" scale oP C s))) (rP (invisible (Point "" rotation sP C a))) ) rP)) (define (Zweig p0 p1 n) (Segment "" extremities p0 p1) (let* ((left-scale (if (odd? n) S1 S2)) (left-angle A1) (right-scale (if (odd? n) S2 S1)) (right-angle A2) ) (if (> n 0) (begin (Zweig p1 (scalerot p0 p1 left-angle left-scale) (dec n)) (Zweig p1 (scalerot p0 p1 right-angle right-scale) (dec n)))))) (lets Point "A" free -3 0) (lets Point "B" free -3 2) (Zweig A B 6) \end{verbatim} \drgeniusFigureSize{Une courbe fractale simulant la représentation d'un arbre}{fig60}{8} \section{Masquer des outils dans l'interface} \label{ui-lock} \drgeo\ offre la possibilité de préparer des sessions\footnote{Fichiers comprenant plusieurs documents \drgeo\ (i.e. figure, macro, texte)} dans lesquelles l'enseignant peut décider, pour certaines figures, de bloquer l'accès à certains outils. Le verrouillage se fait à la figure près avec un mot de passe différent à chaque fois. Cela donne toute la latitude à l'enseignant de préparer une activité avec différentes figures et autant de degrés de verrouillage. \subsection{Verrouiller des outils} \drgeniusIndex{Outils}{Verrouiller}{}{} Le verrouillage se fait à la figure près, aussi depuis l'une d'entre elles, aller au menu \drgeniusMenu{Édition->Adapter l'Interface}. Une grande boîte de dialogue s'affiche, dans celle-ci l'utilisateur reconnaît les icônes utilisées dans la barre d'icônes de \drgeo. Il peut en cliquant sur ces icônes, les désactiver ou activer. Lorsque un outil est désactivé, son icône représentative apparaît légèrement grisée. Il est également possible de désactiver toute une rangée d'outils en cliquant sur l'icône de haut niveau (i.e. celle avec un petit triangle vert). \drgeniusFigureSize{La boîte dialogue pour verrouiller des outils.}{fig53}{8} Lorsque l'utilisateur a fini sa sélection d'outils à verrouiller, il procède au verrouillage à proprement parler en cliquant sur le bouton \drgeniusMenu{Verrouiller} dans la boîte de dialogue, \drgeo\ demande alors un mot de passe. \drgeniusNote{Lors de la sauvegarde d'une figure ou d'une session avec des verrouillages de l'interface, les mots de passe sont également sauvegardés dans le fichier sous une forme cryptée.} \subsection{Déverrouiller des outils} \drgeniusIndex{Outils}{Déverrouiller}{}{} Il est bien sûr possible de déverrouiller une interface, que cela soit pour donner progressivement accès à des outils --~lors d'un travail d'élèves sur une session~-- ou pour retravailler une figure. Pour cela, il faut aller dans le menu \drgeniusMenu{Édition->Adapter l'Interface} et choisir dans la boîte de dialogue le bouton \drgeniusMenu{Déverrouiller}. \drgeo\ demande alors le mot de passe entré précédemment. \drgeniusFigure{La boîte de dialogue pour déverrouiller l'interface d'une figure.}{fig54} \chapter{Fichiers et documents} Les constructions peuvent être enregistrées de deux manières. Une construction par fichier ou un ensemble de constructions par fichier (i.e. une session \drgeo). Nous vous rappelons que les documents contenant des figures doivent être sauvegardés avec une extension \textbf{.fgeo} et ceux contenant uniquement des macro-constructions avec l'extension \textbf{.mgeo}. Pour les documents contenant des figures, macro-constructions et des textes d'explications, utiliser l'extension \textbf{.fgeo}. Ceci n'est qu'indicatif mais suivre ces règles permet de s'y retrouver plus facilement parmi les fichiers. \section{Enregistrement d'une construction} \drgeniusIndex{Figure}{Enregistrer}{}{} À partir du menu \drgeniusMenu{Fichier->Enregistrer} ou \drgeniusMenu{Fichier->Enregistrer sous...}, un fichier contenant la figure de la vue active peut être enregistré. \drgeniusNote{\drgeo\ peut travailler avec plusieurs figures en même temps. L'utilisateur peut passer d'une figure à l'autre en cliquant sur l'onglet correspondant.} Avec le second menu, l'utilisateur peut changer le nom du document enregistré. \drgeniusNote{Le nom de fichier par défaut proposé peut être changé à partir du menu \drgeniusMenu{Édition->Préférences...}. Pour plus d'information, voir la \link{section comportement par défaut}[ Section \Ref, page \Pageref]{default_behaviour}.} \section{Enregistrement d'une session} \drgeniusIndex{Macro-construction}{Enregistrer}{}{} \drgeniusIndex{Session}{Enregistrer}{}{} Une session est un ensemble de données de \drgeo\ que l'utilisateur veut enregistrer d'un seul coup dans un fichier. Cela permet à l'enseignant d'organiser un ensemble de données (figures, macro-constructions, notes) dans un seul fichier, de façon à faciliter leur exploitation. À partir du menu \drgeniusMenu{Fichier->Enregistrement multiple}, l'utilisateur peut ouvrir la boîte de dialogue de session. \drgeniusFigureSize{La boîte dialogue de session \drgenius}{fig51}{8} Dans cette boîte de dialogue, la liste de toutes les données actives est présentée dans un tableau. La première colonne liste les types des données contenues dans \drgeo, la seconde les noms des données. \drgeniusNote{Actuellement, une session peut contenir trois types de données~: figure interactive 2D, macro-construction et texte.} L'utilisateur peut décider de sélectionner une par une les données à enregistrer dans la liste puis appuyer sur le bouton \drgeniusMenu{Enregistrer la sélection}. Autrement, il peut enregistrer toutes les données en appuyant sur le bouton \drgeniusMenu{Enregistrer tout}. \drgeniusNote{Le menu \drgeniusMenu{Fichier->Enregistrement multiple} est le seul moyen d'enregistrer une macro-construction dans un fichier.} \section{Enregistrer une macro-construction} \drgeniusIndex{Macro-construction}{Enregistrer}{}{} Pour enregistrer une ou des macro-constructions dans un fichier, il faut procéder comme pour enregistrer une session -- enregistrement multiple. Depuis la boîte de dialogue de sauvegarde d'une session, sélectionner la ou les macro-constructions à sauvegarder, puis sauver dans un fichier d'extension \textbf{.mgeo}. C'est tout~! Il est ainsi possible de vous composer des librairies de macro-contructions, une par fichier ou plusieurs regroupées selon un même thème dans un seul fichier. \section{Ouvrir un fichier} \drgeniusIndex{Macro-construction}{Ouvrir}{}{} \drgeniusIndex{Session}{Ouvrir}{}{} \drgeniusIndex{Figure}{Ouvrir}{}{} Que l'utilisateur ait sauvegardé une seule figure ou une session avec différents types de documents, la procédure pour l'ouverture est la même par le menu \drgeniusMenu{Fichier->Ouvrir}. Si la session ouverte contient des macro-constructions, celles-ci sont directement disponibles depuis l'outil permettant l'exécution des macro-constructions. Les macro-constructions sont disponibles depuis toutes les figures ouvertes. \section{Exporter une figure} \drgeo\ offre la possibilité d'exporter une figure géométrique vers un document \LaTeX\ ou PostScript. Ces deux formats d'exportation sont de type vectoriel contrairement à des images en plan de bits qui sont de qualité moindre pour une impression. Les commandes d'exportation sont accessibles depuis le sous-menu \drgeniusMenu{Figure->Exporter sous...} \subsection{Exportation \LaTeX} \drgeniusIndex{Figure}{Exporter}{\LaTeX}{} Dans cas d'une exportation vers \LaTeX, le document exporté nécessite le paquet \texttt{pstricks}. Celui-ci est en général distribué avec \LaTeX. Typiquement un document exporté en \LaTeX\ pourra être intégré dans un autre document \LaTeX\ ou même directement compilé~: \begin{verbatim} latex figure.tex dvips figure.dvi \end{verbatim} Cette suite de commandes permet d'obtenir le document figure.ps qui peut être ouvert avec le logiciel GhostView\footnote{GhostView est un logiciel qui permet de visualiser des documents PostScript (.ps ou .eps) ainsi que des documents PDF} \texttt{gv}. \subsection{Exportation PostScript} \label{exporter-ps} \drgeniusIndex{Figure}{Exporter}{PostScript}{} L'exportation au format PostScript -- extension \texttt{eps} pour \emph{Encapsulated PostScript}-- offre l'avantage d'être plus facilement utilisable depuis divers logiciels\footnote{Ce format est reconnu par TeXmacs, OpenOffice.org, Lyx, \LaTeX\, Xfig, The Gimp et bien d'autres encore}. En fait le format \textsc{eps} est plus ou moins un standard de fait en ce qui concerne les images vectorielles. Pour visualiser rapidement ce type d'image, nous utilisons le logiciel GhostView, sa commande est \texttt{gv}. \subsection{Exportation image \textsc{png}} \drgeniusIndex{Figure}{Exporter}{Image PNG}{} Certains logiciels comme OpenOffice.org n'exploitent que partiellement le format \textsc{eps}\footnote{OpenOffice.org permet d'intégrer une image \textsc{eps} mais pas de l'afficher. C'est uniquement à l'impression que celle-ci apparaît.}. Aussi une exportation au format image \textsc{png} est également possible. L'image exportée sous ce format est en haute définition avec le fond de la figure encodé en zone transparente. Depuis un traitement de texte, cela peut permettre de faire un détourage de texte autour de la figure. \subsection{Exportation Fly Draw} \drgeniusIndex{Figure}{Exporter}{Fly Draw/WIMS}{} Le serveur d'exercices WIMS développé par Dr. Xiao Gang à l'université de Nice dispose d'un format de description des figures appelé Fly Draw. \drgeo\ propose également une exportation vers ce format. \subsection{Définir la zone exporter} \drgeniusIndex{Figure}{Exporter}{Définir la zone d'exportation}{} Par défaut, \drgeo\ exporte la zone visible de la figure. Ainsi si nous souhaitons exporter une zone précise de la figure, nous pouvons redimensionner la fenêtre de \drgeo\ jusqu'à obtenir la zone voulue\footnote{Éventuellement, le panneau latéral de l'arbre logique de la figure peut être déplié pour réduire davantage la zone d'exportation.}. Cependant cette solution, si elle rapide et simple, n'est pas toujours suffisamment souple, de plus la zone d'exportation n'est pas enregistrée avec la figure. Une autre façon est donc d'utiliser la commande \drgeniusMenu{Définir la zone d'exportation} accessible depuis le menu \drgeniusMenu{Fichier->Préférences d'exportation}. La commande activée, nous pouvons définir dans la figure un rectangle correspondant à la zone exportée. Cette zone peut être redéfinie autant de fois que nécessaire. Elle est représentée par un rectangle gris clair. Lorsque la figure est sauvegardée cette zone l'est également. Enfin elle peut être supprimée par la commande \drgeniusMenu{Supprimer la zone d'exportation}. \drgeniusFigureSize{Une figure avec une zone d'exportation définie}{fig56}{7} \drgeniusFigureSize{La zone d'exportation a été exportée dans un document PostScript, il est visualisé avec GhostView}{fig57}{7} \chapter{Applications didactiques} Ce chapitre est une aide pour l'utilisateur souhaitant étudier \drgeo{} à partir d'exemples. Contrairement aux chapitres précédents, l'approche est plus concrète par rapport à des situations précises. Le contenu de ce chapitre s'est constitué lors de diverses activités pédagogiques. \section{Pythagore et scripts} Une des possibilités d'utilisation didactique de \drgeo{} consiste dans l'utilisation des \link{scripts Scheme}[ Section \Ref, page \Pageref]{script} pour résoudre des exercices de géométrie. Comme exemple, nous allons montrer la solution d'un problème classique mettant en oeuvre le théorème de Pythagore dont le texte est le suivant~: \begin{quote} \em Soit un trapèze rectangle $ABCD$ où sont connues les bases et la hauteur. Calculer le périmètre et l'aire du trapèze. \end{quote} Il n'est pas difficile, si vous suivez le même modèle, de développer d'autres exemples similaires. \textbf{Solution~:} Commençons par construire la figure dans \drgeo{} qui doit être comme ci-dessous~: \drgeniusFigureSize{Trapèze rectangle}{dafig1}{8} La figure comprend les données à partir des quelles nous pouvons résoudre le problème. D'abord nous pouvons répondre à la première question de l'aire, pour cela nous pouvons écrire le script Scheme suivant ayant comme entrée les deux bases et la hauteur du trapèze~: \drgeniusIndex{Script}{Exemples}{Aire d'un trapèze}{} \begin{quote}{\begin{verbatim} define AB (getLength a1)) (define DC (getLength a2)) (define AD (getLength a3)) (/ ( * AD (+ AB DC )) 2 ) \end{verbatim} } \end{quote} \drgeniusIndex{Script}{Exemples}{Différence de longueur de segments}{} Nous calculons la longueur du segment $BH$ en écrivant un script Scheme avec comme objet en entrée les segments $AB$ et $CD$, et le texte du script est le suivant~: \begin{quote}{\begin{verbatim} (define AB (getLength a1)) (define CD (getLength a2)) (- AB CD) \end{verbatim} } \end{quote} \drgeniusIndex{Script}{Exemples}{Théorème de Pythagore}{} À ce stade, nous pouvons appliquer le théorème de Pythagore dans le triangle rectangle $CHB$. Ici aussi nous utilisons un script Scheme avec comme objets en entrée le segment $CH$ et le script $BH$~: \begin{quote} { \begin{verbatim} (define CH (getLength a1)) (define BH (getValue a2)) (+ (* CH CH) (* BH BH)) \end{verbatim} } \end{quote} \drgeniusIndex{Script}{Exemples}{Racine carrée}{} Finalement nous pouvons obtenir la valeur du segment $BC$ en calculant la racine carrée de la valeur retournée par le script précédent~: \begin{quote} { \begin{verbatim} (define q (getValue a1)) ( sqrt q ) \end{verbatim} } \end{quote} Les deux scripts précédents peuvent être regroupés en un seul script un peu plus élaboré. \drgeniusIndex{Script}{Exemples}{Périmètre}{} Maintenant nous pouvons conclure l'exercice en calculant le périmètre avec un script Scheme~: \begin{quote} { \begin{verbatim} (define AB (getLength a1)) (define CB (getValue a2)) (define DC (getLength a3)) (define AD (getLength a4)) (+ (+ AB CB )(+ DC AD )) \end{verbatim} } \end{quote} \section{Théorème et conjectures} Les \link{scripts Scheme}[ Section \Ref, page \Pageref]{script} permettent de résoudre des exercices mais aussi de comprendre de façon plus approfondie l'énonciation des théorèmes et de vérifier des conjectures. Dans cette section nous commençons par analyser le théorème de Tolomeo~: \begin{quote} \em Étant donné un quadrilatère inscrit dans un cercle la somme du produit des côtés opposés est égale au produit des diagonales. \end{quote} Nous pouvons construire la figure avec \drgeo{} comme ci-dessous~: \drgeniusFigureSize{Théorème de Tolomeo: quadrilatère convexe}{dafig2}{8} où nous avons implémenté deux scripts qui calculent respectivement la somme du produit des côtés opposés et le produit des diagonales. \drgeniusIndex{Script}{Exemples}{Théorème de Tolomeo}{} Le premier script est le suivant~: \begin{quote} { \begin{verbatim} (define AB (getLength a1)) (define DC (getLength a2)) (define BC (getLength a3)) (define AD (getLength a4)) (+ (* AB DC )(* BC AD )) \end{verbatim} } \end{quote} Le second script est~: \begin{quote} { \begin{verbatim} (define DB (getLength a1)) (define AC (getLength a2)) (* DB AC ) \end{verbatim} } \end{quote} Comme nous pouvons le voir les valeurs retournées par les deux scripts, en accord avec le théorème de Tolomeo, sont les mêmes\footnote{Il ne s'agit que d'une vérification numérique.}. Lorsque nous modifions dynamiquement la figure, les valeurs des scripts sont toujours identiques, sauf dans la situation suivante~: \drgeniusFigureSize{Théorème de Tolomeo: quadrilatère non convexe}{dafig3}{8} où la quadrilatère perd sa convexité. Dans ce cas le théorème n'est pas vrai et l'énoncé précédent n'est pas bien énoncé, il doit donc être reformulé comme ci-dessous~: \begin{quote} \em Étant donné un quadrilatère CONVEXE inscrit dans un cercle la somme du produit des côtés opposés est égale au produit des diagonales. \end{quote} À ce stade les conjectures apparaîssent naturellement~: est-ce que le théorème de Tolomeo est valide pour un quadrilatère convexe non inscrit dans un cercle~? Avec \drgeo{} nous pouvons vérifier que cette conjecture est fausse comme le montre la figure suivante~: \drgeniusFigureSize{Réfutation de la conjecture}{dafig4}{8} Le lecteur n'aura pas de difficulté à utiliser \drgeo{} dans la construction d'exemples didactiques, probablement plus connu, relativement aux théorèmes de Pythagore et d'Euclide. \section{Nombre irrationnel} \drgeniusIndex{Figure Scheme de \drgeo{}}{Exemples}{Spirale de Teodoro}{} Une construction classique, relative au nombre irrationnel, connue sous le nom de spirale de Teodoro, permet de construire géométriquement la racine carrée de nombres entiers à partir d'un triangle rectangle isocèle. Considérons le triangle $OAB$ où $OA=1$~: \drgeniusFigureSize{Construction de la racine de 2}{dafig7}{8} Par le théorème de Pythagore nous avons $OB$ égale à la racine carrée de 2. Si maintenant, avec la figure, nous construisons un nouveau triangle rectangle en $B$, avec les côtés $OB$ et $BC$ tel que $BC=1$. \drgeniusFigureSize{Construction de la racine 3}{dafig8}{8} toujours par le théorème de Pythagore, il est clair que l'hypothénuse $OC$ de $OBC$ a pour longueur la racine carrée de 3. En itérant le processus précédent à l'infini nous obtenons toutes les racines carrées des nombres naturels. La nature itérative de la construction s'adapte parfaitement à l'utilisation des FSD. Considérons alors le code suivant~: \begin{quote} { \begin{verbatim} (new-figure "Triangle") (define (triangle p1 p2 p3 n) (let* ((s1 (Segment "" extremities p1 p2)) (s2 (Segment "" extremities p2 p3)) (s3 (Segment "" extremities p3 p1)) (pe (Line "" orthogonal p3 s3)) (ci (Circle "" center-segment p3 s2)) (p4 (Point "" intersection2 pe ci))) (send pe masked) (send ci masked) (send p4 masked) (if (> n 0) (triangle p1 p3 p4 (- n 1))))) (lets Point "O" free 0 0) (lets Point "A" free -1 0) (lets Point "B" free -1 1) (triangle O A B 15) \end{verbatim} } \end{quote} Le triangle du début est défini à travers les coordonnées seulement par commodité. Le code est la transcription littérale de la procédure itérative décrite précédement. Une fois évalué par \drgeo{} le code donne la figure suivante~: \drgeniusFigureSize{Spirale de Teodoro}{dafig9}{8} Les hypothénuses de chaque triangle ont pour longueur les racines carrées des nombres entiers naturels compris entre 2 et 17. \section{Spirale de Baravelle} \drgeniusIndex{Figure Scheme de \drgeo{}}{Exemples}{Spirale de Baravelle}{} Comme nous l'avons vu précédement, à l'aide de FSD il est possible de construire de façon intuitive et simple des figures permettant de \emph{visionner} des situations qui en programmation sont récursives -- ou cycliques. Nous pouvons un peu approfondir cet aspect, en modifiant le code Scheme utilisé pour la construction des nombres irrationnels, afin d'obtenir une figure fameuse de la littérature des mathématiques, à savoir la spirale de Baravelle. Le code Scheme définissant la spirale est le suivant~: \begin{quote} \begin{verbatim} (new-figure "Baravelle") (define (triangle p1 p2 p3 n) (let* ((s1 (Segment "" extremities p1 p2)) (s2 (Segment "" extremities p2 p3)) (s3 (Segment "" extremities p3 p1)) (m (Point "" middle-2pts p1 p3)) (r (Segment "" extremities m p3)) (pe (Line "" orthogonal p3 s3)) (ci (Circle "" center-segment p3 r )) (p4 (Point "" intersection2 pe ci))) (send pe masked) (send ci masked) (send p4 masked) (send m masked) (if (> n 0) (triangle m p3 p4 (- n 1))))) (lets Point "A" free 0 5) (lets Point "B" free 5 5) (lets Point "C" free 5 0) (triangle A B C 9) (lets Point "D" free 0 -5) (lets Point "E" free -5 -5) (lets Point "F" free -5 0) (triangle D E F 9) \end{verbatim} \end{quote} \drgeniusFigureSize{La spirale de Baravelle suite à l'évaluation du code Scheme}{dafig10}{8} À partir de la figure et du code Scheme correspondant nous percevons bien la nature itérative du mécanisme de construction de la figure. Un problème intéressant que nous laissons au lecteur, consiste à établir quand est-ce que les deux rameaux de la spirale convergent. Une petite variation supplémentaire du code précédent~: \begin{quote} \begin{verbatim} (new-figure "Spirale") (define (square p1 p2 p3 p4 n) (let* ((s1 (Segment "" extremities p1 p2)) (s2 (Segment "" extremities p2 p3)) (s3 (Segment "" extremities p3 p4)) (s4 (Segment "" extremities p4 p1)) (A (Point "" on-curve s1 1/10)) (B (Point "" on-curve s2 1/10)) (C (Point "" on-curve s3 1/10)) (D (Point "" on-curve s4 1/10))) (send A masked) (send B masked) (send C masked) (send D masked) (if (> n 0) (square A B C D (- n 1))))) (lets Point "M" free 5 5) (lets Point "N" free -5 5) (lets Point "O" free -5 -5) (lets Point "P" free 5 -5) (square M N O P 30) \end{verbatim} \end{quote} conduit à une spirale simplifiée. \drgeniusFigureSize{Spirale simplifiée}{dafig11}{8} Le lecteur est invité à se divertir en créant de nouvelles variations~! \T \clearpage \section{Catena di Pappo} \drgeniusIndex{Figure Scheme de \drgeo{}}{Exemples}{Catena di Pappo}{} Une utilisation de base de Figure Scheme de \drgeo\ consiste en la reproduction de figure dont nous connaissons les caractéristiques analytiques. L'exemple de construction que nous proposons est représenté par la fameuse ''Catena di Pappo''. \drgeniusFigureSize{Catena di Pappo}{dafig12}{8} Les centres et rayons successifs des cercles qui la constituent ont une expression analytique connue, il est donc aisé de reproduire la figure en tant de FSD. \begin{quote} \begin{verbatim} (new-figure "Pappo") (define (circle n) (let*( (r (Numeric "" free 0 0 (/ 15 ( + 6 (* n n ))))) (c (Point "" free (* 5 (/ 15 ( + 6 (* n n )))) (* 2 (* n (/ 15 ( + 6 (* n n ))))))) (p (Circle "" center-radius c r ))) (send r masked) (if (> n 0) (circle (- n 1))))) (circle 8) (lets Point "A" free 5 0) (lets Point "O" free 0 0) (lets Point "B" free 15 0) (lets Point "M" middle-2pts B O) (lets Circle "" 2points M O) (lets Circle "" 2points A O) (lets Line "" 2points A O) \end{verbatim} \end{quote} le code de la figure est relativement intuitif et ne nécessite pas de commentaire. Un exercice non trivial, que nous laissons au lecteur, consiste à déterminer une construction à la règle et au compas conduisant à une implémentation itérative. \section{Calcul de $\pi$} Le calcul approximatif de $\pi$ a joué un rôle important dans l'histoire des Mathématiques. Les méthodes pour ce type de calcul sont diverses et contiennent souvent des améliorations d'une méthode à l'autre. Nous vous proposons une approche du problème très simplifiée que nous appelons -- même si ce n'est pas tout à fait exacte -- \textbf{Méthode par exhaustion}. Cette approche a toutefois l'avantage de montrer l'essence même de la méthodologie. Nous commençons avec la construction suivante d'un hexagone inscrit dans une cercle à partir du côté $BC$. Nous notons au passage qu'il est possible à partir de cette construction de construire et mémoriser une macro que nous pouvons nommer \textit{Hexagone}. \drgeniusFigureSize{Hexagone régulier inscrit}{dafig5}{8} l'idée de la méthode par exhaustion consiste dans un premier temps à approximer la longueur du cercle avec le périmètre $P_{0}$ de l'hexagone et de calculer une approximation de $\pi$ dividende de $P_{0}$ par le diamètre du cercle. Clairement l'approximation de $\pi$ obtenue sera de 3. Lors d'une deuxième étape nous pouvons, en utilisant \drgeo, construire un côté du dodécagone inscrit dans le cercle. Nous calculons son périmètre $P_{1}$ ainsi qu'une approximation successive de $\pi$ comme dividende de $P_{1}$ par le diamètre. \drgeniusFigureSize{Approximation de $\pi$}{dafig6}{8} En augmentant le nombre de côtés du polygone régulier inscrit nous obtenons de meilleures approximations. \chapter{Astuces diverses} \section{Créer un polygone régulier} \label{polygon_macro} \drgeniusIndex{Macro-construction}{Polygone}{}{} \drgeniusIndex{Polygone}{Macro-construction}{}{} \drgeniusIndex{Macro-construction}{Script}{}{} \drgeo\ peut créer des macro-constructions comportant des éléments de construction indépendants (i.e. des points libres, des valeurs libres, des scripts sans parent). Pour ce faire \drgeo\ prend l'initiative de donner une ou des valeurs aux paramètres libres de ces objets\footnote{Sinon, la macro-construction ne pourrait pas être instanciée. Par exemple quelle valeur donner à un objet de type valeur libre intervenant dans la séquence de construction~?}. La ou les valeur(s) choisie(s) sont en fait celle(s) de l'objet servant de modèle lors de la création de la macro. Dans la suite, un petit exemple permettant de créer des polygones réguliers à $n$ côtés est présenté. En plus des macro-constructions, un script Scheme intervient dans le processus. L'exemple est guidé pas à pas mais le lecteur non familier avec les macro-constructions, les scripts ou plus généralement le fonctionnement de \drgeo\ est fortement invité à lire les sections précédentes. \subsection{Le modèle de polygone} Pour commencer, créer un point libre, puis un script sans parent -- après avoir choisi l'outil script cliquer directement sur le fond de la figure. Éditer le script et lui donner comme valeur~: \begin{verbatim} (/ (* 2 (acos -1)) 7) \end{verbatim} Le résultat de ce script servira pour construire par rotation un polygone régulier à 7 côtés. Placer ensuite une valeur libre de valeur 2, ce sera le rayon de notre polygone. Construire un cercle de centre le point et de rayon la valeur. Sur ce cercle placer un point. Nommer ce point $O$. Maintenant utiliser l'outil rotation pour créer l'image de O par la rotation d'angle la valeur du script et de centre le centre du cercle. Continuer ensuite successivement jusqu'à obtenir les 7 sommets du polygone. Relier les sommets par des segments. \drgeniusFigureSize{Résultat de la construction du polygone régulier à 7 côtés}{fig61}{8} \subsection{La macro-construction du polygone} Ouvrir la boîte de dialogue de création de macro-construction et construire comme suit la macro~: \begin{enumerate} \item \textbf{paramètre d'entrée~:} le centre du cercle~; \item \textbf{paramètres de sortie~:} le point $O$ et les 7 côtés du polygone. \end{enumerate} Voilà, la macro est prête. Pour créer un polygone régulier à 7 côtés, ouvrir la boîte de dialogue d'exécution d'une macro, il suffit de sélectionner un point de la figure. \subsection{Quelques considérations} Lorsque \drgeo\ rencontre des éléments libres dans une macro-construction, il fixe leur valeur en prenant celle du modèle. Dans notre exemple, le script, la valeur et le point O sont de tels éléments libres. Lorsque la macro-construction est exécutée, ils sont fixés comme suit~: \begin{itemize} \item la valeur à 2~; \item le script à \texttt{(/ (* 2 (acos -1)) 7)}~; \item le point sur le cercle avec la même abscisse curviligne que $O$. \end{itemize} C'est ce dernier point qui donne tout son sens à l'utilisation conjointe des macro-constructions avec des scripts ou d'autres objets libres. \section{Imprimer une figure} \drgeniusIndex{Figure}{Imprimer}{}{} \drgeniusIndex{Imprimer}{Figure}{}{} Le plus simple est d'exporter la figure au format PostScript -- \link{Exportation PostScript}[ Section \Ref, page \Pageref]{exporter-ps}. Utiliser ensuite un logiciel permettant de visionner des documents PostScript et imprimer le document. Le document imprimé de la sorte est de qualité vectorielle. Les logiciels GhostView, Gnome GhostView ou encore K GhostView conviennent parfaitement. \section{Placer un paragraphe de texte dans une figure} \drgeniusIndex{Afficher}{Texte}{}{} \drgeniusIndex{Figure}{Afficher}{Texte}{} On peut avantageusement utiliser les scripts, d'une façon certes détournée. Se placer dans le mode de création de script -- \link{Outil Script}[ Section \Ref, page \Pageref]{script-tool} -- cliquer directement sur le fond de l'écran. De cette façon un script sans paramètre d'entrée est créé. Ensuite éditer les propriétés du script -- \link{Propriétés d'un objet}[ Section \Ref, page \Pageref]{property-item}. Dans la zone texte où le code Scheme est normalement écrit, placer un texte entre guillemets précédé de l'apostrophe, par exemple~: \begin{verbatim} '"Animation et observations ================ Déplace les points de la figure pour répondre aux questions suivantes. 1. Où faut-il placer le point A pour que le point A' soit confondu avec le point A ? 2. Où faut-il placer le point A pour que le point A' soit confondu avec le point B ? 3. Comment faut-il placer le point I pour que les points B', C' et I soient alignés ? 4. Quel est le symétrique du point I ? Quel est le symétrique du point A' ?" \end{verbatim} \drgeniusFigureSize{Exemple de paragraphe de texte dans une figure}{fig58}{10} Comme pour tout script, il est également possible de changer la couleur du texte. \W \chapter*{Index} \W \htmlprintindex \W \begin{iftex} \appendix \listoffigures \printindex \W \end{iftex} \chapter{Historique} Rédactions originales de la documentation~: Hilaire Fernandes (anglais et français), Andrea Centomo (italien). 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.#r™ÚWä2%K›¥›·ôLÆ!UoõprŽg‡IEND®B`‚drgeo-doc-1.5/fr/figures/hilaire-email.png0000644000175000017500000000050410117134567014172 ‰PNG  IHDRˆü½á pHYs  ÒÝ~ütIMEÓ  3w¡ä“ãIDATxÚíVу #žÿÿËÙÃnSJ l0ÆCóâ‰i¥5 ¦@ ì+ë|¯Ð³Ì1´Þ³°!í¢fÍ)måü–Ñå«î72g÷¦Ñ”vÎ|ÆÓyŠf–²iLVGÿb–{RØá¶ãJ„êÈÁa¢ð˜‚‘•n³ Û:$ó¾õ9a›g‘w~à-5…Ô< \OãòK|?2ó½²TtDÝ™?>wŽåvÊL¶èâÃÉbuÊq›öÿCòk’w¾6`ÌPYn96#œ8 q ëœ0c·ü?ggH==Ô"X Z\YIEND®B`‚drgeo-doc-1.5/fr/figures/next.png0000644000175000017500000000040210117134567012443 ‰PNG  IHDR TgÇ0PLTE™ÌÿÂõ†¹ì|¯âs¦ÙiœÏ_’ÅV‰¼L²Cv©:m 0c–&YŒPƒ =p3f‚‚“IDATxÚc` %È9sæ0Š×ÿÿÿïÿÿE‰Þÿÿ¿Q˜ÿÿÿ?E$ÿÿÿo(œ@%("çÿÿ¤€¦#À_†ÿ(`Øp$ð… U …ÿÙ ™È¾aZwYÝÿÿ¿ùlïÿÿ/@èÿÿÿ)zø {#x4Ïœ9)@Ó8CÛ|ŽãÁ÷IEND®B`‚drgeo-doc-1.5/fr/figures/previous.png0000644000175000017500000000036510117134567013351 ‰PNG  IHDR D¤ŠÆ3PLTE™ÌÿÂõ†¹ì|¯âs¦ÙiœÏ_’ÅV‰¼L²Cv©:m 0c–&YŒPƒFy =p3fÇœ }IDATxÚÕ’;€ ù(ÈÏpÿÓ vn ;¶å1 ³[Båˆç>C`[˜7Ä]c^-àž˜g¨'<"E/üÕ½ÏÜSOὌó¤ð~Í´Â9’RoÙ19øˆkŒfaÃÑ«ŒâåÆ„k”€IßöH•µ…ÿ£¢±sÿ q ¿/µIEND®B`‚drgeo-doc-1.5/fr/figures/up.png0000644000175000017500000000047110117134567012117 ‰PNG  IHDR D¤ŠÆ3PLTE™ÌÿÂõ†¹ì|¯âs¦ÙiœÏ_’ÅV‰¼L²Cv©:m 0c–&YŒPƒFy =p3fÇœ ÁIDATxÚ•“Y„ DA•5÷?í°¤œ0@¬yZEcènUˆ )X¤÷¼nFW v«›¦CVÝ’×F<Ä¥} ¸I?" œKû3ÚëúU/ÉÍQd_²ºÞ‚è§Ñ¾4>r¶1BNuÕѱd¿QhŽôØ€¯Ý@¡VF=ÌÝÎÆ™‰nÀóR¢ 4„!^ý¸6põ{üÜàH+è`6|C¬Q½è=fý!üâ)zGª¸ÿª½sF×o!ÎßÏhšp8k>DxHÐIEND®B`‚drgeo-doc-1.5/fr/contents.html0000644000175000017500000002344210117134567012047 Manuel utilisateur de Dr. Geo -- Table des matières
CopyrightTopTable des matières

Table des matières
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CopyrightTopTable des matières
drgeo-doc-1.5/fr/default_behaviour.html0000644000175000017500000000733610117134567013706 Manuel utilisateur de Dr. Geo -- Comportement par défaut
Autres préférencesPréférences utilisateursComportement par défaut

Comportement par défaut

Le comportement par défaut de DR. GEO peut être configuré de plusieurs manières. Pour paramétrer les préférences, l'utilisateur accède au menu Édition->Préférences... pour ouvrir la boîte de dialogue des préférences.

Préférences des figures géométriques

La boîte de dialogue est composée en deux parties :
  1. La première partie concerne les préférences des figures géométriques. Des onglets permettent à l'utilisateur de paramétrer le réglage par défaut de chaque type d'objet (géométrique ou numérique). Les réglages concernent l'aspect des objets.
  2. La deuxième partie concerne les préférences globales :
    • Le nombre de niveaux pour Annuler/Refaire ;
    • Le nom par défaut lorsqu'une nouvelle figure est créée. Le %d est remplacé par un entier géré par DR. GEO, cette valeur est incrémentée à chaque nouvelle figure ;
    • Le navigateur Internet - visionneuse - par défaut pour visualiser l'aide en ligne ;
    • Les noms par défaut utilisés lors de la sauvegarde d'une figure et d'une session ;
    • Les noms par défaut utilisés lors d'exportations aux formats LaTeX  et PostScript ;

 

Des commentaires, des remarques ?
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Autres préférencesPréférences utilisateursComportement par défaut
drgeo-doc-1.5/fr/drgenius_100.html0000644000175000017500000000667210117134567012420 Manuel utilisateur de Dr. Geo -- Placer un paragraphe de texte dans une figure
Astuces diversesImprimer une figurePlacer un paragraphe de texte dans une figure

Placer un paragraphe de texte dans une figure

On peut avantageusement utiliser les scripts, d'une façon certes détournée. Se placer dans le mode de création de script - Outil Script - cliquer directement sur le fond de l'écran. De cette façon un script sans paramètre d'entrée est créé.

Ensuite éditer les propriétés du script - Propriétés d'un objet. Dans la zone texte où le code Scheme est normalement écrit, placer un texte entre guillemets précédé de l'apostrophe, par exemple : 

'"Animation et observations
================
Déplace les points de la figure pour répondre aux questions suivantes.

 1. Où faut-il placer le point A pour que le point A' soit confondu avec le point A ?
 2. Où faut-il placer le point A pour que le point A' soit confondu avec le point B ?
 3. Comment faut-il placer le point I pour que les points B', C' et I soient alignés ?
 4. Quel est le symétrique du point I ? Quel est le symétrique du point A' ?"

Exemple de paragraphe de texte dans une figure

Comme pour tout script, il est également possible de changer la couleur du texte.
Des commentaires, des remarques ?
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Astuces diversesImprimer une figurePlacer un paragraphe de texte dans une figure
drgeo-doc-1.5/fr/drgenius_101.html0000644000175000017500000003163010117134567012411 Manuel utilisateur de Dr. Geo -- Index
HistoriqueTopAstuces diversesIndex

Index

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A
Afficher - Texte -
Aide - Préférences par défaut - Visionneuse
Angle - Géométrique -
Angle - Orienté -
Arc de cercle - -
Arc de cercle - Longueur -
C
Cercle - -
Cercle - Périmètre -
D
Demi-droite - -
Droite - -
Droite - Distance -
Droite - Parallèle -
Droite - Pente -
Droite - Perpendiculaire -
E
Editer - Point -
Editer - Propriétés -
Editer - Préférences par défaut -
Editer - Préférences par défaut - Annuler/Refaire
Editer - Préférences par défaut - Noms
Editer - Script -
Editer - Style -
Editer - Style par défaut -
Editer - Valeur -
F
Figure - Afficher - Grille
Figure - Afficher - Texte
Figure - Déplacer -
Figure - Enregistrer -
Figure - Exporter - Définir la zone d'exportation
Figure - Exporter - Fly Draw/WIMS
Figure - Exporter - Image PNG
Figure - Exporter - PostScript
Figure - Exporter - LaTeX
Figure - Imprimer -
Figure - Ouvrir -
Figure - Renommer -
Figure Scheme de DR. GEO - Création d'objets -
Figure Scheme de DR. GEO - Création d'objets - Angle
Figure Scheme de DR. GEO - Création d'objets - Arc de cercle
Figure Scheme de DR. GEO - Création d'objets - Attributs des objets
Figure Scheme de DR. GEO - Création d'objets - Cercle
Figure Scheme de DR. GEO - Création d'objets - Demi-droite
Figure Scheme de DR. GEO - Création d'objets - Droite
Figure Scheme de DR. GEO - Création d'objets - Lieu
Figure Scheme de DR. GEO - Création d'objets - Nombre
Figure Scheme de DR. GEO - Création d'objets - Point
Figure Scheme de DR. GEO - Création d'objets - Polygone
Figure Scheme de DR. GEO - Création d'objets - Segment
Figure Scheme de DR. GEO - Création d'objets - Transformations géométriques
Figure Scheme de DR. GEO - Création d'objets - Vecteur
Figure Scheme de DR. GEO - Evaluer -
Figure Scheme de DR. GEO - Exemples -
Figure Scheme de DR. GEO - Exemples -
Figure Scheme de DR. GEO - Exemples - Catena di Pappo
Figure Scheme de DR. GEO - Exemples - Fractal
Figure Scheme de DR. GEO - Exemples - Polygone régulier
Figure Scheme de DR. GEO - Exemples - Spirale de Baravelle
Figure Scheme de DR. GEO - Exemples - Spirale de Teodoro
Figure Scheme de DR. GEO - Introduction -
Figure Scheme de DR. GEO - Nouvelle figure -
G
Grille - Afficher -
H
Historique - Arbre logique -
I
Imprimer - Figure -
L
Lieu géométrique - -
Lieu géométrique - Script -
M
Macro-construction - -
Macro-construction - Créer -
Macro-construction - Enregistrer -
Macro-construction - Enregistrer -
Macro-construction - Exécuter -
Macro-construction - Exécuter - Boîte de dialogue
Macro-construction - Exécuter - Menu
Macro-construction - Introduction -
Macro-construction - Ouvrir -
Macro-construction - Polygone -
Macro-construction - Script -
N
Nombre - -
Nombre - Valeur libre -
O
Objet - Déplacer -
Objet - Masquer -
Objet - Renommer -
Objet - Supprimer -
Outils - Déverrouiller -
Outils - Verrouiller -
P
Point - Coordonnées -
Point - Défini par coordonnées -
Point - Intersection -
Point - Libre -
Point - Milieu -
Point - Renommer -
Polygone - -
Polygone - Macro-construction -
R
Renommer - Objet -
S
Script - -
Script - Exemples -
Script - Exemples - Aire d'un trapèze
Script - Exemples - Différence de longueur de segments
Script - Exemples - Périmètre
Script - Exemples - Racine carrée
Script - Exemples - Tangente à une courbe
Script - Exemples - Théorème de Pythagore
Script - Exemples - Théorème de Tolomeo
Script - Intervalle -
Script - Introduction -
Script - Paramètres -
Script - getAbscissa -
Script - getAngle -
Script - getCenter -
Script - getCoordinates -
Script - getLength -
Script - getLength -
Script - getNorm -
Script - getRadius -
Script - getSlope -
Script - getUnit -
Script - getValue -
Script - move -
Script - random -
Script - setAbscissa -
Script - setCoordinates -
Script - setValue -
Segment - -
Segment - Longueur -
Session - Enregistrer -
Session - Ouvrir -
T
Transformation - Figure Scheme de DR. GEO -
Transformation - Homothétie -
Transformation - Rotation -
Transformation - Symétrie - Axiale
Transformation - Symétrie - Centrale
Transformation - Translation -
V
Vecteur - -
Vecteur - Coordonnées -
Vecteur - Norme -
Des commentaires, des remarques ?
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HistoriqueTopAstuces diversesIndex
drgeo-doc-1.5/fr/drgenius_102.html0000644000175000017500000000425110117134567012411 Manuel utilisateur de Dr. Geo -- Historique
GNU Free Documentation LicenseTopIndexHistorique

Historique

Rédactions originales de la documentation : Hilaire Fernandes (anglais et français), Andrea Centomo (italien).

Traductions vers le français : Jean-Philippe Georget, Hilaire Fernandes.

Des commentaires, des remarques ?
Vous êtes volontaire pour écrire des parties du manuel ?
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GNU Free Documentation LicenseTopIndexHistorique
drgeo-doc-1.5/fr/drgenius_103.html0000644000175000017500000005657610117134567012433 Manuel utilisateur de Dr. Geo -- GNU Free Documentation License
FootnotesTopHistoriqueGNU Free Documentation License

GNU Free Documentation License


                GNU Free Documentation License
                  Version 1.2, November 2002


 Copyright (C) 2000,2001,2002  Free Software Foundation, Inc.
     59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 Everyone is permitted to copy and distribute verbatim copies
 of this license document, but changing it is not allowed.


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functional and useful document "free" in the sense of freedom: to
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Secondarily, this License preserves for the author and publisher a way
to get credit for their work, while not being considered responsible
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copy along with each Opaque copy, or state in or with each Opaque copy
a computer-network location from which the general network-using
public has access to download using public-standard network protocols
a complete Transparent copy of the Document, free of added material.
If you use the latter option, you must take reasonably prudent steps,
when you begin distribution of Opaque copies in quantity, to ensure
that this Transparent copy will remain thus accessible at the stated
location until at least one year after the last time you distribute an
Opaque copy (directly or through your agents or retailers) of that
edition to the public.

It is requested, but not required, that you contact the authors of the
Document well before redistributing any large number of copies, to give
them a chance to provide you with an updated version of the Document.


4. MODIFICATIONS

You may copy and distribute a Modified Version of the Document under
the conditions of sections 2 and 3 above, provided that you release
the Modified Version under precisely this License, with the Modified
Version filling the role of the Document, thus licensing distribution
and modification of the Modified Version to whoever possesses a copy
of it.  In addition, you must do these things in the Modified Version:

A. Use in the Title Page (and on the covers, if any) a title distinct
   from that of the Document, and from those of previous versions
   (which should, if there were any, be listed in the History section
   of the Document).  You may use the same title as a previous version
   if the original publisher of that version gives permission.
B. List on the Title Page, as authors, one or more persons or entities
   responsible for authorship of the modifications in the Modified
   Version, together with at least five of the principal authors of the
   Document (all of its principal authors, if it has fewer than five),
   unless they release you from this requirement.
C. State on the Title page the name of the publisher of the
   Modified Version, as the publisher.
D. Preserve all the copyright notices of the Document.
E. Add an appropriate copyright notice for your modifications
   adjacent to the other copyright notices.
F. Include, immediately after the copyright notices, a license notice
   giving the public permission to use the Modified Version under the
   terms of this License, in the form shown in the Addendum below.
G. Preserve in that license notice the full lists of Invariant Sections
   and required Cover Texts given in the Document's license notice.
H. Include an unaltered copy of this License.
I. Preserve the section Entitled "History", Preserve its Title, and add
   to it an item stating at least the title, year, new authors, and
   publisher of the Modified Version as given on the Title Page.  If
   there is no section Entitled "History" in the Document, create one
   stating the title, year, authors, and publisher of the Document as
   given on its Title Page, then add an item describing the Modified
   Version as stated in the previous sentence.
J. Preserve the network location, if any, given in the Document for
   public access to a Transparent copy of the Document, and likewise
   the network locations given in the Document for previous versions
   it was based on.  These may be placed in the "History" section.
   You may omit a network location for a work that was published at
   least four years before the Document itself, or if the original
   publisher of the version it refers to gives permission.
K. For any section Entitled "Acknowledgements" or "Dedications",
   Preserve the Title of the section, and preserve in the section all
   the substance and tone of each of the contributor acknowledgements
   and/or dedications given therein.
L. Preserve all the Invariant Sections of the Document,
   unaltered in their text and in their titles.  Section numbers
   or the equivalent are not considered part of the section titles.
M. Delete any section Entitled "Endorsements".  Such a section
   may not be included in the Modified Version.
N. Do not retitle any existing section to be Entitled "Endorsements"
   or to conflict in title with any Invariant Section.
O. Preserve any Warranty Disclaimers.

If the Modified Version includes new front-matter sections or
appendices that qualify as Secondary Sections and contain no material
copied from the Document, you may at your option designate some or all
of these sections as invariant.  To do this, add their titles to the
list of Invariant Sections in the Modified Version's license notice.
These titles must be distinct from any other section titles.

You may add a section Entitled "Endorsements", provided it contains
nothing but endorsements of your Modified Version by various
parties--for example, statements of peer review or that the text has
been approved by an organization as the authoritative definition of a
standard.

You may add a passage of up to five words as a Front-Cover Text, and a
passage of up to 25 words as a Back-Cover Text, to the end of the list
of Cover Texts in the Modified Version.  Only one passage of
Front-Cover Text and one of Back-Cover Text may be added by (or
through arrangements made by) any one entity.  If the Document already
includes a cover text for the same cover, previously added by you or
by arrangement made by the same entity you are acting on behalf of,
you may not add another; but you may replace the old one, on explicit
permission from the previous publisher that added the old one.

The author(s) and publisher(s) of the Document do not by this License
give permission to use their names for publicity for or to assert or
imply endorsement of any Modified Version.


5. COMBINING DOCUMENTS

You may combine the Document with other documents released under this
License, under the terms defined in section 4 above for modified
versions, provided that you include in the combination all of the
Invariant Sections of all of the original documents, unmodified, and
list them all as Invariant Sections of your combined work in its
license notice, and that you preserve all their Warranty Disclaimers.

The combined work need only contain one copy of this License, and
multiple identical Invariant Sections may be replaced with a single
copy.  If there are multiple Invariant Sections with the same name but
different contents, make the title of each such section unique by
adding at the end of it, in parentheses, the name of the original
author or publisher of that section if known, or else a unique number.
Make the same adjustment to the section titles in the list of
Invariant Sections in the license notice of the combined work.

In the combination, you must combine any sections Entitled "History"
in the various original documents, forming one section Entitled
"History"; likewise combine any sections Entitled "Acknowledgements",
and any sections Entitled "Dedications".  You must delete all sections
Entitled "Endorsements".


6. COLLECTIONS OF DOCUMENTS

You may make a collection consisting of the Document and other documents
released under this License, and replace the individual copies of this
License in the various documents with a single copy that is included in
the collection, provided that you follow the rules of this License for
verbatim copying of each of the documents in all other respects.

You may extract a single document from such a collection, and distribute
it individually under this License, provided you insert a copy of this
License into the extracted document, and follow this License in all
other respects regarding verbatim copying of that document.


7. AGGREGATION WITH INDEPENDENT WORKS

A compilation of the Document or its derivatives with other separate
and independent documents or works, in or on a volume of a storage or
distribution medium, is called an "aggregate" if the copyright
resulting from the compilation is not used to limit the legal rights
of the compilation's users beyond what the individual works permit.
When the Document is included in an aggregate, this License does not
apply to the other works in the aggregate which are not themselves
derivative works of the Document.

If the Cover Text requirement of section 3 is applicable to these
copies of the Document, then if the Document is less than one half of
the entire aggregate, the Document's Cover Texts may be placed on
covers that bracket the Document within the aggregate, or the
electronic equivalent of covers if the Document is in electronic form.
Otherwise they must appear on printed covers that bracket the whole
aggregate.


8. TRANSLATION

Translation is considered a kind of modification, so you may
distribute translations of the Document under the terms of section 4.
Replacing Invariant Sections with translations requires special
permission from their copyright holders, but you may include
translations of some or all Invariant Sections in addition to the
original versions of these Invariant Sections.  You may include a
translation of this License, and all the license notices in the
Document, and any Warranty Disclaimers, provided that you also include
the original English version of this License and the original versions
of those notices and disclaimers.  In case of a disagreement between
the translation and the original version of this License or a notice
or disclaimer, the original version will prevail.

If a section in the Document is Entitled "Acknowledgements",
"Dedications", or "History", the requirement (section 4) to Preserve
its Title (section 1) will typically require changing the actual
title.


9. TERMINATION

You may not copy, modify, sublicense, or distribute the Document except
as expressly provided for under this License.  Any other attempt to
copy, modify, sublicense or distribute the Document is void, and will
automatically terminate your rights under this License.  However,
parties who have received copies, or rights, from you under this
License will not have their licenses terminated so long as such
parties remain in full compliance.


10. FUTURE REVISIONS OF THIS LICENSE

The Free Software Foundation may publish new, revised versions
of the GNU Free Documentation License from time to time.  Such new
versions will be similar in spirit to the present version, but may
differ in detail to address new problems or concerns.  See
http://www.gnu.org/copyleft/.

Each version of the License is given a distinguishing version number.
If the Document specifies that a particular numbered version of this
License "or any later version" applies to it, you have the option of
following the terms and conditions either of that specified version or
of any later version that has been published (not as a draft) by the
Free Software Foundation.  If the Document does not specify a version
number of this License, you may choose any version ever published (not
as a draft) by the Free Software Foundation.


ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of
the License in the document and put the following copyright and
license notices just after the title page:

    Copyright (c)  YEAR  YOUR NAME.
    Permission is granted to copy, distribute and/or modify this document
    under the terms of the GNU Free Documentation License, Version 1.2
    or any later version published by the Free Software Foundation;
    with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
    A copy of the license is included in the section entitled "GNU
    Free Documentation License".

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
replace the "with...Texts." line with this:

    with the Invariant Sections being LIST THEIR TITLES, with the
    Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.

If you have Invariant Sections without Cover Texts, or some other
combination of the three, merge those two alternatives to suit the
situation.

If your document contains nontrivial examples of program code, we
recommend releasing these examples in parallel under your choice of
free software license, such as the GNU General Public License,
to permit their use in free software.

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FootnotesTopHistoriqueGNU Free Documentation License
drgeo-doc-1.5/fr/drgenius_104.html0000644000175000017500000001222610117134567012414 Manuel utilisateur de Dr. Geo -- Footnotes
TopGNU Free Documentation LicenseFootnotes

Footnotes

 (1)
Il s'agit de pouvoir, à partir d'une même commande, créer un type d'objet selon des modalités différentes. Par exemple à partir de la commande construction de cercle, l'utilisateur peut créer un cercle à partir de son centre et un point, ou bien une longueur, ou bien un segment, etc. Bien sûr cette commande n'est représentée que par une seule icône, à charge de DR. GEO d'anticiper sur la construction de l'utilisateur. L'effet immédiat est donc une diminution de la charge cognitive de l'interface sur l'utilisateur, tout en proposant un nombre important de modes de construction.
 (2)
Ou procédures pour les amateurs de Pascal.
 (3)
Par exemple sous forme récursive
 (4)
Cette contrainte a depuis été assouplie et permet d'aller encore plus loin avec les macro-constructions. Voir Créer un polygone régulier.
 (5)
Les macro-constructions ont une approche géométrique tandis que les DGS ont une approche numérique mais aussi et surtout nous pouvons les utiliser dans un esprit de bidouillage ("hacking" en anglais).
 (6)
En particulier, les fonctions mathématiques
 (7)
Si par accident vous cliquiez sur un objet, sélectionnez de nouveau l'outil de script. Cela annulera votre sélection.
 (8)
Cette abscisse est dans l'intervalle [0 ; 1], quelque soit le type de ligne
 (9)
D'un point de vue interne au langage Scheme, ces références sont des symboles pointant vers une structure interne à l'objet - un prototype - alors que les noms sont des chaînes de caractères.
 (10)
Fichiers comprenant plusieurs documents DR. GEO (i.e. figure, macro, texte)
 (11)
GhostView est un logiciel qui permet de visualiser des documents PostScript (.ps ou .eps) ainsi que des documents PDF
 (12)
Ce format est reconnu par TeXmacs, OpenOffice.org, Lyx, LaTeX Xfig, The Gimp et bien d'autres encore
 (13)
OpenOffice.org permet d'intégrer une image EPS mais pas de l'afficher. C'est uniquement à l'impression que celle-ci apparaît.
 (14)
Éventuellement, le panneau latéral de l'arbre logique de la figure peut être déplié pour réduire davantage la zone d'exportation.
 (15)
Il ne s'agit que d'une vérification numérique.
 (16)
Sinon, la macro-construction ne pourrait pas être instanciée. Par exemple quelle valeur donner à un objet de type valeur libre intervenant dans la séquence de construction ?
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TopGNU Free Documentation LicenseFootnotes
drgeo-doc-1.5/fr/drgenius_10.html0000644000175000017500000000436210117134567012332 Manuel utilisateur de Dr. Geo -- Milieu
IntersectionOutils de pointPoint libreMilieu

Milieu

 

Crée le milieu de deux points ou d'un segment :

  1. Dans le premier cas, l'utilisateur sélectionne deux points.
  2. Dans le deuxième cas, l'utilisateur sélectionne simplement un segment.
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IntersectionOutils de pointPoint libreMilieu
drgeo-doc-1.5/fr/drgenius_11.html0000644000175000017500000000441410117134567012331 Manuel utilisateur de Dr. Geo -- Intersection
Point défini par ses coordonnéesOutils de pointMilieuIntersection

Intersection

 

Crée le ou les points d'intersection de deux lignes (i.e. droite, demi-droite, segment, arc de cercle, cercle). L'utilisateur doit sélectionner deux lignes.

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Point défini par ses coordonnéesOutils de pointMilieuIntersection
drgeo-doc-1.5/fr/drgenius_12.html0000644000175000017500000000531510117134567012333 Manuel utilisateur de Dr. Geo -- Point défini par ses coordonnées
Outils de pointIntersectionPoint défini par ses coordonnées

Point défini par ses coordonnées

 

Crée un point défini par ses coordonnées. L'utilisateur doit sélectionner deux nombres, le premier correspond à l'abscisse, le second à l'ordonnée.

Comment placer un point contraint par ses coordonnées ?

Cette fonction est largement utilisée lorsque nous souhaitons par exemple construire le lieu d'un point. Cette construction suppose au préalable l'existence de deux valeurs - voir Section numérique - le point est ensuite construit en sélectionnant ces deux valeurs.

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Outils de pointIntersectionPoint défini par ses coordonnées
drgeo-doc-1.5/fr/drgenius_13.html0000644000175000017500000000427610117134567012341 Manuel utilisateur de Dr. Geo -- Demi-droite
SegmentOutils de ligneDroiteDemi-droite

Demi-droite

 

Crée une demi-droite définie par deux points. L'utilisateur sélectionne deux points, le premier est l'origine, le second appartient à la demi-droite.

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SegmentOutils de ligneDroiteDemi-droite
drgeo-doc-1.5/fr/drgenius_14.html0000644000175000017500000000400410117134567012327 Manuel utilisateur de Dr. Geo -- Droite
Demi-droiteOutils de ligneDroite

Droite

Crée une droite définie par deux points. L'utilisateur sélectionne deux points.

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Demi-droiteOutils de ligneDroite
drgeo-doc-1.5/fr/drgenius_15.html0000644000175000017500000000427610117134567012343 Manuel utilisateur de Dr. Geo -- Demi-droite
SegmentOutils de ligneDroiteDemi-droite

Demi-droite

 

Crée une demi-droite définie par deux points. L'utilisateur sélectionne deux points, le premier est l'origine, le second appartient à la demi-droite.

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SegmentOutils de ligneDroiteDemi-droite
drgeo-doc-1.5/fr/drgenius_16.html0000644000175000017500000000407410117134567012340 Manuel utilisateur de Dr. Geo -- Segment
VecteurOutils de ligneDemi-droiteSegment

Segment

 

Crée un segment donné par deux points.

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VecteurOutils de ligneDemi-droiteSegment
drgeo-doc-1.5/fr/drgenius_17.html0000644000175000017500000000463110117134567012340 Manuel utilisateur de Dr. Geo -- Vecteur
CercleOutils de ligneSegmentVecteur

Vecteur

 

Crée un vecteur donné par deux points. L'utilisateur sélectionne deux points, le premier est l'origine, le second est l'extrémité.

Une fois que le vecteur est créé, celui-ci peut être déplacé indépendamment des deux points. Ceci reste vrai pour un vecteur construit par une transformation (Cf. la section Transformations de ce manuel)

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CercleOutils de ligneSegmentVecteur
drgeo-doc-1.5/fr/drgenius_18.html0000644000175000017500000000447210117134567012344 Manuel utilisateur de Dr. Geo -- Cercle
Arc de cercleOutils de ligneVecteurCercle

Cercle

 

Crée un cercle. L'utilisateur peut créer un cercle à partir de différentes sélections :

  1. le centre et un point du cercle ;
  2. le centre et un nombre (le rayon du cercle) ;
  3. le cercle et un segment dont la longueur est le rayon du cercle.
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Arc de cercleOutils de ligneVecteurCercle
drgeo-doc-1.5/fr/drgenius_19.html0000644000175000017500000000430310117134567012336 Manuel utilisateur de Dr. Geo -- Arc de cercle
LieuOutils de ligneCercleArc de cercle

Arc de cercle

 

Crée un arc de cercle défini par trois points. Le premier est l'origine de l'arc, le troisième est l'extrémité, le second est un point de l'arc.

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LieuOutils de ligneCercleArc de cercle
drgeo-doc-1.5/fr/drgenius_20.html0000644000175000017500000000436310117134567012334 Manuel utilisateur de Dr. Geo -- Lieu
PolygoneOutils de ligneArc de cercleLieu

Lieu

 

Crée un lieu défini par deux points. L'utilisateur sélectionne deux points, l'un des deux est un point sur une ligne, l'autre est un point sous contraintes du premier (i.e. quand l'un bouge, l'autre fait de même).

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PolygoneOutils de ligneArc de cercleLieu
drgeo-doc-1.5/fr/drgenius_21.html0000644000175000017500000000473010117134567012333 Manuel utilisateur de Dr. Geo -- Polygone
Outils de ligneLieuPolygone

Polygone

 

Crée un polygone défini par n points. L'utilisateur sélectionne n+1 points limitant le polygone. Le premier et le dernier sont un seul et même point ce qui indique à DR. GEO que la sélection est terminée. L'objet polygone n'est pas un objet comme les autres lignes, il n'est pas possible de placer un point dessus ou de construire une intersection entre un polygone et une autre ligne. En revanche il est possible de construire l'image d'un polygone par une transformation géométrique.

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Outils de ligneLieuPolygone
drgeo-doc-1.5/fr/drgenius_22.html0000644000175000017500000000455710117134567012343 Manuel utilisateur de Dr. Geo -- Droite perpendiculaire
Symétrie axialeOutils de transformationDroite parallèleDroite perpendiculaire

Droite perpendiculaire

 

Crée une droite perpendiculaire à une direction et passant par un point. L'utilisateur sélectionne un point et une direction (i.e. une droite, une demi-droite, un segment ou un vecteur).

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Symétrie axialeOutils de transformationDroite parallèleDroite perpendiculaire
drgeo-doc-1.5/fr/drgenius_23.html0000644000175000017500000000437110117134567012336 Manuel utilisateur de Dr. Geo -- Droite parallèle
Droite perpendiculaireOutils de transformationDroite parallèle

Droite parallèle

 

Crée une ligne parallèle à une direction et passant par un point. L'utilisateur sélectionne un point et une direction (i.e. une droite, une demi-droite, un segment ou un vecteur).

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Droite perpendiculaireOutils de transformationDroite parallèle
drgeo-doc-1.5/fr/drgenius_24.html0000644000175000017500000000455710117134567012345 Manuel utilisateur de Dr. Geo -- Droite perpendiculaire
Symétrie axialeOutils de transformationDroite parallèleDroite perpendiculaire

Droite perpendiculaire

 

Crée une droite perpendiculaire à une direction et passant par un point. L'utilisateur sélectionne un point et une direction (i.e. une droite, une demi-droite, un segment ou un vecteur).

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Symétrie axialeOutils de transformationDroite parallèleDroite perpendiculaire
drgeo-doc-1.5/fr/drgenius_25.html0000644000175000017500000000473310117134567012342 Manuel utilisateur de Dr. Geo -- Symétrie axiale
Symétrie centraleOutils de transformationDroite perpendiculaireSymétrie axiale

Symétrie axiale

 

Crée l'image d'un objet par une symétrie axiale. L'utilisateur sélectionne l'objet à transformer et l'axe de symétrie (une droite). Quand l'utilisateur veut construire l'image d'une droite, la première droite sélectionnée est la droite à transformer.

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Symétrie centraleOutils de transformationDroite perpendiculaireSymétrie axiale
drgeo-doc-1.5/fr/drgenius_26.html0000644000175000017500000000470010117134567012335 Manuel utilisateur de Dr. Geo -- Symétrie centrale
TranslationOutils de transformationSymétrie axialeSymétrie centrale

Symétrie centrale

 

Crée l'image d'un objet par une symétrie centrale. L'utilisateur sélectionne l'objet à transformer et le centre de symétrie (un point). Quand l'utilisateur veut construire l'image d'un point, le premier point sélectionné est le point à transformer.

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TranslationOutils de transformationSymétrie axialeSymétrie centrale
drgeo-doc-1.5/fr/drgenius_27.html0000644000175000017500000000443010117134567012336 Manuel utilisateur de Dr. Geo -- Translation
RotationOutils de transformationSymétrie centraleTranslation

Translation

 

Crée l'image d'un objet par une translation. Quand l'utilisateur veut construire l'image d'un vecteur, le premier vecteur sélectionné est le vecteur à translater.

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RotationOutils de transformationSymétrie centraleTranslation
drgeo-doc-1.5/fr/drgenius_28.html0000644000175000017500000000626210117134567012344 Manuel utilisateur de Dr. Geo -- Rotation
HomothétieOutils de transformationTranslationRotation

Rotation

 

Crée l'image d'un objet par une rotation. L'utilisateur sélectionne l'objet à transformer, le centre et l'angle de la rotation. Quand l'utilisateur veut créer l'image d'un point, le premier point sélectionné est le point à transformer.

L'angle peut être sélectionné à partir de différents types de valeurs :

  • valeur numérique : l'angle est alors exprimé en radians. Exemples de valeurs numériques : valeur libre, distance entre deux points, longueur d'un segment, une coordonnée, une valeur retournée par un script Scheme DR. GEO, etc. ;
  • la mesure d'un angle géométrique formé par trois points : sa mesure est alors exprimée en degrés. Attention, dans ce cas la mesure appartient seulement à l'intervalle [0 ; 180] ;
  • la mesure d'un angle orienté de deux vecteurs : sa mesure est exprimée en degrés et couvre l'intervalle ]-180 ; 180].
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HomothétieOutils de transformationTranslationRotation
drgeo-doc-1.5/fr/drgenius_29.html0000644000175000017500000000445010117134567012342 Manuel utilisateur de Dr. Geo -- Homothétie
Outils de transformationRotationHomothétie

Homothétie

 

Crée l'image d'un objet par une homothétie. L'utilisateur sélectionne l'objet à transformer, le centre et le facteur (i.e. un nombre). Quand l'utilisateur veut créer l'image d'un point, le premier point sélectionné est le point à transformer.

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Outils de transformationRotationHomothétie
drgeo-doc-1.5/fr/drgenius_2.html0000644000175000017500000000501110117134567012243 Manuel utilisateur de Dr. Geo -- Copyright
IntroductionTopTable des matièresCopyright

Copyright

Copyright (c) 2000-2004 OFSET.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".

Other copyright apply to the respective owners of the modified documentations. See the section history for the complet list.

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IntroductionTopTable des matièresCopyright
drgeo-doc-1.5/fr/drgenius_30.html0000644000175000017500000000470510117134567012335 Manuel utilisateur de Dr. Geo -- Angle
CoordonnéesOutils numériquesDistance, longueur & nombreAngle

Angle

 

Calcule la mesure d'un angle défini par trois points ou deux vecteurs. Dans le premier cas, l'angle est considéré comme non orienté (i.e. angle géométrique dont la mesure est dans l'intervalle [0 ; 180]). Dans le second cas, l'angle est orienté et sa mesure est dans l'intervalle ]-180 ; 180].

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CoordonnéesOutils numériquesDistance, longueur & nombreAngle
drgeo-doc-1.5/fr/drgenius_31.html0000644000175000017500000000632210117134567012333 Manuel utilisateur de Dr. Geo -- Distance, longueur & nombre
AngleOutils numériquesDistance, longueur & nombre

Distance, longueur & nombre

 

Crée une valeur numérique. La valeur numérique, selon la sélection de l'utilisateur, peut être calculée ou bien saisie :

  1. deux points : distance entre ces deux points ;
  2. un segment : la longueur de ce segment ;
  3. un vecteur : la norme de ce vecteur ;
  4. un cercle : le périmètre de ce cercle ;
  5. un arc de cercle : la longueur de cet arc ;
  6. une droite : la pente de cette droite ;
  7. une droite et un point : la distance entre ce point et la droite ;
  8. un clic souris directement sur le fond de la figure permet à l'utilisateur d'entrer une nouvelle valeur (i.e. une valeur libre).

Cette dernière possibilité est très intéressante dans certaines situations. Elle permet de fixer une longueur, le rayon d'un cercle, la mesure d'angle (en radian) ou les coordonnées d'un point. La valeur est ensuite utilisée à partir des outils spécifiques de construction de cercle, de rotation et de point défini par ses coordonnées.

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AngleOutils numériquesDistance, longueur & nombre
drgeo-doc-1.5/fr/drgenius_32.html0000644000175000017500000000470510117134567012337 Manuel utilisateur de Dr. Geo -- Angle
CoordonnéesOutils numériquesDistance, longueur & nombreAngle

Angle

 

Calcule la mesure d'un angle défini par trois points ou deux vecteurs. Dans le premier cas, l'angle est considéré comme non orienté (i.e. angle géométrique dont la mesure est dans l'intervalle [0 ; 180]). Dans le second cas, l'angle est orienté et sa mesure est dans l'intervalle ]-180 ; 180].

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CoordonnéesOutils numériquesDistance, longueur & nombreAngle
drgeo-doc-1.5/fr/drgenius_33.html0000644000175000017500000000430710117134567012336 Manuel utilisateur de Dr. Geo -- Coordonnées
Script Scheme DR. GEOOutils numériquesAngleCoordonnées

Coordonnées

 

Crée les coordonnées (abscisse et ordonnée) d'un point ou d'un vecteur.

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Script Scheme DR. GEOOutils numériquesAngleCoordonnées
drgeo-doc-1.5/fr/drgenius_34.html0000644000175000017500000000505410117134567012337 Manuel utilisateur de Dr. Geo -- Script Scheme DR. GEO
Outils numériquesCoordonnéesScript Scheme DR. GEO

Script Scheme DR. GEO

 

Crée un script Scheme DR. GEO. Le script reçoit n objets en entrée. Il retourne éventuellement un nombre, affiché dans la figure. Un script peut être utilisé pour ses effets de bord ou pour sa valeur de retour. Les scripts Scheme DR. GEO sont couverts en détails dans le chapitre des fonctionnalités avancées et exactement à la section script.

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Outils numériquesCoordonnéesScript Scheme DR. GEO
drgeo-doc-1.5/fr/drgenius_35.html0000644000175000017500000000470510117134567012342 Manuel utilisateur de Dr. Geo -- Exécuter une macro-construction
Outil macro-constructionCréer une macro-constructionExécuter une macro-construction

Exécuter une macro-construction

Exécute (i.e. "lance" ou "joue") une macro-construction pré-construite. La macro-construction peut être nouvelle ou chargée depuis un fichier.

(!) Les macro-constructions sont présentées dans la Section macro-construction.
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Outil macro-constructionCréer une macro-constructionExécuter une macro-construction
drgeo-doc-1.5/fr/drgenius_36.html0000644000175000017500000000430210117134567012334 Manuel utilisateur de Dr. Geo -- Créer une macro-construction
Exécuter une macro-constructionOutil macro-constructionCréer une macro-construction

Créer une macro-construction

Extrait une séquence de construction d'une figure et la transforme en macro-construction.

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Exécuter une macro-constructionOutil macro-constructionCréer une macro-construction
drgeo-doc-1.5/fr/drgenius_37.html0000644000175000017500000000470510117134567012344 Manuel utilisateur de Dr. Geo -- Exécuter une macro-construction
Outil macro-constructionCréer une macro-constructionExécuter une macro-construction

Exécuter une macro-construction

Exécute (i.e. "lance" ou "joue") une macro-construction pré-construite. La macro-construction peut être nouvelle ou chargée depuis un fichier.

(!) Les macro-constructions sont présentées dans la Section macro-construction.
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Outil macro-constructionCréer une macro-constructionExécuter une macro-construction
drgeo-doc-1.5/fr/drgenius_38.html0000644000175000017500000000432010117134567012336 Manuel utilisateur de Dr. Geo -- Déplacer la figure
Déplacer un objetAutres fonctionsArbre logique de constructionDéplacer la figure

Déplacer la figure

La figure peut être déplacée en appuyant sur la touche contrôle et le premier bouton de la souris.

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Déplacer un objetAutres fonctionsArbre logique de constructionDéplacer la figure
drgeo-doc-1.5/fr/drgenius_39.html0000644000175000017500000000543610117134567012350 Manuel utilisateur de Dr. Geo -- Arbre logique de construction
Déplacer la figureAutres fonctionsArbre logique de construction

Arbre logique de construction

Chaque figure est associée à un arbre logique de construction. Cet arbre est chronologique, c'est-à-dire qu'il reprend, du haut vers le bas, l'ordre de construction de la figure. Certaines entrées de l'arbre peuvent être dépliées afin de faire apparaître les antécédents - c'est à dire les objets parents - utilisés lors de la définition de l'objet.

Par défaut l'arbre est masqué, il est en fait replié sur le bord gauche de la fenêtre, pour le faire apparaître il faut le déplier à l'aide de la souris. Déplacer le pointeur souris vers le bord gauche de la fenêtre de DR. GEO lorsque celui-ci se transforme en "<->", presser le bouton souris et tirer vers la droite.

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Déplacer la figureAutres fonctionsArbre logique de construction
drgeo-doc-1.5/fr/drgenius_40.html0000644000175000017500000000432010117134567012327 Manuel utilisateur de Dr. Geo -- Déplacer la figure
Déplacer un objetAutres fonctionsArbre logique de constructionDéplacer la figure

Déplacer la figure

La figure peut être déplacée en appuyant sur la touche contrôle et le premier bouton de la souris.

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Déplacer un objetAutres fonctionsArbre logique de constructionDéplacer la figure
drgeo-doc-1.5/fr/drgenius_41.html0000644000175000017500000000517010117134567012334 Manuel utilisateur de Dr. Geo -- Déplacer un objet
Supprimer un objetAutres fonctionsDéplacer la figureDéplacer un objet

Déplacer un objet

 

Un objet peut être déplacé par glisser-déposer. La figure est alors redessinée en respectant ses propriétés. Quasiment tous les objets géométriques peuvent être déplacés. Si nécessaire, DR. GEO déplace les points libres associés. Par exemple, quand l'utilisateur déplace une droite définie par deux points, DR. GEO déplace les deux points simultanément.

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Supprimer un objetAutres fonctionsDéplacer la figureDéplacer un objet
drgeo-doc-1.5/fr/drgenius_42.html0000644000175000017500000000507110117134567012335 Manuel utilisateur de Dr. Geo -- Supprimer un objet
Changer l'aspect d'un objetAutres fonctionsDéplacer un objetSupprimer un objet

Supprimer un objet

 

Un objet d'une figure peut être supprimé en activant ce menu. Éventuellement, l'utilisateur peut annuler la suppression à l'aide de la fonction d'annulation à partir de la barre d'icônes ou du menu de l'application. Par défaut le nombre d'annulations possibles est de 10 mais l'utilisateur peut ajuster cette valeur depuis la boîte de dialogue des préférences.

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Changer l'aspect d'un objetAutres fonctionsDéplacer un objetSupprimer un objet
drgeo-doc-1.5/fr/drgenius_43.html0000644000175000017500000000476110117134567012343 Manuel utilisateur de Dr. Geo -- Afficher une grille
Autres fonctionsChanger les propriétés d'un objetAfficher une grille

Afficher une grille

Il est possible d'afficher une grille unitaire dans toute figure de DR. GEO, la commande est accessible depuis le menu Édition->Montrer ou cacher la grille. Elle peut également être activée par le raccourci clavier Ctrl-G. Si la commande est réactivée, la grille est cachée. La grille est unitaire, chaque subdivision représente une unité. Enfin, si la grille est affichée lors de la sauvegarde, celle-ci l'est aussi.

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Autres fonctionsChanger les propriétés d'un objetAfficher une grille
drgeo-doc-1.5/fr/drgenius_44.html0000644000175000017500000000634610117134567012345 Manuel utilisateur de Dr. Geo -- Changer les propriétés d'un objet
Afficher une grilleAutres fonctionsChanger l'aspect d'un objetChanger les propriétés d'un objet

Changer les propriétés d'un objet

 

Certaines propriétés d'objets sont paramétrables par l'utilisateur. Quand l'utilisateur clique sur ces objets, une boîte de dialogue appropriée apparaît. Actuellement, les objets suivants sont concernés :

  1. point libre : abscisse et ordonnée peuvent être éditées ;

    Changement des coordonnées d'un point libre

  2. valeur libre : sa valeur peut être modifiée ;

    Modification d'une valeur libre

  3. script : son code peut être modifié.

    Modification d'un script

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Afficher une grilleAutres fonctionsChanger l'aspect d'un objetChanger les propriétés d'un objet
drgeo-doc-1.5/fr/drgenius_45.html0000644000175000017500000000476110117134567012345 Manuel utilisateur de Dr. Geo -- Afficher une grille
Autres fonctionsChanger les propriétés d'un objetAfficher une grille

Afficher une grille

Il est possible d'afficher une grille unitaire dans toute figure de DR. GEO, la commande est accessible depuis le menu Édition->Montrer ou cacher la grille. Elle peut également être activée par le raccourci clavier Ctrl-G. Si la commande est réactivée, la grille est cachée. La grille est unitaire, chaque subdivision représente une unité. Enfin, si la grille est affichée lors de la sauvegarde, celle-ci l'est aussi.

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Autres fonctionsChanger les propriétés d'un objetAfficher une grille
drgeo-doc-1.5/fr/drgenius_46.html0000644000175000017500000000420610117134567012340 Manuel utilisateur de Dr. Geo -- Préférences utilisateurs
Fonctions de baseAutres fonctionsPréférences utilisateurs

Préférences utilisateurs

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Fonctions de baseAutres fonctionsPréférences utilisateurs
drgeo-doc-1.5/fr/drgenius_47.html0000644000175000017500000000705010117134567012341 Manuel utilisateur de Dr. Geo -- Fonctionnalités avancées
Figure Scheme de DR. GEOTopFonctions de baseFonctionnalités avancées

Fonctionnalités avancées

Dans ce chapitre, nous présentons les fonctionnalités qui permettent d'étendre les possibilités de DR. GEO ou de l'adapter à une situation pédagogique donnée.

La première est la macro-construction. Elle permet l'extraction d'une construction logique dans un enregistrement. Cet enregistrement peut ensuite être répété ou sauvegardé dans un fichier.

Les scripts Guile DR. GEO - DGS - représentent une autre fonctionnalité pour étendre DR. GEO. Ces scripts sont de véritables items de figure, comme les items géométriques. En entrée, ils reçoivent une ou plusieurs références d'items géométriques et il retourne une valeur placée dans la figure.

Les scripts Guile DR. GEO sont utiles pour la valeur qu'ils retournent ou leur effet de bord, cela dépend de ce que l'utilisateur veut réaliser.

Enfin, l'adaptation de l'interface utilisateur de DR. GEO permet à un enseignant de préparer une session de travail avec des documents dans lesquels certaines fonctions ont été bloquées par un mot de passe.

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Figure Scheme de DR. GEOTopFonctions de baseFonctionnalités avancées
drgeo-doc-1.5/fr/drgenius_48.html0000644000175000017500000000457110117134567012347 Manuel utilisateur de Dr. Geo -- Autres préférences
Préférences utilisateursComportement par défautAutres préférences

Autres préférences

En plus du comportement par défaut de DR. GEO, l'utilisateur peut modifier le nom d'une figure à partir du menu Édition->Renommer.

Changement du nom d'une figure

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Préférences utilisateursComportement par défautAutres préférences
drgeo-doc-1.5/fr/drgenius_49.html0000644000175000017500000001113310117134567012340 Manuel utilisateur de Dr. Geo -- Fonctionnalités avancées
Fichiers et documentsTopFonctions de baseFonctionnalités avancées

Fonctionnalités avancées

Dans ce chapitre, nous présentons les fonctionnalités qui permettent d'étendre les possibilités de DR. GEO ou de l'adapter à une situation pédagogique donnée.

La première est la macro-construction. Elle permet l'extraction d'une construction logique dans un enregistrement. Cet enregistrement peut ensuite être répété ou sauvegardé dans un fichier portant l'extension .mgeo et ouvert lorsque nécessaire.

Les scripts Scheme DR. GEO - DR. GEO Script aka DGS - représentent une autre fonctionnalité pour étendre DR. GEO. Ces scripts sont de véritables items de figure, comme les items géométriques. En entrée, ils reçoivent une ou plusieurs références d'items géométriques et ils retournent une valeur placée dans la figure. Ce sont en fait des fonctions2 greffées dans une figure, elle sont évaluées à chaque mise à jour de la figure (i.e. lorsque la figure a besoin d'être redessinée).

Les scripts Scheme DR. GEO sont utiles pour la valeur qu'ils retournent ou leur effet de bord, cela dépend de ce que l'utilisateur souhaite réaliser.

En extension des scripts Scheme, DR. GEO propose d'aller encore plus loin avec les figures Scheme de DR. GEO. Cette fois il s'agit de décrire une figure géométrique complètement sous la forme d'un code source écrit dans le langage Scheme. La force de cette approche est de permettre une construction fonctionnelle3 des figures et non plus simplement déclarative comme c'est le cas avec l'interface graphique.

Enfin, l'adaptation de l'interface utilisateur de DR. GEO permet à un enseignant de préparer une session de travail avec des documents dans lesquels certaines fonctions ont été bloquées par un mot de passe. L'intérêt est de contrainte à l'utilisation de certains outils pour des situations pédagogiques données.

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Fichiers et documentsTopFonctions de baseFonctionnalités avancées
drgeo-doc-1.5/fr/drgenius_4.html0000644000175000017500000001406710117134567012260 Manuel utilisateur de Dr. Geo -- Avant propos
DR. GEO sur le webIntroductionAvant propos

Avant propos

DR. GEO est un logiciel libre de géométrie interactive et de programmation en Scheme. Il permet de créer des figures géométriques et de les manipuler interactivement en respectant leurs contraintes géométriques. Il offre également la possibilité d'introduire graduellement la programmation. Il est ainsi utilisable dans des situations d'enseignement du niveau primaire au niveau supérieur.

L'interface utilisateur de DR. GEO a été conçue pour allier dans un ensemble harmonieux à la fois simplicité d'utilisation, ergonomie et fonctionnalités avancées.

Ainsi l'interface de DR. GEO, sous une très grande apparence de simplicité, permet au néophyte de se familiariser très rapidement avec les fonctions de base du logiciel. Puis, au fur et à mesure de sa découverte du logiciel, l'utilisateur découvrira des aspects plus avancés de l'interface et du fonctionnement de DR. GEO : multiplicité des modalités de construction d'objet1, macro-construction, sessions, adaptabilité de l'interface, scriptabilité, Figure Scheme de DR. GEO. Ces fonctionnalités avancées génèrent peu de surcharge sur l'interface, c'est pour cela que DR. GEO est très agréablement utilisé en enseignement primaire, cependant il est également très intéressant pour le lycée.

Dans les sections suivantes, les outils de base seront exposés. Ensuite les fonctionnalités avancées seront présentées en détail.

Écran de bienvenue de DR. GEO

L'agencement de l'interface est :
  1. la barre de menu caractéristique avec Fichier, Édition, Macro-constructions, Fenêtres, Aide ;
  2. la barre d'action pour créer une nouvelle figure, un texte d'explication, les outils faire/defaire, etc.

Pour créer une nouvelle figure géométrique, l'utilisateur clique sur le premier bouton de la barre d'action. Alternativement, une nouvelle figure peut être créée en utilisant le menu Fichier->Nouveau->Figure. Lorsqu'une nouvelle figure est créée, une nouvelle barre d'icônes avec un ensemble de six icônes apparaît. Cette barre d'icônes se termine par un menu permettant d'ajuster l'échelle de la figure géométrique courante.

En outre, une barre d'icônes verticale de raccourcis, à gauche de la figure, offre un accès rapide aux outils les plus utilisés.

Une figure géométrique vide

Les six icônes de la barre d'icônes sont des entrées de menu pour des fonctions spécifiques. Ces fonctions sont décrites dans le prochain chapitre.

Une figure DR. GEO et sa description

Pour chaque figure, un panneau synoptique décrivant sa séquence de construction est disponible. Par défaut ce panneau est poussé à l'extrême gauche et seule la représentation de la figure est visible. À tout moment, l'utilisateur peut pousser le panneau vers la droite pour rendre visible sa description. Une description de figure est un arbre composé de tous les éléments de la figure. Les éléments relatifs à d'autres éléments peuvent être développés en cliquant sur le signe `+', de manière à visualiser les parents de ces éléments.
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DR. GEO sur le webIntroductionAvant propos
drgeo-doc-1.5/fr/drgenius_50.html0000644000175000017500000000745310117134567012342 Manuel utilisateur de Dr. Geo -- Exécution d'une macro-construction
Macro-constructionCréation d'une macro-constructionExécution d'une macro-construction

Exécution d'une macro-construction

Pour exécuter une macro-construction, l'utilisateur appelle la fonction Exécuter une macro pré-préconstruite à partir de la barre d'outils ou depuis le menu contextuel de la vue de la figure.

À partir de la boîte de dialogue, l'utilisateur sélectionne la macro-construction. Dans la seconde page, il sélectionne la macro-construction dans la liste en haut de la boîte de dialogue. Une fois la macro sélectionnée, il peut directement cliquer sur les paramètres d'entrée dans la figure. Dès que tous les paramètres d'entrée sont sélectionnés, la macro-construction est exécutée et les paramètres finaux sont affichés.

L'utilisateur sélectionne les paramètres d'entrée dans la figure

Dans notre exemple, la macro-construction nécessite trois paramètres d'entrée (trois points) et elle construit un point et un cercle. Pour exécuter notre macro-construction, il faut une figure avec au moins trois points.

Une figure avec trois points

Une fois que notre macro-construction est appliquée à ces trois points, nous avons le cercle souhaité et son centre.

La figure finale avec le cercle et son centre

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Macro-constructionCréation d'une macro-constructionExécution d'une macro-construction
drgeo-doc-1.5/fr/drgenius_51.html0000644000175000017500000001264010117134567012335 Manuel utilisateur de Dr. Geo -- Création d'une macro-construction
Exécution d'une macro-constructionMacro-constructionCréation d'une macro-construction

Création d'une macro-construction

À cette étape, la séquence de construction est faite. L'utilisateur doit maintenant avertir DR. GEO qu'il veut une macro-construction à partir de cette séquence. Il doit appeler la fonction Construire une macro à partir de la barre d'icônes ou depuis le menu contextuel de la vue de la figure.

Depuis la boîte de dialogue de l'assistant, l'utilisateur sélectionne les paramètres d'entrée et de sortie, le nom et la description de la macro-construction.

Première page de la boîte de dialogue de l'assistant pour construire une macro-construction

La seconde page de la boîte de dialogue sert à sélectionner les paramètres d'entrée. Dans notre exemple, ce sont les trois points initiaux. L'utilisateur a juste besoin d'aller jusqu'à cette seconde page et il peut sélectionner les trois points de la figure. Les items sélectionnés clignotent.

La seconde page, les trois points sont sélectionnés

À partir de la troisième page, l'utilisateur sélectionne les paramètres de sortie. Dans notre exemple, nous voulons le cercle et son centre comme résultat de la macro-construction. Il procède comme dans le cas des paramètres d'entrée pour les sélectionner.

La troisième page, le cercle et son centre sont sélectionnés

À partir de la quatrième page, l'utilisateur entre le nom et la description de la macro-construction. Ces informations sont affichées lorsque l'utilisateur exécute une macro-construction. Ceci permet de distinguer les macro-constructions entre elles.

La quatrième page, le nom et la description de la macro-construction

À partir de la dernière boîte de dialogue de l'assistant (la cinquième), l'utilisateur termine la création en appuyant sur le bouton Terminer. Il peut aussi revenir aux étapes précédentes pour ajuster les paramètres de la macro-construction.

(!) Si la sélection des paramètres d'entrée et de sortie ne correspond pas (DR. GEO ne peut pas extraire la logique de la construction), la macro-construction ne peut pas être créée. Dans ce cas, l'utilisateur doit reconsidérer la sélection des paramètres d'entrée et de sortie. Il peut revenir à la seconde ou la troisième page de la boîte de dialogue de l'assistant pour ajuster ses choix.

À cette étape, la macro-construction est créée et enregistrée dans DR. GEO. Dans la prochaine section, nous verrons comme l'utiliser.

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Exécution d'une macro-constructionMacro-constructionCréation d'une macro-construction
drgeo-doc-1.5/fr/drgenius_52.html0000644000175000017500000000433610117134567012341 Manuel utilisateur de Dr. Geo -- Exécution d'une macro-construction
Macro-constructionCréation d'une macro-constructionExécution d'une macro-construction

Exécution d'une macro-construction

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Macro-constructionCréation d'une macro-constructionExécution d'une macro-construction
drgeo-doc-1.5/fr/drgenius_53.html0000644000175000017500000000770310117134567012343 Manuel utilisateur de Dr. Geo -- À l'aide de la boîte de dialogue
À l'aide du menu Macro-constructionsExécution d'une macro-constructionÀ l'aide de la boîte de dialogue

À l'aide de la boîte de dialogue

Pour exécuter une macro-construction, l'utilisateur peut appeler la fonction Exécuter une macro pré-préconstruite à partir de la barre d'icônes ou depuis le menu contextuel de la vue de la figure. Une boîte de dialogue décrivant la procédure s'affiche alors.

À partir de cette boîte de dialogue, l'utilisateur sélectionne la macro-construction. Dans la seconde page, il sélectionne la macro-construction dans la liste en haut de la boîte de dialogue. Une fois la macro sélectionnée, il peut directement cliquer sur les paramètres d'entrée dans la figure. Dès que tous les paramètres d'entrée sont sélectionnés, la macro-construction est exécutée et les paramètres finaux sont affichés.

L'utilisateur sélectionne les paramètres d'entrée dans la figure

Dans notre exemple, la macro-construction nécessite trois paramètres d'entrée (trois points) et elle construit un point et un cercle. Pour exécuter notre macro-construction, il faut une figure avec au moins trois points.

Une figure avec trois points

Une fois que notre macro-construction est appliquée à ces trois points, nous avons le cercle souhaité et son centre.

La figure finale avec le cercle et son centre

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À l'aide du menu Macro-constructionsExécution d'une macro-constructionÀ l'aide de la boîte de dialogue
drgeo-doc-1.5/fr/drgenius_54.html0000644000175000017500000000575510117134567012351 Manuel utilisateur de Dr. Geo -- À l'aide du menu Macro-constructions
Exécution d'une macro-constructionÀ l'aide de la boîte de dialogueÀ l'aide du menu Macro-constructions

À l'aide du menu Macro-constructions

Il existe une autre procédure - plus rapide - pour exécuter une macro-construction. La barre de menu principale de DR. GEO comporte un menu Macro-constructions. Ce menu est peuplé par les noms des macro-constructions chargées en mémoire dans le programme. Pour exécuter une macro-construction, l'utilisateur sélectionne directement celle de son choix.

En outre un passage du pointeur souris au dessus de chaque item de menu fait apparaître une info-bulle de la description de la macro. L'utilisateur peut ainsi avoir rapidement une explication sur l'ensemble des macro-constructions.

Exécuter une macro-construction directement depuis le menu Macro-constructions

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Exécution d'une macro-constructionÀ l'aide de la boîte de dialogueÀ l'aide du menu Macro-constructions
drgeo-doc-1.5/fr/drgenius_55.html0000644000175000017500000000603310117134567012340 Manuel utilisateur de Dr. Geo -- Droite, Demi-droite, Segment, Vecteur
Cercle, Arc de cercleMéthodes de référence pour les scripts DR. GEOPointDroite, Demi-droite, Segment, Vecteur

Droite, Demi-droite, Segment, Vecteur

valeur (getSlope direction)
direction: Référence vers un objet de type droite, demi-droite, segment ou vecteur
Retourne: La pente de cette direction
Exemple:
(define p (getSlope a1))

  valeur (getNorm vecteur)
vecteur: Référence vers un vecteur
Retourne: La norme de ce vecteur
Exemple:
(define n (getNorm a1))

  valeur (getLength segment)
segment: Référence vers un segment
Retourne: La longueur de ce segment
Exemple:
(define l (getLength a1))

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Cercle, Arc de cercleMéthodes de référence pour les scripts DR. GEOPointDroite, Demi-droite, Segment, Vecteur
drgeo-doc-1.5/fr/drgenius_56.html0000644000175000017500000003132210117134567012340 Manuel utilisateur de Dr. Geo -- DGS par l'exemple
Méthodes de référence pour les scripts DR. GEOScript Scheme DR. GEODGS par l'exemple

DGS par l'exemple

L'outil pour créer un DGS est disponible depuis la section numérique du menu contextuel ou de la barre d'icônes. Un DGS peut recevoir de 0 à n paramètres d'entrée.

Après avoir choisi l'outil, il suffit de cliquer sur les objets souhaités en entrée puis quelque part sur le fond de la figure, le script sera placé à ce dernier endroit.

Dans la suite nous vous proposons de travailler sur quelques exemples de DGS, leurs fonctionnalités et leur puissance seront plus facilement analysées. Les DGS comme les macro-constructions donnent une dimension particulière à DR. GEO, ils permettent - chacun avec un positionnement différent5 - d'aller là où les auteurs du logiciel ne sont pas allés ou ne souhaitent par aller.

Il est aussi important de comprendre que la plupart des fonctionnalités de l'interpréteur GNU Guile sont disponibles depuis les DGS. C'est particulièrement vrai pour ses bibliothèques de fonctions6, nous allons bien sûr les utiliser intensément.

DGS sans paramètre d'entrée

La procédure pour créer un script sans paramètre d'entrée est la suivante :

  1. Après avoir choisi l'outil de script, cliquer directement dans le fond écran, à l'emplacement où vous souhaitez placer le script. Surtout ne cliquez sur aucun objet de la figure, sinon DR. GEO comprendra que vous souhaitez cet objet comme paramètre d'entrée du script7.
  2. Une fois le script placé, vous voyez la chaîne de caractères "Dr. Genius" s'afficher. Tout script nouvellement créé contient une commande par défaut pour afficher cette chaîne de caractères, vous pouvez l'éditer en allant à l'outil propriétés d'objet.
  3. Une fois cet outil choisi, cliquer sur le script - ou pour être plus précis sur sa valeur - de votre choix dans la figure. Une boîte de dialogue contenant le script s'affichera. Dans la suite de cette section, c'est dans ce dialogue que nous saisissons les scripts.
Un générateur de nombres aléatoires et autres :

Si vous souhaitez un générateur de nombres aléatoires, rien de plus simple, saisissez pour tout script le code suivant : 

(random 10)

À chaque mise à jour de la figure, il génère un nombre aléatoire entier dans l'intervalle [0 ; 10[.

Si vous préférez un nombre flottant dans l'intervalle [0 ; 1[, utilisez ce script : 

(random:uniform)

(!) Quelques précisions :
  • La valeur retournée par le script est la valeur calculée par la dernière ligne. Ici en l'occurrence, il s'agit de la valeur retournée par l'appel d'une fonction ;
  • La dernière ligne d'un script doit retourner un nombre réel. Sinon DR. GEO affiche "Résultat non imprimable" ;
  • Si l'on souhaite retourner la valeur d'une variable, il suffit de mettre son nom en dernière ligne.

Calculer des valeurs usuelles :

Pour calculer une valeur approchée de pi : 

(acos -1)

ou de e : 

(exp 1)

Les valeurs retournées par ces DGS sont ensuite utilisables comme toutes les autres valeurs numériques que peut générer DR. GEO. Pour toutes ces petites choses les DGS sont donc vos amis. Mais ils peuvent faire bien plus de choses intéressantes lorsqu'ils reçoivent des paramètres en entrée.

DGS avec au moins un paramètre d'entrée

La procédure pour créer un DGS avec un paramètre d'entrée est sensiblement la même. Juste après avoir sélectionné l'outil script, il suffit de cliquer sur l'objet qui sera passé en paramètre d'entrée, puis de cliquer sur le fond de l'écran, à l'endroit où le script doit être placé.

Ensuite, dans le script, la référence du paramètre d'entrée est placée dans la variable a1. Si nous avions défini deux paramètres d'entrée, leurs références auraient été placées suivant l'ordre de sélection dans les variables a1 et a2. De même pour un nombre de 3, 4, etc. de paramètres d'entrée.

Selon le type d'objet en référence, diverses méthodes sont disponibles qui pour obtenir sa valeur, qui pour obtenir ses coordonnées, etc. Le répertoire des méthodes est disponible depuis la Section Méthodes de référence des DGS.

Dans la suite, nous exposerons graduellement la construction d'une portion de courbe représentative d'une fonction et la tangente en un point mobile à cette portion de courbe.

La figure finale est fournie dans DR. GEO. Elle s'appelle slope.fgeo.

La figure que nous obtiendrons

Définir une valeur dans un intervalle donné :

Dans une nouvelle figure, nous commençons par placer deux points et le segment dont les extrémités sont ces deux points. Sur ce segment nous plaçons un point libre appelé "Move me!". Ce point servira de jauge, à nous de la calibrer avec un script. Ensuite nous créons un script ayant pour unique paramètre d'entrée ce point là.

Lorsque a1 est une référence vers le point "Move me!", le script suivant nous retourne une valeur décimale comprise entre [-10 ; 10] : 

(define x (getAbscissa a1))
(* 20  (- x 0.5))

Quelques explications s'imposent. Dans la première ligne, l'appel (getAbscissa a1) permet d'obtenir l'abscisse curviligne de l'objet référencé par a18 - c'est-à-dire le point "Move me!". Cette abscisse est placée dans une nouvelle variable x. Ensuite à la deuxième ligne nous calibrons, ici l'expression est équivalente en notation algébrique à 20 ×( x - 0.5). Comme c'est la dernière ligne du script le résultat de ce calcul est la valeur retournée et affichée dans la figure.

Enfin, nommons ce script Xo.

Afficher une portion de courbe représentative d'une fonction :

La valeur obtenue par le script précédant nous servira d'abscisse, nous allons nous servir de cette valeur pour calculer avec un deuxième script l'ordonnée en ce point par la fonction x -> cos(x) : 

(define x (getValue a1))
(cos x)

L'appel (getValue a1) permet d'obtenir la valeur numérique de l'objet de référence a1. Ici il s'agit d'obtenir la valeur retournée par le script précédent. Nous nommons ce script Yo.

Ensuite nous créons le point Mo de coordonnées (Xo ; Yo). C'est un point de la courbe représentative de x -> cos(x). Pour afficher sa portion de courbe représentative sur l'intervalle [-10 ; 10], nous créons le lieu du point Mo lorsque le point "Move Me!" décrit le segment. Ça y est nous avons une courbe !

Calculer et afficher la tangente à une courbe :

Pour afficher la tangente en Mo, il nous faut d'abord la pente en ce point. Nous avons donc besoin de la fonction dérivée x -> -sin(x) et de Xo. Nous créons un script avec comme paramètre d'entrée le script Xo : 

(- 0 (sin (getValue a1)))

La notation préfixée utilisée par Scheme/Guile peut dérouter, c'est simplement une question d'habitude. Nommons ce script "pente en Mo". Ainsi lorsque Mo se déplace sur la courbe, la pente est recalculée.

Il nous reste maintenant à afficher la tangente. Pour ce faire nous allons d'abord calculer les coordonnées d'un deuxième point - M1 - de cette droite.

Commençons par son abscisse, par exemple X1 = Xo + 2, pour ce faire créons un script avec comme paramètre d'entrée le script Xo : 

(define x1 (getValue a1))
(+ x1 2)

Nommons ce script X1.

Attaquons-nous maintenant à l'ordonnée de M1. Là nous avons besoin de :

  • Mo (référence a1) ;
  • la pente en Mo (a2) ;
  • l'abscisse X1 (a3).

Dans le script suivant, nous calculons l'ordonnée de M1 par le calcul Yo + m ×(X1 - X0) : 

(define x0 (car (getCoordinates a1)))
(define y0 (cadr (getCoordinates a1)))
(define m (getValue a2))
(define x1 (getValue a3))
(+ (* m (- x1 x0)) y0)

Quelques mots sur l'appel (getCoordinates a1), dans cet appel a1 doit être une référence vers un objet de type point, la méthode retourne une liste contenant les coordonnées du point - ici Mo. car permet d'extraire le premier élément de cette liste, cadr le deuxième. Le reste du script ne devrait pas poser de problème.

Nommons ce script Y1 puis construisons le point M1 de coordonnées (X1 ; Y1) et enfin la tangente (MoM1).

Bien sûr, il aurait été possible de n'utiliser que deux ou trois gros scripts à la place de cette myriade de scripts. Mais nous espérons que ces petits exemples vous ont donné envie d'essayer par vous même les DGS.

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Méthodes de référence pour les scripts DR. GEOScript Scheme DR. GEODGS par l'exemple
drgeo-doc-1.5/fr/drgenius_57.html0000644000175000017500000000521710117134567012345 Manuel utilisateur de Dr. Geo -- Méthodes de référence pour les scripts DR. GEO
Script Scheme DR. GEODGS par l'exempleMéthodes de référence pour les scripts DR. GEO

Méthodes de référence pour les scripts DR. GEO

Les sections suivantes contiennent la description des méthodes disponibles pour les DGS. Elles sont classées par type d'objet géométrique ou numérique.
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Script Scheme DR. GEODGS par l'exempleMéthodes de référence pour les scripts DR. GEO
drgeo-doc-1.5/fr/drgenius_58.html0000644000175000017500000000711710117134567012347 Manuel utilisateur de Dr. Geo -- Point
Droite, Demi-droite, Segment, VecteurMéthodes de référence pour les scripts DR. GEOPoint

Point

valeur (getAbscissa point)
point: Référence d'un point libre sur une ligne
Retourne: L'abscisse de ce point sur la ligne. La valeur appartient à l'intervalle [0 ; 1]
Exemple:
(define x (getAbscissa a1))
(* x 10)

  (setAbscissa point x)
point: Référence d'un point libre sur une ligne
x: Valeur décimale de l'intervalle [0 ; 1] représentant la nouvelle abscisse
Exemple:
(setAbscissa a1 0.5)

 

liste (getCoordinates point|vecteur)
Retourne les coordonnées d'un point ou d'un vecteur.
point|vecteur: Référence vers un point ou un vecteur
Retourne: Liste contenant les coordonnées du point ou du vecteur
Exemple:
(define c (getCoordinates a1))
(define x (car c))
(define y (cadr c))
(+ (* x x) (* y y))

  (setCoordinates point coord)
Positionne les coordonnées d'un point
point: Référence d'un point libre dans le plan
coord: Liste de deux nombres décimaux
Exemple:
(define l (list 1.4 (random 5)))
(setCoordinate a1 l)

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Droite, Demi-droite, Segment, VecteurMéthodes de référence pour les scripts DR. GEOPoint
drgeo-doc-1.5/fr/drgenius_59.html0000644000175000017500000000737710117134567012360 Manuel utilisateur de Dr. Geo -- Droite, Demi-droite, Segment, Vecteur
Cercle, Arc de cercleMéthodes de référence pour les scripts DR. GEOPointDroite, Demi-droite, Segment, Vecteur

Droite, Demi-droite, Segment, Vecteur

valeur (getSlope direction)
direction: Référence vers un objet de type droite, demi-droite, segment ou vecteur
Retourne: La pente de cette direction
Exemple:
(define p (getSlope a1))

  valeur (getUnit direction)
direction: Référence vers un objet de type droite, demi-droite, segment ou vecteur
Retourne: Une liste contenant les coordonnées d'un vecteur unitaire
Exemple:
(define v (getUnit a1))

valeur (getNormal direction)
direction: Référence vers un objet de type droite, demi-droite, segment ou vecteur
Retourne: Une liste contenant les coordonnées d'un vecteur normal à la direction
Exemple:
(define n (getNormal a1))

  valeur (getNorm vecteur)
vecteur: Référence vers un vecteur
Retourne: La norme de ce vecteur
Exemple:
(define n (getNorm a1))

  valeur (getLength segment)
segment: Référence vers un segment
Retourne: La longueur de ce segment
Exemple:
(define l (getLength a1))

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Cercle, Arc de cercleMéthodes de référence pour les scripts DR. GEOPointDroite, Demi-droite, Segment, Vecteur
drgeo-doc-1.5/fr/drgenius_5.html0000644000175000017500000000464010117134567012255 Manuel utilisateur de Dr. Geo -- DR. GEO sur le web
IntroductionAvant proposDR. GEO sur le web

DR. GEO sur le web

DR. GEO dispose de son propre espace web sur le site d'OFSET à l'adresse : http://www.ofset.org/drgeo

Sur cet espace, l'utilisateur trouvera les informations suivantes :

  • les informations pour obtenir DR. GEO ;
  • la documentation sur le logiciel ;
  • des indications pour s'impliquer dans le projet DR. GEO ;
  • des références sur des exploitations pédagogiques du logiciel.
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IntroductionAvant proposDR. GEO sur le web
drgeo-doc-1.5/fr/drgenius_60.html0000644000175000017500000000631110117134567012333 Manuel utilisateur de Dr. Geo -- Cercle, Arc de cercle
NombreMéthodes de référence pour les scripts DR. GEODroite, Demi-droite, Segment, VecteurCercle, Arc de cercle

Cercle, Arc de cercle

liste (getCenter cercle|arc-cercle)
cercle|arc-cercle: Référence vers un cercle ou un arc de cercle
Retourne: Liste contenant les coordonnées du centre du cercle ou de l'arc de cercle
Exemple:
(define c (getCenter a1))
(car c)

  valeur (getRadius cercle|arc-cercle)
cercle|arc-cercle: Référence vers un cercle ou un arc de cercle
Retourne: Rayon du cercle ou de l'arc de cercle
Exemple:
(define r (getRadius a1))

  valeur (getLength cercle|arc-cercle)
cercle|arc-cercle: Référence vers un cercle ou un arc de cercle
Retourne: Périmètre du cercle ou longueur de l'arc de cercle
Exemple:
(define l (getLength a1))

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NombreMéthodes de référence pour les scripts DR. GEODroite, Demi-droite, Segment, VecteurCercle, Arc de cercle
drgeo-doc-1.5/fr/drgenius_61.html0000644000175000017500000000517710117134567012345 Manuel utilisateur de Dr. Geo -- Nombre
AngleMéthodes de référence pour les scripts DR. GEOCercle, Arc de cercleNombre

Nombre

valeur (getValue nombre)
nombre: Référence vers un nombre
Retourne: Valeur de ce nombre
Exemple:
(define a (getValue a1))
(define b (getValue a2))
(+ a b)

  (setValue nombre v)
nombre: Référence vers un nombre
v: Valeur décimale
Exemple:
(define v (getValue a1))
(setValue a2 v)

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AngleMéthodes de référence pour les scripts DR. GEOCercle, Arc de cercleNombre
drgeo-doc-1.5/fr/drgenius_62.html0000644000175000017500000000502110117134567012332 Manuel utilisateur de Dr. Geo -- Angle
AutresMéthodes de référence pour les scripts DR. GEONombreAngle

Angle

valeur (getAngle angle)
angle: Référence vers un angle, orienté ou géométrique
Retourne: Une mesure de cet angle en degré. Pour obtenir une mesure en radian, utiliser la méthode getValue
Exemple:
(define angle1 (getAngle a1))
(define angle2 (getAngle2))
(define angle3 (getAngle a3))
(+ angle1 angle2 angle3)

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AutresMéthodes de référence pour les scripts DR. GEONombreAngle
drgeo-doc-1.5/fr/drgenius_63.html0000644000175000017500000000434210117134567012340 Manuel utilisateur de Dr. Geo -- Autres
Méthodes de référence pour les scripts DR. GEOAngleAutres

Autres

(move item t)
item: Référence vers un objet de la figure
t: Vecteur à deux dimensions
Exemple:
(define v (vector .1 0))
(move a1 v)

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Méthodes de référence pour les scripts DR. GEOAngleAutres
drgeo-doc-1.5/fr/drgenius_64.html0000644000175000017500000000621310117134567012340 Manuel utilisateur de Dr. Geo -- Figure Scheme de DR. GEO
Masquer des outils dans l'interfaceFonctionnalités avancéesScript Scheme DR. GEOFigure Scheme de DR. GEO

Figure Scheme de DR. GEO

Les Figures Scheme de DR. GEO - (FSD) - sont des figures écrites dans un langage relativement naturel. Il ne s'agit donc plus de construire une figure à l'aide de l'interface graphique de DR. GEO mais plutôt de décrire une figure dans le langage Scheme. Nous avons apporté le plus grand soin afin que la syntaxe utilsée soit facile et légère. Aussi l'ensemble des mots clés utilisés pour décrire une figure simple sont adaptables dans différentes langues. Ainsi une figure pourra être décrite en Français, en Anglais, en Espagnol, etc. (Un mélange de langues est même possible mais ce n'est pas souhaitable).

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Masquer des outils dans l'interfaceFonctionnalités avancéesScript Scheme DR. GEOFigure Scheme de DR. GEO
drgeo-doc-1.5/fr/drgenius_65.html0000644000175000017500000002126410117134567012344 Manuel utilisateur de Dr. Geo -- Quelques exemples
Méthodes de référence pour les Figures Scheme DR. GEOFigure Scheme de DR. GEOQuelques exemples

Quelques exemples

En lui même Scheme est un langage de très haut niveau, lorsqu'une figure est définie dans ce langage, nous disposons également de toute sa puissance pour par exemple définir récursivement telle partie de la figure, ou bien pour placer aléatoirement certains objets de telle sorte qu'à chaque ouverture de la figure, celle-ci est légèrement différente. Bref, les FSD sont libérées du carcan de l'interface graphique tout en étant renforcées du langage Scheme. Un FSD est donc un fichier d'extension .scm créé à l'aide d'un éditeur de texte, il est ensuite ouvert dans DR. GEO à l'aide de la commande Fichier->Évaluer.

Commençons par étudier un exemple simple de FSD : 

(nouvelle-figure "Ma figure")

C'est la plus petite FSD que nous puissions définir. Lors de son chargement dans DR. GEO, celle-ci va simplement créer une nouvelle figure vide nommée "Ma figure". Nous pourrions multiplier les commandes (nouvelle-figure "Ma figure") autant de fois que nous le souhaitons, autant de figures seraient créées.

Abordons un deuxième exemple : 

(nouvelle-figure "Ma figure")
(soit Point "A" libre 1.2 -2)

Cette FSD définie une figure avec un point libre A de coordonnées initiales (1,2 ; -2). Comme nous pouvons le voir la syntaxe de définition d'un objet géométrique est relativement agréable, d'autant plus qu'elle est exprimée dans une langue maternelle. Intéressons nous de plus près à la deuxième instruction, en effet celle-ci suit une syntaxe qui est commune à toutes les commandes de définition d'objet. Ce type de commande se décompose comme suit :

  1. Elle commence toujours par le mot-clé soit, il indique que nous souhaitons définir un nouvel objet.
  2. Il est immédiatement suivi de la catégorie de l'objet, ici Point.
  3. Le nom de l'objet vient ensuite, A, il doit toujours être entouré de ". Si nous ne souhaitons pas nommer l'objet, il faut tout de même donner un nom vide comme suit: "".
  4. Enfin, nous précisons le type de l'objet - le type de point dans notre exemple - ici libre. Cela signifie que le point A est libre.
  5. Le type de l'objet est suivi d'une liste d'arguments spécifiques. Dans notre exemple cette liste est composée de deux nombres, les coordonnées du point libre A.

Poursuivons avec un troisième exemple : 

(define (triangle p1 p2 p3)
  (Segment "" extrémités p1 p2)
  (Segment "" extrémités p2 p3)
  (Segment "" extrémités p1 p3))

(define (hasard)
  (- 8 (* 16 (random:uniform))))

(nouvelle-figure "Ma figure")

(soit Point "A" libre (hasard) 0)
(soit Point "B" libre 5 0)
(soit Point "C" libre (hasard) 5)

(triangle A B C)

Cet exemple est particulièrement intéressant, il nous montre trois choses importantes :

  1. L'introduction de construction de plus haut niveau, non prévue au départ par DR. GEO. Ici nous avons défini la fonction triangle qui, à partir de trois points, construit le triangle passant par ces trois points. Nous pouvons comparer ceci avec les macro-constructions mais avec un degré de liberté beaucoup plus important.
  2. La définition de fonctions associées, ici nous avons défini la fonction hasard qui retourne un nombre décimal compris entre -8 et 8. Nous utilisons cette fonction pour placer au hasard certains points de notre figure, ainsi à chaque ouverture la figure est légèrement différente.
  3. En fait l'utilisation du mot clé soit n'est pas obligatoire, nous l'utilisons lorsque nous souhaitons garder une référence de l'objet créé. Par exemple dans la fonction triangle, nous ne gardons pas de références des segments créés, en revanche lorsque nous définissons nos points A, B et C nous avons besoin de garder une référence, ces références ont le même nom9 sans guillemet : A, B et C. Dans la suite nous appellerons symbole ces références, c'est la terminologie exacte du langage Scheme. Ainsi, lors de l'appel de la fonction triangle, nous passons en paramètre les symboles A, B et C qui sont utilisés pour définir nos trois segments.

Noter que lors de la définition des segments, nous ne donnons pas de nom, dans ce cas DR. GEO va attribuer un nom par défaut défini à partir du nom des extrémités. Nos trois segments auront donc comme nom [AB], [BC] et [AC].

Pour clore cette section, voici un dernier exemple : 

(soit Point "A" libre 1 0)
(soit Point "B" libre 5 0)
(soit Droite "d1" 2points A B)

(envoi A couleur jaune)
(envoi A forme rond)
(envoi A taille large)
(envoi B masquer)
(envoi d1 épaisseur tiret)

Les trois premières commandes créent deux points et une droite. La partie qui nous intéresse plus particulièrement est la série de commande envoi. Cette commande permet de communiquer avec un objet dont nous avons gardé un symbole, ici nous avons les symboles A, B et d1. Elle consiste à envoyer un message à un objet, son premier argument est l'objet avec lequel nous communiquons, le deuxième argument le message, le troisième et les suivants sont déterminés par la nature du message. Par exemple (envoi A couleur jaune) envoie le message couleur avec comme paramètre jaune, le point A est peint en jaune. Il est assez facile de comprendre le sens des autres commandes envoi. Elles seront expliquées dans la section suivante.

Nous avons terminé notre petite visite guidée des Figure Scheme Dr. Geo. Dans les sections suivantes nous exposons l'ensemble des commandes disponibles pour définir des FSD.

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Méthodes de référence pour les Figures Scheme DR. GEOFigure Scheme de DR. GEOQuelques exemples
drgeo-doc-1.5/fr/drgenius_66.html0000644000175000017500000000561110117134567012343 Manuel utilisateur de Dr. Geo -- Méthodes de référence pour les Figures Scheme DR. GEO
Galerie d'exemplesFigure Scheme de DR. GEOQuelques exemplesMéthodes de référence pour les Figures Scheme DR. GEO

Méthodes de référence pour les Figures Scheme DR. GEO

La définition d'objets dans un document FSD se fait par l'intermédiare de prototypes. Les prototypes sont en quelque sorte des objets qu'il est possible d'interroger et de modifier comme nous le verrons par la suite.

Cependant, avant toute définition d'objets d'une figure, cette dernière doit être créée avec la commande nouvelle-figure.

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Galerie d'exemplesFigure Scheme de DR. GEOQuelques exemplesMéthodes de référence pour les Figures Scheme DR. GEO
drgeo-doc-1.5/fr/drgenius_67.html0000644000175000017500000000511010117134567012336 Manuel utilisateur de Dr. Geo -- Commandes générales
Définition d'objets d'une figureMéthodes de référence pour les Figures Scheme DR. GEOCommandes générales

Commandes générales

(nouvelle-figure nom)
nom: Chaîne de caractère
Retourne: Ne retourne pas de valeur. L'appel ne produit qu'un effet de bord, à savoir la création d'une nouvelle figure, les objets suivants sont créés dans cette figure, jusqu'au prochain appel de ce type.
Exemple:
(nouvelle-figure "Ma 1er figure")

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Définition d'objets d'une figureMéthodes de référence pour les Figures Scheme DR. GEOCommandes générales
drgeo-doc-1.5/fr/drgenius_68.html0000644000175000017500000005612410117134567012352 Manuel utilisateur de Dr. Geo -- Définition d'objets d'une figure
Modification d'attributs d'objetsMéthodes de référence pour les Figures Scheme DR. GEOCommandes généralesDéfinition d'objets d'une figure

Définition d'objets d'une figure

Un objet peut être défini par l'intermédiaire de différentes syntaxes :

  • (soit Point "p1" type args)

    Le point est créé et sa référence est sauvée dans la variable p1. Cette syntaxe utilise une macro Scheme.

  • (Point "Nom" type args)

    Le point est créé mais aucune référence du point n'est conservée.

  • (define p1 (Point "Nom" type args))

    Le point est créé et sa référence est sauvée dans la variable p1.

  • (set! p1 (Point "Nom" type args))

    Le point est créé et sa référence est copiée dans la variable préexistante p1.

Si des objets sont créés depuis le corps d'une fonction, utiliser soit la forme set! ou la forme spéciale Scheme let. Il est important de remarquer que l'appel de base est celui d'une fonction retournant une référence de l'objet créé.

Pour en savoir plus sur la correspondance entre les noms de commande Scheme en français et en anglais, voir le fichier /usr/share/drgeo/scm/drgeo_scm_interface_constant_fr.scm.

 

Point
prototype (Point nom libre x y)
nom: Chaîne de caractère désignant le nom de l'objet
x: L'abscisse du point
y: L'ordonnée du point
Retourne: Référence d'un point libre du plan de coordonnées initiales x et y.
Exemple:
(define p1 (Point "A" libre 1.2 (acos -1)))

prototype (Point nom sur-courbe ligne x)
nom: Chaîne de caractère désignant le nom de l'objet
ligne: Référence d'une ligne (droite, demi-droite, segment, etc.)
x: Abscisse curviligne du point libre, la valeur appartient à l'intervalle [0 ; 1]
Retourne: Référence d'un point libre sur une ligne.
Exemple:
(Point "M" sur-courbe s1 0.5)

prototype (Point nom milieu-2pts p1 p2)
nom: Chaîne de caractère désignant le nom de l'objet
p1: Référence d'un point
p2: Référence d'un point
Retourne: Référence du milieu des deux points.
Exemple:
(soit Point "A" libre 1 1)
(soit Point "B" libre 4 4)
(Point "I" milieu-2pts A B)

prototype (Point nom milieu-segment s)
nom: Chaîne de caractère désignant le nom de l'objet
s: Référence d'un segment
Retourne: Référence du milieu du segment.
Exemple:
(Point "L" milieu-segment s)

prototype (Point nom intersection l1 l2)
nom: Chaîne de caractère désignant le nom de l'objet
l1: Référence d'une ligne
l2: Référence d'une ligne
Retourne: Référence du point d'intersection des deux lignes.
Exemple:
(Point "I" intersection droite segment)

prototype (Point nom intersection2 l1 l2)
nom: Chaîne de caractère désignant le nom de l'objet
l1: Référence d'une ligne
l2: Référence d'une ligne
Retourne: Référence du 2ème point d'intersection des deux lignes lorsqu'une des deux est du type arc de cercle ou cercle.
Exemple:
(Point "I" intersection2 droite cercle)

 

Droite
prototype (Droite nom 2points p1 p2)
nom: Chaîne de caractère désignant le nom de l'objet
l1: Référence d'un point
l2: Référence d'un point
Retourne: Référence d'une droite passant par deux points.
Exemple:
(soit Point "A" libre 0 0)
(soit Point "M" libre 1 2)
(Droite "" 2points A M)

prototype (Droite nom parallèle p d)
nom: Chaîne de caractère désignant le nom de l'objet
p: Référence d'un point
d: Référence d'une direction (droite, segment, vecteur, ...)
Retourne: Référence d'une droite parallèle à la direction de d et passant par p.
Exemple:
(soit Point "A" libre 1 5)
(soit Droite "d1" parallèle A d)

prototype (Droite nom perpendiculaire p d)
nom: Chaîne de caractère désignant le nom de l'objet
p: Référence d'un point
d: Référence d'une direction (droite, segment, vecteur, ...)
Retourne: Référence d'une droite perpendiculaire à la direction de d et passant par p.
Exemple:
(soit Point "A" libre 1 5)
(soit Droite "d1" perpendiculaire A d)

 

Demi-droite
prototype (Demi-droite nom 2points o p)
nom: Chaîne de caractère désignant le nom de l'objet
o: Référence d'un point, origine de la demi-droite
p: Référence d'un point, point de la demi-droite
Retourne: Référence d'une demi-droite définie par son origine et un point.
Exemple:
(soit Point "A" libre 1 5)
(soit Point "O" libre 0 0)
(soit Demi-droite "dd1" 2points A 0)

 

Segment

prototype (Segment nom extrémités p1 p2)
nom: Chaîne de caractère désignant le nom de l'objet
p1: Référence d'un point
p2: Référence d'un point
Retourne: Référence d'un segment défini par ses extrémités.
Exemple:
(soit Point "A" libre 1 5)
(soit Point "B" libre 10 4)
(soit Segment "" extrémités A B)

 

Cercle
prototype (Cercle nom 2points c p)
nom: Chaîne de caractère désignant le nom de l'objet
c: Référence d'un point, centre du cercle
p: Référence d'un point sur le cercle
Retourne: Référence d'un cercle défini par son centre et un point.
Exemple:
(soit Point "A" libre 1 5)
(soit Point "B" libre 10 4)
(soit Cercle "C1" 2points A B)

prototype (Cercle nom centre-rayon c r)
nom: Chaîne de caractère désignant le nom de l'objet
c: Référence d'un point, centre du cercle
r: Référence d'une valeur numérique, rayon du cercle
Retourne: Référence d'un cercle défini par son centre et son rayon.
Exemple:
(soit Point "A" libre 1 5)
(soit Nombre "r" libre 10)
(soit Cercle "C1" centre-rayon A r)

prototype (Cercle nom centre-segment c s)
nom: Chaîne de caractère désignant le nom de l'objet
c: Référence d'un point, centre du cercle
s: Référence d'un segment dont la longueur est le rayon du cercle
Retourne: Référence d'un cercle défini par son centre et son rayon.
Exemple:
(soit Point "A" libre 1 5)
(soit Cercle "C1" centre-rayon A s)

 

Arc de cercle
prototype (Arc-cercle nom 3points p1 p2 p3)
nom: Chaîne de caractère désignant le nom de l'objet
p1: Référence d'un point, 1ere extrémité de l'arc
p2: Référence d'un point de l'arc
p3: Référence d'un point, 2eme extrémité de l'arc
Retourne: Référence d'un arc de cercle défini par ses extrémités et un point.
Exemple:
(soit Point "A" libre 1 5)
(soit Point "B" libre 0 5)
(soit Point "C" libre -1 -2)
(soit Arc-cercle "arc" 3points A B C)

 

Polygone
prototype (Polygone nom npoints args)
nom: Chaîne de caractère désignant le nom de l'objet
args: Une liste de références de points ; sommets du polygone
Retourne: Référence d'un polygone défini pas ses sommets.
Exemple:
(soit Polygone "quad" npoints A B C D)

 

Les transformations géométriques
Les prototypes des transformations géométriques permettent la construction des tranformés d'objets. Elles s'appliquent à des références d'objets de type point, segment, droite, demi-droite, vecteur, cercle, arc de cercle et polygone.

prototype (TypeObjet nom rotation objet centre angle)
TypeObjet: Point, Segment, Droite, Demi-droite, Vecteur, Cercle, Arc-cercle, Polygone
nom: Chaîne de caractère désignant le nom de l'objet
objet: Référence de l'objet à transformer
centre: Référence d'un point, centre de la rotation
angle: Référence d'une valeur, angle de la rotation
Retourne: Référence de l'objet transformé.
Exemple:
(soit Point "I1" rotation I C a)

prototype (TypeObjet nom homothétie objet centre k)
TypeObjet: Point, Segment, Droite, Demi-droite, Vecteur, Cercle, Arc-cercle, Polygone
nom: Chaîne de caractère désignant le nom de l'objet
objet: Référence de l'objet à transformer
centre: Référence d'un point, centre de l'homothétie
k: Référence d'une valeur, facteur de l'homothétie
Retourne: Référence de l'objet transformé.
Exemple:
(soit Polygone "P1" homothétie P C k1)

prototype (TypeObjet nom symétrie objet centre)
TypeObjet: Point, Segment, Droite, Demi-droite, Vecteur, Cercle, Arc-cercle, Polygone
nom: Chaîne de caractère désignant le nom de l'objet
objet: Référence de l'objet à transformer
centre: Référence d'un point, centre de la symétrie
Retourne: Référence de l'objet transformé.
Exemple:
(soit Segment "S1" symétrie S C)

prototype (TypeObjet nom reflexion objet axe)
TypeObjet: Point, Segment, Droite, Demi-droite, Vecteur, Cercle, Arc-cercle, Polygone
nom: Chaîne de caractère désignant le nom de l'objet
objet: Référence de l'objet à transformer
axe: Référence d'une droite, axe de la réflexion
Retourne: Référence de l'objet transformé.
Exemple:
(soit Polygone "P1" reflexion P d1)

prototype (TypeObjet nom translation objet vecteur)
TypeObjet: Point, Segment, Droite, Demi-droite, Vecteur, Cercle, Arc-cercle, Polygone
nom: Chaîne de caractère désignant le nom de l'objet
objet: Référence de l'objet à transformer
vecteur: Référence d'un vecteur
Retourne: Référence de l'objet transformé.
Exemple:
(soit Cercle "C1" translation C v)

 

Lieu géométrique
prototype (Lieu nom 2points m c)
nom: Chaîne de caractère désignant le nom de l'objet
m: Référence d'un point mobile sur une ligne
c: Référence d'un point fixe dépendant du point m
Retourne: Référence d'un lieu.
Exemple:
(Lieu "lieu1" 2points M I)

 

Vecteur
prototype (Vecteur nom 2points o e)
nom: Chaîne de caractère désignant le nom de l'objet
o: Référence d'un point, origine du vecteur
e: Référence d'un point, extrémité du vecteur
Retourne: Référence d'un vecteur.
Exemple:
(soit Point "B" libre 0 5)
(soit Point "C" libre -1 -2)
(Vecteur "" 2points C B)

 

Nombre
prototype (Nombre nom libre x y v)
nom: Chaîne de caractère désignant le nom de l'objet
x,y: Les coordonnées de l'emplacement du nombre
v: La valeur initiale du nombre
Retourne: Référence d'un nombre libre.
Exemple:
(soit Nombre "pi" libre 5 5 (acos -1))

prototype (Nombre nom longueur-segment x y s)
nom: Chaîne de caractère désignant le nom de l'objet
x,y: Les coordonnées de l'emplacement du nombre
s: Référence d'un segment
Retourne: Référence d'un nombre, longueur d'un segment.
Exemple:
(soit Nombre "l" longueur-segment 5 5 S)

prototype (Nombre nom norme-vecteur x y v)
nom: Chaîne de caractère désignant le nom de l'objet
x,y: Les coordonnées de l'emplacement du nombre
s: Référence d'un vecteur
Retourne: Référence d'un nombre, norme d'un vecteur.
Exemple:
(soit Nombre "l" norme-vecteur 5 5 V)

prototype (Nombre nom point-cercle x y p c)
nom: Chaîne de caractère désignant le nom de l'objet
x,y: Les coordonnées de l'emplacement du nombre
p: Référence d'un point
c: Référence d'un cercle
Retourne: Référence d'un nombre, distance entre le point et le cercle.
Exemple:
(soit Nombre "l" point-cercle 5 5 P C)

prototype (Nombre nom point-droite x y p d)
nom: Chaîne de caractère désignant le nom de l'objet
x,y: Les coordonnées de l'emplacement du nombre
p: Référence d'un point
c: Référence d'une droite
Retourne: Référence d'un nombre, distance entre le point et la droite.
Exemple:
(soit Nombre "d" point-droite 5 5 M D1)

prototype (Nombre nom point-point x y p1 p2)
nom: Chaîne de caractère désignant le nom de l'objet
x,y: Les coordonnées de l'emplacement du nombre
p1: Référence d'un point
p2: Référence d'un point
Retourne: Référence d'un nombre, distance entre les deux points.
Exemple:
(soit Nombre "d" point-point 5 5 A B)

prototype (Nombre nom longueur-cercle x y c)
nom: Chaîne de caractère désignant le nom de l'objet
x,y: Les coordonnées du nombre
c: Référence d'un cercle
Retourne: Référence d'un nombre, longueur d'un cercle.
Exemple:
(soit Nombre "p" longueur-cercle 5 5 C)

prototype (Nombre nom pente-droite x y d)
nom: Chaîne de caractère désignant le nom de l'objet
x,y: Les coordonnées du nombre
d: Référence d'une droite
Retourne: Référence d'un nombre, pente d'une droite.
Exemple:
(soit Nombre "p" pente-droite 5 5 d1)

prototype (Nombre nom longueur-arc x y arc)
nom: Chaîne de caractère désignant le nom de l'objet
x,y: Les coordonnées du nombre
arc: Référence d'un arc de cercle
Retourne: Référence d'un nombre, longueur d'un arc de cercle.
Exemple:
(soit Nombre "l" longueur-arc 5 5 ABC)

 

Angle
prototype (Angle nom géométrique A B C)
nom: Chaîne de caractère désignant le nom de l'objet
A: Référence d'un point
B: Référence d'un point, sommet de l'angle
C: Référence d'un point
Retourne: Référence d'un angle géométrique.
Exemple:
(soit Angle "a" géométrique A B C)

prototype (Angle nom orienté x y v1 v2)
nom: Chaîne de caractère désignant le nom de l'objet
x,y: Les coordonnées de l'emplacement de l'angle
v1: Référence d'un vecteur
v2: Référence d'un vecteur
Retourne: Référence d'un angle orienté formé par les deux vecteurs.
Exemple:
(define v1 (Vecteur "" 2points A B))
(define v2 (Vecteur "" 2points A C))
(Angle "a" orienté 1 1 v1 v2)

Des commentaires, des remarques ?
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Modification d'attributs d'objetsMéthodes de référence pour les Figures Scheme DR. GEOCommandes généralesDéfinition d'objets d'une figure
drgeo-doc-1.5/fr/drgenius_69.html0000644000175000017500000001030210117134567012337 Manuel utilisateur de Dr. Geo -- Modification d'attributs d'objets
Méthodes de référence pour les Figures Scheme DR. GEODéfinition d'objets d'une figureModification d'attributs d'objets

Modification d'attributs d'objets

Pour modifier les attributs d'un objet déjà créé, nous utilisons un système de messages envoyés directement au prototype représentant l'objet en question. La modification des attributs se fait donc toujours à posteriori.

(envoi objet couleur valeur)
objet: Référence d'un objet
valeur: La couleur, les valeurs possibles sont noir, gris-noir, gris, blanc, vert-noir, vert, bleu-noir, bleu, rouge, bordeaux, jaune, orange
Exemple:
(soit Point "A" libre 1 2)
(envoi A couleur vert)

(envoi ligne épaisseur valeur)
ligne: Référence d'une ligne (droite, demi-droite, cercle, lieu, etc.)
valeur: L'épaisseur, les valeurs possibles sont tiret, normal, large
Exemple:
(soit Point "A" libre 1 2)
(soit Point "O" libre 0 0)
(soit Droite "d" 2points A B)
(envoi d épaisseur tiret)

(envoi point taille valeur)
point: Référence d'un point
valeur: La taille du point, les valeurs possibles sont petit, normal, large
Exemple:
(soit Point "A" libre 1 2)
(envoi A taille petit)

(envoi point forme valeur)
point: Référence d'un point
valeur: La forme du point, les valeurs possibles sont rond, croix, rond-vide, rec, rec-vide
Exemple:
(soit Point "A" libre 1 2)
(envoi A forme rond)

(envoi objet masquer)
objet: Référence d'un objet à masquer
Exemple:
(soit Point "A" libre 1 2)
(envoi A masquer)

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Méthodes de référence pour les Figures Scheme DR. GEODéfinition d'objets d'une figureModification d'attributs d'objets
drgeo-doc-1.5/fr/drgenius_6.html0000644000175000017500000000464210117134567012260 Manuel utilisateur de Dr. Geo -- Fonctions de base
Fonctionnalités avancéesTopIntroductionFonctions de base

Fonctions de base

Ce chapitre décrit les outils utilisés pour construire une figure géométrique. Il se termine par la présentation de la configuration des préférences par l'utilisateur.

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Fonctionnalités avancéesTopIntroductionFonctions de base
drgeo-doc-1.5/fr/drgenius_70.html0000644000175000017500000000531610117134567012340 Manuel utilisateur de Dr. Geo -- Galerie d'exemples
Figure Scheme de DR. GEOMéthodes de référence pour les Figures Scheme DR. GEOGalerie d'exemples

Galerie d'exemples

Pour illustrer l'utilisation des Figures Scheme DR. GEO, nous vous proposons une petite série d'exemples. Ceux-ci vous montrent leurs importantes possibilités et nous espérons qu'ils seront également une source d'inspiration. Pour chacun de ces exemples, nous donnons le code source Scheme de la figure puis son résultat. Le code source peut être copié dans un éditeur de texte puis sauvegardé dans un fichier d'extension .scm pour l'évaluer avec DR. GEO.

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Figure Scheme de DR. GEOMéthodes de référence pour les Figures Scheme DR. GEOGalerie d'exemples
drgeo-doc-1.5/fr/drgenius_71.html0000644000175000017500000000545210117134567012342 Manuel utilisateur de Dr. Geo -- Polygone régulier
FractalGalerie d'exemplesPolygone régulier

Polygone régulier

Construire un polygone régulier, avec un nombre de cotés arbitraire, peut se faire par l'intermédiaire d'une fonction récursive Scheme. 

(define pi (acos -1))
(define n 15)
(define x0 0)
(define y0 0)
(define p1 0)

(define (polygon center p a n)
  (if (> n 0)
      (begin
        (set! p1 (Point "" rotation p center a))
        (send p1 masked)
        (Segment "" extremities p p1)
        (polygon center p1 a (- n 1)))))

(new-figure "Regular Polygon!")
(lets Point "C" free x0 y0)
(lets Numeric "a" free 0 0 (* 2 (/ pi n)))
(send a masked)

(set! p1 (Point "I" free 5 0))

(lets Segment "S" extremities C p1)
(Segment ""  rotation S C a)

(polygon C p1 a n)

Un polygone régulier à 15 côtés

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FractalGalerie d'exemplesPolygone régulier
drgeo-doc-1.5/fr/drgenius_72.html0000644000175000017500000000630110117134567012335 Manuel utilisateur de Dr. Geo -- Fractal
Galerie d'exemplesPolygone régulierFractal

Fractal

La construction d'une courbe fractale de la forme d'un arbre se fait très aisément avec une figure Scheme. Le code source de la figure est étonnement compact, surtout comparé à une construction "à la main" depuis l'interface graphique. 

(new-figure "Baum")
(lets Numeric "A1" free 2 2 +3.4)
(lets Numeric "A2" free 2 3 -3.7)
(lets Numeric "S1" free 2 4 +0.5)
(lets Numeric "S2" free 2 5 +0.9)

(define (dec n)
  (- n 1))
(define (inc n)
  (+ n 1))
(define (invisible p)
  (send p masked)
  p)
(define (scalerot oP C a s)
  (let* ((sP (invisible (Point "" scale oP C s)))
         (rP (invisible (Point "" rotation sP C a))) )
    rP))
(define (Zweig p0 p1 n)
  (Segment "" extremities p0 p1)
  (let* ((left-scale (if (odd? n) S1 S2))
         (left-angle A1)
         (right-scale (if (odd? n) S2 S1))
         (right-angle A2) )
    (if (> n 0)
      (begin
        (Zweig p1 (scalerot p0 p1  left-angle  left-scale) (dec n))
        (Zweig p1 (scalerot p0 p1 right-angle right-scale) (dec n))))))
        
(lets Point "A" free -3 0)
(lets Point "B" free -3 2)
(Zweig A B 6)

Une courbe fractale simulant la représentation d'un arbre

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Galerie d'exemplesPolygone régulierFractal
drgeo-doc-1.5/fr/drgenius_73.html0000644000175000017500000000531210117134567012337 Manuel utilisateur de Dr. Geo -- Masquer des outils dans l'interface
Fonctionnalités avancéesFigure Scheme de DR. GEOMasquer des outils dans l'interface

Masquer des outils dans l'interface

DR. GEO offre la possibilité de préparer des sessions10 dans lesquelles l'enseignant peut décider, pour certaines figures, de bloquer l'accès à certains outils. Le verrouillage se fait à la figure près avec un mot de passe différent à chaque fois. Cela donne toute la latitude à l'enseignant de préparer une activité avec différentes figures et autant de degrés de verrouillage.

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Fonctionnalités avancéesFigure Scheme de DR. GEOMasquer des outils dans l'interface
drgeo-doc-1.5/fr/drgenius_74.html0000644000175000017500000000660110117134567012342 Manuel utilisateur de Dr. Geo -- Verrouiller des outils
Déverrouiller des outilsMasquer des outils dans l'interfaceVerrouiller des outils

Verrouiller des outils

Le verrouillage se fait à la figure près, aussi depuis l'une d'entre elles, aller au menu Édition->Adapter l'Interface. Une grande boîte de dialogue s'affiche, dans celle-ci l'utilisateur reconnaît les icônes utilisées dans la barre d'icônes de DR. GEO. Il peut en cliquant sur ces icônes, les désactiver ou activer. Lorsque un outil est désactivé, son icône représentative apparaît légèrement grisée. Il est également possible de désactiver toute une rangée d'outils en cliquant sur l'icône de haut niveau (i.e. celle avec un petit triangle vert).

La boîte dialogue pour verrouiller des outils.

Lorsque l'utilisateur a fini sa sélection d'outils à verrouiller, il procède au verrouillage à proprement parler en cliquant sur le bouton Verrouiller dans la boîte de dialogue, DR. GEO demande alors un mot de passe.

(!) Lors de la sauvegarde d'une figure ou d'une session avec des verrouillages de l'interface, les mots de passe sont également sauvegardés dans le fichier sous une forme cryptée.
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Déverrouiller des outilsMasquer des outils dans l'interfaceVerrouiller des outils
drgeo-doc-1.5/fr/drgenius_75.html0000644000175000017500000000533110117134567012342 Manuel utilisateur de Dr. Geo -- Déverrouiller des outils
Masquer des outils dans l'interfaceVerrouiller des outilsDéverrouiller des outils

Déverrouiller des outils

Il est bien sûr possible de déverrouiller une interface, que cela soit pour donner progressivement accès à des outils - lors d'un travail d'élèves sur une session - ou pour retravailler une figure. Pour cela, il faut aller dans le menu Édition->Adapter l'Interface et choisir dans la boîte de dialogue le bouton Déverrouiller. DR. GEO demande alors le mot de passe entré précédemment.

La boîte de dialogue pour déverrouiller l'interface d'une figure.

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Masquer des outils dans l'interfaceVerrouiller des outilsDéverrouiller des outils
drgeo-doc-1.5/fr/drgenius_76.html0000644000175000017500000000576710117134567012360 Manuel utilisateur de Dr. Geo -- Fichiers et documents
Applications didactiquesTopFonctionnalités avancéesFichiers et documents

Fichiers et documents

Les constructions peuvent être enregistrées de deux manières. Une construction par fichier ou un ensemble de constructions par fichier (i.e. une session DR. GEO). Nous vous rappelons que les documents contenant des figures doivent être sauvegardés avec une extension .fgeo et ceux contenant uniquement des macro-constructions avec l'extension .mgeo. Pour les documents contenant des figures, macro-constructions et des textes d'explications, utiliser l'extension .fgeo.

Ceci n'est qu'indicatif mais suivre ces règles permet de s'y retrouver plus facilement parmi les fichiers.

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Applications didactiquesTopFonctionnalités avancéesFichiers et documents
drgeo-doc-1.5/fr/drgenius_77.html0000644000175000017500000000547610117134567012356 Manuel utilisateur de Dr. Geo -- Enregistrement d'une construction
Enregistrement d'une sessionFichiers et documentsEnregistrement d'une construction

Enregistrement d'une construction

À partir du menu Fichier->Enregistrer ou Fichier->Enregistrer sous..., un fichier contenant la figure de la vue active peut être enregistré.

(!) DR. GEO peut travailler avec plusieurs figures en même temps. L'utilisateur peut passer d'une figure à l'autre en cliquant sur l'onglet correspondant.

Avec le second menu, l'utilisateur peut changer le nom du document enregistré.

(!) Le nom de fichier par défaut proposé peut être changé à partir du menu Édition->Préférences.... Pour plus d'information, voir la section comportement par défaut.
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Enregistrement d'une sessionFichiers et documentsEnregistrement d'une construction
drgeo-doc-1.5/fr/drgenius_78.html0000644000175000017500000000724710117134567012355 Manuel utilisateur de Dr. Geo -- Enregistrement d'une session
Enregistrer une macro-constructionFichiers et documentsEnregistrement d'une constructionEnregistrement d'une session

Enregistrement d'une session

Une session est un ensemble de données de DR. GEO que l'utilisateur veut enregistrer d'un seul coup dans un fichier. Cela permet à l'enseignant d'organiser un ensemble de données (figures, macro-constructions, notes) dans un seul fichier, de façon à faciliter leur exploitation.

À partir du menu Fichier->Enregistrement multiple, l'utilisateur peut ouvrir la boîte de dialogue de session.

La boîte dialogue de session DR. GEO

Dans cette boîte de dialogue, la liste de toutes les données actives est présentée dans un tableau. La première colonne liste les types des données contenues dans DR. GEO, la seconde les noms des données.

(!) Actuellement, une session peut contenir trois types de données : figure interactive 2D, macro-construction et texte.

L'utilisateur peut décider de sélectionner une par une les données à enregistrer dans la liste puis appuyer sur le bouton Enregistrer la sélection. Autrement, il peut enregistrer toutes les données en appuyant sur le bouton Enregistrer tout.

(!) Le menu Fichier->Enregistrement multiple est le seul moyen d'enregistrer une macro-construction dans un fichier.
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Enregistrer une macro-constructionFichiers et documentsEnregistrement d'une constructionEnregistrement d'une session
drgeo-doc-1.5/fr/drgenius_79.html0000644000175000017500000000521210117134567012344 Manuel utilisateur de Dr. Geo -- Enregistrer une macro-construction
Ouvrir un fichierFichiers et documentsEnregistrement d'une sessionEnregistrer une macro-construction

Enregistrer une macro-construction

Pour enregistrer une ou des macro-constructions dans un fichier, il faut procéder comme pour enregistrer une session - enregistrement multiple. Depuis la boîte de dialogue de sauvegarde d'une session, sélectionner la ou les macro-constructions à sauvegarder, puis sauver dans un fichier d'extension .mgeo. C'est tout !

Il est ainsi possible de vous composer des librairies de macro-contructions, une par fichier ou plusieurs regroupées selon un même thème dans un seul fichier.

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Ouvrir un fichierFichiers et documentsEnregistrement d'une sessionEnregistrer une macro-construction
drgeo-doc-1.5/fr/drgenius_7.html0000644000175000017500000000633610117134567012263 Manuel utilisateur de Dr. Geo -- Outils de construction
Autres fonctionsFonctions de baseOutils de construction

Outils de construction

Ces outils sont partagés en six groupes accessibles à partir de la seconde barre d'icônes de DR. GEO.

Catégories d'outils de DR. GEO et leur description

Lorsque l'utilisateur clique sur une des icônes décorées d'un petit triangle vert, une nouvelle barre verticale d'icônes s'affiche immédiatement. Celle-ci regroupe des fonctions d'une même famille.

De la gauche vers la droite, nous avons accès aux barres d'icônes verticales pour construire des points et des lignes, utiliser des transformations, calculer des valeurs, gérer des macro-constructions, et utiliser les outils d'édition - Divers outils dans la figure.

Ces fonctions se retrouvent à l'identique dans le menu contextuel d'une figure appelée par un clic droit dans le fond de celle-ci.

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Autres fonctionsFonctions de baseOutils de construction
drgeo-doc-1.5/fr/drgenius_80.html0000644000175000017500000000501410117134567012334 Manuel utilisateur de Dr. Geo -- Ouvrir un fichier
Exporter une figureFichiers et documentsEnregistrer une macro-constructionOuvrir un fichier

Ouvrir un fichier

Que l'utilisateur ait sauvegardé une seule figure ou une session avec différents types de documents, la procédure pour l'ouverture est la même par le menu Fichier->Ouvrir. Si la session ouverte contient des macro-constructions, celles-ci sont directement disponibles depuis l'outil permettant l'exécution des macro-constructions. Les macro-constructions sont disponibles depuis toutes les figures ouvertes.

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Exporter une figureFichiers et documentsEnregistrer une macro-constructionOuvrir un fichier
drgeo-doc-1.5/fr/drgenius_81.html0000644000175000017500000000515710117134567012345 Manuel utilisateur de Dr. Geo -- Exporter une figure
Fichiers et documentsOuvrir un fichierExporter une figure

Exporter une figure

DR. GEO offre la possibilité d'exporter une figure géométrique vers un document LaTeX ou PostScript. Ces deux formats d'exportation sont de type vectoriel contrairement à des images en plan de bits qui sont de qualité moindre pour une impression. Les commandes d'exportation sont accessibles depuis le sous-menu Figure->Exporter sous...

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Fichiers et documentsOuvrir un fichierExporter une figure
drgeo-doc-1.5/fr/drgenius_82.html0000644000175000017500000000476410117134567012351 Manuel utilisateur de Dr. Geo -- Exportation LaTeX
Exportation PostScriptExporter une figureExportation LaTeX

Exportation LaTeX

Dans cas d'une exportation vers LaTeX, le document exporté nécessite le paquet pstricks. Celui-ci est en général distribué avec LaTeX. Typiquement un document exporté en LaTeX pourra être intégré dans un autre document LaTeX ou même directement compilé : 

latex figure.tex
dvips figure.dvi

Cette suite de commandes permet d'obtenir le document figure.ps qui peut être ouvert avec le logiciel GhostView11 gv.

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Exportation PostScriptExporter une figureExportation LaTeX
drgeo-doc-1.5/fr/drgenius_83.html0000644000175000017500000000475310117134567012350 Manuel utilisateur de Dr. Geo -- Exportation PostScript
Exportation image PNGExporter une figureExportation LaTeXExportation PostScript

Exportation PostScript

L'exportation au format PostScript - extension eps pour Encapsulated PostScript- offre l'avantage d'être plus facilement utilisable depuis divers logiciels12. En fait le format EPS est plus ou moins un standard de fait en ce qui concerne les images vectorielles. Pour visualiser rapidement ce type d'image, nous utilisons le logiciel GhostView, sa commande est gv.

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Exportation image PNGExporter une figureExportation LaTeXExportation PostScript
drgeo-doc-1.5/fr/drgenius_84.html0000644000175000017500000000476310117134567012352 Manuel utilisateur de Dr. Geo -- Exportation image PNG
Exportation Fly DrawExporter une figureExportation PostScriptExportation image PNG

Exportation image PNG

Certains logiciels comme OpenOffice.org n'exploitent que partiellement le format EPS13. Aussi une exportation au format image PNG est également possible. L'image exportée sous ce format est en haute définition avec le fond de la figure encodé en zone transparente. Depuis un traitement de texte, cela peut permettre de faire un détourage de texte autour de la figure.

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Exportation Fly DrawExporter une figureExportation PostScriptExportation image PNG
drgeo-doc-1.5/fr/drgenius_85.html0000644000175000017500000000447410117134567012352 Manuel utilisateur de Dr. Geo -- Exportation Fly Draw
Définir la zone exporterExporter une figureExportation image PNGExportation Fly Draw

Exportation Fly Draw

Le serveur d'exercices WIMS développé par Dr. Xiao Gang à l'université de Nice dispose d'un format de description des figures appelé Fly Draw. DR. GEO propose également une exportation vers ce format.

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Définir la zone exporterExporter une figureExportation image PNGExportation Fly Draw
drgeo-doc-1.5/fr/drgenius_86.html0000644000175000017500000000677510117134567012361 Manuel utilisateur de Dr. Geo -- Définir la zone exporter
Exporter une figureExportation Fly DrawDéfinir la zone exporter

Définir la zone exporter

Par défaut, DR. GEO exporte la zone visible de la figure. Ainsi si nous souhaitons exporter une zone précise de la figure, nous pouvons redimensionner la fenêtre de DR. GEO jusqu'à obtenir la zone voulue14.

Cependant cette solution, si elle rapide et simple, n'est pas toujours suffisamment souple, de plus la zone d'exportation n'est pas enregistrée avec la figure. Une autre façon est donc d'utiliser la commande Définir la zone d'exportation accessible depuis le menu Fichier->Préférences d'exportation.

La commande activée, nous pouvons définir dans la figure un rectangle correspondant à la zone exportée. Cette zone peut être redéfinie autant de fois que nécessaire. Elle est représentée par un rectangle gris clair. Lorsque la figure est sauvegardée cette zone l'est également. Enfin elle peut être supprimée par la commande Supprimer la zone d'exportation.

Une figure avec une zone d'exportation définie

La zone d'exportation a été exportée dans un document PostScript, il est visualisé avec GhostView

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Exporter une figureExportation Fly DrawDéfinir la zone exporter
drgeo-doc-1.5/fr/drgenius_87.html0000644000175000017500000000532610117134567012351 Manuel utilisateur de Dr. Geo -- Applications didactiques
Astuces diversesTopFichiers et documentsApplications didactiques

Applications didactiques

Ce chapitre est une aide pour l'utilisateur souhaitant étudier DR. GEO à partir d'exemples. Contrairement aux chapitres précédents, l'approche est plus concrète par rapport à des situations précises. Le contenu de ce chapitre s'est constitué lors de diverses activités pédagogiques.

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Astuces diversesTopFichiers et documentsApplications didactiques
drgeo-doc-1.5/fr/drgenius_88.html0000644000175000017500000001163710117134567012354 Manuel utilisateur de Dr. Geo -- Pythagore et scripts
Théorème et conjecturesApplications didactiquesPythagore et scripts

Pythagore et scripts

Une des possibilités d'utilisation didactique de DR. GEO consiste dans l'utilisation des scripts Scheme pour résoudre des exercices de géométrie.

Comme exemple, nous allons montrer la solution d'un problème classique mettant en oeuvre le théorème de Pythagore dont le texte est le suivant :

Soit un trapèze rectangle ABCD où sont connues les bases et la hauteur. Calculer le périmètre et l'aire du trapèze.

Il n'est pas difficile, si vous suivez le même modèle, de développer d'autres exemples similaires.

Solution :

Commençons par construire la figure dans DR. GEO qui doit être comme ci-dessous :

Trapèze rectangle

La figure comprend les données à partir des quelles nous pouvons résoudre le problème. D'abord nous pouvons répondre à la première question de l'aire, pour cela nous pouvons écrire le script Scheme suivant ayant comme entrée les deux bases et la hauteur du trapèze :

  

define AB (getLength a1))
(define DC (getLength a2))
(define AD (getLength a3))
(/ ( * AD (+ AB DC )) 2 )

Nous calculons la longueur du segment BH en écrivant un script Scheme avec comme objet en entrée les segments AB et CD, et le texte du script est le suivant : 

(define AB (getLength a1))
(define CD (getLength a2))
(- AB CD)

À ce stade, nous pouvons appliquer le théorème de Pythagore dans le triangle rectangle CHB. Ici aussi nous utilisons un script Scheme avec comme objets en entrée le segment CH et le script BH : 

(define CH (getLength a1))
(define BH (getValue a2))
(+ (* CH CH) (* BH BH))

Finalement nous pouvons obtenir la valeur du segment BC en calculant la racine carrée de la valeur retournée par le script précédent : 

(define q (getValue a1))
( sqrt q )

Les deux scripts précédents peuvent être regroupés en un seul script un peu plus élaboré.

Maintenant nous pouvons conclure l'exercice en calculant le périmètre avec un script Scheme : 

(define AB (getLength a1))
(define CB (getValue  a2))
(define DC (getLength a3))
(define AD (getLength a4))
(+ (+ AB CB )(+ DC AD ))

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Théorème et conjecturesApplications didactiquesPythagore et scripts
drgeo-doc-1.5/fr/drgenius_89.html0000644000175000017500000001231410117134567012346 Manuel utilisateur de Dr. Geo -- Théorème et conjectures
Nombre irrationnelApplications didactiquesPythagore et scriptsThéorème et conjectures

Théorème et conjectures

Les scripts Scheme permettent de résoudre des exercices mais aussi de comprendre de façon plus approfondie l'énonciation des théorèmes et de vérifier des conjectures.

Dans cette section nous commençons par analyser le théorème de Tolomeo :

Étant donné un quadrilatère inscrit dans un cercle la somme du produit des côtés opposés est égale au produit des diagonales.

Nous pouvons construire la figure avec DR. GEO comme ci-dessous :

Théorème de Tolomeo: quadrilatère convexe

où nous avons implémenté deux scripts qui calculent respectivement la somme du produit des côtés opposés et le produit des diagonales.  

Le premier script est le suivant : 

(define AB (getLength a1))
(define DC (getLength a2))
(define BC (getLength a3))
(define AD (getLength a4))
(+ (* AB DC )(* BC AD ))

Le second script est : 

(define DB (getLength a1))
(define AC (getLength a2))
(* DB AC )

Comme nous pouvons le voir les valeurs retournées par les deux scripts, en accord avec le théorème de Tolomeo, sont les mêmes15. Lorsque nous modifions dynamiquement la figure, les valeurs des scripts sont toujours identiques, sauf dans la situation suivante :

Théorème de Tolomeo: quadrilatère non convexe

où la quadrilatère perd sa convexité.

Dans ce cas le théorème n'est pas vrai et l'énoncé précédent n'est pas bien énoncé, il doit donc être reformulé comme ci-dessous :

Étant donné un quadrilatère CONVEXE inscrit dans un cercle la somme du produit des côtés opposés est égale au produit des diagonales.

À ce stade les conjectures apparaîssent naturellement : est-ce que le théorème de Tolomeo est valide pour un quadrilatère convexe non inscrit dans un cercle ?

Avec DR. GEO nous pouvons vérifier que cette conjecture est fausse comme le montre la figure suivante :

Réfutation de la conjecture

Le lecteur n'aura pas de difficulté à utiliser DR. GEO dans la construction d'exemples didactiques, probablement plus connu, relativement aux théorèmes de Pythagore et d'Euclide.
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Nombre irrationnelApplications didactiquesPythagore et scriptsThéorème et conjectures
drgeo-doc-1.5/fr/drgenius_8.html0000644000175000017500000000432010117134567012253 Manuel utilisateur de Dr. Geo -- Milieu
IntersectionOutils de pointPoint libreMilieu

Milieu

 

Crée le milieu de deux points ou d'un segment. Dans le premier cas, l'utilisateur sélectionne deux points. Dans le dernier cas, l'utilisateur sélectionne simplement un segment.

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IntersectionOutils de pointPoint libreMilieu
drgeo-doc-1.5/fr/drgenius_90.html0000644000175000017500000001122410117134567012335 Manuel utilisateur de Dr. Geo -- Nombre irrationnel
Spirale de BaravelleApplications didactiquesThéorème et conjecturesNombre irrationnel

Nombre irrationnel

Une construction classique, relative au nombre irrationnel, connue sous le nom de spirale de Teodoro, permet de construire géométriquement la racine carrée de nombres entiers à partir d'un triangle rectangle isocèle.

Considérons le triangle OAB où OA=1 :

Construction de la racine de 2

Par le théorème de Pythagore nous avons OB égale à la racine carrée de 2. Si maintenant, avec la figure, nous construisons un nouveau triangle rectangle en B, avec les côtés OB et BC tel que BC=1.

Construction de la racine 3

toujours par le théorème de Pythagore, il est clair que l'hypothénuse OC de OBC a pour longueur la racine carrée de 3. En itérant le processus précédent à l'infini nous obtenons toutes les racines carrées des nombres naturels.

La nature itérative de la construction s'adapte parfaitement à l'utilisation des FSD. Considérons alors le code suivant : 

(new-figure "Triangle")

(define (triangle p1 p2 p3 n)
  (let* ((s1 (Segment "" extremities    p1 p2))
         (s2 (Segment "" extremities    p2 p3))
         (s3 (Segment "" extremities    p3 p1))
         (pe (Line    "" orthogonal     p3 s3))
         (ci (Circle  "" center-segment p3 s2))
         (p4 (Point   "" intersection2  pe ci)))
    (send pe masked)
    (send ci masked)
    (send p4 masked)
    (if (> n 0)
       (triangle p1 p3 p4 (- n 1)))))


(lets Point "O" free  0  0)
(lets Point "A" free -1  0)
(lets Point "B" free -1  1)
(triangle O A B 15)

Le triangle du début est défini à travers les coordonnées seulement par commodité. Le code est la transcription littérale de la procédure itérative décrite précédement. Une fois évalué par DR. GEO le code donne la figure suivante :

Spirale de Teodoro

Les hypothénuses de chaque triangle ont pour longueur les racines carrées des nombres entiers naturels compris entre 2 et 17.
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Spirale de BaravelleApplications didactiquesThéorème et conjecturesNombre irrationnel
drgeo-doc-1.5/fr/drgenius_91.html0000644000175000017500000001207010117134567012336 Manuel utilisateur de Dr. Geo -- Spirale de Baravelle
Catena di PappoApplications didactiquesNombre irrationnelSpirale de Baravelle

Spirale de Baravelle

Comme nous l'avons vu précédement, à l'aide de FSD il est possible de construire de façon intuitive et simple des figures permettant de visionner des situations qui en programmation sont récursives - ou cycliques.

Nous pouvons un peu approfondir cet aspect, en modifiant le code Scheme utilisé pour la construction des nombres irrationnels, afin d'obtenir une figure fameuse de la littérature des mathématiques, à savoir la spirale de Baravelle.

Le code Scheme définissant la spirale est le suivant : 

 
(new-figure "Baravelle")
 
(define (triangle p1 p2 p3 n)   
  (let* ((s1  (Segment "" extremities    p1 p2))
         (s2  (Segment "" extremities    p2 p3))
         (s3  (Segment "" extremities    p3 p1))
         (m   (Point   "" middle-2pts    p1 p3))
         (r   (Segment "" extremities    m  p3))
         (pe  (Line    "" orthogonal     p3 s3))
         (ci  (Circle  "" center-segment p3 r ))
         (p4  (Point   "" intersection2  pe ci)))
    (send pe  masked)
    (send ci  masked)
    (send p4  masked)
    (send m   masked)
    (if (> n 0)
      (triangle  m  p3  p4 (- n 1)))))
   
 
(lets Point "A" free  0  5)
(lets Point "B" free  5  5)
(lets Point "C" free  5  0)
(triangle A B C 9)
 
(lets Point "D" free  0 -5)
(lets Point "E" free -5 -5)
(lets Point "F" free -5  0)
(triangle D E F 9)

La spirale de Baravelle suite à l'évaluation du code Scheme

À partir de la figure et du code Scheme correspondant nous percevons bien la nature itérative du mécanisme de construction de la figure. Un problème intéressant que nous laissons au lecteur, consiste à établir quand est-ce que les deux rameaux de la spirale convergent.

Une petite variation supplémentaire du code précédent : 

(new-figure "Spirale")

(define (square p1 p2 p3 p4 n)
  (let* ((s1 (Segment "" extremities p1 p2))
         (s2 (Segment "" extremities p2 p3))
         (s3 (Segment "" extremities p3 p4))
         (s4 (Segment "" extremities p4 p1))
         (A (Point "" on-curve s1 1/10))
         (B (Point "" on-curve s2 1/10))
         (C (Point "" on-curve s3 1/10))
         (D (Point "" on-curve s4 1/10)))
     (send A masked)
     (send B masked)
     (send C masked)
     (send D masked)
     (if (> n 0)
       (square A B C D (- n 1)))))

(lets Point "M" free 5 5)
(lets Point "N" free -5 5)
(lets Point "O" free -5 -5)
(lets Point "P" free 5 -5)

(square M N O P 30)

conduit à une spirale simplifiée.

Spirale simplifiée

Le lecteur est invité à se divertir en créant de nouvelles variations !
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Catena di PappoApplications didactiquesNombre irrationnelSpirale de Baravelle
drgeo-doc-1.5/fr/drgenius_92.html0000644000175000017500000000670510117134567012347 Manuel utilisateur de Dr. Geo -- Catena di Pappo
Calcul de piApplications didactiquesSpirale de BaravelleCatena di Pappo

Catena di Pappo

Une utilisation de base de Figure Scheme de DR. GEO consiste en la reproduction de figure dont nous connaissons les caractéristiques analytiques.

L'exemple de construction que nous proposons est représenté par la fameuse "Catena di Pappo".

Catena di Pappo

Les centres et rayons successifs des cercles qui la constituent ont une expression analytique connue, il est donc aisé de reproduire la figure en tant de FSD. 

(new-figure "Pappo")

(define (circle n)
(let*(
  (r (Numeric "" free 0 0 (/ 15 ( + 6 (* n n )))))
  (c (Point   "" free (* 5 (/ 15 ( + 6 (* n n )))) 
                      (* 2 (* n (/ 15 ( + 6 (* n n )))))))
  (p (Circle "" center-radius c r )))
 (send r masked)
 (if (> n 0)
    (circle (- n 1)))))

(circle 8)

(lets Point "A" free 5 0)
(lets Point "O" free 0   0)
(lets Point "B" free 15 0)
(lets Point "M" middle-2pts B O)
(lets Circle "" 2points M O)
(lets Circle "" 2points A O)
(lets Line   "" 2points A O)

le code de la figure est relativement intuitif et ne nécessite pas de commentaire.

Un exercice non trivial, que nous laissons au lecteur, consiste à déterminer une construction à la règle et au compas conduisant à une implémentation itérative.

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Calcul de piApplications didactiquesSpirale de BaravelleCatena di Pappo
drgeo-doc-1.5/fr/drgenius_93.html0000644000175000017500000000761010117134567012344 Manuel utilisateur de Dr. Geo -- Calcul de pi
Applications didactiquesCatena di PappoCalcul de pi

Calcul de pi

Le calcul approximatif de pi a joué un rôle important dans l'histoire des Mathématiques. Les méthodes pour ce type de calcul sont diverses et contiennent souvent des améliorations d'une méthode à l'autre. Nous vous proposons une approche du problème très simplifiée que nous appelons - même si ce n'est pas tout à fait exacte - Méthode par exhaustion. Cette approche a toutefois l'avantage de montrer l'essence même de la méthodologie.

Nous commençons avec la construction suivante d'un hexagone inscrit dans une cercle à partir du côté BC. Nous notons au passage qu'il est possible à partir de cette construction de construire et mémoriser une macro que nous pouvons nommer Hexagone.

Hexagone régulier inscrit

l'idée de la méthode par exhaustion consiste dans un premier temps à approximer la longueur du cercle avec le périmètre P0 de l'hexagone et de calculer une approximation de pi dividende de P0 par le diamètre du cercle. Clairement l'approximation de pi obtenue sera de 3.

Lors d'une deuxième étape nous pouvons, en utilisant DR. GEO, construire un côté du dodécagone inscrit dans le cercle. Nous calculons son périmètre P1 ainsi qu'une approximation successive de pi comme dividende de P1 par le diamètre.

Approximation de pi

En augmentant le nombre de côtés du polygone régulier inscrit nous obtenons de meilleures approximations.
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Applications didactiquesCatena di PappoCalcul de pi
drgeo-doc-1.5/fr/drgenius_94.html0000644000175000017500000000426610117134567012351 Manuel utilisateur de Dr. Geo -- Astuces diverses
IndexTopApplications didactiquesAstuces diverses

Astuces diverses

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IndexTopApplications didactiquesAstuces diverses
drgeo-doc-1.5/fr/drgenius_95.html0000644000175000017500000000632410117134567012347 Manuel utilisateur de Dr. Geo -- Créer un polygone régulier
Imprimer une figureAstuces diversesCréer un polygone régulier

Créer un polygone régulier

DR. GEO peut créer des macro-constructions comportant des éléments de construction indépendants (i.e. des points libres, des valeurs libres, des scripts sans parent). Pour ce faire DR. GEO prend l'initiative de donner une ou des valeurs aux paramètres libres de ces objets16. La ou les valeur(s) choisie(s) sont en fait celle(s) de l'objet servant de modèle lors de la création de la macro.

Dans la suite, un petit exemple permettant de créer des polygones réguliers à n côtés est présenté. En plus des macro-constructions, un script Scheme intervient dans le processus.

L'exemple est guidé pas à pas mais le lecteur non familier avec les macro-constructions, les scripts ou plus généralement le fonctionnement de DR. GEO est fortement invité à lire les sections précédentes.

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Imprimer une figureAstuces diversesCréer un polygone régulier
drgeo-doc-1.5/fr/drgenius_96.html0000644000175000017500000000611510117134567012346 Manuel utilisateur de Dr. Geo -- Le modèle de polygone
La macro-construction du polygoneCréer un polygone régulierLe modèle de polygone

Le modèle de polygone

Pour commencer, créer un point libre, puis un script sans parent - après avoir choisi l'outil script cliquer directement sur le fond de la figure. Éditer le script et lui donner comme valeur : 

(/ (* 2 (acos -1)) 7)

Le résultat de ce script servira pour construire par rotation un polygone régulier à 7 côtés. Placer ensuite une valeur libre de valeur 2, ce sera le rayon de notre polygone.

Construire un cercle de centre le point et de rayon la valeur. Sur ce cercle placer un point. Nommer ce point O.

Maintenant utiliser l'outil rotation pour créer l'image de O par la rotation d'angle la valeur du script et de centre le centre du cercle. Continuer ensuite successivement jusqu'à obtenir les 7 sommets du polygone. Relier les sommets par des segments.

Résultat de la construction du polygone régulier à 7 côtés

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La macro-construction du polygoneCréer un polygone régulierLe modèle de polygone
drgeo-doc-1.5/fr/drgenius_97.html0000644000175000017500000000532010117134567012344 Manuel utilisateur de Dr. Geo -- La macro-construction du polygone
Quelques considérationsCréer un polygone régulierLe modèle de polygoneLa macro-construction du polygone

La macro-construction du polygone

Ouvrir la boîte de dialogue de création de macro-construction et construire comme suit la macro :

  1. paramètre d'entrée : le centre du cercle ;
  2. paramètres de sortie : le point O et les 7 côtés du polygone.

Voilà, la macro est prête.

Pour créer un polygone régulier à 7 côtés, ouvrir la boîte de dialogue d'exécution d'une macro, il suffit de sélectionner un point de la figure.

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Quelques considérationsCréer un polygone régulierLe modèle de polygoneLa macro-construction du polygone
drgeo-doc-1.5/fr/drgenius_98.html0000644000175000017500000000531710117134567012353 Manuel utilisateur de Dr. Geo -- Quelques considérations
Créer un polygone régulierLa macro-construction du polygoneQuelques considérations

Quelques considérations

Lorsque DR. GEO rencontre des éléments libres dans une macro-construction, il fixe leur valeur en prenant celle du modèle. Dans notre exemple, le script, la valeur et le point O sont de tels éléments libres. Lorsque la macro-construction est exécutée, ils sont fixés comme suit :

  • la valeur à 2 ;
  • le script à (/ (* 2 (acos -1)) 7) ;
  • le point sur le cercle avec la même abscisse curviligne que O.

C'est ce dernier point qui donne tout son sens à l'utilisation conjointe des macro-constructions avec des scripts ou d'autres objets libres.

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Créer un polygone régulierLa macro-construction du polygoneQuelques considérations
drgeo-doc-1.5/fr/drgenius_99.html0000644000175000017500000000500210117134567012343 Manuel utilisateur de Dr. Geo -- Imprimer une figure
Placer un paragraphe de texte dans une figureAstuces diversesCréer un polygone régulierImprimer une figure

Imprimer une figure

Le plus simple est d'exporter la figure au format PostScript - Exportation PostScript. Utiliser ensuite un logiciel permettant de visionner des documents PostScript et imprimer le document. Le document imprimé de la sorte est de qualité vectorielle. Les logiciels GhostView, Gnome GhostView ou encore K GhostView conviennent parfaitement.

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Placer un paragraphe de texte dans une figureAstuces diversesCréer un polygone régulierImprimer une figure
drgeo-doc-1.5/fr/drgenius_9.html0000644000175000017500000000677710117134567012276 Manuel utilisateur de Dr. Geo -- Point libre
MilieuOutils de pointPoint libre

Point libre

 

Crée un point libre dans le plan ou sur un objet unidimensionnel (segment, demi-droite, droite, arc de cercle, cercle, lieu) :

  1. Dans le premier cas, le point créé peut être déplacé n'importe où dans le plan de la figure. Pour le construire l'utilisateur clique simplement sur le fond.
  2. Dans le deuxième cas, le point n'est libre que dans l'objet unidimensionnel (ligne) où il a été crée ; il est collé sur l'objet. Pour construire ce type de point, l'utilisateur clique sur une ligne (i.e. droite, demi-droite, segment, cercle, arc de cercle, etc.).
Comment placer un point avec des coordonnées données ?

Le plus simple est de placer un point libre puis d'éditer ses propriétés - outil Propriété - afin d'ajuster ses coordonnées comme souhaité.

Une autre possibilité - moins souple pour ce cas de figure - est de placer deux valeurs libres dans la figure - outils Numériques - puis de construire le point ayant pour coordonnées ces deux valeurs - outil Point défini par ses coordonnées. Cette possibilité a un avantage sur la précédente, le point ainsi construit ne peut pas être déplacé directement à la souris, le point est en quelque sorte bloqué dans sa position.

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MilieuOutils de pointPoint libre
drgeo-doc-1.5/fr/drgenius_guile_script.html0000644000175000017500000001027710117134567014605 Manuel utilisateur de Dr. Geo -- Script Scheme DR. GEO
Figure Scheme de DR. GEOFonctionnalités avancéesMacro-constructionScript Scheme DR. GEO

Script Scheme DR. GEO

DR. GEO est compatible Guile. Cela signifie qu'il est possible d'exécuter des scripts Scheme avec DR. GEO. Mais qu'est-ce que Guile ? Extrait du manuel de Guile :

Guile est un interpréteur pour le langage de programmation Scheme, prévu pour être utilisé dans une grande variété d'environnements.

Les citations suivantes décrivent précisément comment Guile est utilisé dans DR. GEO :

Comme un shell, Guile peut être lancé de manière interactive, recevoir des expressions de l'utilisateur, les évaluer et afficher les résultats, ou comme un interpréteur de scripts, lire et exécuter du code Scheme à partir d'un fichier. Cependant, Guile est disponible sous forme de bibliothèque permettant à d'autres applications d'incorporer facilement un interpréteur Scheme complet. Une application peut utiliser Guile comme un langage d'extension, un langage de configuration propre et puissant, ou comme une "colle" multi-usages, liant des primitives fournies par l'application.

Dans DR. GEO, une API est disponible à partir de l'interpréteur Guile. C'est un ensemble de "crochets" dans le moteur géométrique. C'est pourquoi l'utilisateur peut écrire des scripts pour manipuler les items (géométriques ou numériques) des figures. Aussi, puisque les scripts sont des items de figure au même titre que d'autres, ils n'ont pas besoin d'être dans un fichier séparé, ils sont enregistrés dans le fichier de la figure. Dans ce qui suit, nous allons utiliser l'acronyme DGS pour désigner un script Guile DR. GEO ("DR. GEO Script").

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Figure Scheme de DR. GEOFonctionnalités avancéesMacro-constructionScript Scheme DR. GEO
drgeo-doc-1.5/fr/drgenius.html0000644000175000017500000000370210117134567012027 Manuel utilisateur de Dr. Geo

Manuel utilisateur de DR. GEO

Hilaire Fernandes, Andrea Centomo,
Jean-Philippe Georget,
OFSET
http://www.ofset.org

29 août 2004

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drgeo-doc-1.5/fr/editing_object_styles.html0000644000175000017500000001064410117134567014566 Manuel utilisateur de Dr. Geo -- Changer l'aspect d'un objet
Changer les propriétés d'un objetAutres fonctionsSupprimer un objetChanger l'aspect d'un objet

Changer l'aspect d'un objet

 

Chaque objet géométrique a ses propres attributs de style comme la couleur, l'épaisseur, l'étiquette, la taille et la forme. De plus, il est possible de cacher temporairement un objet sans le supprimer. Par exemple, il peut être utile de cacher des constructions intermédiaires sans les supprimer. Tous ces attributs sont ajustables depuis la boîte de dialogue qui s'affiche lorsque l'utilisateur clique sur un objet de la figure. Pour cela il faut d'abord se mettre dans le mode d'édition de style en sélectionnant Autres->Aspect du menu contextuel de la figure, ou bien en cliquant sur l'icône ci-dessus, du 6ème tiroir d'icônes.

 

La boîte de dialogue du style d'un point concerne tous les types de point. Il est possible d'ajuster la couleur, la forme, la taille, le nom et la visibilité.

Boîte de dialogue pour le style d'un objet point

La boîte de dialogue du style d'une ligne concerne les droites, les demi-droites, les segments, les vecteurs, les cercles, les arcs de cercle, les lieux de points. Il est possible d'ajuster la couleur, le style, le nom et la visibilité. Lorsqu'une droite, une demi-droite, un vecteur ou un segment sont définis par deux points ayant des noms non vides, leur nom est automatiquement déduit à partir de celui des deux points. Dans ce cas, l'utilisateur ne peut pas les renommer.

Boîte de dialogue pour le style d'un objet ligne

La boîte de dialogue du style d'un nombre ou d'un polygone concerne toutes les sortes de valeur (saisie par l'utilisateur, calculée par un script Scheme DR. GEO ou représentant une mesure géométrique) et les formes polygonales.

Boîte de dialogue pour les nombres & les objets polygones

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Changer les propriétés d'un objetAutres fonctionsSupprimer un objetChanger l'aspect d'un objet
drgeo-doc-1.5/fr/introduction.html0000644000175000017500000000406310117134567012731 Manuel utilisateur de Dr. Geo -- Introduction
Fonctions de baseTopCopyrightIntroduction

Introduction

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Fonctions de baseTopCopyrightIntroduction
drgeo-doc-1.5/fr/line_tools.html0000644000175000017500000000461110117134567012356 Manuel utilisateur de Dr. Geo -- Outils de ligne
Outils de transformationOutils de constructionOutils de pointOutils de ligne

Outils de ligne

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Outils de transformationOutils de constructionOutils de pointOutils de ligne
drgeo-doc-1.5/fr/macroconstruction_tools.html0000644000175000017500000000416510117134567015207 Manuel utilisateur de Dr. Geo -- Outil macro-construction
Outils de constructionOutils numériquesOutil macro-construction

Outil macro-construction

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Outils de constructionOutils numériquesOutil macro-construction
drgeo-doc-1.5/fr/numeric_tools.html0000644000175000017500000000453110117134567013072 Manuel utilisateur de Dr. Geo -- Outils numériques
Outil macro-constructionOutils de constructionOutils de transformationOutils numériques

Outils numériques

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Outil macro-constructionOutils de constructionOutils de transformationOutils numériques
drgeo-doc-1.5/fr/other_tools.html0000644000175000017500000000477610117134567012564 Manuel utilisateur de Dr. Geo -- Autres fonctions
Préférences utilisateursFonctions de baseOutils de constructionAutres fonctions

Autres fonctions

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Préférences utilisateursFonctions de baseOutils de constructionAutres fonctions
drgeo-doc-1.5/fr/point_tools.html0000644000175000017500000000416510117134567012564 Manuel utilisateur de Dr. Geo -- Outils de point
Outils de ligneOutils de constructionOutils de point

Outils de point

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Outils de ligneOutils de constructionOutils de point
drgeo-doc-1.5/fr/transformation_tools.html0000644000175000017500000000467210117134567014504 Manuel utilisateur de Dr. Geo -- Outils de transformation
Outils numériquesOutils de constructionOutils de ligneOutils de transformation

Outils de transformation

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Outils numériquesOutils de constructionOutils de ligneOutils de transformation
drgeo-doc-1.5/fr/using_macro.html0000644000175000017500000001066010117134567012516 Manuel utilisateur de Dr. Geo -- Macro-construction
Script Scheme DR. GEOFonctionnalités avancéesMacro-construction

Macro-construction

Une macro-construction ressemble un peu à une procédure qui reçoit des items d'une figure en entrée et qui retourne un ou plusieurs items de figure, construits par la macro-construction. Une macro est construite à partir d'un modèle défini par l'utilisateur. Cela signifie que l'utilisateur doit réaliser la séquence de construction une première fois dans une figure puis demander à DR. GEO de l'enregistrer dans une macro-construction. La macro-construction peut ensuite être sauvegardée dans un fichier d'extension .mgeo.

Pour enregistrer une séquence de construction, DR. GEO doit connaître les items initiaux de la séquence ainsi que les items finaux. Évidemment, les items finaux ne doivent dépendre que des items initiaux4, sinon DR. GEO ne sera pas capable de déduire les items finaux à partir des items initiaux.

Ainsi, DR. GEO déduit la logique de la séquence de construction et l'enregistre dans une macro-construction. L'utilisateur peut exécuter cette macro-construction, elle demande seulement les items initiaux (du bon type) de la figure et construit les items résultants.

(!) Les items de figure intermédiaires et invisibles sont aussi construits par la macro-construction. Ils sont nécessaires pour construire les items résultants.

Pour illustrer la fonctionnalité macro-construction, nous utiliserons l'exemple de l'utilisateur qui souhaite enregistrer la construction du cercle passant par trois points ainsi que son centre.

La figure initiale

 

Avant la création de la macro-construction, l'utilisateur doit construire la figure finale, elle est considérée comme modèle par la macro-construction.

La figure avec la construction finale

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Script Scheme DR. GEOFonctionnalités avancéesMacro-construction
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do \ basename = `basename $$file`; \ $(INSTALL_DATA) $(srcdir)/$$file $(DESTDIR)$(drgenius_helpdir)/$$basefile; \ done -for file in $(srcdir)/figures/*.png; do \ basename = `basename $$file`; \ $(INSTALL_DATA) $(srcdir)/$$file $(DESTDIR)$(drgenius_helpdir)/figures/$$basefile; \ done drgeo-doc-1.5/it/drgenius.tex0000644000175000017500000030220610113164061011655 % This is the documentation of DrGeo % Copyright 2002-2004 Ofset % Licensed under the terms of the FDL % Traduction and Italian version by Andrea Centomo \documentclass[a4paper,11pt]{book} \usepackage{hyperlatex} \T \usepackage[pdftex]{color,graphicx} \usepackage{makeidx} \usepackage[latin1]{inputenc} \usepackage[italian]{babel} \usepackage{hyperref} \captionsitalian \dateitalian \extrasitalian \W \htmlpanelitalian % Prepare macro \newcommand{\drgeniusImagePath}{../it/figures} \newcommand{\drgeoApiOutLocale}{output} \newcommand{\drgeoApiExampleLocale}{Esempio} % Include common definitions \input{../drgeniusCommon.tex} \makeindex \htmltitle{Manuale di Dr. Geo} \htmladdress{\small Hai domande o commenti da fare? \\ Vuoi partecipare alla stesura di parti di questo manuale?\\ -> Contatta Andrea Centomo all'OFSET (acentomo at ofset dot org) o aggiungiti alla lista per la diffusione di \drgeo.} \title{Manuale di \drgeo \\ \drgeniusImage{fig0} } \author{Hilaire Fernandes \\ Andrea Centomo \\ \textit{OFSET}\\ \texttt{http://www.ofset.org} } \begin{document} \W \begin{center} \maketitle \W \end{center} \xname{contents} \tableofcontents \chapter*{Copyright} Copyright (c) 2000-2004 OFSET. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Other copyright apply to the respective owners of the modified documentations. See the section history for the complet list. \xname{introduction} \chapter{Introduzione} \drgeo\ \`e un programma Gnome per lo studio interattivo della geometria euclidea e della programmazione Scheme. Utilizzando \drgeo\ \`e possibile creare costruzioni geometriche e manipolarle in modo da mantenere inalterate le loro propriet\`a geometriche fondamentali ed introdurre lo studente in modo graduale alla programmazione. \drgeo\ rappresenta, in questo senso, un ottimo ausilio per la didattica della Matematica nel ciclo di istruzione primario e secondario. \drgeniusFigureSize{La schermata iniziale di \drgeo}{fig1}{8} La schermata iniziale evidenzia in alto due barre: \begin{enumerate} \item la \textit{barra dei menu} caratterizzata dalle voci File, Modifica, Aiuto; \item la \textit{barra delle azioni}: aprire una nuova figura, aprire un nuovo foglio di testo, annullare o ripetere un comando. \end{enumerate} Per creare una nuova figura geometrica \`e sufficiente cliccare sul primo bottone nella barra delle azioni. Alternativamente si pu\`o cliccare sull'opzione \drgeniusMenu{File -> Nuovo -> Figura} della barra dei menu. Non appena creata una nuova figura geometrica, oltre ad un foglio da disegno bianco, comparir\`a la \textit{barra delle icone}, che contiene sette icone fondamentali e che si conclude con un menu per l'aggiustamento della scala della figura geometrica corrente. \drgeniusFigureSize{Schermata iniziale di una costruzione geometrica}{fig2}{8} Le prime sei icone della barra delle icone contengono dei sottomenu a tendina relativi alle funzioni base e avanzate di \drgeo\ per la cui descrizione si rimanda al capitolo successivo. \drgeniusFigureSize{Una figura geometrica in \drgeo\ e la sua descrizione}{fig50}{9} Ogni figura \`e accompagnata da un \textit{albero sinottico} che riassume le costruzioni eseguite. Inizialmente l'albero \`e coperto in modo che solo il foglio di lavoro risulti visibile. In ogni momento l'utilizzatore pu\`o aprirlo con la seguente procedura: si porta il mouse a sinistra del righello verticale che delimita il foglio di lavoro fino a quando, nella zona centrale, la freccia del puntatore assume la forma $<->$; si clicca quindi con il tasto sinistro del mouse e tenendo premuto ci si sposta verso destra quanto si desidera allargare l'albero. L'albero, che descrive la figura geometrica corrente, presenta dei \textit{nodi} che possono essere espansi o compressi cliccando su linguette triangolari. \chapter{Funzioni Base} In questo capitolo vengono descritti gli strumenti necessari per la costruzione delle figure geometriche e gli elementi fondamentali per la personalizzazione delle preferenze dell'utilizzatore. \section{Strumenti di Costruzione} Questi strumenti sono suddivisi in sei menu visualizzabili cliccando con il mouse su ciascuna delle prime sei icone della barra delle icone di \drgeo. \drgeniusFigureSize{Gli strumenti di \drgeo\ e la loro descrizione}{fig3}{12} \xname{point_tools} \subsection{Costruzione di punti } \subsubsection{Punto libero} \drgeniusIcon{fig4} \label{free_point} \drgeniusIndex{Punto:}{libero}{}{} Selezionando questo comando si possono creare sul foglio di lavoro un punto o un punto su un oggetto (retta, semiretta, ...) tracciato in precedenza. Nel primo caso il punto si costruisce cliccando con il mouse nel punto del foglio di lavoro desiderato e, se necessario, potr\`a essere successivamente spostato dinamicamente all'interno del foglio di lavoro. Nel secondo caso il punto si costruisce cliccando sull'oggetto geometrico desiderato e, se necessario, potr\`a essere successivamente spostato, rimanendo tuttavia vincolato all'oggetto geometrico su cui \`e stato creato. \subsubsection{Punto medio} \drgeniusIcon{fig5} \drgeniusIndex{Punto:}{medio}{}{} Selezionando questo comando si pu\`o costruire il punto medio o di un segmento o di una coppia di punti dati. Nel primo caso il punto medio si ottiene cliccando con il mouse direttamente sul segmento. Nel secondo caso il punto medio si ottiene cliccando in sequenza sui due punti dati. \subsubsection{Punti di intersezione} \drgeniusIcon{fig6} \drgeniusIndex{Punto:}{di intersezione}{}{} Selezionando questo comando si ottengono uno o pi\`u punti di intersezione tra due oggetti geometrici dati. Per creare i punti di intersezione \`e necessario cliccare con il mouse in sequenza sui due oggetti geometrici da intersecare. \subsubsection{Punto definito attraverso coordinate} \drgeniusIcon{fig7} \label{coordinate_point} \drgeniusIndex{Punto:}{definito attraverso coordinate}{}{} Selezionando questo comando si definisce un punto precisando le sue coordinate cartesiane (ascissa e ordinata). Le coordinate devono essere state scritte precedentemente nel foglio di lavoro utilizzando le modalit\`a per editare un numero descritte nel paragrafo Strumenti numerici. \xname{line_tools} \subsection{Costruzione di linee} \subsubsection{Retta} \drgeniusIcon{fig8} \drgeniusIndex{Retta}{}{}{} Selezionando questo comando si costruisce una retta passante per due punti dati. Si clicca con il mouse sui due punti dati. \subsubsection{Semiretta} \drgeniusIcon{fig9} \drgeniusIndex{Semiretta}{}{}{} Selezionando questo comando si costruisce una semiretta. Si clicca con il mouse in sequenza su due punti di cui il primo \`e l'origine della semiretta. \subsubsection{Segmento} \drgeniusIcon{fig10} \drgeniusIndex{Segmento}{}{}{} Selezionando questo comando si costruisce un segmento. Si clicca con il mouse su due punti dati che rappresentano gli estremi del segmento. \subsubsection{Vettore} \drgeniusIcon{fig11} \drgeniusIndex{Vettore}{}{}{} Selezionando questo comando si costruisce un vettore. Si clicca con il mouse su due punti dati che rappresentano nell'ordine coda e punta del vettore. \subsubsection{Circonferenza} \drgeniusIcon{fig12} \drgeniusIndex{Circonferenza}{}{}{} Selezionando questo comando si costruisce una circonferenza secondo tre possibili modalit\`a: \begin{enumerate} \item si clicca con il mouse in sequenza su due punti dati che sono, nell'ordine, il centro della circonferenza e un punto ad essa appartenente; \item si clicca con il mouse su un punto che rappresenta il centro della circonferenza e si seleziona un numero che rappresenta il raggio della circonferenza; \item si clicca con il mouse in sequenza su un punto, che rappresenta il centro della circonferenza, e su un segmento la cui lunghezza rappresenta il raggio della circonferenza. \end{enumerate} \subsubsection{Arco di circonferenza} \drgeniusIcon{fig13} \drgeniusIndex{Arco di circonferenza}{}{}{} Selezionando questo comando si costruisce un arco di circonferenza. Si clicca con il mouse su tre punti di cui il primo e il terzo sono gli estremi dell'arco mentre il secondo \`e un punto appartenente all'arco. \subsubsection{Luogo} \drgeniusIcon{fig14} \drgeniusIndex{Luogo}{}{}{} Selezionando questo comando si costruisce un luogo geometrico definito da due punti. Si clicca con il mouse su due punti di cui il primo \`e libero di muoversi su una linea mentre il secondo \`e vincolato a muoversi con il secondo. \subsubsection{Poligono} \drgeniusIcon{fig15} \drgeniusIndex{Poligono}{}{}{} Selezionando questo comando si costruisce un poligono dati i suoi $n$ vertici. Si clicca con il mouse $n+1$ volte in sequenza su tutti i vertici del poligono avendo cura di cliccare all'inizio e alla fine sul medesimo vertice; in questo modo \drgeo\ comprende che la costruzione del poligono \`e conclusa. In \drgeo\ i poligoni sono oggetti geometrici speciali in quanto su essi non \`e possibile disegnare un punto cos\`{\i} come non \`e possibile determinare i punti di intersezione tra due qualsiasi di essi. \xname{transformation_tools} \subsection{Trasformazioni del piano} Questo menu permette di studiare le isometrie del piano euclideo e le trasformazioni omotetiche. \subsubsection{Retta parallela} \drgeniusIcon{fig16} \drgeniusIndex{Retta}{parallela}{}{} Selezionando questo comando, dati una retta e un punto ad essa esterna, si costruisce la retta parallela alla data passante per quel punto. Si clicca con il mouse su un punto e una retta dati. \subsubsection{Retta perpendicolare} \drgeniusIcon{fig17} \drgeniusIndex{Retta}{perpendicolare}{}{} Selezionando questo comando, dati una retta e un punto ad essa esterna, si costruisce la retta perpendicolare alla data passante per quel punto. Si clicca con il mouse su un punto e una retta dati. \subsubsection{Riflessione} \drgeniusIcon{fig18} \drgeniusIndex{Trasformazioni del piano:}{riflessione}{}{} Selezionando questo comando si esegue una riflessione intorno ad una retta (asse di riflessione) di un qualsiasi oggetto geometrico. Si clicca con il mouse sull'oggetto e sull'asse di riflessione. Se l'oggetto da riflettere \`e una retta prima si deve selezionare la retta da riflettere e solo dopo l'asse di riflessione. \subsubsection{Simmetria centrale} \drgeniusIcon{fig19} \drgeniusIndex{Trasformazioni del piano:}{simmetria}{centrale}{} Selezionando questo comando si esegue una simmetria rispetto ad un punto (centro di simmetria) di un qualsiasi oggetto geometrico. Si clicca con il mouse sull'oggetto e sul punto che \`e centro di simmetria. Se l'oggetto da riflettere \`e un punto prima si deve selezionare il punto da trasformare e solo dopo il centro di simmetria. \subsubsection{Traslazione} \drgeniusIcon{fig20} \drgeniusIndex{Trasformazioni del piano:}{traslazione}{}{} Selezionando questo comando si esegue una traslazione di un qualsiasi oggetto geometrico. Si clicca con il mouse sull'oggetto da traslare e sul vettore che rappresenta la traslazione. Se l'oggetto da traslare \`e un vettore prima si deve selezionare il vettore da trasformare e solo dopo il vettore che individua la traslazione. \subsubsection{Rotazione} \drgeniusIcon{fig21} \drgeniusIndex{Tranformazioni del piano:}{rotazione}{}{} Selezionando questo comando si esegue una rotazione di un angolo fissato rispetto ad un centro (centro di rotazione) di un qualsiasi oggetto geometrico. Si clicca con il mouse sull'oggetto e sul punto che \`e centro di rotazione. Se l'oggetto da ruotare \`e un punto prima si deve selezionare il punto da ruotare e solo dopo il centro di rotazione. Il valore dell'angolo di rotazione pu\`o essere definito in diversi modi: \begin{itemize} \item \textbf{valore numerico}: in questo caso l'angolo viene espresso in radianti. Esempi di valori numerici sono: le lunghezze di segmenti, le distanze tra punti, le coordinate di un punto, i valori numerici restituiti da script Guile per \drgeo, ecc.; \item \textbf{angolo formato da tre punti}: in questo caso l'angolo si esprime in gradi e il suo valore appartiene all'intervallo $[0^{o};180^{o}]$; \item \textbf{angolo orientato tra vettori}: in questo caso l'angolo si esprime in gradi e il suo valore appartiene all'intervallo $]-180^{o};+180^{o}]$; \end{itemize} \subsubsection{Omotetia} \drgeniusIcon{fig22} \drgeniusIndex{Trasformazioni del piano:}{omotetia}{}{} Selezionando questo comando si esegue una omotetia di un qualsiasi oggetto geometrico. Si clicca con il mouse sull'oggetto da trasformare, sul punto che rappresenta il centro di omotetia e su un numero che rappresenta il fattore di scala. \xname{numeric_tools} \subsection{Strumenti numerici} \label{strumenti numerici} Questo menu permette di editare e manipolare valori numerici. \subsubsection{Distanze, lunghezze e numeri} \drgeniusIcon{fig23} \label{numeric_tool} \drgeniusIndex{Numero}{}{}{} \drgeniusIndex{Retta:}{pendenza}{}{} \drgeniusIndex{Retta:}{distanza da}{}{} \drgeniusIndex{Circonferenza:}{lunghezza}{}{} \drgeniusIndex{Segmento:}{lunghezza}{}{} \drgeniusIndex{Vettore:}{norma}{}{} \drgeniusIndex{Arco di circonferenza:}{lunghezza}{}{} \drgeniusIndex{Numero:}{valore libero}{}{} Selezionando questo comando viene creato un valore numerico in molti modi diversi: \begin{enumerate} \item cliccando con il mouse su due punti viene visualizzata la loro distanza; \item cliccando con il mouse su un vettore o su un segmento viene visualizzata la sua lunghezza; \item cliccando con il mouse su una circonferenza viene visualizzata la sua lunghezza; \item cliccando con il mouse su un arco viene visualizzata la sua lunghezza; \item cliccando con il mouse su una retta viene visualizzato il suo coefficiente angolare; \item cliccando con il mouse su una retta e su un punto viene visualizzata la distanza tra il punto e la retta stessa; \item \textbf{cliccando con il tasto sinistro del mouse sullo sfondo} si pu\`o inserire nel foglio di lavoro un valore numerico qualsiasi. \end{enumerate} L'ultima modalit\`a risulta molto utile nella pratica in quanto capita spesso di aver bisogno di inserire nel foglio di lavoro un numero che potr\`a rappresentare una coordinata, una lunghezza o l'ampiezza di un angolo prefissato. \subsubsection{Angolo} \drgeniusIcon{fig24} \drgeniusIndex{Angolo:}{geometrico}{}{}{} \drgeniusIndex{Angolo:}{orientato}{}{}{} Selezionando questo comando \`e possibile misurare l'ampiezza di un angolo o dell'angolo compreso tra due vettori. Nel primo caso si clicca in sequenza su tre punti: il primo e il terzo appartengono ai lati dell'angolo e il secondo \`e il vertice dell'angolo. Nel secondo caso si clicca con il mouse sui due vettori. Osserviamo che nel primo caso l'angolo non \`e orientato e il valore della sua ampiezza non supera l'ampiezza di un angolo piatto. Nel caso dei vettori l'angolo \`e orientato e varia tra $]-180^{o};+180^{o}]$. \subsubsection{Coordinate cartesiane} \drgeniusIcon{fig25} \drgeniusIndex{Punto:}{coordinate di}{}{} \drgeniusIndex{Vettore:}{coordinate di}{}{} Selezionando questo comando si possono visualizzare le coordinate cartesiane di un punto o di un vettore. Si clicca con il mouse su un punto (o su un vettore) e vengono visualizzate, sovrapposte verticalmente, la sua ascissa e la sua ordinata. \subsubsection{Script Guile per \drgeo} \label{script-tool} \drgeniusIcon{fig49} \drgeniusIndex{Script}{}{}{} Selezionando questo comando si attiva la funzione per creare script Guile per \drgeo. In generale uno script riceve in ingresso un certo numero di oggetti geometrici e in uscita fornisce un numero che viene visualizzato nell'area di lavoro. Per gli approfondimenti su questo importante argomento si rinvia ai contenuti dedicati alle \link{Funzioni Avanzate}[ Capitolo \Ref]{advancedFeatures} e in particolare alla \link{script}[ Sezione \Ref, pagina \Pageref]{script}. \xname{macroconstruction_tools} \subsection{Strumenti per la costruzione di macro} \drgeniusIndex{Macro-costruzione}{}{}{} La costruzione di macro rappresenta uno degli aspetti essenziali di \drgeo\ in quanto in questo modo possiamo ampliare indefinitamente il numero degli strumenti di costruzione in esso presenti. \subsubsection{Creare una macro-costruzione} \drgeniusIcon{fig26} Selezionando questo comando inizia il procedimento guidato di realizzazione di una macro. \drgeniusNote{Le macro-costruzioni sono esposte nella sezione \link{macro-costruzioni}[ \Ref, pagina \Pageref]{macroConstruction}.} \subsubsection{Eseguire una macro-costruzione} \drgeniusIcon{fig27} Selezionando questo comando inizia il procedimento guidato per l'esecuzione di una Macro precedentemente costruita. \drgeniusNote{Le macro-costruzioni sono esposte nella sezione \link{macro-costruzioni}[ \Ref, pagina \Pageref]{macroConstruction}.} \xname{other_tools} \section{Altre funzioni} In questo capitolo si analizzano le funzioni per manipolare dinamicamente i diversi oggetti geometrici. \subsection{Spostamento di un oggetto geometrico} \drgeniusIcon{fig28} \drgeniusIndex{Oggetto geometrico:}{spostamento di}{}{} Questa funzionalit\`a \`e molto importante e rappresenta uno dei punti di forza di \drgeo. Dopo aver selezionato questo comando e dopo aver spostato il mouse su un qualsiasi oggetto geometrico, tenendo premuto il tasto sinistro del mouse e contemporaneamente muovendo il mouse stesso, si sposta l'oggetto geometrico selezionato mantenendo tuttavia invariate le caratteristiche geometriche della costruzione. \subsection{Cancellazione di un oggetto geometrico} \drgeniusIcon{fig30} \drgeniusIndex{Oggetto geometrico:}{cancella}{}{} Questa funzionalit\`a permette di cancellare oggetti geometrici precedentemente creati. Dopo aver selezionato il comando, cliccando con il mouse su un oggetto si ottiene l'apertura di una finestra che chiede la conferma per l'eliminazione dell'oggetto stesso. Se per errore si elimina un oggetto che invece si desiderava mantenere \`e possibile rigenerarlo selezionando il comando ``Annulla'' nella barra delle icone o nel menu ``Modifica''. Di default si possono ricostruire fino a 5 oggetti cancellati tuttavia questo numero pu\`o essere modificato andando a modificare le Preferenze. \xname{editing_object_styles} \subsection{Modificare lo stile di un oggetto} \label{object-style} \drgeniusIcon{fig29} \drgeniusIndex{Modifica:}{stile}{}{} \drgeniusIndex{Oggetto geometrico:}{rinomina}{}{} \drgeniusIndex{Oggetto geometrico:}{nascondi}{}{} Selezionando questo comando si pu\`o modificare lo stile proprio di un oggetto che \`e definito dalle seguenti caratteristiche: colore, spessore, etichetta, dimensione e forma. Oltre a questo \`e possibile nascondere temporaneamente un oggetto presente in una costruzione senza tuttavia cancellarlo. Ci\`o pu\`o essere utile per gli oggetti geometrici che dopo essere stati usati in una costruzione geometrica non si desidera siano visibili. Quando, dopo aver selezionato questo comando, si clicca con il mouse su un oggetto, compare una finestra di dialogo che permette di modificare tutte le sue propriet\`a. La finestra di dialogo ha preferenze leggermente diverse in relazione al particolare tipo di oggetto geometrico. La finestra di dialogo relativa ai punti \`e rappresentata in figura: \drgeniusFigure{Finestra di dialogo stile Punto}{fig31} e si nota che questa finestra \`e diversa da quella relativa alle linee (retta, semiretta, vettore, ecc...) rappresentata pi\`u in basso. Dal momento che questi oggetti vengono definiti specificando una coppia di punti essi non possono essere rinominati in quanto il loro nome viene riferito al nome della coppia di punti che li definisce. \drgeniusFigure{Finestra di dialogo stile Linea}{fig32} Una finestra del tutto analoga permette di modificare anche lo stile di una circonferenza, di un arco e di un luogo. Una terza finestra di dialogo permette di modificare lo stile in cui vengono presentati i diversi valori numerici (direttamente editati dall'utente, generati da uno script Guile per \drgeo\ o altro) e l'aspetto dei poligoni: \drgeniusFigure{Finestra di dialogo stile Numeri e Poligoni}{fig33} \subsection{Modificare le propriet\`a di un oggetto} \label{property-item} \drgeniusIcon{fig52} \drgeniusIndex{Modifica:}{propriet\`a}{}{} \drgeniusIndex{Modifica:}{punto}{}{} \drgeniusIndex{Modifica:}{script}{}{} \drgeniusIndex{Modifica:}{valore}{}{} L'utilizzatore di \drgeo\ \`e libero di modificare, attraverso questo comando, le propriet\`a di alcuni oggetti. Cliccando con il mouse su essi si apre una finestra di dialogo per la modifica delle propriet\`a. Allo stato attuale di sviluppo del programma possono essere modificate le propriet\`a dei seguenti oggetti: \begin{enumerate} \item punto libero: si possono modificare ascissa e ordinata\\ \drgeniusFigure{Cambiamento delle coordinate di un punto}{fig34} \item valore numerico: si pu\`o modificare un valore numerico libero\\ \drgeniusFigure{Modifica di un valore numerico}{fig36} \item script: si pu\`o modificare il codice di uno script\\ \drgeniusFigure{Modifica di uno script}{fig35} \end{enumerate} \T \clearpage \section{Preferenze} \xname{default_behaviour} \subsection{Preferenze di default} \label{default_behaviour} \drgeniusIndex{Modifica:}{preferenze di default}{}{} Le preferenze di default di \drgeo\ possono essere configurate in pi\`u modi. Per parametrizzare le preferenze si accede al menu \drgeniusMenu{Modifica -> Preferenze} e si apre la seguente finestra di dialogo: \drgeniusFigureSize{Preferenze globali}{fig37}{8} La finestra di dialogo \`e articolata in due sezioni: \begin{enumerate} \item La prima sezione riguarda le preferenze relative agli oggetti geometrici e permette di modificare l'aspetto di ciascuno di essi; \drgeniusIndex{Modifica:}{stile di default}{}{} \item La seconda sezione permette di modificare alcune preferenze globali come:\\ \begin{itemize} \drgeniusIndex{Modifica:}{preferenze di default:}{annulla/rifai}{}{} \item il numero di oggetti cancellati per errore e ricostruibili utilizzando il comando Annulla/Rifai; \drgeniusIndex{Modifica:}{preferenze di default:}{nomi}{} \item il nome di default che si attiva ogni volta che un dato oggetto viene costruito. Il \%d viene rimpiazzato da un numero intero generato da \drgeo; questo valore viene incrementato di una unit\`a ad ogni nuova costruzione di un oggetto dello stesso tipo; \item i nomi di default per l'esportazione in formato \LaTeX\ e PostScript ; \end{itemize} \end{enumerate} \subsection{Altre preferenze} \drgeniusIndex{Figura:}{rinomina}{}{} Oltre alle preferenze di default di \drgeo\ \`e possibile modificare il nome di un oggetto geometrico a partire dal menu \drgeniusMenu{Modifica -> Rinomina}. \drgeniusFigure{Modifica nome di una figura}{fig39} \chapter{Funzioni Avanzate} \label{advancedFeatures} In questo capitolo vengono presentate le funzionalit\`a che permettono di estendere in modo sostanzialmente indefinito le potenzialit\`a di \drgeo\ o di adattarne l'uso alle pi\`u svariate situazioni pedagogiche. La prima funzione avanzata che si considera riguarda la creazione di \textit{macro-costruzioni} o, pi\`u brevemente, di macro. Attraverso la costruzione di una macro \`e possibile definire in \drgeo\ una nuova costruzione geometrica, salvarla in un file con estensione \textbf{.mgeo} e richiamarla quando necessario. La seconda funzione avanzata che si considera consiste nella stesura di \textit{script Guile} per \drgeo\ o, pi\`u brevemente, di DGS. Questa funzionalit\`a, come la costruzione di macro, permette di estendere le potenzialit\`a di \drgeo\ permettendo all'utilizzatore di familiarizzare con la stesura di script in linguaggio Scheme. Uno script DGS generalmente ha in ingresso valori numerici relativi ad uno o pi\`u oggetti geometrici (lunghezza di un segmento, coordinata di un punto) e restituisce sempre in uscita un numero. Per fare un esempio, come vedremo, si pu\`o scrivere un DGS per calcolare l'area di un triangolo. In questo caso in ingresso sono date le lunghezze di base e altezza del triangolo e in uscita si ottiene l'area del triangolo. Un ultimo aspetto avanzato di \drgeo\ riguarda la possibilit\`a di \textit{modificare l'interfaccia utente} in modo da escludere una o pi\`u costruzioni geometriche normalmente disponibili. Ci\`o potrebbe essere di interesse in alcune situazioni didattiche in cui si vuole costringere l'utilizzatore a lavorare in un ambiente con un set di costruzioni limitato. \xname{using_macro} \section{Macro-costruzioni} \label{macroConstruction} \drgeniusIndex{Macro-costruzione:}{introduzione}{}{} La costruzione di una macro \`e una procedura attraverso la quale \`e possibile aggiungere a \drgeo\ una nuova costruzione. Come in ogni costruzione geometrica si definiscono un certo numero di oggetti geometrici in ingresso e si ottengono alcuni oggetti geometrici in uscita. L'utilizzatore di \drgeo\ stabilisce gli oggetti iniziali e finali della macro-costruzione, che poi verr\`a salvata in un file con estensione .mgeo. La costruzione di una macro deve essere logicamente coerente: gli oggetti finali della macro devono dipendere in modo esclusivo dagli oggetti iniziali in modo che \drgeo\ possa ricostruire senza ambiguit\`a l'intera costruzione. Da questo punto di vista \drgeo\ \`e in grado di memorizzare la sequenza della costruzione e di riprodurla ogni volta che l'utilizzatore, dopo aver azionato il comando di esecuzione di una macro, andr\`a a cliccare su oggetti geometrici che coincidono con gli oggetti in ingresso della macro. \drgeniusNote{Quando si esegue una macro vengono ricostruiti tutti gli oggetti geometrici intermedi necessari per la costruzione degli oggetti finali della macro.} Per illustrare il modo in cui avviene la costruzione di una macro analizziamo in dettaglio, come esempio, la costruzione di una circonferenza passante per tre punti dati. \drgeniusFigureSize{Figura iniziale}{fig40}{4} \drgeniusIndex{Macro-costruzione:}{crea}{}{} Prima di creare una macro-costruzione \`e necessario eseguire la costruzione che porta agli oggetti finali in modo da rendere disponibile a \drgeo\ un modello. Nel nostro caso la costruzione \`e la seguente: \drgeniusFigureSize{Figura finale}{fig41}{4} \subsection{Realizzare una macro-costruzione} A questo punto la sequenza di costruzione \`e completa ed \`e necessario avvertire \drgeo\ che, a partire da questa sequenza, si desidera costruire una macro. Per fare questo si seleziona, nella barra delle icone, il comando \drgeniusMenu{Costruire una macro} \drgeniusIcon{fig26} o si seleziona l'analogo comando dal menu azionabile cliccando con il tasto destro del mouse in un punto dello sfondo. Si apre allora una finestra di dialogo che riassume i passaggi necessari per costruire una macro: definizione degli oggetti iniziali e finali, scelta del nome e descrizione. \drgeniusFigureSize{Prima pagina della finestra di dialogo per costruire una macro}{fig42}{6} Procedendo si apre una seconda pagina in cui vengono selezionati gli oggetti iniziali della macro. Nel nostro esempio sono i tre punti iniziali. Per inserirli \`e sufficiente cliccare su ciascuno di essi. \drgeniusFigureSize{Seconda pagina: i tre punti sono stati selezionati}{fig43}{6} Procedendo si apre una terza pagina in cui vengono selezionati gli oggetti finali della macro. Nel nostro esempio gli oggetti finali sono la circonferenza e il suo centro. Per inserirli \`e sufficiente, come in precedenza, cliccare su ciscuno di essi. \drgeniusFigureSize{Terza pagina: circonferenza e suo centro sono stati selezionati}{fig44}{6} Procedendo si apre una quarta pagina in cui vengono inseriti il nome e la descrizione della macro. Queste informazioni sono utili quando la macro-costruzione verr\`a nuovamente utilizzata, magari a distanza di tempo, durante altre sessioni di lavoro. A questo proposito si consiglia di scegliere opportunamente il nome delle macro in modo da non confonderle tra loro. \drgeniusFigureSize{Quarta pagina: nome e descrizione della macro sono stati inseriti}{fig45}{6} Procedendo ancora si apre una quinta pagina con i bottoni per conludere la costruzione o per tornare indietro ed emendare possibili errori. \drgeniusNote{Se oggetti iniziali e finali non trovano corrispondenza (\drgeo\ non riesce a comprendere la logica della costruzione), la macro non pu\`o essere costruita. In questo caso \`e necessario fare marcia indietro e modificare il contenuto di alcune pagine precedenti.} Nel caso in cui la costruzione sia corretta la macro viene creata e memorizzata in \drgeo. Vedremo ora come sia possibile riutilizzare una macro costruita in precedenza e salvata. \subsection{Eseguire una macro-costruzione} \drgeniusIndex{Macro-costruzione:}{esegui}{}{} Per eseguire una macro-costruzione \`e necessario selezionare nella barra delle icone il comando \drgeniusMenu{Eseguire una macro precostruita} \drgeniusIcon{fig27} o selezionare l'analogo comando dal menu azionabile cliccando con il tasto destro del mouse in un punto dello sfondo. Si apre allora una finestra di dialogo che riassume i passaggi necessari per eseguire una macro: scelta della macro dalla lista macro, selezione, nella vista corrente, degli oggetti geometrici necessari per eseguire la macro. Procedendo si apre una seconda pagina con un elenco da cui \`e possibile selezionare la macro desiderata. A questo punto, per eseguire la macro, basta cliccare con il mouse sugli oggetti geometrici della figura corrispondenti agli oggetti iniziali della macro stessa. \drgeniusFigureSize{Seconda pagina: selezione di una macro}{fig46}{6} Se ci riferiamo all'esempio precedente della circonferenza per tre punti per eseguire la macro dobbiamo avere a disposizione sul foglio di lavoro almeno tre punti. \drgeniusFigureSize{Foglio di lavoro con tre punti}{fig47}{4} Cliccando sui tre punti la macro viene eseguita e compare la circonferenza passante per i tre punti e il suo centro. \drgeniusFigureSize{Figura finale: circonferenza e centro}{fig48}{4} \T \clearpage \xname{drgenius_guile_script} \section{Script Guile per \drgeo } \label{script} \drgeniusIndex{Script:}{introduzione}{}{} Il software \drgeo\ \`e compatible con Guile; ci\`o significa che con \drgeo\ \`e possibile eseguire degli script Scheme che si appoggiano all'interprete Guile. Ma, che cos'\`e Guile? Se andiamo a leggere l'inizio del manuale di Guile troviamo scritto: \begin{quote}{\em Guile \`e un interprete per il linguaggio di programmazione Scheme che pu\`o essere utilizzato in molti ambienti. } \end{quote} La citazione seguente descrive in modo pi\`u preciso come utilizzare Guile in \drgeo: \begin{quote}{\em Analogamente ad un terminale, Guile pu\`o essere lanciato in modo interattivo, pu\`o ricevere espressioni scritte dall'utilizzatore, elaborarle e restituire dei risultati. Alternativamente come interprete di script, Guile \`e in grado di leggere ed eseguire un codice Scheme contenuto in un file. In questo modo Guile \`e disponibile, sotto forma di biblioteca, per permettere ad applicazioni di vario tipo di incorporare facilmente e in modo completo un interprete Scheme. Una applicazione pu\`o utilizzare Guile come un languaggio potente di estensione o di autoconfigurazione, o come un adesivo universale per ``incollare'' funzioni primitive fornite dall'applicazione. } \end{quote} In \drgeo, una API viene resa disponibile a partire dall'interprete Guile. L'utilizzatore di \drgeo, attraverso gli script pu\`o manipolare opportunamente oggetti (geometrici o numerici) contenuti in una figura. Oltre a questo, dal momento che uno script viene considerato un oggetto come altri non vi \`e alcun bisogno di salvarlo separatamente dalla figura in cui \`e contenuto. D'ora in poi, per indicare uno script Guile, utilizzeremo sempre l'acronimo DGS (``\drgeo\ Guile Script''). \subsection{DGS attraverso esempi} \drgeniusIndex{Script:}{esempi}{}{} Il comando per creare un DGS \`e disponibile all'interno della sezione riguardante i numeri del menu azionabile cliccando con il tasto destro del mouse in un punto dello sfondo o nella barra delle icone. Un DGS pu\`o ricevere da 0 a $n$ parametri di ingresso. Conviene a questo punto passare direttamente all'analisi di qualche esempio di DGS che permetta di comprendere facilmente le potenzialit\`a di questo strumento. Macro e DGS conferiscono a \drgeo\ un aspetto speciale\footnote{Le macro costituiscono l'aspetto geometrico, gli script, quello numerico di un programma nato all'insegna di uno spirito ``hacker''} nel panorama dei programmi di studio interattivo della geometria euclidea. Oltre a questo \`e importante comprendere come, attraverso i DGS, vengano messe a dispozione la maggior parte delle funzionalit\`a dell'interprete GNU Guile. Ci\`o vale in particolare per la libreria delle funzioni matematiche di cui qui viene fatto largo uso. \paragraph{DGS senza parametri di ingresso} La procedura per la creazione di un DGS senza parametri in ingresso \`e la seguente: \begin{enumerate} \item si seleziona il \link{comando script}[ Sezione \Ref, pagina \Pageref]{script-tool}; \item si clicca con il mouse \textit{direttamente} sullo sfondo del foglio di lavoro nel punto in cui si desidera che compaia il valore di uscita dello script prestando attenzione a \textbf{non cliccare} erroneamente su oggetti della figura, in quanto questi verrebbero considerati da \drgeo\ come parametri di ingresso dello script\footnote{Se per errore sono stati selezionati oggetti indesiderati per annullare la selezione \`e sufficiente cliccare nuovamente sul comando per attivare uno script.}; \item una volta collocato lo script appare per default la scritta celeste ``Dr.~Genius'' ed \`e ora il momento di editare lo script azionando il \link{comando per modificare le propriet\`a di un oggetto}[ Sezione \Ref, pagina \Pageref]{property-item} e quindi cliccando con il mouse sulla scritta stessa. A questo punto si apre automaticamente una finestra di dialogo, che mostra il contenuto dello script (\texttt{``Dr. Genius''}), dove si pu\`o cancellare il contenuto di default dello script e sostituirlo con il desiderato. \end{enumerate} \subparagraph{Un generatore di numeri casuali e altro} \drgeniusIndex{Script:}{numeri casuali}{}{} Il codice da editare, dopo aver seguito la procedura illustrata sopra, per ottenere un numero casuale \`e semplicemente: \begin{verbatim} (random 10) \end{verbatim} Ogni volta che si clicca sullo script comparir\`a un numero casuale tra 0 e 9. Se si desidera generare un numero casuale appartenente all'intervallo $[0;1[$, basta utilizzare lo script: \begin{verbatim} (random:uniform) \end{verbatim} \drgeniusNote{Qualche osservazione: \begin{itemize} \item Il valore restituito da uno script coincide con il valore calcolato nell'ultima linea di codice. Nel nostro caso questo valore coincide con il valore ritornato dalla chiamata ad una funzione. \item L'ultima linea di uno script deve ritornare un numero reale. In caso contrario comparir\`a la scritta ``Risultato non stampabile''~; \item Se si desidera visualizzare il valore di una variabile \`e sufficiente scrivere il suo nome nell'ultima riga dello script. \end{itemize} } \subparagraph{Calcolo di costanti} Per calcolare un valore approssimato di pigreco \`e sufficiente scrivere: \begin{verbatim} (acos -1) \end{verbatim} mentre per calcolare un valore approssimato del numero di Neper: \begin{verbatim} (exp 1) \end{verbatim} I valori restituiti da questi DGS si possono utilizzare alla stregua di un qualsiasi altro valore numerico editabile in \drgeo. L'importanza pedagogica dei DGS si sente maggiormente quando, come ora vedremo, vengono loro passati dei parametri in ingresso. \paragraph{DGS con uno o pi\`u parametri in ingresso} \drgeniusIndex{Script:}{parametri}{}{} Il procedimento per creare un DGS con un parametro in ingresso \`e simile, ma non identico, a quanto visto in precedenza. L'unica diversit\`a consiste nel fatto che in questo caso, subito \textbf{dopo} aver selezionato il comando per attivare uno script, si deve \textbf{cliccare sugli oggetti geometrici di ingresso} che si desidera passare allo stesso e solo \textbf{successivamente} si deve cliccare in un punto del foglio di lavoro dove si desidera venga visualizzato l'output dello script. All'interno dello script il riferimento al primo parametro di entrata \`e rappresentato per default dalla variabile $a1$. In caso di due o pi\`u parametri di ingresso si utilizzeranno, rispettando l'ordine in cui sono stati selezionati gli oggetti, le variabili $a1, a2\ldots , an$. A seconda del tipo di oggetto a cui si fa riferimento sono disponibili diversi metodi per ottenere valori numerici, coordinate, lunghezze e via di seguito i cui codici sono contenuti nel capitolo \link{Metodi di riferimento per DGS}[ \Ref, pagina \Pageref]{api-dgs}. \subparagraph{Area del triangolo} Iniziamo ora a trattare un esempio molto semplice di utilizzo di un DGS per il calcolo dell'area di un triangolo. La figura a cui ci riferiamo \`e la seguente: \drgeniusFigureSize{Area del triangolo}{fig38}{8} In essa sono rappresentati un triangolo $ABC$ e l'altezza $CH$ relativa alla base $AB$. Per calcolare l'area $S(ABC)$ del triangolo utilizziamo un DGS con parametri in ingresso i segmenti $AB$ e $CH$ della figura. Seguendo la procedura precedente si clicca innazitutto sul bottone che aziona la funzionalit\`a di \link{script}[ Sezione \Ref, pagina \Pageref]{script-tool} e subito dopo, nell'ordine, sui due segmenti che risulteranno lampeggiare. Si clicca quindi su un punto dello schermo dove si desidera collocare l'uscita dello script e comparir\`a la scritta azzurra Dr. Genius. A questo punto, dopo aver azionato il comando per \link{modificare le propriet\`a di un oggetto}[ Sezione \Ref, pagina \Pageref]{property-item} e dopo aver cliccato sulla scritta Dr. Genius, si aprir\`a una finestra in cui scriveremo il seguente codice Scheme: \begin{verbatim} (define AB (getLength a1)) (define BC (getLength a2)) (/ (* AB CH ) 2 ) \end{verbatim} ottenendo il valore dell'area del triangolo. Per assegnare il nome $S(ABC)$ allo script e per cambiarne il colore da azzurro a rosso scuro basta utilizzare la funzionalit\`a di \link{modifica dello stile di un oggetto}[ Sezione \Ref, pagina \Pageref]{object-style} vista in precedenza. Altri esempi didattici elementari sono comunque contenuti nel capitolo dedicato alle \link{Applicazioni Didattiche}[ Sezione \Ref, pagina \Pageref]{education}. \subparagraph{Tangente ad una curva} In quanto segue proponiamo un esempio articolato in cui si esamina pi\`u volte la procedura di creazione di uno script. L'esempio, che svilupperemo in modo graduale, riguarda la costruzione del grafico di una funzione e della tangente in un punto variabile del suo grafico. La figura finale \`e contenuta nella documentazione di \drgeo\ e prende il nome di \xlink{slope.fgeo}[(/usr/local/share/drgeo/examples/figures/slope.fgeo)] {/usr/local/share/drgeo/examples/figures/slope.fgeo} \drgeniusFigureSize{La figura che otterremo}{fig55}{8} \subparagraph{Definire un valore in un dato intervallo} \drgeniusIndex{Script:}{intervallo}{}{} In un foglio di lavoro bianco disegnamo due punti e il segmento che li congiunge. Su questo segmento sistemiamo un punto che chiamiamo ``Move me!''. Questo punto ci serve per determinare valori numerici in un dato intervallo. Infatti il seguente script, il cui parametro $a1$ si riferisce a ``Move me!'', restituisce un numero decimale nell'intervallo $[-10;+10]$: \begin{verbatim} (define x (getAbscissa a1)) (* 20 (- x 0.5)) \end{verbatim} La prima linea dello script definisce una variabile \texttt{x} il cui valore \texttt{(getAbscissa a1)} coincide con l'ascissa curvilinea dell'oggetto geometrico a cui si riferisce $a1$\footnote{Indipendentemente dal tipo di segmento di curva l'ascissa curvilinea \`e un numero reale appartenente all'intervallo $[0;1]$} ossia del punto ``Move me!''. Nella seconda riga dello script, che traduce l'espressione algebrica $20 \cdot ( x - 0.5)$, si fa in modo che il valore restituito dallo script appartenga all'intervallo $[-10;+10]$. Finalmente chiamiamo questo script $X_{0}$. \subparagraph{Disegnare il grafico di una funzione} \drgeniusIndex{Luogo:}{script}{}{} Il valore numerico generato dallo script precedente ci serve ora per calcolare, attraverso un secondo script, la sua immagine attraverso la funzione $x \rightarrow cos(x)$ : \begin{verbatim} (define x (getValue a1)) (cos x) \end{verbatim} Sottolineiamo che in \texttt{(getValue a1)} l'oggetto a cui si riferisce $a1$ non \`e il punto ``Move me!'' ma lo script $X_{0}$. Chiamiamo questo secondo script $Y_{0}$. Infine creiamo il punto $M_{0}$ di coordinate $(X_{0};Y_{0})$ che \`e un punto del grafico della funzione $x \rightarrow cos(x)$. Per disegnare il grafico costruiamo il luogo del punto $M_{0}$ quando ``Move me!'' descrive tutto il segmento su cui giace. \subparagraph{Calcolare e disegnare la tangente al grafico} \drgeniusIndex{Script:}{tangente a un grafico}{}{} Per determinare la tangente nel punto $M_{0}$ del grafico calcoliamo in primo luogo la pendenza della retta tangente. Consideriamo allora la derivata prima della funzione $x \rightarrow -sin(x)$ nel punto $X_{0}$ e scriviamo lo script: \begin{verbatim} (- 0 (sin (getValue a1))) \end{verbatim} che ha come riferimento l'ascissa $X_{0}$. Le notazioni di tipo Scheme/Guile possono sembrare inizialmente poco intuitive ma dopo aver familiarizzato con esse appariranno semplici. Chiamiamo lo script ``pendenza in $M_{0}$''. Nel momento in cui $M_{0}$ viene spostato sul grafico la pendenza viene ricalcolata. Non resta che disegnare la tangente. Per fare questo calcoliamo le coordinate di un secondo punto $M_{1}$ di questa retta. Iniziamo dall'ascissa ponendo, ad esempio, $X_{1} = X_{0} + 2$ e scriviamo uno script, che chiamiamo $X_{1}$, con parametro d'ingresso lo script $X_{0}$: \begin{verbatim} (define x1 (getValue a1)) (+ x1 2) \end{verbatim} Per determinare l'ordinata di $M_{1}$ abbiamo bisogno di: \begin{itemize} \item $M_{0}$ (riferimento $a1$); \item pendenza in $M_{0}$ ($a2$); \item ascissa $X_{1}$ ($a3$). \end{itemize} Nello script seguente calcoliamo l'ordinata di $M_{1}$ calcolando $Y_{0} + m(X_{1} - X_{0})$: \begin{verbatim} (define x0 (car (getCoordinates a1))) (define y0 (cadr (getCoordinates a1))) (define m (getValue a2)) (define x1 (getValue a3)) (+ (* m (- x1 x0)) y0) \end{verbatim} Qualche parola relativamente alla chiamata \texttt{(getCoordinates a1)}, in essa \texttt{a1} deve riferirsi a un oggetto di tipo punto. Il metodo restituisce in questo caso una lista contenente le coordinate del punto che per noi \`e $M_{0}$. Scrivendo \texttt{car} si estrae dalla lista il primo valore, scrivendo \texttt{cadr} il secondo. La parte rimanente dello script dovrebbe risultare chiara. Chiamiamo questo script $Y_{1}$ e costruiamo il punto $M_{1}$ di coordinate $(X_{1};Y_{1})$ e finalmente la tangente $M_{0}M_{1}$. Osserviamo che, al posto di tutti questi script, sarebbe stato possibile scriverne solo due o tre, anche se pi\`u complessi. \subsection{Metodi di riferimento per DGS} \label{api-dgs} % DGS API is exposed here Quanto segue \`e una descrizione dei metodi disponibili per DGS. La classificazione \`e fatta secondo il tipo di oggetti geometrici o numerici cui si riferiscono. \subsubsection{Punto} \drgeniusIndex{Script:}{\texttt{getAbscissa}}{}{}{} \begin{drgeoApi}{valore (getAbscissa punto)} \drgeoApiIn{punto}{punto su una curva} \drgeoApiOut{ascissa curvilinea del punto sulla curva. Il valore appartiene all'intervallo chiuso $[0;1]$} \drgeoApiExample{(define x (getAbscissa a1))\\ (* x 10)} \end{drgeoApi} \drgeniusIndex{Script:}{\texttt{setAbscissa}}{}{}{} \begin{drgeoApi}{(setAbscissa punto x)} \drgeoApiIn{punto}{punto su una curva} \drgeoApiIn{x}{valore decimale nell'intervallo $[0;1]$ che rappresenta l'ascissa del punto} \drgeoApiExample{(setAbscissa a1 0.5)} \end{drgeoApi} \drgeniusIndex{Script:}{\texttt{getCoordinates}}{}{} \begin{drgeoApi}{liste (getCoordinates punto|vettore)} Restituisce le coordinate di un punto o di un vettore.\\ \drgeoApiIn{punto|vettore}{punto o vettore} \drgeoApiOut{lista contenente le coordinate del punto o del vettore} \drgeoApiExample{(define c (getCoordinates a1))\\ (define x (car c))\\ (define y (cadr c))\\ (+ (* x x) (* y y))} \end{drgeoApi} \drgeniusIndex{Script:}{\texttt{setCoordinates}}{}{} \begin{drgeoApi}{(setCoordinates punto coord)} Posiziona le coordinate di un punto\\ \drgeoApiIn{punto}{punto libero nel piano} \drgeoApiIn{coord}{lista di numeri decimali} \drgeoApiExample{(define l (list 1.4 (random 5)))\\ (setCoordinate a1 l)} \end{drgeoApi} \subsubsection{Retta, Semiretta, Segmento, Vettore, Angolo} \drgeniusIndex{Script:}{\texttt{getSlope}}{}{}{} \begin{drgeoApi}{valore (getSlope direzione)} \drgeoApiIn{direzione}{retta, semiretta, segmento o vettore} \drgeoApiOut{pendenza relativa alla direzione} \drgeoApiExample{(define p (getSlope a1))} \end{drgeoApi} \drgeniusIndex{Script:}{\texttt{getNorm}}{}{} \begin{drgeoApi}{valore (getNorm vettore)} \drgeoApiIn{vettore}{vettore} \drgeoApiOut{norma del vettore} \drgeoApiExample{(define n (getNorm a1))} \end{drgeoApi} \drgeniusIndex{Script:}{\texttt{getLength}}{}{} \begin{drgeoApi}{valore (getLength segmento)} \drgeoApiIn{segmento}{segmento} \drgeoApiOut{lunghezza segmento} \drgeoApiExample{(define l (getLength a1))} \end{drgeoApi} \drgeniusIndex{Script:}{\texttt{getAngle}}{}{} \begin{drgeoApi}{valore (getAngle angolo)} \drgeoApiIn{angolo geometrico}{angolo geometrico} \drgeoApiOut{ampiezza in gradi dell'angolo} \drgeoApiExample{(define ABC (getAngle a1))} \end{drgeoApi} \subsubsection{Circonferenza, Arco di circonferenza} \drgeniusIndex{Script:}{\texttt{getCenter}}{}{} \begin{drgeoApi}{lista (getCenter circonferenza|arco)} \drgeoApiIn{circonferenza|arco}{circonferenza o suo arco} \drgeoApiOut{lista contenente le coordinate del centro} \drgeoApiExample{(define c (getCenter a1))\\ (car c)} \end{drgeoApi} \drgeniusIndex{Script:}{\texttt{getRadius}}{}{} \begin{drgeoApi}{valore (getRadius circonferenza|arco)} \drgeoApiIn{circonferenza|arco}{circonferenza o suo arco} \drgeoApiOut{raggio} \drgeoApiExample{(define r (getRadius a1))} \end{drgeoApi} \drgeniusIndex{Script:}{\texttt{getLength}}{}{} \begin{drgeoApi}{valore (getLength circonferenza|arco)} \drgeoApiIn{circonferenza|arco}{circonferenza o suo arco} \drgeoApiOut{lunghezza circonferenza o arco} \drgeoApiExample{(define l (getLength a1))} \end{drgeoApi} \subsubsection{Numeri} \drgeniusIndex{Script:}{\texttt{getValue}}{}{} \begin{drgeoApi}{valore (getValue numero)} \drgeoApiIn{numero}{numero} \drgeoApiOut{valore del numero} \drgeoApiExample{(define a (getValue a1))\\ (define b (getValue a2))\\ (+ a b)} \end{drgeoApi} \drgeniusIndex{Script:}{\texttt{setValue}}{}{} \begin{drgeoApi}{(setValue numero v)} \drgeoApiIn{numero}{numero} \drgeoApiIn{v}{valore decimale} \drgeoApiExample{(define v (getValue a1))\\ (setValue a2 v)} \end{drgeoApi} \subsubsection{Altro} \drgeniusIndex{Script:}{\texttt{move}}{}{} \begin{drgeoApi}{(move item u)} \drgeoApiIn{item}{oggetto} \drgeoApiIn{u}{vettore} \drgeoApiExample{(define v (vector .1 0))\\ (move a1 v)} \end{drgeoApi} \section{Blocco di strumenti dell'interfaccia} \label{ui-lock} \drgeo\ offre la possibilit\`a di predisporre delle sessioni\footnote{File che comprendono pi\`u documenti di \drgeo\ (figure e/o testi)} in cui l'insegnante pu\`o decidere, in merito ad alcune costruzioni da eseguire, di impedire l'accesso ad alcuni strumenti normalmente disponibili. Il blocco degli strumenti avviene attraverso un sistema di password. In questo modo l'insegnante ha la possibilit\`a di predisporre attivit\`a didattiche che prevedono gradi diversi di blocco degli strumenti di costruzione. \subsection{Impedire l'uso di strumenti} \drgeniusIndex{Strumenti:}{blocco}{}{} Per impedire l'accesso agli strumenti di costruzione si ricorre al comando \drgeniusMenu{Modifica -> Personalizza Interfaccia}. Dopo aver selezionato il comando si apre una grande finestra di dialogo in cui si riconoscono tutte le icone relative agli strumenti di \drgeo. Cliccando direttamente sulle icone \`e possibile attivare o disattivare la loro funzionalit\`a. Le icone disattivate appariranno pi\`u sbiadite. Allo stesso tempo, cliccando sull'icona principale di un menu (riconoscibile per la presenza di un triangolino verde in basso a destra), \`e possibile disattivare tutti gli strumenti afferenti a quel menu. \drgeniusFigureSize{Finestra di dialogo per bloccare l'interfaccia.}{fig53}{8} Dopo aver completato la scelta degli strumenti di cui impedire l'uso si procede alla loro effettiva disattivazione cliccando sul bottone \drgeniusMenu{Blocca} della finestra di dialogo. A quel punto \drgeo\ richiede una password. \drgeniusNote{Quando si salva in un file una figura o una sessione con blocco dell'interfaccia anche le password sono salvate in forma criptata nello stesso file.} \subsection{Sblocco degli strumenti} \drgeniusIndex{Strumenti:}{sblocco}{}{} Analogamente a come vengono bloccate delle funzionalit\`a dell'interfaccia \`e possibile, a seconda delle necessit\`a, sbloccare le stesse funzionalit\`a. Sempre ricorrendo al comando \drgeniusMenu{ Modifica -> Personalizza Interfaccia} una volta aperta la finestra di dialogo si utilizza il bottone \drgeniusMenu{Sblocca}. Come in precedenza per poter sbloccare uno strumento \`e necessario inserire una pasword. \drgeniusFigure{Finestra di dialogo per sbloccare l'interfaccia}{fig54} \chapter{Figure Scheme per \drgeo} \drgeniusIndex{Figure Scheme per \drgeo\ :}{introduzione}{}{} Le \emph{Figure Scheme in \drgeo} -- (FSD) -- sono figure scritte in un linguaggio relativamente naturale. Non si tratta pi\`u di costruire una figura utilizzando gli strumenti messi a disposizione dall'interfaccia grafica di \drgeo\ ma piuttosto di descrivere una figura utilizzando il linguaggio di programmazione Scheme. Abbiamo profuso il massimo sforzo per rendere la sintassi del linguaggio semplice e non intricata. Oltre a questo le parole chiave utili per descrivere una figura si possono adattare a differenti lingue in quanto sono ridefinibili. Per coerenza, nonostante sia possibile utilizzare istruzioni in lingue diverse, \`e preferibile, una volta scelta una lingua, uniformare tutti i comandi a quella stessa lingua. \section{Alcuni esempi} \drgeniusIndex{Figure Scheme per \drgeo\ :}{esempi}{}{} Scheme \`e per sua natura un linguaggio di alto livello, per questa ragione, una volta definita una figura, avremo a disposizione tutta la sua potenza per eseguire, ad esempio, azioni ricorsive su parti della figura o per utilizzare funzioni aleatorie per modificarla ad ogni sua comparsa sul foglio di lavoro. In altri termini le FSD sono allo stesso tempo svincolate dall'interfaccia grafica e potenziate dalla presenza di Scheme. Una FSD \`e un file con estensione .scm creato attraverso un editore di testo che, una volta aperto in \drgeo\ attraverso il comando \drgeniusMenu{File->Valuta}, genera una figura sul foglio di lavoro. Iniziamo studiando un semplice esempio di FSD: % Note to the translator, most of the DSF commands can be translated % in various languages, this is why you can see the command % written in French, feel free to translate in your language, however % you will also have to maintain the corresponding % scm/drgeo_scm_interface_constant_xx.scm file \drgeniusIndex{Figure Scheme per \drgeo\ :}{nuova figura}{}{} \begin{verbatim} (new-figure "Figura") \end{verbatim} Si tratta della pi\`u semplice FSD che si possa definire. Una volta valutato il file in \drgeo\ appare una nuova figura vuota con nome ``Figura''. Ripetendo il comando \texttt{(new-figure "Figura")} verranno create quante figure si desiderano. Vediamo un secondo esempio: \begin{verbatim} (new-figure "Figura") (lets Point "A" free 1.2 -2) \end{verbatim} Questa FSD definisce una figura con un punto libero $A$ di coordinate $(1,2~;~-2)$. Come si pu\`o vedere la sintassi utile per la definizione dell'oggetto geometrico \`e intuitiva e espressa in un linguaggio molto vicino a quello comune. Osserviamo inoltre come questa definizione sia sostanzialmente identica nella forma a quella di tutti i comandi che permettono di definire i rimanenti oggetti: \begin{enumerate} \item inizia con la parola chiave \texttt{lets} che indica che si desidera costruire un nuovo oggetto; \item segue la categoria a cui appartiene l'oggetto, in questo caso \texttt{Point}. \item quindi si scrive il nome dell'oggetto, nel nostro caso $A$, sempre tra virgolette ". Se non si desidera dare alcun nome all'oggetto \`e sufficiente scrivere: \begin{verbatim}""\end{verbatim} \item infine si precisa il tipo di oggetto, ossia il tipo di punto, che nel nostro caso \`e libero \texttt{free}; \item il tipo di oggetto \`e seguito da una lista di argomenti specifici che, nel nostro esempio, coincide con la coppia di coordinate che definiscono il punto $A$. \end{enumerate} Vediamo un terzo esempio: \begin{verbatim} (define (triangolo p1 p2 p3) (Segment "" extremities p1 p2) (Segment "" extremities p2 p3) (Segment "" extremities p1 p3)) (define (casuale) (- 8 (* 16 (random:uniform)))) (new-figure "Figura") (lets Point "A" free (casuale) 0) (lets Point "B" free 5 0) (lets Point "C" free (casuale) 5) (triangolo A B C) \end{verbatim} Questo esempio \`e di particolare interesse in quanto ci mostra tre aspetti essenziali: \begin{enumerate} \item come introdurre costruzioni di pi\`u alto livello non previste inizialmente in \drgeo. Qui abbiamo definito la funzione \texttt{triangolo} che a partire da tre punti qualsiasi costruisce un triangolo. Possiamo confrontare questa costruzione con quella che potremmo definire attraverso una macro concludendo che il primo metodo \`e pi\`u potente; \item come definire funzioni associate: nel nostro caso la funzione \texttt{casuale} che ritorna un numero decimale casuale compreso tra -8 e 8. Attraverso questa funzione, ogni volta che viene aperta la figura, il disegno apparir\`a diverso; \item l'uso della parola chiave \texttt{lets} non \`e obbligatorio, ma legato alla necessit\`a di definire o meno dei riferimenti per l'oggetto creato. Ad esempio nella funzione \texttt{triangolo} non abbiamo bisogno di alcun riferimento ai segmenti creati; al contrario quando definiamo i punti $A$, $B$ e $C$ sono necessari dei riferimenti. In questo caso i riferimenti hanno lo stesso nome\footnote{Da un punto di vista interno al linguaggio Scheme, i riferimenti sono dei simboli che puntano ad una struttura interna all'oggetto -- un prototipo -- nel momento in cui i nomi sono stringhe di caratteri.} senza virgolette: \texttt{A}, \texttt{B} e \texttt{C}. Nel seguito chiameremo questi riferimenti \textbf{simboli}; ci\`o per utilizzare in modo corretto la terminologia del linguaggio Scheme. In questo modo quando la funzione \texttt{triangolo} viene chiamata vengono passati ad essa come parametri i simboli \texttt{A}, \texttt{B} e \texttt{C}, che vengono utilizzati per definire i vertici del triangolo. \end{enumerate} Osserviamo che quando si definiscono i segmenti non vengono assegnati ad essi dei nomi in quanto \drgeo\ fa questo automaticamente: nel nostro caso i segmenti saranno $[AB]$, $[BC]$ e $[AC]$. Per concludere questa sezione vediamo un ultimo esempio: \begin{verbatim} (lets Point "A" free 1 0) (lets Point "B" free 5 0) (lets Line "d1" 2points A B) (send A color yellow) (send A shape round) (send A size large) (send B masked) (send d1 thickness dashed) \end{verbatim} I primi tre comandi permettono di costruire due punti e una retta. La parte che qui maggiormente interessa riguarda la serie di comandi preceduti da \texttt{send}. Questo comando permette di comunicare con un oggetto di cui si dispone del simbolo relativo. In questo caso i simboli di cui disponiamo sono \texttt{A}, \texttt{B} e \texttt{d1}. La struttura di \texttt{send} consiste in primo luogo di un primo argomento che identifica l'oggetto con cui si vuole comunicare e di un secondo argomento che definisce il messaggio. Dal terzo argomento in poi seguono informazioni legate alla natura del messaggio. Ad esempio \texttt{(send A color yellow)} invia il messagio \texttt{color} con parametro \texttt{yellow}: in questo caso il punto viene dipinto di giallo. Il significato dei rimanenti comandi dovrebbe a questo punto risultare ovvio. In ogni caso ritorneremo su essi nel seguito. Terminata questa breve visita guidata alle \emph{Figure Scheme per Dr. Geo} nella sezione seguente verranno esposti i comandi disponibili per definire le diverse FSD. \section{Metodi di riferimento per le Figure Scheme per \drgeo} La definizione di oggetti in un file FSD avviene attraverso dei prototipi. I prototipi sono un genere di oggetti che, come chiariremo nel seguito, \`e possibile interrogare e modificare. Tuttavia, prima di ogni definizione di un oggetto in una figura questa deve essere stata precedentemente creata con il comando \texttt{new-figure}. \subsection{Comandi generali} \begin{drgeoApi}{(new-figure nome)} \drgeoApiIn{nome}{stringa di caratteri} \drgeoApiOut{non viene restituito alcun valore. La chiamata non produce che un effetto di contorno per indicare la creazione di una figura; successivamente in essa verranno creati degli oggetti fino ad una nuova chiamata dello stesso tipo} \drgeoApiExample{(new-figure ``Figura 1'')} \end{drgeoApi} \subsection{Definizione di oggetti in una figura} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti}{}{} Un oggetto pu\`o essere definito ricorrendo a strutture sintattiche assai diverse~: \begin{itemize} \item \texttt{(lets Point ``p1'' type args)} In questo modo viene creato un punto e il suo riferimento \`e contenuto nella variabile \texttt{p1}. Questo tipo di sintassi utilizza una macro di Scheme. \item \texttt{(Point ``Nome'' type args)} In queto modo viene creato un punto senza che venga conservato alcun riferimento. \item \texttt{(define p1 (Point ``Nome'' type args))} In questo modo viene creato un punto e il suo riferimento \`e contenuto nella variabile \texttt{p1}. \item \texttt{(set! p1 (Point ``Nome'' type args))} In questo modo viene creato un punto e il suo riferimento viene copiato nella variabile preesistente \texttt{p1}. \end{itemize} Se alcuni oggetti vengono creati nel corpo di una funzione \`e possibile utilizzare sia la forma \texttt{set!} che la forma speciale di Scheme \texttt{lets}. Ci\`o che importa sottolineare \`e che la chiamata base consiste in una chiamata ad una funzione che ritorna il riferimento all'oggetto creato. \subsubsection{Punto} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{punto}{} \begin{drgeoApi}{prototipo (Point nome free x y)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{x}{ascissa del punto} \drgeoApiIn{y}{ordinata del punto} \drgeoApiOut{riferimento per un punto libero nel piano con coordinate iniziali \texttt{x} e \texttt{y}.} \drgeoApiExample{(define p1 (Point ``A'' free 1.2 (acos -1)))} \end{drgeoApi} \begin{drgeoApi}{prototipo (Point nome on-curve linea x)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{linea}{riferimento ad una linea (retta, semiretta, segmento, ecc.)} \drgeoApiIn{x}{ascissa curvilinea di un punto libero il cui valore appartiene all'intervallo [0~;~1]} \drgeoApiOut{riferimento per un punto libero su una curva.} \drgeoApiExample{(Point ``M'' on-curve s1 0.5)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Point nome middle-2pts p1 p2)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{p1}{riferimento ad un punto} \drgeoApiIn{p2}{riferimento ad un punto} \drgeoApiOut{riferimento al punto medio tra due punti.} \drgeoApiExample{(lets Point ``A'' free 1 1)\\ (lets Point ``B'' free 4 4)\\ (Point ``I'' middle-2pts A B)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Point nome middle-segment s)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{s}{riferimento ad un segmento} \drgeoApiOut{riferimento al punto medio di un segmento.} \drgeoApiExample{(Point ``L'' middle-segment s)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Point nome intersection l1 l2)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{l1}{riferimento ad una linea} \drgeoApiIn{l2}{riferimento ad una linea} \drgeoApiOut{riferimento al punto di intersezione di due linee.} \drgeoApiExample{(Point ``I'' intersection line segment)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Point nome intersection2 l1 l2)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{l1}{riferimento ad una linea} \drgeoApiIn{l2}{riferimento ad una curva} \drgeoApiOut{riferimento al secondo punto d'intersezione di due curve quando una delle due \`e un arco o una circonferenza.} \drgeoApiExample{(Point ``I'' intersection2 line circle)} \end{drgeoApi} \subsubsection{Retta} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{retta}{} \begin{drgeoApi}{prototipo (Line nome 2points p1 p2)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{p1}{riferimento ad un punto} \drgeoApiIn{p2}{riferimento ad un punto} \drgeoApiOut{riferimento ad una retta passante per due punti.} \drgeoApiExample{(lets Point ``A'' free 0 0)\\ (lets Point ``M'' free 1 2)\\ (Line ``'' 2points A M)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Line nome parallel p d)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{p}{riferimento ad un punto} \drgeoApiIn{d}{riferimento ad una direzione (retta, segmento, vettore ...)} \drgeoApiOut{riferimento ad una retta parallela alla direzione \texttt{d} e passante per \texttt{p}.} \drgeoApiExample{(lets Point ``A'' free 1 5)\\ (lets Line ``d1'' parallel A d)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Line nome orthogonal p d)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{p}{riferimento ad un punto} \drgeoApiIn{d}{riferimento ad una direzione (retta, segmento, vettore ...)} \drgeoApiOut{riferimento ad una retta perpendicolare alla direzione \texttt{d} e passante per \texttt{p}.} \drgeoApiExample{(lets Point ``A'' free 1 5)\\ (lets Line ``d1'' orthogonal A d)} \end{drgeoApi} \subsubsection{Semiretta} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{semiretta}{} \begin{drgeoApi}{prototipo (Ray nome 2points o p)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{o}{riferimento ad un punto origine della semiretta} \drgeoApiIn{p}{riferimento ad un punto appartenente alla semiretta} \drgeoApiOut{riferimento ad una semiretta definita dall'origine e un punto.} \drgeoApiExample{(lets Point ``A'' free 1 5)\\ (lets Point ``O'' free 0 0)\\ (lets Ray ``dd1'' 2points A 0)} \end{drgeoApi} \subsubsection{Segmento} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{segmento}{} \begin{drgeoApi}{prototipo (Segment nome extremities p1 p2)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{p1}{riferimento ad un punto estremo del segmento} \drgeoApiIn{p2}{riferimento ad un punto estremo del segmento} \drgeoApiOut{riferimento ad un segmento definito dai suoi estremi.} \drgeoApiExample{(lets Point ``A'' free 1 5)\\ (lets Point ``B'' free 10 4)\\ (lets Segment ``'' extremities A B)} \end{drgeoApi} \subsubsection{Circonferenza} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{circonferenza}{} \begin{drgeoApi}{prototipo (Circle nome 2points c p)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{c}{riferimento ad un punto: centro della circonferenza} \drgeoApiIn{p}{riferimento ad un punto appartenente alla circonferenza} \drgeoApiOut{riferimento ad una circonferenza definita da centro e punto ad essa appartenente.} \drgeoApiExample{(lets Point ``A'' free 1 5)\\ (lets Point ``B'' free 10 4)\\ (lets Circle ``C1'' 2points A B)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Circle nome center-radius c r)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{c}{riferimento ad un punto: centro della circonferenza} \drgeoApiIn{r}{riferimento ad un valore numerico: raggio della circonferenza} \drgeoApiOut{riferimento ad una circonferenza definita da centro e raggio.} \drgeoApiExample{(lets Point ``A'' free 1 5)\\ (lets Numeric ``r'' free 10 4)\\ (lets Circle ``C1'' center-radius A r)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Circle nome center-segment c s)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{c}{riferimento ad un punto: centro della circonferenza} \drgeoApiIn{s}{riferimento ad un segmento la cui lunghezza definisce il raggio della circonferenza} \drgeoApiOut{riferimento ad una circonferenza definita da centro e raggio.} \drgeoApiExample{(lets Point ``A'' free 1 5)\\ (lets Point ``B'' free 10 4)\\ (lets Segment ``s'' extremities A B)\\ (lets Circle ``C1'' center-segment A s)} \end{drgeoApi} \subsubsection{Arco} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{arco}{} \begin{drgeoApi}{prototipo (Arc nome 3points p1 p2 p3)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{p1}{riferimento ad un punto primo estremo del'arco} \drgeoApiIn{p2}{riferimento ad un punto centro dell'arco} \drgeoApiIn{p3}{riferimento ad un punto secondo estremo dell'arco} \drgeoApiOut{riferimento ad un arco di circonferenza definito dai suoi estremi e da un punto} \drgeoApiExample{(lets Point ``A'' free 1 5)\\ (lets Point ``B'' free 0 5)\\ (lets Point ``C'' free -1 -2)\\ (lets Arc ``arc'' 3points A B C)} \end{drgeoApi} \subsubsection{Poligono} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{poligono}{} \begin{drgeoApi}{prototipo (Polygon nome npoints args)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{args}{una lista di riferimenti a punti che rappresentano i vertici del poligono} \drgeoApiOut{riferimento ad un poligono definito dai suoi vertici} \drgeoApiExample{(lets Point ``A'' free 1 1)\\ (lets Point ``B'' free 1 5)\\ (lets Point ``C'' free 5 1)\\ (lets Point ``D'' free 5 5)\\ (lets Polygon ``quad'' npoints A B C D)} \end{drgeoApi} \subsubsection{Trasformazioni geometriche} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{trasformazioni geometriche}{} \drgeniusIndex{Trasformazioni:}{figure Scheme per \drgeo}{}{} I prototipi relativi alle trasformazioni geometriche permettono di eseguire trasformazioni geometriche di diversi oggetti. Essi si applicano in riferimento agli oggetti punto, segmento, retta, semiretta, vettore, circonferenza, arco e poligono. \begin{drgeoApi}{prototipo (TipoOggetto nome rotation oggetto centro angolo)} \drgeoApiIn{TipoOggetto}{Point, Segment, Line, Ray, Vector, Circle, Arc, Polygon} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{oggetto}{riferimento all'oggetto da trasformare} \drgeoApiIn{centro}{riferimento ad un punto: il centro di rotazione} \drgeoApiIn{angolo}{riferimento ad un valore: l'angolo di rotazione} \drgeoApiOut{riferimento all'oggetto trasformato.} \drgeoApiExample{(lets Point ``I1'' rotation I C a)} \end{drgeoApi} \begin{drgeoApi}{prototipo (TipoOggetto nome scale oggetto centro k)} \drgeoApiIn{TipoOggetto}{Point, Segment, Line, Ray, Vector, Circle, Arc, Polygon} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{oggetto}{riferimento all'oggetto da trasformare} \drgeoApiIn{centro}{riferimento ad un punto: il centro di omotetia} \drgeoApiIn{k}{riferimento ad un valore: rapporto di omotetia} \drgeoApiOut{riferimento all'oggetto trasformato.} \drgeoApiExample{(lets Polygon ``P1'' scale P C k1)} \end{drgeoApi} \begin{drgeoApi}{prototipo (TipoOggetto nome symmetry oggetto centro)} \drgeoApiIn{TipoOggetto}{Point, Segment, Line, Ray, Vector, Circle, Arc, Polygon} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{oggetto}{riferimento all'oggetto da trasformare} \drgeoApiIn{centro}{riferimento ad un punto: il centro di simmetria} \drgeoApiOut{riferimento all'oggetto trasformato.} \drgeoApiExample{(lets Segment ``S1'' symmetry S C)} \end{drgeoApi} \begin{drgeoApi}{prototipo (TipoOggetto nome reflexion oggetto asse)} \drgeoApiIn{TipoOggetto}{Point, Segment, Line, Ray, Vector, Circle, Arc, Polygon} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{oggetto}{riferimento all'oggetto da trasformare} \drgeoApiIn{asse}{riferimento ad una retta: l'asse di riflessione} \drgeoApiOut{riferimento all'oggetto trasformato.} \drgeoApiExample{(lets Polygon ``P1'' reflexion P d1)} \end{drgeoApi} \begin{drgeoApi}{prototipo (TipoOggetto nome translation oggetto vettore)} \drgeoApiIn{TipoOggetto}{Point, Segment, Line, Ray, Vector, Circle, Arc, Polygon} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{oggetto}{riferimento all'oggetto da trasformare} \drgeoApiIn{vettore}{riferimento ad un vettore: il vettore di traslazione} \drgeoApiOut{riferimento all'oggetto trasformato.} \drgeoApiExample{(lets Circle ``C1'' translation C v)} \end{drgeoApi} \subsubsection{Luogo geometrico} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{luogo}{} \begin{drgeoApi}{prototipo (Locus nome 2points m c)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{m}{riferimento ad un punto mobile su una curva} \drgeoApiIn{c}{riferimento ad un punto fisso dipendente dal punto \texttt{m}} \drgeoApiOut{riferimento ad un luogo.} \drgeoApiExample{(Locus ``luogo'' 2points M I)} \end{drgeoApi} \subsubsection{Vettore} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{vettore}{} \begin{drgeoApi}{prototipo (Vector nome 2points o e)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{o}{riferimento ad un punto: origine del vettore} \drgeoApiIn{e}{riferimento ad un punto: estremo del vettore} \drgeoApiOut{riferimento ad un vettore.} \drgeoApiExample{(lets Point ``B'' free 0 5)\\ (lets Point ``C'' free -1 -2)\\ (Vector ``'' 2points C B)} \end{drgeoApi} \subsubsection{Numeri} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{numeri}{} \begin{drgeoApi}{prototipo (Numeric nome free x y v)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{x,y}{le coordinate che determinano la posizione del numero} \drgeoApiIn{v}{il valore del numero} \drgeoApiOut{riferimento a un numero.} \drgeoApiExample{(lets Numeric ``pi'' free 5 5 (acos -1))} \end{drgeoApi} \begin{drgeoApi}{prototipo (Numeric nome segment-length x y s)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{x,y}{le coordinate che determinano la posizione del numero} \drgeoApiIn{s}{riferimento ad un numero: la lunghezza di un segmento} \drgeoApiOut{riferimento alla lunghezza di un segmento.} \drgeoApiExample{(lets Numeric ``l'' segment-length 5 5 S)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Numeric nome vector-norm x y v)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{x,y}{le coordinate che determinano la posizione del numero} \drgeoApiIn{v}{riferimento ad un vettore} \drgeoApiOut{riferimento alla norma di un vettore.} \drgeoApiExample{(lets Numeric ``l'' vector-norm 5 5 V)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Nombre nome point-circle x y p c)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{x,y}{le coordinate che determinano la posizione del numero} \drgeoApiIn{p}{riferimento ad un punto} \drgeoApiIn{c}{riferimento ad una circonferenza} \drgeoApiOut{riferimento al valore che esprime la distanza tra punto e circonferenza.} \drgeoApiExample{(lets Numeric ``l'' point-circle 5 5 P C)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Numeric nome point-line x y p d)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{x,y}{le coordinate che determinano la posizione del numero} \drgeoApiIn{p}{riferimento ad un punto} \drgeoApiIn{d}{riferimento ad una retta} \drgeoApiOut{riferimento al valore che esprime la distanza tra punto e retta.} \drgeoApiExample{(lets Numeric ``d'' point-line 5 5 M D1)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Numeric nome point-point x y p1 p2)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{x,y}{le coordinate che determinano la posizione del numero} \drgeoApiIn{p1}{riferimento ad un punto} \drgeoApiIn{p2}{riferimento ad un punto} \drgeoApiOut{riferimento al valore che esprime la distanza tra i due punti.} \drgeoApiExample{(lets Numeric ``d'' point-point 5 5 A B)} \end{drgeoApi} \begin{drgeoApi}{prototipo (Numeric nome circle-length x y c)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{x,y}{le coordinate che determinano la posizione del numero} \drgeoApiIn{c}{riferimento ad una circonferenza} \drgeoApiOut{riferimento alla lunghezza della circonferenza.} \drgeoApiExample{(lets Numeric ``p'' circle-length 5 5 C)} \end{drgeoApi} \subsubsection{Angolo} \begin{drgeoApi}{prototipo (Angle nome geometric A B C)} \drgeoApiIn{nome}{stringa di caratteri che designa il nome dell'oggetto} \drgeoApiIn{A}{riferimento a un punto} \drgeoApiIn{B}{riferimento a un punto: vertice dell'angolo} \drgeoApiIn{C}{riferimento a un punto} \drgeoApiOut{riferimento ad un angolo geometrico.} \drgeoApiExample{(lets Angle ``a'' geometric A B C)} \end{drgeoApi} \subsection{Modifiche agli attributi di un oggetto} \drgeniusIndex{Figure Scheme per \drgeo\ :}{costruzione di oggetti:}{attributi oggetto}{} Per modificare gli attributi di un oggetto creato in precedenza si utilizza un sistema di messaggi che vengono inviati direttamente al prototipo che rappresenta l'oggetto in questione. Le modifiche agli attributi si eseguono quindi a posteriori della costruzione dei diversi oggetti. \begin{drgeoApi}{(send oggetto color valore)} \drgeoApiIn{oggetto}{riferimento ad un oggetto} \drgeoApiIn{valore}{un colore tra i seguenti: \texttt{black, dark-grey, grey, white, dark-green, green, dark-blue, bleu, red, yellow}} \drgeoApiExample{(lets Point ``A'' free 1 2)\\ (send A color green)} \end{drgeoApi} \begin{drgeoApi}{(send linea thickness valore)} \drgeoApiIn{linea}{riferimento ad una linea (retta, semiretta, circonferenza, luogo, ecc.)} \drgeoApiIn{valore}{lo spessore i cui valori possibili sono: \texttt{dashed, normal, large}} \drgeoApiExample{(lets Point ``A'' free 1 2)\\ (lets Point ``O'' free 0 0)\\ (lets Line ``d'' 2points A B)\\ (send d thickness dashed)} \end{drgeoApi} \begin{drgeoApi}{(send punto size valore)} \drgeoApiIn{punto}{riferimento ad un punto} \drgeoApiIn{valore}{la dimensione di un punto i cui valori possibili sono: \texttt{small, normal, large}} \drgeoApiExample{(lets Point ``A'' free 1 2)\\ (send A size small)} \end{drgeoApi} \begin{drgeoApi}{(send punto shape valore)} \drgeoApiIn{punto}{riferimento ad un punto} \drgeoApiIn{valore}{la forma di un punto i cui valori possibibili sono: \texttt{round, cross, round-empty, rec-empty}} \drgeoApiExample{(lets Point ``A'' free 1 2)\\ (send A shape rond)} \end{drgeoApi} \begin{drgeoApi}{(send oggetto masked)} \drgeoApiIn{oggetto}{riferimento ad un oggetto nascosto} \drgeoApiExample{(lets Point ``A'' free 1 2)\\ (send A masked)} \end{drgeoApi} \T \clearpage \section{Galleria di esempi} \drgeniusIndex{Figure Scheme per \drgeo\ :}{esempi}{}{} Per illustrare l'utilizzo di Figure Scheme per \drgeo\ proponiamo alcuni esempi. Gli esempi hanno lo scopo di mostrare le potenzialit\`a delle FSD e allo stesso tempo ci auguriamo siano fonte di ispirazione per costruire altri esempi. Ogni esempio \`e accompagnato dal codice Scheme che genera la figura corrispondente. Il codice sorgente pu\`o essere copiato in un editore di testo, salvato con estensione .scm e quindi valutato in \drgeo. Altri esempi, forse pi\`u semplici, sono disponibili al \link{Capitolo 6}[ Capitolo \Ref, pagina \Pageref]{education}. \subsection{Poligoni regolari} \drgeniusIndex{Figure Scheme per \drgeo\ :}{esempi:}{poligono regolare}{} La costruzione di un poligono regolare con un numero arbitrario di lati, che non \`e prevista come costruzione base in \drgeo, pu\`o essere eseguita attraverso una FSD che sfrutta alcune funzioni ricorsive del linguaggio Scheme. \begin{verbatim} (define pi (acos -1)) (define n 15) (define x0 0) (define y0 0) (define p1 0) (define (polygon center p a n) (if (> n 0) (begin (set! p1 (Point "" rotation p center a)) (send p1 masked) (Segment "" extremities p p1) (polygon center p1 a (- n 1))))) (new-figure "Poligono Regolare") (lets Point "C" free x0 y0) (lets Numeric "a" free 0 0 (* 2 (/ pi n))) (send a masked) (set! p1 (Point "I" free 5 0)) (lets Segment "S" extremities C p1) (Segment "" rotation S C a) (polygon C p1 a n) \end{verbatim} \drgeniusFigureSize{Un poligono regolare con 15 lati}{fig59}{8} \subsection{Frattali} \drgeniusIndex{Figure Scheme per \drgeo\ :}{esempi:}{frattale}{} La costruzione di una curva frattale a forma d'albero si pu\`o realizzare facilmente utilizzando una FSD. Il codice sorgente della figura \`e incredibilmente compatto e incomparabilmente pi\`u efficiente rispetto all'esecuzione della figura attraverso l'interfaccia grafica. \begin{verbatim} (new-figure "Albero") (lets Numeric "A1" free 2 2 +3.4) (lets Numeric "A2" free 2 3 -3.7) (lets Numeric "S1" free 2 4 +0.5) (lets Numeric "S2" free 2 5 +0.9) (define (dec n) (- n 1)) (define (inc n) (+ n 1)) (define (invisible p) (send p masked) p) (define (scalerot oP C a s) (let* ((sP (invisible (Point "" scale oP C s))) (rP (invisible (Point "" rotation sP C a))) ) rP)) (define (Ramo p0 p1 n) (Segment "" extremities p0 p1) (let* ((left-scale (if (odd? n) S1 S2)) (left-angle A1) (right-scale (if (odd? n) S2 S1)) (right-angle A2) ) (if (> n 0) (begin (Ramo p1 (scalerot p0 p1 left-angle left-scale) (dec n)) (Ramo p1 (scalerot p0 p1 right-angle right-scale) (dec n)))))) (lets Point "A" free -3 0) (lets Point "B" free -3 2) (Ramo A B 6) \end{verbatim} \drgeniusFigureSize{Curva frattale}{fig60}{10} \chapter{Gestione Documenti} Le costruzioni geometriche si possono salvare sia singolarmente sia a gruppi (salvataggio di una sessione di \drgenius). Ricordiamo che le macro vengono salvate come file con estensione .mgeo e le rimanenti costruzioni come file con estensione .fgeo. \section{Salvare una costruzione} \drgeniusIndex{Figura:}{salva}{}{} Partendo dal menu \drgeniusMenu{File -> Salva} o \drgeniusMenu{File -> Salva come} \`e possibile salvare come file una qualsiasi costruzione. \drgeniusNote{\drgenius\ \`e in grado di lavorare contemporaneamente con pi\`u costruzioni. Si pu\`o passare da una all'altra cliccando con il mouse.} Selezionando l'opzione \drgeniusMenu{File -> Salva come} \`e possibile cambiare il nome di una costruzione salvata in precedenza. \drgeniusNote{ Il nome del file proposto di default pu\`o essere modificato utilizzando il comando \drgeniusMenu{Modifica -> Preferenze}. Per maggiori informazioni vedere la sezione relativa al \link{funzionamento di default}[ Sezione \Ref, pagina \Pageref]{default_behaviour}.} \section{Salvare una sessione} \drgeniusIndex{Macro-costruzione:}{salva}{}{} \drgeniusIndex{Sessione:}{salva}{}{} Una sessione \`e un insieme di costruzioni di \drgenius\ che possono essere registrate tutte in un unico file. Il salvataggio di sessioni pu\`o essere particolarmente utile per l'organizzazione didattica di materiali. Partendo dal menu \drgeniusMenu{File -> Salvataggio multiplo}, possibile aprire la seguente finestra di dialogo. \drgeniusFigureSize{La finestra di dialogo per una sessione di \drgenius}{fig51}{8} La finestra di dialogo mostra la lista di tutte le costruzioni realizzate durante la sessione di lavoro e il loro genere (macro, costruzioni interattive, ecc...). \drgeniusNote{Attualmente una sessione pu\`o contenere tre generi di costruzioni: figure piane costruite interattivamente, macro e testi.} E' possibile selezionare una ad una le costruzioni utilizzando il comando \drgeniusMenu{Salva selezionato} oppure salvare tutte le costruzioni utilizzando il comando \drgeniusMenu{Salva tutto}. \drgeniusNote{Il menu \drgeniusMenu{File -> Salvataggio multiplo} rappresenta l'unico mezzo disponibile per salvare una macro in un file.} \section{Aprire un file} \drgeniusIndex{Macro-costruzione:}{apri}{}{} \drgeniusIndex{Sessione:}{apri}{}{} \drgeniusIndex{Figura:}{apri}{}{} Dal momento che costruzioni e sessioni vengono salvate sempre su un unico file. La procedura di apertura di una sessione o di una costruzione sono identiche in quanto si tratta sempre di aprire un file. A questo scopo si utilizza il comando \drgeniusMenu{File -> Apri}. Se si apre una sessione che contiene delle macro esse sono disponibili dopo l'apertura di tutte le costruzioni. \chapter{Applicazioni didattiche} \label{education} Questo capitolo \`e di aiuto per chi vuole iniziare ad usare \drgeo\ studiando direttamente degli esempi didattici applicativi. Diversamente dai capitoli precedenti qui l'approccio \`e pi\`u diretto e si analizzano situazioni concrete. I materiali contenuti in questo capitolo sono stati elaborati nell'ambito di alcuni periodi di attivit\`a didattica. \section{Soluzione di esercizi} Uno dei possibili utilizzi didattici di \drgenius\ consiste nella possibilit\`a di risolvere, ricorrendo agli \link{script Guile}[ Sezione \Ref, pagina \Pageref]{script} esercizi di geometria. Come esempio mostriamo ora la soluzione di un classico problema di geometria, in cui si applica il teorema di Pitagora, e il cui testo \`e il seguente: \begin{quote}{\em Sia dato un trapezio rettangolo $ABCD$ di cui sono note le lunghezze delle due basi e dell'altezza. Calcolare perimetro e area del trapezio.} \end{quote} Non \`e difficile, sulla scia di quanto trattiamo, sviluppare molti altri esempi non necessariamente ristretti all'ambito della Matematica. \textbf{Soluzione:} Iniziamo costruendo con \drgeo\ la figura: \drgeniusFigureSize{Trapezio rettangolo}{dafig1}{8} Essa comprende i dati e da questi possiamo procedere per risolvere il problema. Innanzitutto possiamo rispondere subito alla domanda riguardante l'area. Per fare questo scriviamo il seguente script Guile che ha come parametri in ingresso basi e altezza del trapezio: \drgeniusIndex{Script:}{\texttt{area trapezio}}{}{} \begin{quote}{\begin{verbatim} (define AB (getLength a1)) (define DC (getLength a2)) (define AD (getLength a3)) (/ ( * AD (+ AB DC )) 2 ) \end{verbatim} } \end{quote} ci calcoliamo quindi la lunghezza del segmento $BH$ scrivendo uno script in Guile i cui oggetti in ingresso sono i segmenti $AB$ e $CD$: \drgeniusIndex{Script:}{\texttt{segmento differenza}}{}{} \begin{quote}{\begin{verbatim} (define AB (getLength a1)) (define CD (getLength a2)) (- AB CD) \end{verbatim} } \end{quote} A questo punto possiamo applicare il teorema di Pitagora al triangolo rettangolo $CHB$. Anche qui usiamo uno script Guile che ha come oggetti in ingresso il segmento $CH$ e lo script $BH$: \drgeniusIndex{Script:}{\texttt{teorema di Pitagora}}{}{} \begin{quote} { \begin{verbatim} (define CH (getLength a1)) (define BH (getValue a2)) (+ (* CH CH) (* BH BH)) \end{verbatim} } \end{quote} Finalmente possiamo ricavare la lunghezza del lato obliquo $BC$ calcolando la radice quadrata del valore restituito dallo script precedente: \drgeniusIndex{Script:}{\texttt{radice quadrata}}{}{} \begin{quote} { \begin{verbatim} (define q (getValue a1)) ( sqrt q ) \end{verbatim} } \end{quote} I due script precedenti potevano essere compendiati in un unico script, ma leggermente pi\`u complesso. A questo punto possiamo concludere l'esercizio calcolando il perimetro con lo script Guile: \drgeniusIndex{Script:}{\texttt{perimetro}}{}{} \begin{quote} { \begin{verbatim} (define AB (getLength a1)) (define CB (getValue a2)) (define DC (getLength a3)) (define AD (getLength a4)) (+ (+ AB CB )(+ DC AD )) \end{verbatim} } \end{quote} \section{Teoremi e congetture} Gli \link{script Guile}[ Sezione \Ref, pagina \Pageref]{script} permettono, altre alla soluzione di esercizi vista sopra, di comprendere con maggiore profondit\`a gli enunciati di teoremi e di verificare congetture. In questa sezione iniziamo analizzando, a titolo di esempio, il teorema di Tolomeo: \begin{quote}{\em Dato un quadrilatero inscritto in una circonferenza la somma dei prodotti dei lati opposti \`e uguale al prodotto delle diagonali. } \end{quote} Possiamo facilmente disegnare la figura con \drgeo\ ottenendo: \drgeniusFigureSize{Teorema di Tolomeo: quadrilatero convesso}{dafig2}{9} dove sono anche stati implementati due script che calcolano rispettivamente la somma dei prodotti dei lati opposti del quadrilatero e il prodotto delle diagonali. Lo script per il calcolo della somma dei prodotti dei lati opposti \`e il seguente \drgeniusIndex{Script:}{\texttt{teorema di Tolomeo}}{}{} \begin{quote} { \begin{verbatim} (define AB (getLength a1)) (define DC (getLength a2)) (define BC (getLength a3)) (define AD (getLength a4)) (+ (* AB DC )(* BC AD )) \end{verbatim} } \end{quote} mentre lo script per il calcolo del prodotto delle diagonali \`e: \begin{quote} { \begin{verbatim} ( define DB (getLength a1)) ( define AC (getLength a2)) ( * DB AC ) \end{verbatim} } \end{quote} Come si vede i valori restituiti dagli script, in accordo con il teorema di Tolomeo, coincidono. Se modifichiamo dinamicamente la figura gli script continuano a concidere a meno che non ci si imbatta nella seguente situazione: \drgeniusFigureSize{Teorema di Tolomeo: quadrilatero non convesso}{dafig3}{9} ossia quando il quadrilatero perde la convessit\`a. In questo caso il teorema non vale e quindi l'enunciato precedente non \`e stato ben formulato e andrebbe precisato meglio scrivendolo come segue: \begin{quote}{\em Dato un quadrilatero CONVESSO inscritto in una circonferenza la somma dei prodotti dei lati opposti \`e uguale al prodotto delle diagonali. } \end{quote} A questo punto potrebbe venire spontanea la seguente congettura: il teorema di Tolomeo rimane valido per un quadrilatero convesso non inscritto in una circonferenza? Con \drgeo\ possiamo verificare immediatamente la falsit\`a di questa congettura come mostrato in figura: \drgeniusFigureSize{Falsifichiamo una congettura}{dafig4}{8} Il lettore non avr\`a difficolt\`a ad utilizzare il programma per costruire esempi didattici, magari pi\`u conosciuti, relativamente ai teoremi di Pitagora e di Euclide. \section{Numeri Irrazionali} \drgeniusIndex{Figure Scheme per \drgeo\ :}{esempi:}{spirale di Teodoro}{} Una costruzione classica riguardante i numeri irrazionali e nota come Spirale di Teodoro permette di costruire geometricamente le radici quadrate dei numeri interi a partire da un triangolo rettangolo isoscele avente cateti di lunghezza unitaria. Consideriamo il triangolo $OAB$ di figura in cui $OA=1$: \drgeniusFigureSize{Costruzione di radice di 2}{dafig7}{8} Per il teorema di Pitagora si ha allora che $OB$ ha lunghezza pari a radice quadrata di 2. Se ora, come in figura, si costruisce un nuovo triangolo rettangolo, retto in $B$, con cateti $OB$ e $BC$, di cui l'ultimo di lunghezza unitaria; \drgeniusFigureSize{Costruzione di radice di 3}{dafig8}{8} sempre per il teorema di Pitagora \`e chiaro che l'ipotenusa $OC$ di $OBC$ ha lunghezza radice quadrata di 3. Iterando il procedimento si ottengono facilmente tutte le radici quadrate dei numeri naturali. La natura iterativa della costruzione si presta ad un trattamento tramite FSD. Consideriamo allora il seguente codice Scheme: \begin{quote} { \begin{verbatim} (new-figure "Triangoli") (define (triangle p1 p2 p3 n) (let* ((s1 (Segment "" extremities p1 p2)) (s2 (Segment "" extremities p2 p3)) (s3 (Segment "" extremities p3 p1)) (pe (Line "" orthogonal p3 s3)) (ci (Circle "" center-segment p3 s2)) (p4 (Point "" intersection2 pe ci))) (send pe masked) (send ci masked) (send p4 masked) (if (> n 0) (triangle p1 p3 p4 (- n 1))))) (lets Point "O" free 0 0) (lets Point "A" free -1 0) (lets Point "B" free -1 1) (triangle O A B 15) \end{verbatim} } \end{quote} Il triangolo di partenza \`e definito attraverso le coordinate esclusivamente per comodit\`a. Il codice \`e la trascrizione letterale del procedimento iterativo descritto sopra. Una volta valutato da \drgeo\ viene restituita la figura seguente: \drgeniusFigureSize{Spirale di Teodoro}{dafig9}{8} L'ipotenusa di ogni triangolo ha lunghezza eguale alla radice quadrata di un numero naturale compreso tra 2 e 17. \section{Spirale di Baravelle} \drgeniusIndex{Figure Scheme per \drgeo\ :}{esempi:}{spirale di Baravelle}{} Come abbiamo visto in precedenza, attraverso una FSD \`e possibile costruire in modo semplice e intuitivo, una figura che permette di ``visualizzare'' ci\`o che in programmazione \`e un ciclo. Possiamo approfondire questo aspetto, modificando di poco il codice Scheme utilizzato per la costruzione dei numeri irrazionali, per ottenere una figura nota in letteratura come spirale di Baravelle. Il codice Scheme che definisce la spirale \`e il seguente: \begin{quote} { \begin{verbatim} (new-figure "Baravelle") (define (triangle p1 p2 p3 n) (let* ((s1 (Segment "" extremities p1 p2)) (s2 (Segment "" extremities p2 p3)) (s3 (Segment "" extremities p3 p1)) (m (Point "" middle-2pts p1 p3)) (r (Segment "" extremities m p3)) (pe (Line "" orthogonal p3 s3)) (ci (Circle "" center-segment p3 r )) (p4 (Point "" intersection2 pe ci))) (send pe masked) (send ci masked) (send p4 masked) (send m masked) (if (> n 0) (triangle m p3 p4 (- n 1))))) (lets Point "A" free 0 5) (lets Point "B" free 5 5) (lets Point "C" free 5 0) (triangle A B C 9) (lets Point "D" free 0 -5) (lets Point "E" free -5 -5) (lets Point "F" free -5 0) (triangle D E F 9) \end{verbatim} } \end{quote} La figura nota come spirale di Baravelle \`e: \drgeniusFigureSize{Spirale di Baravelle}{dafig10}{8} Dalla figura e dal codice Scheme si intuisce la struttura iterativa alla base della costruzione. Un problema interessante, che lasciamo al lettore, consiste nello stabilire dove convergono i due rami della spirale. Una variazione ulteriore del codice precedente: \begin{quote} { \begin{verbatim} (new-figure "Spiral") (define (square p1 p2 p3 p4 n) (let* ((s1 (Segment "" extremities p1 p2)) (s2 (Segment "" extremities p2 p3)) (s3 (Segment "" extremities p3 p4)) (s4 (Segment "" extremities p4 p1)) (A (Point "" on-curve s1 1/10)) (B (Point "" on-curve s2 1/10)) (C (Point "" on-curve s3 1/10)) (D (Point "" on-curve s4 1/10))) (send A masked) (send B masked) (send C masked) (send D masked) (if (> n 0) (square A B C D (- n 1))))) (lets Point "M" free 5 5) (lets Point "N" free -5 5) (lets Point "O" free -5 -5) (lets Point "P" free 5 -5) (square M N O P 30) \end{verbatim} } \end{quote} conduce alla spirale rappresentata in figura: \drgeniusFigureSize{Spirale}{dafig11}{8} Il lettore \`e invitato a divertirsi creandone di nuove generalizzando la costruzione precedente! \section{Catena di Pappo} \drgeniusIndex{Figure Scheme per \drgeo\ :}{esempi:}{catena di Pappo}{} Un utilizzo base delle Figure Scheme per Dr. Geo consiste nella riproduzione di figure di cui sono note le caratteristiche analitiche. L'esempio di costruzione che proponiamo è rappresentato dalla famosa catena di Pappo. \drgeniusFigureSize{Catena di Pappo}{dafig12}{8} Centri e raggi della successione di circonferenze che la formano hanno un'espressione analitica nota ed quindi è molto semplice implementarla per riprodurre la figura come FSD. \begin{quote} { \begin{verbatim} (new-figure "Pappo") (define (circle n) (let*( (r (Numeric "" free 0 0 (/ 15 ( + 6 (* n n ))))) (c (Point "" free (* 5 (/ 15 ( + 6 (* n n )))) (* 2 (* n (/ 15 ( + 6 (* n n ))))))) (p (Circle "" center-radius c r ))) (send r masked) (if (> n 0) (circle (- n 1))))) (circle 8) (lets Point "A" free 5 0) (lets Point "O" free 0 0) (lets Point "B" free 15 0) (lets Point "M" middle-2pts B O) (lets Circle "" 2points M O) (lets Circle "" 2points A O) (lets Line "" 2points A O) \end{verbatim} } \end{quote} Il significato del codice è molto intuitivo e non ha bisogno di commenti. Un esercizio, che fa leva sull'inversione circolare, consiste nel determinare una costruzione con riga e compasso che permetta di generare la catena. Il lettore interessato a questo pu\`o consultare il libro di Maria Ded\`o intitolato \textit{Trasformazioni Geometriche}. \section{Calcolo di Pigreco} Il calcolo approssimato di pigreco riveste nella storia della Matematica un ruolo importante. I metodi di approccio a questo tipo di calcolo sono risultati tra i pi\`u diversi e spesso contengono raffinatezze. Qui proponiamo un approccio molto semplificato al problema che chiamiamo, anche se non del tutto propriamente, \textbf{Metodo di esaustione} che contiene l'essenza della questione. Iniziamo con la seguente costruzione di un esagono inscritto in una circonferenza a partire dal lato $BC$. Notiamo di passaggio che da questa costruzione \`e possibile costruire e memorizzare una macro che possiamo chiamare \textit{Esagono}. \drgeniusFigureSize{Esagono regolare inscritto}{dafig5}{9} L'idea del metodo di esaustione consiste, al primo passo, nell'approssimare la lunghezza della circonferenza con il perimetro $P_{0}$ dell'esagono e nel calcolare un'approssimazione di Pigreco dividendo $P_{0}$ per il diametro della circonferenza. Chiaramente l'approssimazione che si ottiene per Pigreco \`e 3. Al secondo passo possiamo, utilizzando Dr. Geo, costruire il lato del dodecagono inscritto nella circonferenza, calcolarci il perimetro $P_{1}$, e calcolare una successiva approssimazione di Pigreco dividendo $P_{1}$ per il diametro. \drgeniusFigureSize{Approssimazione di Pigreco}{dafig6}{9} Aumentando il numero di lati del poligono inscritto si otterranno chiaramente approssimazioni sempre migliori. \section{Esportazione di figure e testi} Spesso per uso didattico \`e utile poter stampare le figure o esportarle come immagini in qualche formato che permetta il loro inserimento in documenti di altro genere. \subsection{Stampa di una figura} \drgeniusIndex{Figura:}{stampa}{}{} \drgeniusIndex{Stampa:}{figura}{}{} Il modo pi\`u semplice per stampare una figura consiste prima nell'esportarla in PostScript e quindi di utilizzare un sostware come Ghostview o un suo derivato per stamparla direttamente. Naturalmente la figura esportata pu\`o essere, se necessario, inserita in altri documenti come immagine. Si ricorda che il formato PostScript garantisce all'immagine una qualit\`a vettoriale. Per gli utilizzatori di \TeX\ \`e disponibile l'esportazione di figure attraverso il pacchetto Pstrick. L'immagine che si ottiene si integra perfettamente nel testo \TeX\ tuttavia di essa non si pu\`o eseguire, o almeno sembra, alcun rididmensionamento. Un ultimo tipo di esportazione, recentemente introdotto in \drgeo, riguarda l'esportazione in formato PNG attraverso il pacchetto Image Magick. In tutti questi casi l'utilizzatore pu\`o preventivamente selezionare, attraverso il comando \drgeniusMenu{File -> Preferenze Esportazione -> Definisci l'area di stampa}, la porzione di figura da stampare e, successivamente, attraverso il comando \drgeniusMenu{File -> Preferenze Esportazione -> Rimuovi l'area di stampa}, rimuovere l'area di stampa definita in precedenza. \subsection{Inserire un testo in una figura} \drgeniusIndex{Inserire}{Testo}{}{} \drgeniusIndex{Figura}{Inserire}{Testo}{} Per inserire un testo all'interno di una figura \`e possibile utilizzare l'utilit\`a script -- \link{script Guile}[ Sezione \Ref, pagina \Pageref]{script} -- creando uno script senza passare ad esso alcun oggetto. Per fare questo \`e sufficiente cliccare sul comando che attiva la funzionalit\`a di script e cliccare direttamente in un punto del foglio di lavoro dove si desidera collocare il testo. A questo punto comparir\`a la scritta ``Drgenius'' e potremo editare lo script andando ad inserire tra le virgolette, dove tipicamente viene inserito il codice Guile/Scheme da eseguire, il testo desiderato. Nell'esempio che segue una tassellazione di Keplero viene accompagnata dal seguente richiamo: \begin{verbatim} "Il Motivo Z =========================== Tratto dall'Harmonice Mundi di Johannes Kepler si costruisce un pentagono formato da oggetti a simmetria pentagonale." \end{verbatim} \drgeniusFigureSize{Un esempio di testo in una figura}{fig58}{9} Come per ogni script \`e stato possibile modificare il colore del testo. \W \chapter*{Indice Analitico} \W \htmlprintindex \W \begin{iftex} \appendix \listoffigures \printindex \W \end{iftex} \chapter{GNU Free Documentation License} \input{../fdl} \end{document} % LocalWords: Guile Homothétie homothétie macro-construction glisser-déposer % LocalWords: redessinée drgeo-doc-1.5/it/figures/0002777000175000017500000000000010117134567011056 5drgeo-doc-1.5/it/figures/blank.png0000644000175000017500000000012410117134567012562 ‰PNG  IHDR I´è·PLTE™ÌÿõÉj IDATxÚc`Ü Žû±´IEND®B`‚drgeo-doc-1.5/it/figures/dafig10.png0000644000175000017500000007703110117134567012721 ‰PNG  IHDR?g ê- IDATxœìÝwxTÅúðwNݾ›dÓ;„„.U@¤#MŠ@@ ÂÄ.¢ˆ¨ˆþ°‹…+ˆHQŠ€ ‚\z/RHHHïÙl9u~,ÄH !Ù4ÏsŸÜÍÙ³sÞ³øì73gÎ,êxoG8zä(•pÿý÷×u AÿF¥v;Ë2e¿^{´åpbÕSƒxš+´$']Ü¿åÇâ¼èÚµë¤I“ÂÃÃëº4‚ âîÌ›?ÿÈáÃù……ŽÔñÞŽs®®ëªj(EÂå„ÓY_’Ÿ«×ëW­ZU×eAwG’¤§§OOJJÒðêxoÇg^[Q×%Õ € Œ! •U’öûê/l$  I’1BUdôåÚSwõJY´‰.GnVrxtç*Σеûë1B,UàHß»î«Ò‚\??¿¯¿þº. $‚¨yv»½¸¸Øn·;NEQ†ÑétƒÁb±ð<߀A½½páîÝ»ÑûßÜÅ| {q:Ïky­A–UDk*ÿºðµqC !Œ0„-sùòþ“Û€Áƒ?þøãuX)AD ‘e¹¸¸8//ÏåraŒ1.ûƒhšÖëõ¾¾¾ƒ¢¨zÞÆ* Œ}àСóßdJbeß±øO›$ª€åxõ!VëWù×Ö€1„#@€1\ 1»èmj×÷ñ–7|¼uëÖóçÏ/\¸P£©÷‘LQi’(efeªŠ QDIQŠ¢8Žãy¾¤¤ØétúúúúúúÞ.6êI#Q4,DZ,c³W6½ä’“ƒû·Q:((¼¨¸ùö‰6ÕRÉ×Ö õ½0 ®¥Ø_ŠvÔîÁ’OoL>{xÊ”)K—.ÕjµuT.A„')Š’™™YPX@!$Ërqq‘Š±^¯§iZ–å‚‚°úX)šÉÎÎF€¬¾V„P½m¤ ˲!Ææ*ùFøê ®^aÒÓòzö¶ìØ~ ))Å/¦• WÔO¬[!Àp½ß…ÿ~ ̽†R§è2XUqÆù#O<ñÄÊ•+ë¨^‚ Á–––rg+)).) 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=p3f‚‚“IDATxÚc` %È9sæ0Š×ÿÿÿïÿÿE‰Þÿÿ¿Q˜ÿÿÿ?E$ÿÿÿo(œ@%("çÿÿ¤€¦#À_†ÿ(`Øp$ð… U …ÿÙ ™È¾aZwYÝÿÿ¿ùlïÿÿ/@èÿÿÿ)zø {#x4Ïœ9)@Ó8CÛ|ŽãÁ÷IEND®B`‚drgeo-doc-1.5/it/figures/previous.png0000644000175000017500000000036510117134567013356 ‰PNG  IHDR D¤ŠÆ3PLTE™ÌÿÂõ†¹ì|¯âs¦ÙiœÏ_’ÅV‰¼L²Cv©:m 0c–&YŒPƒFy =p3fÇœ }IDATxÚÕ’;€ ù(ÈÏpÿÓ vn ;¶å1 ³[Båˆç>C`[˜7Ä]c^-àž˜g¨'<"E/üÕ½ÏÜSOὌó¤ð~Í´Â9’RoÙ19øˆkŒfaÃÑ«ŒâåÆ„k”€IßöH•µ…ÿ£¢±sÿ q ¿/µIEND®B`‚drgeo-doc-1.5/it/figures/up.png0000644000175000017500000000047110117134567012124 ‰PNG  IHDR D¤ŠÆ3PLTE™ÌÿÂõ†¹ì|¯âs¦ÙiœÏ_’ÅV‰¼L²Cv©:m 0c–&YŒPƒFy =p3fÇœ ÁIDATxÚ•“Y„ DA•5÷?í°¤œ0@¬yZEcènUˆ )X¤÷¼nFW v«›¦CVÝ’×F<Ä¥} ¸I?" œKû3ÚëúU/ÉÍQd_²ºÞ‚è§Ñ¾4>r¶1BNuÕѱd¿QhŽôØ€¯Ý@¡VF=ÌÝÎÆ™‰nÀóR¢ 4„!^ý¸6põ{üÜàH+è`6|C¬Q½è=fý!üâ)zGª¸ÿª½sF×o!ÎßÏhšp8k>DxHÐIEND®B`‚drgeo-doc-1.5/it/contents.html0000644000175000017500000001763210117134567012060 Manuale di Dr. Geo -- Indice
CopyrightIndiceIndice

Indice

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CopyrightIndiceIndice
drgeo-doc-1.5/it/default_behaviour.html0000644000175000017500000000612510117134567013706 Manuale di Dr. Geo -- Preferenze di default
Altre preferenzePreferenzePreferenze di default

Preferenze di default

Le preferenze di default di DR. GEO possono essere configurate in più modi. Per parametrizzare le preferenze si accede al menu Modifica -> Preferenze e si apre la seguente finestra di dialogo:

Preferenze globali

La finestra di dialogo è articolata in due sezioni:
  1. La prima sezione riguarda le preferenze relative agli oggetti geometrici e permette di modificare l'aspetto di ciascuno di essi;  
  2. La seconda sezione permette di modificare alcune preferenze globali come:
       
    • il numero di oggetti cancellati per errore e ricostruibili utilizzando il comando Annulla/Rifai;  
    • il nome di default che si attiva ogni volta che un dato oggetto viene costruito. Il %d viene rimpiazzato da un numero intero generato da DR. GEO; questo valore viene incrementato di una unità ad ogni nuova costruzione di un oggetto dello stesso tipo;
    • i nomi di default per l'esportazione in formato LaTeX e PostScript ;
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Altre preferenzePreferenzePreferenze di default
drgeo-doc-1.5/it/drgenius_10.html0000644000175000017500000000451410117134567012336 Manuale di Dr. Geo -- Punto definito attraverso coordinate
Costruzione di punti Punti di intersezionePunto definito attraverso coordinate

Punto definito attraverso coordinate

 

Selezionando questo comando si definisce un punto precisando le sue coordinate cartesiane (ascissa e ordinata). Le coordinate devono essere state scritte precedentemente nel foglio di lavoro utilizzando le modalità per editare un numero descritte nel paragrafo Strumenti numerici.

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Costruzione di punti Punti di intersezionePunto definito attraverso coordinate
drgeo-doc-1.5/it/drgenius_11.html0000644000175000017500000000407110117134567012335 Manuale di Dr. Geo -- Retta
SemirettaCostruzione di lineeRetta

Retta

 

Selezionando questo comando si costruisce una retta passante per due punti dati. Si clicca con il mouse sui due punti dati.

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SemirettaCostruzione di lineeRetta
drgeo-doc-1.5/it/drgenius_12.html0000644000175000017500000000401110117134567012330 Manuale di Dr. Geo -- Retta
SemirettaCostruzione di lineeRetta

Retta

 

Selezionando questo comando si costruisce una retta passante per due punti dati. Si clicca con il mouse sui due punti dati.

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SemirettaCostruzione di lineeRetta
drgeo-doc-1.5/it/drgenius_13.html0000644000175000017500000000421710117134567012341 Manuale di Dr. Geo -- Semiretta
SegmentoCostruzione di lineeRettaSemiretta

Semiretta

 

Selezionando questo comando si costruisce una semiretta. Si clicca con il mouse in sequenza su due punti di cui il primo è l'origine della semiretta.

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SegmentoCostruzione di lineeRettaSemiretta
drgeo-doc-1.5/it/drgenius_14.html0000644000175000017500000000420110117134567012333 Manuale di Dr. Geo -- Segmento
VettoreCostruzione di lineeSemirettaSegmento

Segmento

 

Selezionando questo comando si costruisce un segmento. Si clicca con il mouse su due punti dati che rappresentano gli estremi del segmento.

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VettoreCostruzione di lineeSemirettaSegmento
drgeo-doc-1.5/it/drgenius_15.html0000644000175000017500000000422110117134567012336 Manuale di Dr. Geo -- Vettore
CirconferenzaCostruzione di lineeSegmentoVettore

Vettore

 

Selezionando questo comando si costruisce un vettore. Si clicca con il mouse su due punti dati che rappresentano nell'ordine coda e punta del vettore.

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CirconferenzaCostruzione di lineeSegmentoVettore
drgeo-doc-1.5/it/drgenius_16.html0000644000175000017500000000515710117134567012350 Manuale di Dr. Geo -- Circonferenza
Arco di circonferenzaCostruzione di lineeVettoreCirconferenza

Circonferenza

 

Selezionando questo comando si costruisce una circonferenza secondo tre possibili modalità:

  1. si clicca con il mouse in sequenza su due punti dati che sono, nell'ordine, il centro della circonferenza e un punto ad essa appartenente;
  2. si clicca con il mouse su un punto che rappresenta il centro della circonferenza e si seleziona un numero che rappresenta il raggio della circonferenza;
  3. si clicca con il mouse in sequenza su un punto, che rappresenta il centro della circonferenza, e su un segmento la cui lunghezza rappresenta il raggio della circonferenza.
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Arco di circonferenzaCostruzione di lineeVettoreCirconferenza
drgeo-doc-1.5/it/drgenius_17.html0000644000175000017500000000440610117134567012345 Manuale di Dr. Geo -- Arco di circonferenza
LuogoCostruzione di lineeCirconferenzaArco di circonferenza

Arco di circonferenza

 

Selezionando questo comando si costruisce un arco di circonferenza. Si clicca con il mouse su tre punti di cui il primo e il terzo sono gli estremi dell'arco mentre il secondo è un punto appartenente all'arco.

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LuogoCostruzione di lineeCirconferenzaArco di circonferenza
drgeo-doc-1.5/it/drgenius_18.html0000644000175000017500000000436610117134567012353 Manuale di Dr. Geo -- Luogo
PoligonoCostruzione di lineeArco di circonferenzaLuogo

Luogo

 

Selezionando questo comando si costruisce un luogo geometrico definito da due punti. Si clicca con il mouse su due punti di cui il primo è libero di muoversi su una linea mentre il secondo è vincolato a muoversi con il secondo.

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PoligonoCostruzione di lineeArco di circonferenzaLuogo
drgeo-doc-1.5/it/drgenius_19.html0000644000175000017500000000471310117134567012350 Manuale di Dr. Geo -- Poligono
Costruzione di lineeLuogoPoligono

Poligono

 

Selezionando questo comando si costruisce un poligono dati i suoi n vertici. Si clicca con il mouse n+1 volte in sequenza su tutti i vertici del poligono avendo cura di cliccare all'inizio e alla fine sul medesimo vertice; in questo modo DR. GEO comprende che la costruzione del poligono è conclusa. In DR. GEO i poligoni sono oggetti geometrici speciali in quanto su essi non è possibile disegnare un punto così come non è possibile determinare i punti di intersezione tra due qualsiasi di essi.

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Costruzione di lineeLuogoPoligono
drgeo-doc-1.5/it/drgenius_20.html0000644000175000017500000000433410117134567012337 Manuale di Dr. Geo -- Retta parallela
Retta perpendicolareTrasformazioni del pianoRetta parallela

Retta parallela

 

Selezionando questo comando, dati una retta e un punto ad essa esterna, si costruisce la retta passante per il punto dato ad essa parallela. Si clicca con il mouse su un punto e una retta dati.

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Retta perpendicolareTrasformazioni del pianoRetta parallela
drgeo-doc-1.5/it/drgenius_21.html0000644000175000017500000000425210117134567012337 Manuale di Dr. Geo -- Retta parallela
Retta perpendicolareTrasformazioni del pianoRetta parallela

Retta parallela

 

Selezionando questo comando, dati una retta e un punto ad essa esterna, si costruisce la retta parallela alla data passante per quel punto. Si clicca con il mouse su un punto e una retta dati.

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Retta perpendicolareTrasformazioni del pianoRetta parallela
drgeo-doc-1.5/it/drgenius_22.html0000644000175000017500000000443310117134567012341 Manuale di Dr. Geo -- Retta perpendicolare
RiflessioneTrasformazioni del pianoRetta parallelaRetta perpendicolare

Retta perpendicolare

 

Selezionando questo comando, dati una retta e un punto ad essa esterna, si costruisce la retta perpendicolare alla data passante per quel punto. Si clicca con il mouse su un punto e una retta dati.

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RiflessioneTrasformazioni del pianoRetta parallelaRetta perpendicolare
drgeo-doc-1.5/it/drgenius_23.html0000644000175000017500000000462210117134567012342 Manuale di Dr. Geo -- Riflessione
Simmetria centraleTrasformazioni del pianoRetta perpendicolareRiflessione

Riflessione

 

Selezionando questo comando si esegue una riflessione intorno ad una retta (asse di riflessione) di un qualsiasi oggetto geometrico. Si clicca con il mouse sull'oggetto e sull'asse di riflessione. Se l'oggetto da riflettere è una retta prima si deve selezionare la retta da riflettere e solo dopo l'asse di riflessione.

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Simmetria centraleTrasformazioni del pianoRetta perpendicolareRiflessione
drgeo-doc-1.5/it/drgenius_24.html0000644000175000017500000000464010117134567012343 Manuale di Dr. Geo -- Simmetria centrale
TraslazioneTrasformazioni del pianoRiflessioneSimmetria centrale

Simmetria centrale

 

Selezionando questo comando si esegue una simmetria rispetto ad un punto (centro di simmetria) di un qualsiasi oggetto geometrico. Si clicca con il mouse sull'oggetto e sul punto che è centro di simmetria. Se l'oggetto da riflettere è un punto prima si deve selezionare il punto da trasformare e solo dopo il centro di simmetria.

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TraslazioneTrasformazioni del pianoRiflessioneSimmetria centrale
drgeo-doc-1.5/it/drgenius_25.html0000644000175000017500000000460310117134567012343 Manuale di Dr. Geo -- Traslazione
RotazioneTrasformazioni del pianoSimmetria centraleTraslazione

Traslazione

 

Selezionando questo comando si esegue una traslazione di un qualsiasi oggetto geometrico. Si clicca con il mouse sull'oggetto da traslare e sul vettore che rappresenta la traslazione. Se l'oggetto da traslare è un vettore prima si deve selezionare il vettore da trasformare e solo dopo il vettore che individua la traslazione.

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RotazioneTrasformazioni del pianoSimmetria centraleTraslazione
drgeo-doc-1.5/it/drgenius_26.html0000644000175000017500000000606710117134567012352 Manuale di Dr. Geo -- Rotazione
OmotetiaTrasformazioni del pianoTraslazioneRotazione

Rotazione

 

Selezionando questo comando si esegue una rotazione di un angolo fissato rispetto ad un centro (centro di rotazione) di un qualsiasi oggetto geometrico. Si clicca con il mouse sull'oggetto e sul punto che è centro di rotazione. Se l'oggetto da ruotare è un punto prima si deve selezionare il punto da ruotare e solo dopo il centro di rotazione.

Il valore dell'angolo di rotazione può essere definito in diversi modi:

  • valore numerico: in questo caso l'angolo viene espresso in radianti. Esempi di valori numerici sono: le lunghezze di segmenti, le distanze tra punti, le coordinate di un punto, i valori numerici restituiti da script Guile per DR. GEO, ecc.;
  • angolo formato da tre punti: in questo caso l'angolo si esprime in gradi e il suo valore appartiene all'intervallo [0o;180o];
  • angolo orientato tra vettori: in questo caso l'angolo si esprime in gradi e il suo valore appartiene all'intervallo ]-180o;+180o];
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OmotetiaTrasformazioni del pianoTraslazioneRotazione
drgeo-doc-1.5/it/drgenius_27.html0000644000175000017500000000425610117134567012351 Manuale di Dr. Geo -- Omotetia
Trasformazioni del pianoRotazioneOmotetia

Omotetia

 

Selezionando questo comando si esegue una omotetia di un qualsiasi oggetto geometrico. Si clicca con il mouse sull'oggetto da trasformare, sul punto che rappresenta il centro di omotetia e su un numero che rappresenta il fattore di scala.

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Trasformazioni del pianoRotazioneOmotetia
drgeo-doc-1.5/it/drgenius_28.html0000644000175000017500000000544310117134567012351 Manuale di Dr. Geo -- Distanze, lunghezze e numeri
AngoloStrumenti numericiDistanze, lunghezze e numeri

Distanze, lunghezze e numeri

 

Selezionando questo comando viene creato un valore numerico in molti modi diversi:

  1. cliccando con il mouse su due punti viene visualizzata la loro distanza;
  2. cliccando con il mouse su un vettore o su un segmento viene visualizzata la sua lunghezza;
  3. cliccando con il mouse su una circonferenza viene visualizzata la sua lunghezza;
  4. cliccando con il mouse su un arco viene visualizzata la sua lunghezza;
  5. cliccando con il mouse su una retta viene visualizzato il suo coefficiente angolare;
  6. cliccando con il mouse su una retta e su un punto viene visualizzata la distanza tra il punto e la retta stessa;
  7. cliccando con il tasto sinistro del mouse sullo sfondo si può scrivere un valore numerico qualsiasi.
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AngoloStrumenti numericiDistanze, lunghezze e numeri
drgeo-doc-1.5/it/drgenius_29.html0000644000175000017500000000600610117134567012346 Manuale di Dr. Geo -- Distanze, lunghezze e numeri
AngoloStrumenti numericiDistanze, lunghezze e numeri

Distanze, lunghezze e numeri

 

Selezionando questo comando viene creato un valore numerico in molti modi diversi:

  1. cliccando con il mouse su due punti viene visualizzata la loro distanza;
  2. cliccando con il mouse su un vettore o su un segmento viene visualizzata la sua lunghezza;
  3. cliccando con il mouse su una circonferenza viene visualizzata la sua lunghezza;
  4. cliccando con il mouse su un arco viene visualizzata la sua lunghezza;
  5. cliccando con il mouse su una retta viene visualizzato il suo coefficiente angolare;
  6. cliccando con il mouse su una retta e su un punto viene visualizzata la distanza tra il punto e la retta stessa;
  7. cliccando con il tasto sinistro del mouse sullo sfondo si può inserire nel foglio di lavoro un valore numerico qualsiasi.

L'ultima modalità risulta molto utile nella pratica in quanto capita spesso di aver bisogno di inserire nel foglio di lavoro un numero che potrà rappresentare una coordinata, una lunghezza o l'ampiezza di un angolo prefissato.

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AngoloStrumenti numericiDistanze, lunghezze e numeri
drgeo-doc-1.5/it/drgenius_2.html0000644000175000017500000000470610117134567012262 Manuale di Dr. Geo -- Copyright
IntroduzioneIndiceIndiceCopyright

Copyright

Copyright (c) 2000-2004 OFSET.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".

Other copyright apply to the respective owners of the modified documentations. See the section history for the complet list.

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IntroduzioneIndiceIndiceCopyright
drgeo-doc-1.5/it/drgenius_30.html0000644000175000017500000000515610117134567012343 Manuale di Dr. Geo -- Angolo
Coordinate cartesianeStrumenti numericiDistanze, lunghezze e numeriAngolo

Angolo

 

Selezionando questo comando è possibile misurare l'ampiezza di un angolo o dell'angolo compreso tra due vettori. Nel primo caso si clicca in sequenza su tre punti: il primo e il terzo appartengono ai lati dell'angolo e il secondo è il vertice dell'angolo. Nel secondo caso si clicca con il mouse sui due vettori. Osserviamo che nel primo caso l'angolo non è orientato e il valore della sua ampiezza non supera l'ampiezza di un angolo piatto. Nel caso dei vettori l'angolo è orientato e varia tra ]-180o;+180o].

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Coordinate cartesianeStrumenti numericiDistanze, lunghezze e numeriAngolo
drgeo-doc-1.5/it/drgenius_31.html0000644000175000017500000000451110117134567012336 Manuale di Dr. Geo -- Coordinate cartesiane
Script Guile per DR. GEOStrumenti numericiAngoloCoordinate cartesiane

Coordinate cartesiane

 

Selezionando questo comando si possono visualizzare le coordinate cartesiane di un punto o di un vettore. Si clicca con il mouse su un punto (o su un vettore) e vengono visualizzate, sovrapposte verticalmente, la sua ascissa e la sua ordinata.

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Script Guile per DR. GEOStrumenti numericiAngoloCoordinate cartesiane
drgeo-doc-1.5/it/drgenius_32.html0000644000175000017500000000473710117134567012351 Manuale di Dr. Geo -- Script Guile per DR. GEO
Strumenti numericiCoordinate cartesianeScript Guile per DR. GEO

Script Guile per DR. GEO

 

Selezionando questo comando si attiva la funzione per creare script Guile per DR. GEO. In generale uno script riceve in ingresso un certo numero di oggetti geometrici e in uscita fornisce un numero che viene visualizzato nell'area di lavoro. Per gli approfondimenti su questo importante argomento si rinvia ai contenuti dedicati alle Funzioni Avanzate e in particolare alla script.

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Strumenti numericiCoordinate cartesianeScript Guile per DR. GEO
drgeo-doc-1.5/it/drgenius_33.html0000644000175000017500000000451610117134567012345 Manuale di Dr. Geo -- Creare una macro-costruzione
Eseguire una macro-costruzioneStrumenti per la costruzione di macroCreare una macro-costruzione

Creare una macro-costruzione

Selezionando questo comando inizia il procedimento guidato di realizzazione di una macro.

(!) Le macro-costruzioni sono esposte nella sezione macro-costruzioni.
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Eseguire una macro-costruzioneStrumenti per la costruzione di macroCreare una macro-costruzione
drgeo-doc-1.5/it/drgenius_34.html0000644000175000017500000000443610117134567012347 Manuale di Dr. Geo -- Creare una macro-costruzione
Eseguire una macro-costruzioneStrumenti per la costruzione di macroCreare una macro-costruzione

Creare una macro-costruzione

Selezionando questo comando inizia il procedimento guidato di realizzazione di una macro.

(!) Le macro-costruzioni sono esposte nella sezione macro-costruzioni.
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Eseguire una macro-costruzioneStrumenti per la costruzione di macroCreare una macro-costruzione
drgeo-doc-1.5/it/drgenius_35.html0000644000175000017500000000450310117134567012343 Manuale di Dr. Geo -- Eseguire una macro-costruzione
Strumenti per la costruzione di macroCreare una macro-costruzioneEseguire una macro-costruzione

Eseguire una macro-costruzione

Selezionando questo comando inizia il procedimento guidato per l'esecuzione di una Macro precedentemente costruita.

(!) Le macro-costruzioni sono esposte nella sezione macro-costruzioni.
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Strumenti per la costruzione di macroCreare una macro-costruzioneEseguire una macro-costruzione
drgeo-doc-1.5/it/drgenius_36.html0000644000175000017500000000502410117134567012343 Manuale di Dr. Geo -- Spostamento di un oggetto geometrico
Cancellazione di un oggetto geometricoAltre funzioniSpostamento di un oggetto geometrico

Spostamento di un oggetto geometrico

 

Questa funzionalità è molto importante e rappresenta uno dei punti di forza di DR. GEO. Dopo aver selezionato questo comando e dopo aver spostato il mouse su un qualsiasi oggetto geometrico, tenendo premuto il tasto sinistro del mouse e contemporaneamente muovendo il mouse stesso, si sposta l'oggetto geometrico selezionato mantenendo tuttavia invariate le caratteristiche geometriche della costruzione.

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Cancellazione di un oggetto geometricoAltre funzioniSpostamento di un oggetto geometrico
drgeo-doc-1.5/it/drgenius_37.html0000644000175000017500000000474410117134567012354 Manuale di Dr. Geo -- Spostamento di un oggetto geometrico
Cancellazione di un oggetto geometricoAltre funzioniSpostamento di un oggetto geometrico

Spostamento di un oggetto geometrico

 

Questa funzionalità è molto importante e rappresenta uno dei punti di forza di DR. GEO. Dopo aver selezionato questo comando e dopo aver spostato il mouse su un qualsiasi oggetto geometrico, tenendo premuto il tasto sinistro del mouse e contemporaneamente muovendo il mouse stesso, si sposta l'oggetto geometrico selezionato mantenendo tuttavia invariate le caratteristiche geometriche della costruzione.

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Cancellazione di un oggetto geometricoAltre funzioniSpostamento di un oggetto geometrico
drgeo-doc-1.5/it/drgenius_38.html0000644000175000017500000000547010117134567012352 Manuale di Dr. Geo -- Cancellazione di un oggetto geometrico
Modificare lo stile di un oggettoAltre funzioniSpostamento di un oggetto geometricoCancellazione di un oggetto geometrico

Cancellazione di un oggetto geometrico

 

Questa funzionalità permette di cancellare oggetti geometrici precedentemente creati. Dopo aver selezionato il comando, cliccando con il mouse su un oggetto si ottiene l'apertura di una finestra che chiede la conferma per l'eliminazione dell'oggetto stesso. Se per errore si elimina un oggetto che invece si desiderava mantenere è possibile rigenerarlo selezionando il comando "Annulla" nella barra delle icone o nel menu "Modifica". Di default si possono ricostruire fino a 5 oggetti cancellati tuttavia questo numero può essere modificato andando a modificare le Preferenze.

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Modificare lo stile di un oggettoAltre funzioniSpostamento di un oggetto geometricoCancellazione di un oggetto geometrico
drgeo-doc-1.5/it/drgenius_39.html0000644000175000017500000000626510117134567012356 Manuale di Dr. Geo -- Modificare le proprietà di un oggetto
Altre funzioniModificare lo stile di un oggettoModificare le proprietà di un oggetto

Modificare le proprietà di un oggetto

 

L'utilizzatore di DR. GEO è libero di modificare le proprietà di alcuni oggetti. Cliccando con il mouse su alcuni oggetti si apre una finestra di dialogo per la modifica delle proprietà. Allo stato attuale di sviluppo del programma possono essere modificate le proprietà dei seguenti oggetti:

  1. punto libero: si possono modificare ascissa e ordinata

    Cambiamento delle coordinate di un punto

  2. valore numerico: si può modificare un valore numerico libero

    Modifica di un valore numerico

  3. script: si può modificare il codice di uno script

    Modifica di uno script

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Altre funzioniModificare lo stile di un oggettoModificare le proprietà di un oggetto
drgeo-doc-1.5/it/drgenius_3.html0000644000175000017500000000451310117134567012257 Manuale di Dr. Geo -- Funzioni Base
Funzioni AvanzateIndiceIntroduzioneFunzioni Base

Funzioni Base

In questo capitolo vengono descritti gli strumenti necessari per la costruzione delle figure geometriche e gli elementi fondamentali per la personalizzazione delle preferenze dell'utilizzatore.

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Funzioni AvanzateIndiceIntroduzioneFunzioni Base
drgeo-doc-1.5/it/drgenius_40.html0000644000175000017500000000622710117134567012344 Manuale di Dr. Geo -- Modificare le proprietà di un oggetto
Altre funzioniModificare lo stile di un oggettoModificare le proprietà di un oggetto

Modificare le proprietà di un oggetto

 

L'utilizzatore di DR. GEO è libero di modificare, attraverso questo comando, le proprietà di alcuni oggetti. Cliccando con il mouse su essi si apre una finestra di dialogo per la modifica delle proprietà. Allo stato attuale di sviluppo del programma possono essere modificate le proprietà dei seguenti oggetti:

  1. punto libero: si possono modificare ascissa e ordinata

    Cambiamento delle coordinate di un punto

  2. valore numerico: si può modificare un valore numerico libero

    Modifica di un valore numerico

  3. script: si può modificare il codice di uno script

    Modifica di uno script

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Altre funzioniModificare lo stile di un oggettoModificare le proprietà di un oggetto
drgeo-doc-1.5/it/drgenius_41.html0000644000175000017500000000371710117134567012346 Manuale di Dr. Geo -- Preferenze
Funzioni BaseAltre funzioniPreferenze

Preferenze

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drgeo-doc-1.5/it/drgenius_42.html0000644000175000017500000000437710117134567012352 Manuale di Dr. Geo -- Altre preferenze
PreferenzePreferenze di defaultAltre preferenze

Altre preferenze

Oltre alle preferenze di default di DR. GEO è possibile modificare il nome di un oggetto geometrico a partire dal menu Modifica -> Rinomina.

Modifica nome di una figura

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PreferenzePreferenze di defaultAltre preferenze
drgeo-doc-1.5/it/drgenius_43.html0000644000175000017500000000431710117134567012345 Manuale di Dr. Geo -- Altre preferenze
PreferenzePreferenze di defaultAltre preferenze

Altre preferenze

Oltre alle preferenze di default di DR. GEO è possibile modificare il nome di un oggetto geometrico a partire dal menu Modifica -> Rinomina.

Modifica nome di una figura

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PreferenzePreferenze di defaultAltre preferenze
drgeo-doc-1.5/it/drgenius_44.html0000644000175000017500000000763710117134567012356 Manuale di Dr. Geo -- Funzioni Avanzate
Figure Scheme per DR. GEOIndiceFunzioni BaseFunzioni Avanzate

Funzioni Avanzate

In questo capitolo vengono presentate le funzionalità che permettono di estendere in modo sostanzialmente indefinito le potenzialità di DR. GEO o di adattarne l'uso alle più svariate situazioni pedagogiche.

La prima funzione avanzata che si considera riguarda la creazione di macro-costruzioni o, più brevemente, di macro. Attraverso la costruzione di una macro è possibile definire in DR. GEO una nuova costruzione geometrica, salvarla in un file con estensione .mgeo e richiamarla quando necessario.

La seconda funzione avanzata che si considera consiste nella stesura di script Guile per DR. GEO o, più brevemente, di DGS. Questa funzionalità, come la costruzione di macro, permette di estendere le potenzialità di DR. GEO permettendo all'utilizzatore di familiarizzare con la stesura di script in linguaggio Scheme. Uno script DGS generalmente ha in ingresso valori numerici relativi ad uno o più oggetti geometrici (lunghezza di un segmento, coordinata di un punto) e restituisce sempre in uscita un numero. Per fare un esempio, come vedremo, si può scrivere un DGS per calcolare l'area di un triangolo. In questo caso in ingresso sono date le lunghezze di base e altezza del triangolo e in uscita si ottiene l'area del triangolo.

Un ultimo aspetto avanzato di DR. GEO riguarda la possibilità di modificare l'interfaccia utente in modo da escludere una o più costruzioni geometriche normalmente disponibili. Ciò potrebbe essere di interesse in alcune situazioni didattiche in cui si vuole costringere l'utilizzatore a lavorare in un ambiente con un set di costruzioni limitato.

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Figure Scheme per DR. GEOIndiceFunzioni BaseFunzioni Avanzate
drgeo-doc-1.5/it/drgenius_45.html0000644000175000017500000001155410117134567012350 Manuale di Dr. Geo -- Realizzare una macro-costruzione
Eseguire una macro-costruzioneMacro-costruzioniRealizzare una macro-costruzione

Realizzare una macro-costruzione

A questo punto la sequenza di costruzione è completa ed è necessario avvertire DR. GEO che, a partire da questa sequenza, si desidera costruire una macro. Per fare questo si seleziona, nella barra degli strumenti, il comando Costruire una macro o si seleziona l'analogo comando dal menu azionabile cliccando con il tasto destro del mouse in un punto dello sfondo. Si apre allora una finestra di dialogo che riassume i passaggi necessari per costruire una macro: definizione degli oggetti iniziali e finali, scelta del nome e descrizione.

Prima pagina della finestra di dialogo per costruire una macro

Procedendo si apre una seconda pagina in cui vengono selezionati gli oggetti iniziali della macro. Nel nostro esempio sono i tre punti iniziali. Per inserirli è sufficiente cliccare su ciascuno di essi.

Seconda pagina: i tre punti sono stati selezionati

Procedendo si apre una terza pagina in cui vengono selezionati gli oggetti finali della macro. Nel nostro esempio gli oggetti finali sono la circonferenza e il suo centro. Per inserirli è sufficiente, come in precedenza, cliccare su ciscuno di essi.

Terza pagina: circonferenza e suo centro sono stati selezionati

Procedendo si apre una quarta pagina in cui vengono inseriti il nome e la descrizione della macro. Queste informazioni sono utili quando la macro-costruzione verrà nuovamente utilizzata, magari a distanza di tempo, durante altre sessioni di lavoro. A questo proposito si consiglia di scegliere opportunamente il nome delle macro in modo da non confonderle tra loro.

Quarta pagina: nome e descrizione della macro sono stati inseriti

Procedendo ancora si apre una quinta pagina con i bottoni per conludere la costruzione o per tornare indietro ed emendare possibili errori.

(!) Se oggetti iniziali e finali non trovano corrispondenza (DR. GEO non riesce a comprendere la logica della costruzione), la macro non può essere costruita. In questo caso è necessario fare marcia indietro e modificare il contenuto di alcune pagine precedenti.

Nel caso in cui la costruzione sia corretta la macro viene creata e memorizzata in DR. GEO. Vedremo ora come sia possibile riutilizzare una macro costruita in precedenza e salvata.

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Eseguire una macro-costruzioneMacro-costruzioniRealizzare una macro-costruzione
drgeo-doc-1.5/it/drgenius_46.html0000644000175000017500000001147010117134567012346 Manuale di Dr. Geo -- Realizzare una macro-costruzione
Eseguire una macro-costruzioneMacro-costruzioniRealizzare una macro-costruzione

Realizzare una macro-costruzione

A questo punto la sequenza di costruzione è completa ed è necessario avvertire DR. GEO che, a partire da questa sequenza, si desidera costruire una macro. Per fare questo si seleziona, nella barra delle icone, il comando Costruire una macro o si seleziona l'analogo comando dal menu azionabile cliccando con il tasto destro del mouse in un punto dello sfondo. Si apre allora una finestra di dialogo che riassume i passaggi necessari per costruire una macro: definizione degli oggetti iniziali e finali, scelta del nome e descrizione.

Prima pagina della finestra di dialogo per costruire una macro

Procedendo si apre una seconda pagina in cui vengono selezionati gli oggetti iniziali della macro. Nel nostro esempio sono i tre punti iniziali. Per inserirli è sufficiente cliccare su ciascuno di essi.

Seconda pagina: i tre punti sono stati selezionati

Procedendo si apre una terza pagina in cui vengono selezionati gli oggetti finali della macro. Nel nostro esempio gli oggetti finali sono la circonferenza e il suo centro. Per inserirli è sufficiente, come in precedenza, cliccare su ciscuno di essi.

Terza pagina: circonferenza e suo centro sono stati selezionati

Procedendo si apre una quarta pagina in cui vengono inseriti il nome e la descrizione della macro. Queste informazioni sono utili quando la macro-costruzione verrà nuovamente utilizzata, magari a distanza di tempo, durante altre sessioni di lavoro. A questo proposito si consiglia di scegliere opportunamente il nome delle macro in modo da non confonderle tra loro.

Quarta pagina: nome e descrizione della macro sono stati inseriti

Procedendo ancora si apre una quinta pagina con i bottoni per conludere la costruzione o per tornare indietro ed emendare possibili errori.

(!) Se oggetti iniziali e finali non trovano corrispondenza (DR. GEO non riesce a comprendere la logica della costruzione), la macro non può essere costruita. In questo caso è necessario fare marcia indietro e modificare il contenuto di alcune pagine precedenti.

Nel caso in cui la costruzione sia corretta la macro viene creata e memorizzata in DR. GEO. Vedremo ora come sia possibile riutilizzare una macro costruita in precedenza e salvata.

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Eseguire una macro-costruzioneMacro-costruzioniRealizzare una macro-costruzione
drgeo-doc-1.5/it/drgenius_47.html0000644000175000017500000000705710117134567012355 Manuale di Dr. Geo -- Eseguire una macro-costruzione
Macro-costruzioniRealizzare una macro-costruzioneEseguire una macro-costruzione

Eseguire una macro-costruzione

Per eseguire una macro-costruzione è necessario selezionare nella barra delle icone il comando Eseguire una macro precostruita o selezionare l'analogo comando dal menu azionabile cliccando con il tasto destro del mouse in un punto dello sfondo.

Si apre allora una finestra di dialogo che riassume i passaggi necessari per eseguire una macro: scelta della macro dalla lista macro, selezione, nella vista corrente, degli oggetti geometrici necessari per eseguire la macro.

Procedendo si apre una seconda pagina con un elenco da cui è possibile selezionare la macro desiderata. A questo punto, per eseguire la macro, basta cliccare con il mouse sugli oggetti geometrici della figura corrispondenti agli oggetti iniziali della macro stessa.

Seconda pagina: selezione di una macro

Se ci riferiamo all'esempio precedente della circonferenza per tre punti per eseguire la macro dobbiamo avere a disposizione sul foglio di lavoro almeno tre punti.

Foglio di lavoro con tre punti

Cliccando sui tre punti la macro viene eseguita e compare la circonferenza passante per i tre punti e il suo centro.

Figura finale: circonferenza e centro

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Macro-costruzioniRealizzare una macro-costruzioneEseguire una macro-costruzione
drgeo-doc-1.5/it/drgenius_48.html0000644000175000017500000002711410117134567012352 Manuale di Dr. Geo -- DGS attraverso esempi
Metodi di riferimento per DGSScript Guile per DR. GEODGS attraverso esempi

DGS attraverso esempi

Il comando per creare un DGS è disponibile all'interno della sezione riguardante i numeri del menu azionabile cliccando con il tasto destro del mouse in un punto dello sfondo o nella barra delle applicazioni. Un DGS può ricevere da 0 a n parametri di ingresso.

Subito dopo aver selezionato il comando per attivare uno script si deve cliccare sugli oggetti geometrici di ingresso e, successivamente, cliccare in un punto del foglio di lavoro dove si desidera venga visualizzata l'output dello script.

Conviene a questo punto passare direttamente all'analisi di qualche esempio di DGS che permetta di comprendere facilmente le potenzialità di questo strumento. Macro e DGS conferiscono a DR. GEO un aspetto speciale1 nel panorama dei programmi di studio interattivo della geometria euclidea. Oltre a questo è importante comprendere come, attraverso i DGS, vengono messe a dispozione la maggior parte delle funzionalità dell'interprete GNU Guile. Ciò vale in particolare per la libreria delle funzioni matematiche di cui qui viene fatto largo uso.

DGS senza parametri di ingresso

Dopo aver selezionato il comando script, clicchiamo sullo sfondo del foglio di lavoro nel punto in cui desideriamo compaia il valore di uscita dello script. Se lo script non ha parametri in ingresso si deve prestare attenzione a non cliccare erroneamente su oggetti della figura in quanto questi verrebbero considerati da DR. GEO come parametri di ingresso dello script2. Una volta collocato lo script appare la scritta "Dr. Genius". Ogni volta che viene generato un nuovo script di default viene fatta comparire questa scritta. Per editare lo script si deve azionare il comando per modificare le proprietà di un oggetto. Azionato questo comando si clicca sullo script o, più precisamente, sul suo valore e automaticamente si aprirà una finestra di dialogo con il contenuto dello script. In questa finestra è possibile editare lo script stesso.

Un generatore di numeri casuali e altro

Il codice da editare per ottenere un numero casuale è molto semplice: 

(random 10)

Ogni volta che si clicca sullo script compare un numero casuale tra 0 e 9.

Se si vuole generare un numero casuale appartenente all'intervallo [0;1[, possiamo utilizzare lo script: 

(random:uniform)

(!) Qualche osservazione:
  • Il valore restituito da uno script coincide con il valore calcolato nell'ultima linea di codice. Nel nostro caso questo valore coincide con il valore ritornato dalla chiamata ad una funzione.
  • L'ultima linea di uno script deve ritornare un numero reale. In caso contrario comparirà la scritta "Risultato non stampabile" ;
  • Se si desidera visualizzare il valore di una variabile è sufficiente scrivere il suo nome nell'ultima riga dello script.

Calcolo di costanti

Per calcolare un valore approssimato di pigreco è sufficiente scrivere: 

(acos -1)
mentre per calcolare un valore approssimato di e : 
(exp 1)

I valori restituita da questi DGS si possono utilizzare alla stregua di un qualsiasi altro valore numerico editabile in DR. GEO. I DGS sono vostri amici per tutte queste piccole cose. Tuttavia la loro amicizia si sente maggiormente quando vengono loro passati dei parametri in ingresso.

DGS con uno o più parametri in ingresso

Il procedimento per creare un DGS con un parametro in ingresso è simile a quanto visto in precedenza. Dopo aver selezionato il comando per attivare uno script, si clicca sugli oggetti che vengono passati allo script come parametri di ingresso, quindi si clicca in un punto del foglio di lavoro dove si desidera venga visualizzato il numero che rappresenta l'uscita dello script.

All'interno dello script il riferimento al primo parametro di entrata è rappresentato dalla variabile a1. In caso di due o più parametri di ingresso si utilizzeranno, rispettando l'ordine in cui sono stati selezionati gli oggetti, le variabili a1, a2..., an.

A seconda del tipo di oggetto a cui si fa riferimento sono disponibili diversi metodi per ottenere valori numerici, coordinate, lunghezze ecc... e i loro codici sono contenuti nel capitolo Metodi di riferimento per DGS.

In quanto segue proponiamo un esempio - non il più semplice - esaustivo della procedura di creazione di uno script. L'esempio, che svilupperemo gradualmente, riguarda la costruzione del grafico di una funzione e della tangente in un punto variabile del grafico.

La figure finale è contenuta nella documentazione di DR. GEO e prende il nome di slope.drgenius

La figura che otterremo

Definire un valore in un dato intervallo

In un foglio di lavoro bianco disegnamo due punti e il segmento che li congiunge. Su questo segmento sistemiamo un punto che chiamiamo "Move me!".

Questo punto ci serve per determinare valori numerici in un dato intervallo. Infatti il seguente script, il cui parametro a1 si riferisce a "Move me!", restituisce un numero decimale nell'intervallo [-10;+10]: 

(define x (getAbscissa a1))
(* 20  (- x 0.5))

La prima linea dello script definisce una variabile x il cui valore (getAbscissa a1) coincide con l'ascissa curvilinea dell'oggetto geometrico a cui si riferisce a13 ossia del punto "Move me!". Nella seconda riga dello script, che traduce l'espressione algebrica 20 ·( x - 0.5), si fa in modo che il valore restituito dallo script appartenga all'intervallo [-10;+10]. Finalmente chiamiamo questo script X0.

Disegnare il grafico di una funzione

Il valore numerico generato dallo script precedente ci serve ora per calcolare, attraverso un secondo script, la sua immagine attraverso la funzione x -> cos(x) : 

(define x (getValue a1))
(cos x)

Sottolineiamo che in (getValue a1) l'oggetto a cui si riferisce a1 non è il punto "Move me!" ma lo script X0. Chiamiamo questo secondo script Y0.

Infine creiamo il punto M0 di coordinate (X0;Y0) che è un punto del grafico della funzione x -> cos(x). Per disegnare il grafico costruiamo il luogo del punto M0 quando "Move me!" descrive tutto il segmento su cui giace.

Calcolare e disegnare la tangente al grafico

Per determinare la tangente nel punto M0 del grafico calcoliamo in primo luogo la pendenza della retta tangente. Consideriamo allora la derivata prima della funzione x -> -sin(x) nel punto X0 e scriviamo lo script: 

(- 0 (sin (getValue a1)))

che ha come riferimento l'ascissa X0. Le notazioni di tipo Scheme/Guile possono sembrare inizialmente poco intuitive ma dopo aver familiarizzato con esse appariranno semplici. Chiamiamo lo script "pendenza in M0". Nel momento in cui M0 viene spostato sul grafico la pendenza viene ricalcolata.

Non resta che disegnare la tangente. Per fare questo calcoliamo le coordinate di un secondo punto M1 di questa retta.

Iniziamo dall'ascissa ponendo, ad esempio, X1 = X0 + 2 e scriviamo uno script, che chiamiamo X1, con parametro d'ingresso lo script X0: 

(define x1 (getValue a1))
(+ x1 2)

Per determinare l'ordinata di M1 abbiamo bisogno di:

  • M0 (riferimento a1);
  • pendenza in M0 (a2);
  • ascissa X1 (a3).

Nello script seguente calcoliamo l'ordinata di M1 calcolando Y0 + m(X1 - X0): 

(define x0 (car (getCoordinates a1)))
(define y0 (cadr (getCoordinates a1)))
(define m (getValue a2))
(define x1 (getValue a3))
(+ (* m (- x1 x0)) y0)

Qualche parola relativamente alla chiamata (getCoordinates a1), in essa a1 deve riferirsi a un oggetto di tipo punto. Il metodo restituisce in questo caso una lista contenente le coordinate del punto che per noi è M0. Scrivendo car si estrae dalla lista il primo valore, scrivendo cadr il secondo. La parte rimanente dello script dovrebbe risultare chiara.

Chiamiamo questo script Y1 e costruiamo il punto M1 di coordinate (X1;Y1) e finalmente la tangente M0M1.

Osserviamo che, al posto di tutti questi script, sarebbe stato possibile scriverne solo due o tre, anche se più complessi. La speranza è comunque di aver dato un quadro complessivo ed esaustivo di utilizzo dei DGS.

Hai domande o commenti da fare ?
Vuoi partecipare alla stesura di parti di questo manuale ?
-> Contatta Hilaire Fernandes all'OFSET ( ) o aggiungiti alla lista per la diffusione di DR. GEO.

Metodi di riferimento per DGSScript Guile per DR. GEODGS attraverso esempi
drgeo-doc-1.5/it/drgenius_49.html0000644000175000017500000003225010117134567012350 Manuale di Dr. Geo -- DGS attraverso esempi
Metodi di riferimento per DGSScript Guile per DR. GEODGS attraverso esempi

DGS attraverso esempi

Il comando per creare un DGS è disponibile all'interno della sezione riguardante i numeri del menu azionabile cliccando con il tasto destro del mouse in un punto dello sfondo o nella barra delle icone. Un DGS può ricevere da 0 a n parametri di ingresso.

Conviene a questo punto passare direttamente all'analisi di qualche esempio di DGS che permetta di comprendere facilmente le potenzialità di questo strumento. Macro e DGS conferiscono a DR. GEO un aspetto speciale1 nel panorama dei programmi di studio interattivo della geometria euclidea. Oltre a questo è importante comprendere come, attraverso i DGS, vengano messe a dispozione la maggior parte delle funzionalità dell'interprete GNU Guile. Ciò vale in particolare per la libreria delle funzioni matematiche di cui qui viene fatto largo uso.

DGS senza parametri di ingresso

La procedura per la creazione di un DGS senza parametri in ingresso è la seguente:

  1. si seleziona il comando script;
  2. si clicca con il mouse direttamente sullo sfondo del foglio di lavoro nel punto in cui si desidera che compaia il valore di uscita dello script prestando attenzione a non cliccare erroneamente su oggetti della figura, in quanto questi verrebbero considerati da DR. GEO come parametri di ingresso dello script2;
  3. una volta collocato lo script appare per default la scritta celeste "Dr. Genius" ed è ora il momento di editare lo script azionando il comando per modificare le proprietà di un oggetto e quindi cliccando con il mouse sulla scritta stessa. A questo punto si apre automaticamente una finestra di dialogo, che mostra il contenuto dello script ("Dr. Genius"), dove si può cancellare il contenuto di default dello script e sostituirlo con il desiderato.
Un generatore di numeri casuali e altro

Il codice da editare, dopo aver seguito la procedura illustrata sopra, per ottenere un numero casuale è semplicemente: 

(random 10)

Ogni volta che si clicca sullo script comparirà un numero casuale tra 0 e 9.

Se si desidera generare un numero casuale appartenente all'intervallo [0;1[, basta utilizzare lo script: 

(random:uniform)

(!) Qualche osservazione:
  • Il valore restituito da uno script coincide con il valore calcolato nell'ultima linea di codice. Nel nostro caso questo valore coincide con il valore ritornato dalla chiamata ad una funzione.
  • L'ultima linea di uno script deve ritornare un numero reale. In caso contrario comparirà la scritta "Risultato non stampabile" ;
  • Se si desidera visualizzare il valore di una variabile è sufficiente scrivere il suo nome nell'ultima riga dello script.

Calcolo di costanti

Per calcolare un valore approssimato di pigreco è sufficiente scrivere: 

(acos -1)
mentre per calcolare un valore approssimato del numero di Neper: 
(exp 1)

I valori restituiti da questi DGS si possono utilizzare alla stregua di un qualsiasi altro valore numerico editabile in DR. GEO.

L'importanza pedagogica dei DGS si sente maggiormente quando, come ora vedremo, vengono loro passati dei parametri in ingresso.

DGS con uno o più parametri in ingresso

Il procedimento per creare un DGS con un parametro in ingresso è simile, ma non identico, a quanto visto in precedenza.

L'unica diversità consiste nel fatto che in questo caso, subito dopo aver selezionato il comando per attivare uno script, si deve cliccare sugli oggetti geometrici di ingresso che si desidera passare allo stesso e solo successivamente si deve cliccare in un punto del foglio di lavoro dove si desidera venga visualizzato l'output dello script.

All'interno dello script il riferimento al primo parametro di entrata è rappresentato per default dalla variabile a1. In caso di due o più parametri di ingresso si utilizzeranno, rispettando l'ordine in cui sono stati selezionati gli oggetti, le variabili a1, a2..., an.

A seconda del tipo di oggetto a cui si fa riferimento sono disponibili diversi metodi per ottenere valori numerici, coordinate, lunghezze e via di seguito i cui codici sono contenuti nel capitolo Metodi di riferimento per DGS.

Area del triangolo

Iniziamo ora a trattare un esempio molto semplice di utilizzo di un DGS per il calcolo dell'area di un triangolo. La figura a cui ci riferiamo è la seguente:

Area del triangolo

In essa sono rappresentati un triangolo ABC e l'altezza CH relativa alla base AB.

Per calcolare l'area S(ABC) del triangolo utilizziamo un DGS con parametri in ingresso i segmenti AB e CH della figura.

Seguendo la procedura precedente si clicca innazitutto sul bottone che aziona la funzionalità di script e subito dopo, nell'ordine, sui due segmenti che risulteranno lampeggiare. Si clicca quindi su un punto dello schermo dove si desidera collocare l'uscita dello script e comparirà la scritta azzurra Dr. Genius.

A questo punto, dopo aver azionato il comando per modificare le proprietà di un oggetto e dopo aver cliccato sulla scritta Dr. Genius, si aprirà una finestra in cui scriveremo il seguente codice Scheme: 

(define AB (getLength a1))
(define BC (getLength a2))
(/ (* AB CH ) 2 )

ottenendo il valore dell'area del triangolo. Per assegnare il nome S(ABC) allo script e per cambiarne il colore da azzurro a rosso scuro basta utilizzare la funzionalità di modifica dello stile di un oggetto vista in precedenza.

Altri esempi didattici elementari sono comunque contenuti nel capitolo dedicato alle Applicazioni Didattiche.

Tangente ad una curva

In quanto segue proponiamo un esempio articolato in cui si esamina più volte la procedura di creazione di uno script. L'esempio, che svilupperemo in modo graduale, riguarda la costruzione del grafico di una funzione e della tangente in un punto variabile del suo grafico.

La figura finale è contenuta nella documentazione di DR. GEO e prende il nome di slope.fgeo

La figura che otterremo

Definire un valore in un dato intervallo

In un foglio di lavoro bianco disegnamo due punti e il segmento che li congiunge. Su questo segmento sistemiamo un punto che chiamiamo "Move me!".

Questo punto ci serve per determinare valori numerici in un dato intervallo. Infatti il seguente script, il cui parametro a1 si riferisce a "Move me!", restituisce un numero decimale nell'intervallo [-10;+10]: 

(define x (getAbscissa a1))
(* 20  (- x 0.5))

La prima linea dello script definisce una variabile x il cui valore (getAbscissa a1) coincide con l'ascissa curvilinea dell'oggetto geometrico a cui si riferisce a13 ossia del punto "Move me!". Nella seconda riga dello script, che traduce l'espressione algebrica 20 ·( x - 0.5), si fa in modo che il valore restituito dallo script appartenga all'intervallo [-10;+10]. Finalmente chiamiamo questo script X0.

Disegnare il grafico di una funzione

Il valore numerico generato dallo script precedente ci serve ora per calcolare, attraverso un secondo script, la sua immagine attraverso la funzione x -> cos(x) : 

(define x (getValue a1))
(cos x)

Sottolineiamo che in (getValue a1) l'oggetto a cui si riferisce a1 non è il punto "Move me!" ma lo script X0. Chiamiamo questo secondo script Y0.

Infine creiamo il punto M0 di coordinate (X0;Y0) che è un punto del grafico della funzione x -> cos(x). Per disegnare il grafico costruiamo il luogo del punto M0 quando "Move me!" descrive tutto il segmento su cui giace.

Calcolare e disegnare la tangente al grafico

Per determinare la tangente nel punto M0 del grafico calcoliamo in primo luogo la pendenza della retta tangente. Consideriamo allora la derivata prima della funzione x -> -sin(x) nel punto X0 e scriviamo lo script: 

(- 0 (sin (getValue a1)))

che ha come riferimento l'ascissa X0. Le notazioni di tipo Scheme/Guile possono sembrare inizialmente poco intuitive ma dopo aver familiarizzato con esse appariranno semplici. Chiamiamo lo script "pendenza in M0". Nel momento in cui M0 viene spostato sul grafico la pendenza viene ricalcolata.

Non resta che disegnare la tangente. Per fare questo calcoliamo le coordinate di un secondo punto M1 di questa retta.

Iniziamo dall'ascissa ponendo, ad esempio, X1 = X0 + 2 e scriviamo uno script, che chiamiamo X1, con parametro d'ingresso lo script X0: 

(define x1 (getValue a1))
(+ x1 2)

Per determinare l'ordinata di M1 abbiamo bisogno di:

  • M0 (riferimento a1);
  • pendenza in M0 (a2);
  • ascissa X1 (a3).

Nello script seguente calcoliamo l'ordinata di M1 calcolando Y0 + m(X1 - X0): 

(define x0 (car (getCoordinates a1)))
(define y0 (cadr (getCoordinates a1)))
(define m (getValue a2))
(define x1 (getValue a3))
(+ (* m (- x1 x0)) y0)

Qualche parola relativamente alla chiamata (getCoordinates a1), in essa a1 deve riferirsi a un oggetto di tipo punto. Il metodo restituisce in questo caso una lista contenente le coordinate del punto che per noi è M0. Scrivendo car si estrae dalla lista il primo valore, scrivendo cadr il secondo. La parte rimanente dello script dovrebbe risultare chiara.

Chiamiamo questo script Y1 e costruiamo il punto M1 di coordinate (X1;Y1) e finalmente la tangente M0M1.

Osserviamo che, al posto di tutti questi script, sarebbe stato possibile scriverne solo due o tre, anche se più complessi.

Hai domande o commenti da fare?
Vuoi partecipare alla stesura di parti di questo manuale?
-> Contatta Andrea Centomo all'OFSET (acentomo at ofset dot org) o aggiungiti alla lista per la diffusione di DR. GEO.

Metodi di riferimento per DGSScript Guile per DR. GEODGS attraverso esempi
drgeo-doc-1.5/it/drgenius_4.html0000644000175000017500000000443310117134567012261 Manuale di Dr. Geo -- Funzioni Base
Funzioni AvanzateIndiceIntroduzioneFunzioni Base

Funzioni Base

In questo capitolo vengono descritti gli strumenti necessari per la costruzione delle figure geometriche e gli elementi fondamentali per la personalizzazione delle preferenze dell'utilizzatore.

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Funzioni AvanzateIndiceIntroduzioneFunzioni Base
drgeo-doc-1.5/it/drgenius_50.html0000644000175000017500000000465510117134567012350 Manuale di Dr. Geo -- Metodi di riferimento per DGS
Script Guile per DR. GEODGS attraverso esempiMetodi di riferimento per DGS

Metodi di riferimento per DGS

Quanto segue è una descrizione dei metodi disponibili per DGS. La classificazione è fatta secondo il tipo di oggetti geometrici o numerici cui si riferiscono.
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Script Guile per DR. GEODGS attraverso esempiMetodi di riferimento per DGS
drgeo-doc-1.5/it/drgenius_51.html0000644000175000017500000000644110117134567012344 Manuale di Dr. Geo -- Punto
Retta, Semiretta, Segmento, Vettore, AngoloMetodi di riferimento per DGSPunto

Punto

valore (getAbscissa punto)
punto: punto su una curva
output: ascissa curvilinea del punto sulla curva. Il valore appartiene all'intervallo chiuso [0;1]
Esempio:
(define x (getAbscissa a1))
(* x 10)

  (setAbscissa punto x)
punto: punto su una curva
x: valore decimale nell'intervallo [0;1] che rappresenta l'ascissa del punto
Esempio:
(setAbscissa a1 0.5)

 

liste (getCoordinates punto|vettore)
Restituisce le coordinate di un punto o di un vettore.
punto|vettore: punto o vettore
output: lista contenente le coordinate del punto o del vettore
Esempio:
(define c (getCoordinates a1))
(define x (car c))
(define y (cadr c))
(+ (* x x) (* y y))

  (setCoordinates punto coord)
Posiziona le coordinate di un punto
punto: punto libero nel piano
coord: lista di numeri decimali
Esempio:
(define l (list 1.4 (random 5)))
(setCoordinate a1 l)

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Retta, Semiretta, Segmento, Vettore, AngoloMetodi di riferimento per DGSPunto
drgeo-doc-1.5/it/drgenius_52.html0000644000175000017500000000615610117134567012350 Manuale di Dr. Geo -- Retta, Semiretta, Segmento, Vettore, Angolo
Circonferenza, Arco di circonferenzaMetodi di riferimento per DGSPuntoRetta, Semiretta, Segmento, Vettore, Angolo

Retta, Semiretta, Segmento, Vettore, Angolo

valore (getSlope direzione)
direzione: retta, semiretta, segmento o vettore
output: pendenza relativa alla direzione
Esempio:
(define p (getSlope a1))

  valore (getNorm vettore)
vettore: vettore
output: norma del vettore
Esempio:
(define n (getNorm a1))

  valore (getLength segmento)
segmento: segmento
output: lunghezza segmento
Esempio:
(define l (getLength a1))

  valore (getAngle angolo)
angolo geometrico: angolo geometrico
output: ampiezza in gradi dell'angolo
Esempio:
(define ABC (getAngle a1))

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Circonferenza, Arco di circonferenzaMetodi di riferimento per DGSPuntoRetta, Semiretta, Segmento, Vettore, Angolo
drgeo-doc-1.5/it/drgenius_53.html0000644000175000017500000000567310117134567012354 Manuale di Dr. Geo -- Circonferenza, Arco di circonferenza
NumeriMetodi di riferimento per DGSRetta, Semiretta, Segmento, Vettore, AngoloCirconferenza, Arco di circonferenza

Circonferenza, Arco di circonferenza

lista (getCenter circonferenza|arco)
circonferenza|arco: circonferenza o suo arco
output: lista contenente le coordinate del centro
Esempio:
(define c (getCenter a1))
(car c)

  valore (getRadius circonferenza|arco)
circonferenza|arco: circonferenza o suo arco
output: raggio
Esempio:
(define r (getRadius a1))

  valore (getLength circonferenza|arco)
circonferenza|arco: circonferenza o suo arco
output: lunghezza circonferenza o arco
Esempio:
(define l (getLength a1))

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NumeriMetodi di riferimento per DGSRetta, Semiretta, Segmento, Vettore, AngoloCirconferenza, Arco di circonferenza
drgeo-doc-1.5/it/drgenius_54.html0000644000175000017500000000473210117134567012350 Manuale di Dr. Geo -- Numeri
AltroMetodi di riferimento per DGSCirconferenza, Arco di circonferenzaNumeri

Numeri

valore (getValue numero)
numero: numero
output: valore del numero
Esempio:
(define a (getValue a1))
(define b (getValue a2))
(+ a b)

  (setValue numero v)
numero: numero
v: valore decimale
Esempio:
(define v (getValue a1))
(setValue a2 v)

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AltroMetodi di riferimento per DGSCirconferenza, Arco di circonferenzaNumeri
drgeo-doc-1.5/it/drgenius_55.html0000644000175000017500000000404410117134567012345 Manuale di Dr. Geo -- Altro
Metodi di riferimento per DGSNumeriAltro

Altro

(move item u)
item: oggetto
u: vettore
Esempio:
(define v (vector .1 0))
(move a1 v)

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Metodi di riferimento per DGSNumeriAltro
drgeo-doc-1.5/it/drgenius_56.html0000644000175000017500000000517310117134567012352 Manuale di Dr. Geo -- Blocco di strumenti dell'interfaccia
Funzioni AvanzateScript Guile per DR. GEOBlocco di strumenti dell'interfaccia

Blocco di strumenti dell'interfaccia

DR. GEO offre la possibilità di predisporre delle sessioni4 in cui l'insegnante può decidere, in merito ad alcune costruzioni da eseguire, di impedire l'accesso ad alcuni strumenti normalmente disponibili. Il blocco degli strumenti avviene attraverso un sistema di password. In questo modo l'insegnante ha la possibilità di predisporre attività didattiche che prevedono gradi diversi di blocco degli strumenti di costruzione.

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Funzioni AvanzateScript Guile per DR. GEOBlocco di strumenti dell'interfaccia
drgeo-doc-1.5/it/drgenius_57.html0000644000175000017500000000631410117134567012351 Manuale di Dr. Geo -- Impedire l'uso di strumenti
Sblocco degli strumentiBlocco di strumenti dell'interfacciaImpedire l'uso di strumenti

Impedire l'uso di strumenti

Per impedire l'accesso agli strumenti di costruzione si ricorre al comando Modifica -> Personalizza Interfaccia. Dopo aver selezionato il comando si apre una grande finestra di dialogo in cui si riconoscono tutte le icone relative agli strumenti di DR. GEO. Cliccando direttamente sulle icone è possibile attivare o disattivare la loro funzionalità. Le icone disattivate appariranno più sbiadite. Allo stesso tempo, cliccando sull'icona principale di un menu (riconoscibile per la presenza di un triangolino verde in basso a destra), è possibile disattivare tutti gli strumenti afferenti a quel menu.

Finestra di dialogo per bloccare l'interfaccia.

Dopo aver completato la scelta degli strumenti di cui impedire l'uso si procede alla loro effettiva disattivazione cliccando sul bottone Blocca della finestra di dialogo. A quel punto DR. GEO richiede una password.

(!) Quando si salva in un file una figura o una sessione con blocco dell'interfaccia anche le password sono salvate in forma criptata nello stesso file.
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Sblocco degli strumentiBlocco di strumenti dell'interfacciaImpedire l'uso di strumenti
drgeo-doc-1.5/it/drgenius_58.html0000644000175000017500000000507410117134567012354 Manuale di Dr. Geo -- Sblocco degli strumenti
Blocco di strumenti dell'interfacciaImpedire l'uso di strumentiSblocco degli strumenti

Sblocco degli strumenti

Analogamente a come vengono bloccate delle funzionalità dell'interfaccia è possibile, a seconda delle necessità, sbloccare le stesse funzionalità.

Sempre ricorrendo al comando Modifica -> Personalizza Interfaccia una volta aperta la finestra di dialogo si utilizza il bottone Sblocca. Come in precedenza per poter sbloccare uno strumento è necessario inserire una pasword.

Finestra di dialogo per sbloccare l'interfaccia

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Blocco di strumenti dell'interfacciaImpedire l'uso di strumentiSblocco degli strumenti
drgeo-doc-1.5/it/drgenius_59.html0000644000175000017500000000572410117134567012357 Manuale di Dr. Geo -- Figure Scheme per DR. GEO
Gestione DocumentiIndiceFunzioni AvanzateFigure Scheme per DR. GEO

Figure Scheme per DR. GEO

Le Figure Scheme in DR. GEO - (FSD) - sono figure scritte in un linguaggio relativamente naturale. Non si tratta più di costruire una figura utilizzando gli strumenti messi a disposizione dall'interfaccia grafica di DR. GEO ma piuttosto di descrivere una figura utilizzando il linguaggio di programmazione Scheme. Abbiamo profuso il massimo sforzo per rendere la sintassi del linguaggio semplice e non intricata. Oltre a questo le parole chiave utili per descrivere una figura si possono adattare a differenti lingue in quanto sono ridefinibili. Per coerenza, nonostante sia possibile utilizzare istruzioni in lingue diverse, è preferibile, una volta scelta una lingua, uniformare tutti i comandi a quella stessa lingua.

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Gestione DocumentiIndiceFunzioni AvanzateFigure Scheme per DR. GEO
drgeo-doc-1.5/it/drgenius_5.html0000644000175000017500000000505410117134567012262 Manuale di Dr. Geo -- Strumenti di Costruzione
Altre funzioniFunzioni BaseStrumenti di Costruzione

Strumenti di Costruzione

Questi strumenti sono suddivisi in sei menu visualizzabili cliccando con il mouse su ciascuna delle prime sei icone della barra delle icone di DR. GEO.

Gli strumenti di DR. GEO e la loro descrizione

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Altre funzioniFunzioni BaseStrumenti di Costruzione
drgeo-doc-1.5/it/drgenius_60.html0000644000175000017500000001723610117134567012350 Manuale di Dr. Geo -- Alcuni esempi
Metodi di riferimento per le Figure Scheme per DR. GEOFigure Scheme per DR. GEOAlcuni esempi

Alcuni esempi

Scheme è per sua natura un linguaggio di alto livello, per questa ragione, una volta definita una figura, avremo a disposizione tutta la sua potenza per eseguire, ad esempio, azioni ricorsive su parti della figura o per utilizzare funzioni aleatorie per modificarla ad ogni sua comparsa sul foglio di lavoro. In altri termini le FSD sono allo stesso tempo svincolate dall'interfaccia grafica e potenziate dalla presenza di Scheme.

Una FSD è un file con estensione .scm creato attraverso un editore di testo che, una volta aperto in DR. GEO attraverso il comando File->Valuta, genera una figura sul foglio di lavoro.

Iniziamo studiando un semplice esempio di FSD:

  

(new-figure "Figura")

Si tratta della più semplice FSD che si possa definire. Una volta valutato il file in DR. GEO appare una nuova figura vuota con nome "Figura". Ripetendo il comando (new-figure "Figura") verranno create quante figure si desiderano.

Vediamo un secondo esempio: 

(new-figure "Figura")
(lets Point "A" free 1.2 -2)

Questa FSD definisce una figura con un punto libero A di coordinate (1,2 ; -2). Come si può vedere la sintassi utile per la definizione dell'oggetto geometrico è intuitiva e espressa in un linguaggio molto vicino a quello comune. Osserviamo inoltre come questa definizione sia sostanzialmente identica nella forma a quella di tutti i comandi che permettono di definire i rimanenti oggetti:

  1. inizia con la parola chiave lets che indica che si desidera costruire un nuovo oggetto;
  2. segue la categoria a cui appartiene l'oggetto, in questo caso Point.
  3. quindi si scrive il nome dell'oggetto, nel nostro caso A, sempre tra virgolette ". Se non si desidera dare alcun nome all'oggetto è sufficiente scrivere: 
    ""
  4. infine si precisa il tipo di oggetto, ossia il tipo di punto, che nel nostro caso è libero free;
  5. il tipo di oggetto è seguito da una lista di argomenti specifici che, nel nostro esempio, coincide con la coppia di coordinate che definiscono il punto A.

Vediamo un terzo esempio: 

(define (triangolo p1 p2 p3)
  (Segment "" extremities p1 p2)
  (Segment "" extremities p2 p3)
  (Segment "" extremities p1 p3))

(define (casuale)
  (- 8 (* 16 (random:uniform))))

(new-figure "Figura")

(lets Point "A" free (casuale) 0)
(lets Point "B" free 5 0)
(lets Point "C" free (casuale) 5)

(triangolo A B C)

Questo esempio è di particolare interesse in quanto ci mostra tre aspetti essenziali:

  1. come introdurre costruzioni di più alto livello non previste inizialmente in DR. GEO. Qui abbiamo definito la funzione triangolo che a partire da tre punti qualsiasi costruisce un triangolo. Possiamo confrontare questa costruzione con quella che potremmo definire attraverso una macro concludendo che il primo metodo è più potente;
  2. come definire funzioni associate: nel nostro caso la funzione casuale che ritorna un numero decimale casuale compreso tra -8 e 8. Attraverso questa funzione, ogni volta che viene aperta la figura, il disegno apparirà diverso;
  3. l'uso della parola chiave lets non è obbligatorio, ma legato alla necessità di definire o meno dei riferimenti per l'oggetto creato. Ad esempio nella funzione triangolo non abbiamo bisogno di alcun riferimento ai segmenti creati; al contrario quando definiamo i punti A, B e C sono necessari dei riferimenti. In questo caso i riferimenti hanno lo stesso nome5 senza virgolette: A, B e C. Nel seguito chiameremo questi riferimenti simboli; ciò per utilizzare in modo corretto la terminologia del linguaggio Scheme. In questo modo quando la funzione triangolo viene chiamata vengono passati ad essa come parametri i simboli A, B e C, che vengono utilizzati per definire i vertici del triangolo.

Osserviamo che quando si definiscono i segmenti non vengono assegnati ad essi dei nomi in quanto DR. GEO fa questo automaticamente: nel nostro caso i segmenti saranno [AB], [BC] e [AC].

Per concludere questa sezione vediamo un ultimo esempio: 

(lets Point "A" free 1 0)
(lets Point "B" free 5 0)
(lets Line "d1" 2points A B)

(send A color yellow)
(send A shape round)
(send A size large)
(send B masked)
(send d1 thickness dashed)

I primi tre comandi permettono di costruire due punti e una retta. La parte che qui maggiormente interessa riguarda la serie di comandi preceduti da send. Questo comando permette di comunicare con un oggetto di cui si dispone del simbolo relativo. In questo caso i simboli di cui disponiamo sono A, B e d1. La struttura di send consiste in primo luogo di un primo argomento che identifica l'oggetto con cui si vuole comunicare e di un secondo argomento che definisce il messaggio. Dal terzo argomento in poi seguono informazioni legate alla natura del messaggio. Ad esempio (send A color yellow) invia il messagio color con parametro yellow: in questo caso il punto viene dipinto di giallo. Il significato dei rimanenti comandi dovrebbe a questo punto risultare ovvio. In ogni caso ritorneremo su essi nel seguito.

Terminata questa breve visita guidata alle Figure Scheme per Dr. Geo nella sezione seguente verranno esposti i comandi disponibili per definire le diverse FSD.

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Metodi di riferimento per le Figure Scheme per DR. GEOFigure Scheme per DR. GEOAlcuni esempi
drgeo-doc-1.5/it/drgenius_61.html0000644000175000017500000000531310117134567012342 Manuale di Dr. Geo -- Metodi di riferimento per le Figure Scheme per DR. GEO
Galleria di esempiFigure Scheme per DR. GEOAlcuni esempiMetodi di riferimento per le Figure Scheme per DR. GEO

Metodi di riferimento per le Figure Scheme per DR. GEO

La definizione di oggetti in un file FSD avviene attraverso dei prototipi. I prototipi sono un genere di oggetti che, come chiariremo nel seguito, è possibile interrogare e modificare.

Tuttavia, prima di ogni definizione di un oggetto in una figura questa deve essere stata precedentemente creata con il comando new-figure.

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Galleria di esempiFigure Scheme per DR. GEOAlcuni esempiMetodi di riferimento per le Figure Scheme per DR. GEO
drgeo-doc-1.5/it/drgenius_62.html0000644000175000017500000000463410117134567012350 Manuale di Dr. Geo -- Comandi generali
Definizione di oggetti in una figuraMetodi di riferimento per le Figure Scheme per DR. GEOComandi generali

Comandi generali

(new-figure nome)
nome: stringa di caratteri
output: non viene restituito alcun valore. La chiamata non produce che un effetto di contorno per indicare la creazione di una figura; successivamente in essa verranno creati degli oggetti fino ad una nuova chiamata dello stesso tipo
Esempio:
(new-figure "Figura 1")

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Definizione di oggetti in una figuraMetodi di riferimento per le Figure Scheme per DR. GEOComandi generali
drgeo-doc-1.5/it/drgenius_63.html0000644000175000017500000000746110117134567012352 Manuale di Dr. Geo -- Definizione di oggetti in una figura
Modifiche agli attributi di un oggettoMetodi di riferimento per le Figure Scheme per DR. GEOComandi generaliDefinizione di oggetti in una figura

Definizione di oggetti in una figura

Un oggetto può essere definito ricorrendo a strutture sintattiche assai diverse :

  • (lets Point "p1" type args)

    In questo modo viene creato un punto e il suo riferimento è contenuto nella variabile p1. Questo tipo di sintassi utilizza una macro di Scheme.

  • (Point "Nome" type args)

    In queto modo viene creato un punto senza che venga conservato alcun riferimento.

  • (define p1 (Point "Nome" type args))

    In questo modo viene creato un punto e il suo riferimento è contenuto nella variabile p1.

  • (set! p1 (Point "Nome" type args))

    In questo modo viene creato un punto e il suo riferimento viene copiato nella variabile preesistente p1.

Se alcuni oggetti vengono creati nel corpo di una funzione è possibile utilizzare sia la forma set! che la forma speciale di Scheme lets. Ciò che importa sottolineare è che la chiamata base consiste in una chiamata ad una funzione che ritorna il riferimento all'oggetto creato.

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Modifiche agli attributi di un oggettoMetodi di riferimento per le Figure Scheme per DR. GEOComandi generaliDefinizione di oggetti in una figura
drgeo-doc-1.5/it/drgenius_64.html0000644000175000017500000001067610117134567012355 Manuale di Dr. Geo -- Punto
RettaDefinizione di oggetti in una figuraPunto

Punto

prototipo (Point nome free x y)
nome: stringa di caratteri che designa il nome dell'oggetto
x: ascissa del punto
y: ordinata del punto
output: riferimento per un punto libero nel piano con coordinate iniziali x e y.
Esempio:
(define p1 (Point "A" free 1.2 (acos -1)))

prototipo (Point nome on-curve linea x)
nome: stringa di caratteri che designa il nome dell'oggetto
linea: riferimento ad una linea (retta, semiretta, segmento, ecc.)
x: ascissa curvilinea di un punto libero il cui valore appartiene all'intervallo [0 ; 1]
output: riferimento per un punto libero su una curva.
Esempio:
(Point "M" on-curve s1 0.5)

prototipo (Point nome middle-2pts p1 p2)
nome: stringa di caratteri che designa il nome dell'oggetto
p1: riferimento ad un punto
p2: riferimento ad un punto
output: riferimento al punto medio tra due punti.
Esempio:
(lets Point "A" free 1 1)
(lets Point "B" free 4 4)
(Point "I" middle-2pts A B)

prototipo (Point nome middle-segment s)
nome: stringa di caratteri che designa il nome dell'oggetto
s: riferimento ad un segmento
output: riferimento al punto medio di un segmento.
Esempio:
(Point "L" middle-segment s)

prototipo (Point nome intersection l1 l2)
nome: stringa di caratteri che designa il nome dell'oggetto
l1: riferimento ad una linea
l2: riferimento ad una linea
output: riferimento al punto di intersezione di due linee.
Esempio:
(Point "I" intersection line segment)

prototipo (Point nome intersection2 l1 l2)
nome: stringa di caratteri che designa il nome dell'oggetto
l1: riferimento ad una linea
l2: riferimento ad una curva
output: riferimento al secondo punto d'intersezione di due curve quando una delle due è un arco o una circonferenza.
Esempio:
(Point "I" intersection2 line circle)

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RettaDefinizione di oggetti in una figuraPunto
drgeo-doc-1.5/it/drgenius_65.html0000644000175000017500000000657710117134567012363 Manuale di Dr. Geo -- Retta
SemirettaDefinizione di oggetti in una figuraPuntoRetta

Retta

prototipo (Line nome 2points p1 p2)
nome: stringa di caratteri che designa il nome dell'oggetto
p1: riferimento ad un punto
p2: riferimento ad un punto
output: riferimento ad una retta passante per due punti.
Esempio:
(lets Point "A" free 0 0)
(lets Point "M" free 1 2)
(Line "" 2points A M)

prototipo (Line nome parallel p d)
nome: stringa di caratteri che designa il nome dell'oggetto
p: riferimento ad un punto
d: riferimento ad una direzione (retta, segmento, vettore ...)
output: riferimento ad una retta parallela alla direzione d e passante per p.
Esempio:
(lets Point "A" free 1 5)
(lets Line "d1" parallel A d)

prototipo (Line nome orthogonal p d)
nome: stringa di caratteri che designa il nome dell'oggetto
p: riferimento ad un punto
d: riferimento ad una direzione (retta, segmento, vettore ...)
output: riferimento ad una retta perpendicolare alla direzione d e passante per p.
Esempio:
(lets Point "A" free 1 5)
(lets Line "d1" orthogonal A d)

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SemirettaDefinizione di oggetti in una figuraPuntoRetta
drgeo-doc-1.5/it/drgenius_66.html0000644000175000017500000000472110117134567012351 Manuale di Dr. Geo -- Semiretta
SegmentoDefinizione di oggetti in una figuraRettaSemiretta

Semiretta

prototipo (Ray nome 2points o p)
nome: stringa di caratteri che designa il nome dell'oggetto
o: riferimento ad un punto origine della semiretta
p: riferimento ad un punto appartenente alla semiretta
output: riferimento ad una semiretta definita dall'origine e un punto.
Esempio:
(lets Point "A" free 1 5)
(lets Point "O" free 0 0)
(lets Ray "dd1" 2points A 0)

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SegmentoDefinizione di oggetti in una figuraRettaSemiretta
drgeo-doc-1.5/it/drgenius_67.html0000644000175000017500000000473610117134567012360 Manuale di Dr. Geo -- Segmento
CirconferenzaDefinizione di oggetti in una figuraSemirettaSegmento

Segmento

prototipo (Segment nome extremities p1 p2)
nome: stringa di caratteri che designa il nome dell'oggetto
p1: riferimento ad un punto estremo del segmento
p2: riferimento ad un punto estremo del segmento
output: riferimento ad un segmento definito dai suoi estremi.
Esempio:
(lets Point "A" free 1 5)
(lets Point "B" free 10 4)
(lets Segment "" extremities A B)

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CirconferenzaDefinizione di oggetti in una figuraSemirettaSegmento
drgeo-doc-1.5/it/drgenius_68.html0000644000175000017500000000722610117134567012356 Manuale di Dr. Geo -- Circonferenza
ArcoDefinizione di oggetti in una figuraSegmentoCirconferenza

Circonferenza

prototipo (Circle nome 2points c p)
nome: stringa di caratteri che designa il nome dell'oggetto
c: riferimento ad un punto: centro della circonferenza
p: riferimento ad un punto appartenente alla circonferenza
output: riferimento ad una circonferenza definita da centro e punto ad essa appartenente.
Esempio:
(lets Point "A" free 1 5)
(lets Point "B" free 10 4)
(lets Circle "C1" 2points A B)

prototipo (Circle nome center-radius c r)
nome: stringa di caratteri che designa il nome dell'oggetto
c: riferimento ad un punto: centro della circonferenza
r: riferimento ad un valore numerico: raggio della circonferenza
output: riferimento ad una circonferenza definita da centro e raggio.
Esempio:
(lets Point "A" free 1 5)
(lets Numeric "r" free 10 4)
(lets Circle "C1" center-radius A r)

prototipo (Circle nome center-segment c s)
nome: stringa di caratteri che designa il nome dell'oggetto
c: riferimento ad un punto: centro della circonferenza
s: riferimento ad un segmento la cui lunghezza definisce il raggio della circonferenza
output: riferimento ad una circonferenza definita da centro e raggio.
Esempio:
(lets Point "A" free 1 5)
(lets Point "B" free 10 4)
(lets Segment "s" extremities A B)
(lets Circle "C1" center-segment A s)

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ArcoDefinizione di oggetti in una figuraSegmentoCirconferenza
drgeo-doc-1.5/it/drgenius_69.html0000644000175000017500000000511210117134567012347 Manuale di Dr. Geo -- Arco
PoligonoDefinizione di oggetti in una figuraCirconferenzaArco

Arco

prototipo (Arc nome 3points p1 p2 p3)
nome: stringa di caratteri che designa il nome dell'oggetto
p1: riferimento ad un punto primo estremo del'arco
p2: riferimento ad un punto centro dell'arco
p3: riferimento ad un punto secondo estremo dell'arco
output: riferimento ad un arco di circonferenza definito dai suoi estremi e da un punto
Esempio:
(lets Point "A" free 1 5)
(lets Point "B" free 0 5)
(lets Point "C" free -1 -2)
(lets Arc "arc" 3points A B C)

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PoligonoDefinizione di oggetti in una figuraCirconferenzaArco
drgeo-doc-1.5/it/drgenius_6.html0000644000175000017500000000511010117134567012254 Manuale di Dr. Geo -- Punto libero
Punto medioCostruzione di punti Punto libero

Punto libero

 

Selezionando questo comando si possono creare sul foglio di lavoro un punto o un punto su un oggetto (retta, semiretta, ...) tracciato in precedenza. Nel primo caso il punto si costruisce cliccando con il mouse nel punto del foglio di lavoro desiderato e, se necessario, potrà essere successivamente spostato ovunque nel foglio di lavoro utilizzando un comando opportuno. Nel secondo caso il punto si costruisce cliccando sull'oggetto geometrico desiderato e, se necessario, potrà essere successivamente spostato, rimanendo tuttavia vincolato all'oggetto geometrico su cui è stato creato.

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Punto medioCostruzione di punti Punto libero
drgeo-doc-1.5/it/drgenius_70.html0000644000175000017500000000500410117134567012337 Manuale di Dr. Geo -- Poligono
Trasformazioni geometricheDefinizione di oggetti in una figuraArcoPoligono

Poligono

prototipo (Polygon nome npoints args)
nome: stringa di caratteri che designa il nome dell'oggetto
args: una lista di riferimenti a punti che rappresentano i vertici del poligono
output: riferimento ad un poligono definito dai suoi vertici
Esempio:
(lets Point "A" free 1 1)
(lets Point "B" free 1 5)
(lets Point "C" free 5 1)
(lets Point "D" free 5 5)
(lets Polygon "quad" npoints A B C D)

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Trasformazioni geometricheDefinizione di oggetti in una figuraArcoPoligono
drgeo-doc-1.5/it/drgenius_71.html0000644000175000017500000001221710117134567012344 Manuale di Dr. Geo -- Trasformazioni geometriche
Luogo geometricoDefinizione di oggetti in una figuraPoligonoTrasformazioni geometriche

Trasformazioni geometriche

I prototipi relativi alle trasformazioni geometriche permettono di eseguire trasformazioni geometriche di diversi oggetti. Essi si applicano in riferimento agli oggetti punto, segmento, retta, semiretta, vettore, circonferenza, arco e poligono.

prototipo (TipoOggetto nome rotation oggetto centro angolo)
TipoOggetto: Point, Segment, Line, Ray, Vector, Circle, Arc, Polygon
nome: stringa di caratteri che designa il nome dell'oggetto
oggetto: riferimento all'oggetto da trasformare
centro: riferimento ad un punto: il centro di rotazione
angolo: riferimento ad un valore: l'angolo di rotazione
output: riferimento all'oggetto trasformato.
Esempio:
(lets Point "I1" rotation I C a)

prototipo (TipoOggetto nome scale oggetto centro k)
TipoOggetto: Point, Segment, Line, Ray, Vector, Circle, Arc, Polygon
nome: stringa di caratteri che designa il nome dell'oggetto
oggetto: riferimento all'oggetto da trasformare
centro: riferimento ad un punto: il centro di omotetia
k: riferimento ad un valore: rapporto di omotetia
output: riferimento all'oggetto trasformato.
Esempio:
(lets Polygon "P1" scale P C k1)

prototipo (TipoOggetto nome symmetry oggetto centro)
TipoOggetto: Point, Segment, Line, Ray, Vector, Circle, Arc, Polygon
nome: stringa di caratteri che designa il nome dell'oggetto
oggetto: riferimento all'oggetto da trasformare
centro: riferimento ad un punto: il centro di simmetria
output: riferimento all'oggetto trasformato.
Esempio:
(lets Segment "S1" symmetry S C)

prototipo (TipoOggetto nome reflexion oggetto asse)
TipoOggetto: Point, Segment, Line, Ray, Vector, Circle, Arc, Polygon
nome: stringa di caratteri che designa il nome dell'oggetto
oggetto: riferimento all'oggetto da trasformare
asse: riferimento ad una retta: l'asse di riflessione
output: riferimento all'oggetto trasformato.
Esempio:
(lets Polygon "P1" reflexion P d1)

prototipo (TipoOggetto nome translation oggetto vettore)
TipoOggetto: Point, Segment, Line, Ray, Vector, Circle, Arc, Polygon
nome: stringa di caratteri che designa il nome dell'oggetto
oggetto: riferimento all'oggetto da trasformare
vettore: riferimento ad un vettore: il vettore di traslazione
output: riferimento all'oggetto trasformato.
Esempio:
(lets Circle "C1" translation C v)

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Luogo geometricoDefinizione di oggetti in una figuraPoligonoTrasformazioni geometriche
drgeo-doc-1.5/it/drgenius_72.html0000644000175000017500000000466710117134567012357 Manuale di Dr. Geo -- Luogo geometrico
VettoreDefinizione di oggetti in una figuraTrasformazioni geometricheLuogo geometrico

Luogo geometrico

prototipo (Locus nome 2points m c)
nome: stringa di caratteri che designa il nome dell'oggetto
m: riferimento ad un punto mobile su una curva
c: riferimento ad un punto fisso dipendente dal punto m
output: riferimento ad un luogo.
Esempio:
(Locus "luogo" 2points M I)

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VettoreDefinizione di oggetti in una figuraTrasformazioni geometricheLuogo geometrico
drgeo-doc-1.5/it/drgenius_73.html0000644000175000017500000000465610117134567012356 Manuale di Dr. Geo -- Vettore
NumeriDefinizione di oggetti in una figuraLuogo geometricoVettore

Vettore

prototipo (Vector nome 2points o e)
nome: stringa di caratteri che designa il nome dell'oggetto
o: riferimento ad un punto: origine del vettore
e: riferimento ad un punto: estremo del vettore
output: riferimento ad un vettore.
Esempio:
(lets Point "B" free 0 5)
(lets Point "C" free -1 -2)
(Vector "" 2points C B)

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NumeriDefinizione di oggetti in una figuraLuogo geometricoVettore
drgeo-doc-1.5/it/drgenius_74.html0000644000175000017500000001231110117134567012342 Manuale di Dr. Geo -- Numeri
AngoloDefinizione di oggetti in una figuraVettoreNumeri

Numeri

prototipo (Numeric nome free x y v)
nome: stringa di caratteri che designa il nome dell'oggetto
x,y: le coordinate che determinano la posizione del numero
v: il valore del numero
output: riferimento a un numero.
Esempio:
(lets Numeric "pi" free 5 5 (acos -1))

prototipo (Numeric nome segment-length x y s)
nome: stringa di caratteri che designa il nome dell'oggetto
x,y: le coordinate che determinano la posizione del numero
s: riferimento ad un numero: la lunghezza di un segmento
output: riferimento alla lunghezza di un segmento.
Esempio:
(lets Numeric "l" segment-length 5 5 S)

prototipo (Numeric nome vector-norm x y v)
nome: stringa di caratteri che designa il nome dell'oggetto
x,y: le coordinate che determinano la posizione del numero
v: riferimento ad un vettore
output: riferimento alla norma di un vettore.
Esempio:
(lets Numeric "l" vector-norm 5 5 V)

prototipo (Nombre nome point-circle x y p c)
nome: stringa di caratteri che designa il nome dell'oggetto
x,y: le coordinate che determinano la posizione del numero
p: riferimento ad un punto
c: riferimento ad una circonferenza
output: riferimento al valore che esprime la distanza tra punto e circonferenza.
Esempio:
(lets Numeric "l" point-circle 5 5 P C)

prototipo (Numeric nome point-line x y p d)
nome: stringa di caratteri che designa il nome dell'oggetto
x,y: le coordinate che determinano la posizione del numero
p: riferimento ad un punto
d: riferimento ad una retta
output: riferimento al valore che esprime la distanza tra punto e retta.
Esempio:
(lets Numeric "d" point-line 5 5 M D1)

prototipo (Numeric nome point-point x y p1 p2)
nome: stringa di caratteri che designa il nome dell'oggetto
x,y: le coordinate che determinano la posizione del numero
p1: riferimento ad un punto
p2: riferimento ad un punto
output: riferimento al valore che esprime la distanza tra i due punti.
Esempio:
(lets Numeric "d" point-point 5 5 A B)

prototipo (Numeric nome circle-length x y c)
nome: stringa di caratteri che designa il nome dell'oggetto
x,y: le coordinate che determinano la posizione del numero
c: riferimento ad una circonferenza
output: riferimento alla lunghezza della circonferenza.
Esempio:
(lets Numeric "p" circle-length 5 5 C)

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AngoloDefinizione di oggetti in una figuraVettoreNumeri
drgeo-doc-1.5/it/drgenius_75.html0000644000175000017500000000445410117134567012354 Manuale di Dr. Geo -- Angolo
Definizione di oggetti in una figuraNumeriAngolo

Angolo

prototipo (Angle nome geometric A B C)
nome: stringa di caratteri che designa il nome dell'oggetto
A: riferimento a un punto
B: riferimento a un punto: vertice dell'angolo
C: riferimento a un punto
output: riferimento ad un angolo geometrico.
Esempio:
(lets Angle "a" geometric A B C)

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Definizione di oggetti in una figuraNumeriAngolo
drgeo-doc-1.5/it/drgenius_76.html0000644000175000017500000001003210117134567012342 Manuale di Dr. Geo -- Modifiche agli attributi di un oggetto
Metodi di riferimento per le Figure Scheme per DR. GEODefinizione di oggetti in una figuraModifiche agli attributi di un oggetto

Modifiche agli attributi di un oggetto

Per modificare gli attributi di un oggetto creato in precedenza si utilizza un sistema di messaggi che vengono inviati direttamente al prototipo che rappresenta l'oggetto in questione. Le modifiche agli attributi si eseguono quindi a posteriori della costruzione dei diversi oggetti.

(send oggetto color valore)
oggetto: riferimento ad un oggetto
valore: un colore tra i seguenti: black, dark-grey, grey, white, dark-green, green, dark-blue, bleu, red, yellow
Esempio:
(lets Point "A" free 1 2)
(send A color green)

(send linea thickness valore)
linea: riferimento ad una linea (retta, semiretta, circonferenza, luogo, ecc.)
valore: lo spessore i cui valori possibili sono: dashed, normal, large
Esempio:
(lets Point "A" free 1 2)
(lets Point "O" free 0 0)
(lets Line "d" 2points A B)
(send d thickness dashed)

(send punto size valore)
punto: riferimento ad un punto
valore: la dimensione di un punto i cui valori possibili sono: small, normal, large
Esempio:
(lets Point "A" free 1 2)
(send A size small)

(send punto shape valore)
punto: riferimento ad un punto
valore: la forma di un punto i cui valori possibibili sono: round, cross, round-empty, rec-empty
Esempio:
(lets Point "A" free 1 2)
(send A shape rond)

(send oggetto masked)
oggetto: riferimento ad un oggetto nascosto
Esempio:
(lets Point "A" free 1 2)
(send A masked)

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Metodi di riferimento per le Figure Scheme per DR. GEODefinizione di oggetti in una figuraModifiche agli attributi di un oggetto
drgeo-doc-1.5/it/drgenius_77.html0000644000175000017500000000524210117134567012352 Manuale di Dr. Geo -- Galleria di esempi
Figure Scheme per DR. GEOMetodi di riferimento per le Figure Scheme per DR. GEOGalleria di esempi

Galleria di esempi

Per illustrare l'utilizzo di Figure Scheme per DR. GEO proponiamo alcuni esempi. Gli esempi hanno lo scopo di mostrare le potenzialità delle FSD e allo stesso tempo ci auguriamo siano fonte di ispirazione per costruire altri esempi. Ogni esempio è accompagnato dal codice Scheme che genera la figura corrispondente. Il codice sorgente può essere copiato in un editore di testo, salvato con estensione .scm e quindi valutato in DR. GEO. Altri esempi, forse più semplici, sono disponibili al Capitolo 6.

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Figure Scheme per DR. GEOMetodi di riferimento per le Figure Scheme per DR. GEOGalleria di esempi
drgeo-doc-1.5/it/drgenius_78.html0000644000175000017500000000545410117134567012360 Manuale di Dr. Geo -- Poligoni regolari
FrattaliGalleria di esempiPoligoni regolari

Poligoni regolari

La costruzione di un poligono regolare con un numero arbitrario di lati, che non è prevista come costruzione base in DR. GEO, può essere eseguita attraverso una FSD che sfrutta alcune funzioni ricorsive del linguaggio Scheme. 

(define pi (acos -1))
(define n 15)
(define x0 0)
(define y0 0)
(define p1 0)

(define (polygon center p a n)
  (if (> n 0)
      (begin
        (set! p1 (Point "" rotation p center a))
        (send p1 masked)
        (Segment "" extremities p p1)
        (polygon center p1 a (- n 1)))))

(new-figure "Poligono Regolare")
(lets Point "C" free x0 y0)
(lets Numeric "a" free 0 0 (* 2 (/ pi n)))
(send a masked)

(set! p1 (Point "I" free 5 0))

(lets Segment "S" extremities C p1)
(Segment ""  rotation S C a)

(polygon C p1 a n)

Un poligono regolare con 15 lati

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FrattaliGalleria di esempiPoligoni regolari
drgeo-doc-1.5/it/drgenius_79.html0000644000175000017500000000616210117134567012356 Manuale di Dr. Geo -- Frattali
Galleria di esempiPoligoni regolariFrattali

Frattali

La costruzione di una curva frattale a forma d'albero si può realizzare facilmente utilizzando una FSD. Il codice sorgente della figura è incredibilmente compatto e incomparabilmente più efficiente rispetto all'esecuzione della figura attraverso l'interfaccia grafica. 

(new-figure "Albero")
(lets Numeric "A1" free 2 2 +3.4)
(lets Numeric "A2" free 2 3 -3.7)
(lets Numeric "S1" free 2 4 +0.5)
(lets Numeric "S2" free 2 5 +0.9)

(define (dec n)
  (- n 1))
(define (inc n)
  (+ n 1))
(define (invisible p)
  (send p masked)
  p)
(define (scalerot oP C a s)
  (let* ((sP (invisible (Point "" scale oP C s)))
         (rP (invisible (Point "" rotation sP C a))) )
    rP))
(define (Ramo p0 p1 n)
  (Segment "" extremities p0 p1)
  (let* ((left-scale (if (odd? n) S1 S2))
         (left-angle A1)
         (right-scale (if (odd? n) S2 S1))
         (right-angle A2) )
    (if (> n 0)
      (begin
        (Ramo p1 (scalerot p0 p1  left-angle  left-scale) (dec n))
        (Ramo p1 (scalerot p0 p1 right-angle right-scale) (dec n))))))
        
(lets Point "A" free -3 0)
(lets Point "B" free -3 2)
(Ramo A B 6)

Curva frattale

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Galleria di esempiPoligoni regolariFrattali
drgeo-doc-1.5/it/drgenius_7.html0000644000175000017500000000501610117134567012262 Manuale di Dr. Geo -- Punto libero
Punto medioCostruzione di punti Punto libero

Punto libero

 

Selezionando questo comando si possono creare sul foglio di lavoro un punto o un punto su un oggetto (retta, semiretta, ...) tracciato in precedenza.

Nel primo caso il punto si costruisce cliccando con il mouse nel punto del foglio di lavoro desiderato e, se necessario, potrà essere successivamente spostato dinamicamente all'interno del foglio di lavoro.

Nel secondo caso il punto si costruisce cliccando sull'oggetto geometrico desiderato e, se necessario, potrà essere successivamente spostato, rimanendo tuttavia vincolato all'oggetto geometrico su cui è stato creato.

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Punto medioCostruzione di punti Punto libero
drgeo-doc-1.5/it/drgenius_80.html0000644000175000017500000000463710117134567012353 Manuale di Dr. Geo -- Gestione Documenti
Applicazioni didatticheIndiceFigure Scheme per DR. GEOGestione Documenti

Gestione Documenti

Le costruzioni geometriche si possono salvare sia singolarmente sia a gruppi (salvataggio di una sessione di DR. GEO). Ricordiamo che le macro vengono salvate come file con estensione .mgeo e le rimanenti costruzioni come file con estensione .fgeo.
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Applicazioni didatticheIndiceFigure Scheme per DR. GEOGestione Documenti
drgeo-doc-1.5/it/drgenius_81.html0000644000175000017500000000525410117134567012350 Manuale di Dr. Geo -- Salvare una costruzione
Salvare una sessioneGestione DocumentiSalvare una costruzione

Salvare una costruzione

Partendo dal menu File -> Salva o File -> Salva come è possibile salvare come file una qualsiasi costruzione.

(!) DR. GEO è in grado di lavorare contemporaneamente con più costruzioni. Si può passare da una all'altra cliccando con il mouse.

Selezionando l'opzione File -> Salva come è possibile cambiare il nome di una costruzione salvata in precedenza.

(!) Il nome del file proposto di default può essere modificato utilizzando il comando Modifica -> Preferenze. Per maggiori informazioni vedere la sezione relativa al funzionamento di default.
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Salvare una sessioneGestione DocumentiSalvare una costruzione
drgeo-doc-1.5/it/drgenius_82.html0000644000175000017500000000634110117134567012347 Manuale di Dr. Geo -- Salvare una sessione
Aprire un fileGestione DocumentiSalvare una costruzioneSalvare una sessione

Salvare una sessione

Una sessione è un insieme di costruzioni di DR. GEO che possono essere registrate tutte in un unico file. Il salvataggio di sessioni può essere particolarmente utile per l'organizzazione didattica di materiali.

Partendo dal menu File -> Salvataggio multiplo, possibile aprire la seguente finestra di dialogo.

La finestra di dialogo per una sessione di DR. GEO

La finestra di dialogo mostra la lista di tutte le costruzioni realizzate durante la sessione di lavoro e il loro genere (macro, costruzioni interattive, ecc...).

(!) Attualmente una sessione può contenere tre generi di costruzioni: figure piane costruite interattivamente, macro e testi.

E' possibile selezionare una ad una le costruzioni utilizzando il comando Salva selezionato oppure salvare tutte le costruzioni utilizzando il comando Salva tutto.

(!) Il menu File -> Salvataggio multiplo rappresenta l'unico mezzo disponibile per salvare una macro in un file.
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Aprire un fileGestione DocumentiSalvare una costruzioneSalvare una sessione
drgeo-doc-1.5/it/drgenius_83.html0000644000175000017500000000441110117134567012344 Manuale di Dr. Geo -- Aprire un file
Gestione DocumentiSalvare una sessioneAprire un file

Aprire un file

Dal momento che costruzioni e sessioni vengono salvate sempre su un unico file. La procedura di apertura di una sessione o di una costruzione sono identiche in quanto si tratta sempre di aprire un file. A questo scopo si utilizza il comando File -> Apri. Se si apre una sessione che contiene delle macro esse sono disponibili dopo l'apertura di tutte le costruzioni.
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Gestione DocumentiSalvare una sessioneAprire un file
drgeo-doc-1.5/it/drgenius_84.html0000644000175000017500000000537310117134567012355 Manuale di Dr. Geo -- Applicazioni didattiche
Indice AnaliticoIndiceGestione DocumentiApplicazioni didattiche

Applicazioni didattiche

Questo capitolo è di aiuto per chi vuole iniziare ad usare DR. GEO studiando direttamente degli esempi didattici applicativi. Diversamente dai capitoli precedenti qui l'approccio è più diretto e si analizzano situazioni concrete. I materiali contenuti in questo capitolo sono stati elaborati nell'ambito di alcuni periodi di attività didattica.

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Indice AnaliticoIndiceGestione DocumentiApplicazioni didattiche
drgeo-doc-1.5/it/drgenius_85.html0000644000175000017500000001107510117134567012352 Manuale di Dr. Geo -- Soluzione di esercizi
Teoremi e congettureApplicazioni didatticheSoluzione di esercizi

Soluzione di esercizi

Uno dei possibili utilizzi didattici di DR. GEO consiste nella possibilità di risolvere, ricorrendo agli script Guile esercizi di geometria. Come esempio mostriamo ora la soluzione di un classico problema di geometria, in cui si applica il teorema di Pitagora, e il cui testo è il seguente:

Sia dato un trapezio rettangolo ABCD di cui sono note le lunghezze delle due basi e dell'altezza. Calcolare perimetro e area del trapezio.

Non è difficile, sulla scia di quanto trattiamo, sviluppare molti altri esempi non necessariamente ristretti all'ambito della Matematica.

Soluzione: Iniziamo costruendo con DR. GEO la figura:

Trapezio rettangolo

Essa comprende i dati e da questi possiamo procedere per risolvere il problema. Innanzitutto possiamo rispondere subito alla domanda riguardante l'area. Per fare questo scriviamo il seguente script Guile che ha come parametri in ingresso basi e altezza del trapezio:

  

(define AB (getLength a1))
(define DC (getLength a2))
(define AD (getLength a3))
(/ ( * AD (+ AB DC )) 2 )

ci calcoliamo quindi la lunghezza del segmento BH scrivendo uno script in Guile i cui oggetti in ingresso sono i segmenti AB e CD:

  

(define AB (getLength a1))
(define CD (getLength a2))
(- AB CD)

A questo punto possiamo applicare il teorema di Pitagora al triangolo rettangolo CHB. Anche qui usiamo uno script Guile che ha come oggetti in ingresso il segmento CH e lo script BH:

  

(define CH (getLength a1))
(define BH (getValue a2))
(+ (* CH CH) (* BH BH))

Finalmente possiamo ricavare la lunghezza del lato obliquo BC calcolando la radice quadrata del valore restituito dallo script precedente:

  

(define q (getValue a1))
( sqrt q )

I due script precedenti potevano essere compendiati in un unico script, ma leggermente più complesso. A questo punto possiamo concludere l'esercizio calcolando il perimetro con lo script Guile:

  

(define AB (getLength a1))
(define CB (getValue  a2))
(define DC (getLength a3))
(define AD (getLength a4))
(+ (+ AB CB )(+ DC AD ))

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Teoremi e congettureApplicazioni didatticheSoluzione di esercizi
drgeo-doc-1.5/it/drgenius_86.html0000644000175000017500000001145410117134567012354 Manuale di Dr. Geo -- Teoremi e congetture
Numeri IrrazionaliApplicazioni didatticheSoluzione di eserciziTeoremi e congetture

Teoremi e congetture

Gli script Guile permettono, altre alla soluzione di esercizi vista sopra, di comprendere con maggiore profondità gli enunciati di teoremi e di verificare congetture.

In questa sezione iniziamo analizzando, a titolo di esempio, il teorema di Tolomeo:

Dato un quadrilatero inscritto in una circonferenza la somma dei prodotti dei lati opposti è uguale al prodotto delle diagonali.

Possiamo facilmente disegnare la figura con DR. GEO ottenendo:

Teorema di Tolomeo: quadrilatero convesso

dove sono anche stati implementati due script che calcolano rispettivamente la somma dei prodotti dei lati opposti del quadrilatero e il prodotto delle diagonali. Lo script per il calcolo della somma dei prodotti dei lati opposti è il seguente

  

(define AB (getLength a1))
(define DC (getLength a2))
(define BC (getLength a3))
(define AD (getLength a4))
(+ (* AB DC )(* BC AD ))

mentre lo script per il calcolo del prodotto delle diagonali è: 

( define DB (getLength a1))
( define AC (getLength a2))
( * DB AC )

Come si vede i valori restituiti dagli script, in accordo con il teorema di Tolomeo, coincidono. Se modifichiamo dinamicamente la figura gli script continuano a concidere a meno che non ci si imbatta nella seguente situazione:

Teorema di Tolomeo: quadrilatero non convesso

ossia quando il quadrilatero perde la convessità.

In questo caso il teorema non vale e quindi l'enunciato precedente non è stato ben formulato e andrebbe precisato meglio scrivendolo come segue:

Dato un quadrilatero CONVESSO inscritto in una circonferenza la somma dei prodotti dei lati opposti è uguale al prodotto delle diagonali.

A questo punto potrebbe venire spontanea la seguente congettura: il teorema di Tolomeo rimane valido per un quadrilatero convesso non inscritto in una circonferenza?

Con DR. GEO possiamo verificare immediatamente la falsità di questa congettura come mostrato in figura:

Falsifichiamo una congettura

Il lettore non avrà difficoltà ad utilizzare il programma per costruire esempi didattici, magari più conosciuti, relativamente ai teoremi di Pitagora e di Euclide.
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Numeri IrrazionaliApplicazioni didatticheSoluzione di eserciziTeoremi e congetture
drgeo-doc-1.5/it/drgenius_87.html0000644000175000017500000001057410117134567012357 Manuale di Dr. Geo -- Numeri Irrazionali
Spirale di BaravelleApplicazioni didatticheTeoremi e congettureNumeri Irrazionali

Numeri Irrazionali

Una costruzione classica riguardante i numeri irrazionali e nota come Spirale di Teodoro permette di costruire geometricamente le radici quadrate dei numeri interi a partire da un triangolo rettangolo isoscele avente cateti di lunghezza unitaria.

Consideriamo il triangolo OAB di figura in cui OA=1:

Costruzione di radice di 2

Per il teorema di Pitagora si ha allora che OB ha lunghezza pari a radice quadrata di 2. Se ora, come in figura, si costruisce un nuovo triangolo rettangolo, retto in B, con cateti OB e BC, di cui l'ultimo di lunghezza unitaria;

Costruzione di radice di 3

sempre per il teorema di Pitagora è chiaro che l'ipotenusa OC di OBC ha lunghezza radice quadrata di 3. Iterando il procedimento si ottengono facilmente tutte le radici quadrate dei numeri naturali.

La natura iterativa della costruzione si presta ad un trattamento tramite FSD. Consideriamo allora il seguente codice Scheme: 

(new-figure "Triangoli")

(define (triangle p1 p2 p3 n)
  
  (let* ((s1 (Segment "" extremities    p1 p2))
         (s2 (Segment "" extremities    p2 p3))
         (s3 (Segment "" extremities    p3 p1))
         (pe (Line    "" orthogonal     p3 s3))
         (ci (Circle  "" center-segment p3 s2))
         (p4 (Point   "" intersection2  pe ci)))

    (send pe masked)
    (send ci masked)
    (send p4 masked)

(if (> n 0)

    (triangle p1 p3 p4 (- n 1)))))


(lets Point "O" free  0  0)
(lets Point "A" free -1  0)
(lets Point "B" free -1  1)

(triangle O A B 15)

Il triangolo di partenza è definito attraverso le coordinate esclusivamente per comodità. Il codice è la trascrizione letterale del procedimento iterativo descritto sopra. Una volta valutato da DR. GEO viene restituita la figura seguente:

Spirale di Teodoro

L'ipotenusa di ogni triangolo ha lunghezza eguale alla radice quadrata di un numero naturale compreso tra 2 e 17.
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Spirale di BaravelleApplicazioni didatticheTeoremi e congettureNumeri Irrazionali
drgeo-doc-1.5/it/drgenius_88.html0000644000175000017500000001134710117134567012357 Manuale di Dr. Geo -- Spirale di Baravelle
Catena di PappoApplicazioni didatticheNumeri IrrazionaliSpirale di Baravelle

Spirale di Baravelle

Come abbiamo visto in precedenza, attraverso una FSD è possibile costruire in modo semplice e intuitivo, una figura che permette di "visualizzare" ciò che in programmazione è un ciclo.

Possiamo approfondire questo aspetto, modificando di poco il codice Scheme utilizzato per la costruzione dei numeri irrazionali, per ottenere una figura nota in letteratura come spirale di Baravelle. Il codice Scheme che definisce la spirale è il seguente: 

(new-figure "Baravelle")
 
 (define (triangle p1 p2 p3 n)
   
   (let* ((s1  (Segment "" extremities    p1 p2))
          (s2  (Segment "" extremities    p2 p3))
          (s3  (Segment "" extremities    p3 p1))
          (m   (Point   "" middle-2pts    p1 p3))
          (r   (Segment "" extremities    m  p3))
          (pe  (Line    "" orthogonal     p3 s3))
          (ci  (Circle  "" center-segment p3 r ))
          (p4  (Point   "" intersection2  pe ci)))
 
     (send pe  masked)
     (send ci  masked)
     (send p4  masked)
     (send m   masked)
 
 (if (> n 0)
 
     (triangle  m  p3  p4 (- n 1)))))
   
 
 (lets Point "A" free  0  5)
 (lets Point "B" free  5  5)
 (lets Point "C" free  5  0)
 
 (triangle A B C 9)
 
 (lets Point "D" free  0 -5)
 (lets Point "E" free -5 -5)
 (lets Point "F" free -5  0)
 
 (triangle D E F 9)

La figura nota come spirale di Baravelle è:

Spirale di Baravelle

Dalla figura e dal codice Scheme si intuisce la struttura iterativa alla base della costruzione.

Un problema interessante, che lasciamo al lettore, consiste nello stabilire dove convergono i due rami della spirale.

Una variazione ulteriore del codice precedente: 

(new-figure "Spiral")

 (define (square p1 p2 p3 p4 n)

 (let* ((s1 (Segment "" extremities p1 p2))
 (s2 (Segment "" extremities p2 p3))
 (s3 (Segment "" extremities p3 p4))
 (s4 (Segment "" extremities p4 p1))
 (A (Point "" on-curve s1 1/10))
 (B (Point "" on-curve s2 1/10))
 (C (Point "" on-curve s3 1/10))
 (D (Point "" on-curve s4 1/10)))

 (send A masked)
 (send B masked)
 (send C masked)
 (send D masked)

 (if (> n 0)

 (square A B C D (- n 1)))))


 (lets Point "M" free 5 5)
 (lets Point "N" free -5 5)
 (lets Point "O" free -5 -5)
 (lets Point "P" free 5 -5)

(square M N O P 30)

conduce alla spirale rappresentata in figura:

Spirale

Il lettore è invitato a divertirsi creandone di nuove generalizzando la costruzione precedente!
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Catena di PappoApplicazioni didatticheNumeri IrrazionaliSpirale di Baravelle
drgeo-doc-1.5/it/drgenius_89.html0000644000175000017500000000667010117134567012363 Manuale di Dr. Geo -- Catena di Pappo
Calcolo di PigrecoApplicazioni didatticheSpirale di BaravelleCatena di Pappo

Catena di Pappo

Un utilizzo base delle Figure Scheme per Dr. Geo consiste nella riproduzione di figure di cui sono note le caratteristiche analitiche.

L'esempio di costruzione che proponiamo è rappresentato dalla famosa catena di Pappo.

Catena di Pappo

Centri e raggi della successione di circonferenze che la formano hanno un'espressione analitica nota ed quindi è molto semplice implementarla per riprodurre la figura come FSD. 

(new-figure "Pappo")

(define (circle n)
(let*(
(r (Numeric "" free 0 0 (/ 15 ( + 6 (* n n )))))
(c (Point   "" free (* 5 (/ 15 ( + 6 (* n n )))) 
(* 2 (* n (/ 15 ( + 6 (* n n )))))))
(p (Circle "" center-radius c r )))

(send r masked)

(if (> n 0)
    (circle (- n 1)))))

(circle 8)

(lets Point "A" free 5 0)
(lets Point "O" free 0   0)
(lets Point "B" free 15 0)
(lets Point "M" middle-2pts B O)
(lets Circle "" 2points M O)
(lets Circle "" 2points A O)
(lets Line   "" 2points A O)

Il significato del codice è molto intuitivo e non ha bisogno di commenti. Un esercizio, che fa leva sull'inversione circolare, consiste nel determinare una costruzione con riga e compasso che permetta di generare la catena. Il lettore interessato a questo può consultare il libro di Maria Dedò intitolato Trasformazioni Geometriche.

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Calcolo di PigrecoApplicazioni didatticheSpirale di BaravelleCatena di Pappo
drgeo-doc-1.5/it/drgenius_8.html0000644000175000017500000000450710117134567012267 Manuale di Dr. Geo -- Punto medio
Punti di intersezioneCostruzione di punti Punto liberoPunto medio

Punto medio

 

Selezionando questo comando si può costruire il punto medio o di un segmento o di una coppia di punti dati. Nel primo caso il punto medio si ottiene cliccando con il mouse direttamente sul segmento. Nel secondo caso il punto medio si ottiene cliccando in sequenza sui due punti dati.

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Punti di intersezioneCostruzione di punti Punto liberoPunto medio
drgeo-doc-1.5/it/drgenius_90.html0000644000175000017500000000725310117134567012351 Manuale di Dr. Geo -- Calcolo di Pigreco
Esportazione di figure e testiApplicazioni didatticheCatena di PappoCalcolo di Pigreco

Calcolo di Pigreco

Il calcolo approssimato di pigreco riveste nella storia della Matematica un ruolo importante. I metodi di approccio a questo tipo di calcolo sono risultati tra i più diversi e spesso contengono raffinatezze. Qui proponiamo un approccio molto semplificato al problema che chiamiamo, anche se non del tutto propriamente, Metodo di esaustione che contiene l'essenza della questione.

Iniziamo con la seguente costruzione di un esagono inscritto in una circonferenza a partire dal lato BC. Notiamo di passaggio che da questa costruzione è possibile costruire e memorizzare una macro che possiamo chiamare Esagono.

Esagono regolare inscritto

L'idea del metodo di esaustione consiste, al primo passo, nell'approssimare la lunghezza della circonferenza con il perimetro P0 dell'esagono e nel calcolare un'approssimazione di Pigreco dividendo P0 per il diametro della circonferenza. Chiaramente l'approssimazione che si ottiene per Pigreco è 3.

Al secondo passo possiamo, utilizzando Dr. Geo, costruire il lato del dodecagono inscritto nella circonferenza, calcolarci il perimetro P1, e calcolare una successiva approssimazione di Pigreco dividendo P1 per il diametro.

Approssimazione di Pigreco

Aumentando il numero di lati del poligono inscritto si otterranno chiaramente approssimazioni sempre migliori.
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Esportazione di figure e testiApplicazioni didatticheCatena di PappoCalcolo di Pigreco
drgeo-doc-1.5/it/drgenius_91.html0000644000175000017500000000436710117134567012355 Manuale di Dr. Geo -- Esportazione di figure e testi
Applicazioni didatticheCalcolo di PigrecoEsportazione di figure e testi

Esportazione di figure e testi

Spesso per uso didattico è utile poter stampare le figure o esportarle come immagini in qualche formato che permetta il loro inserimento in documenti di altro genere.

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Applicazioni didatticheCalcolo di PigrecoEsportazione di figure e testi
drgeo-doc-1.5/it/drgenius_92.html0000644000175000017500000000620210117134567012344 Manuale di Dr. Geo -- Stampa di una figura
Inserire un testo in una figuraEsportazione di figure e testiStampa di una figura

Stampa di una figura

Il modo più semplice per stampare una figura consiste prima nell'esportarla in PostScript e quindi di utilizzare un sostware come Ghostview o un suo derivato per stamparla direttamente. Naturalmente la figura esportata può essere, se necessario, inserita in altri documenti come immagine. Si ricorda che il formato PostScript garantisce all'immagine una qualità vettoriale.

Per gli utilizzatori di TeX è disponibile l'esportazione di figure attraverso il pacchetto Pstrick. L'immagine che si ottiene si integra perfettamente nel testo TeX tuttavia di essa non si può eseguire, o almeno sembra, alcun rididmensionamento.

Un ultimo tipo di esportazione, recentemente introdotto in DR. GEO, riguarda l'esportazione in formato PNG attraverso il pacchetto Image Magick.

In tutti questi casi l'utilizzatore può preventivamente selezionare, attraverso il comando File -> Preferenze Esportazione -> Definisci l'area di stampa, la porzione di figura da stampare e, successivamente, attraverso il comando File -> Preferenze Esportazione -> Rimuovi l'area di stampa, rimuovere l'area di stampa definita in precedenza.

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Inserire un testo in una figuraEsportazione di figure e testiStampa di una figura
drgeo-doc-1.5/it/drgenius_93.html0000644000175000017500000000614510117134567012353 Manuale di Dr. Geo -- Inserire un testo in una figura
Esportazione di figure e testiStampa di una figuraInserire un testo in una figura

Inserire un testo in una figura

Per inserire un testo all'interno di una figura è possibile utilizzare l'utilità script - script Guile - creando uno script senza passare ad esso alcun oggetto. Per fare questo è sufficiente cliccare sul comando che attiva la funzionalità di script e cliccare direttamente in un punto del foglio di lavoro dove si desidera collocare il testo.

A questo punto comparirà la scritta "Drgenius" e potremo editare lo script andando ad inserire tra le virgolette, dove tipicamente viene inserito il codice Guile/Scheme da eseguire, il testo desiderato.

Nell'esempio che segue una tassellazione di Keplero viene accompagnata dal seguente richiamo: 


"Il Motivo Z 
===========================

Tratto dall'Harmonice Mundi  di Johannes Kepler
si costruisce un pentagono formato da oggetti
a simmetria pentagonale."

Un esempio di testo in una figura

Come per ogni script è stato possibile modificare il colore del testo.
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Esportazione di figure e testiStampa di una figuraInserire un testo in una figura
drgeo-doc-1.5/it/drgenius_94.html0000644000175000017500000002614310117134567012354 Manuale di Dr. Geo -- Indice Analitico
GNU Free Documentation LicenseIndiceApplicazioni didatticheIndice Analitico

Indice Analitico

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A
Angolo: - geometrico -
Angolo: - orientato -
Arco di circonferenza - -
Arco di circonferenza: - lunghezza -
C
Circonferenza - -
Circonferenza: - lunghezza -
F
Figura - Inserire - Testo
Figura: - apri -
Figura: - rinomina -
Figura: - salva -
Figura: - stampa -
Figure Scheme per DR. GEO : - costruzione di oggetti -
Figure Scheme per DR. GEO : - costruzione di oggetti: - arco
Figure Scheme per DR. GEO : - costruzione di oggetti: - attributi oggetto
Figure Scheme per DR. GEO : - costruzione di oggetti: - circonferenza
Figure Scheme per DR. GEO : - costruzione di oggetti: - luogo
Figure Scheme per DR. GEO : - costruzione di oggetti: - numeri
Figure Scheme per DR. GEO : - costruzione di oggetti: - poligono
Figure Scheme per DR. GEO : - costruzione di oggetti: - punto
Figure Scheme per DR. GEO : - costruzione di oggetti: - retta
Figure Scheme per DR. GEO : - costruzione di oggetti: - segmento
Figure Scheme per DR. GEO : - costruzione di oggetti: - semiretta
Figure Scheme per DR. GEO : - costruzione di oggetti: - trasformazioni geometriche
Figure Scheme per DR. GEO : - costruzione di oggetti: - vettore
Figure Scheme per DR. GEO : - esempi -
Figure Scheme per DR. GEO : - esempi -
Figure Scheme per DR. GEO : - esempi: - catena di Pappo
Figure Scheme per DR. GEO : - esempi: - frattale
Figure Scheme per DR. GEO : - esempi: - poligono regolare
Figure Scheme per DR. GEO : - esempi: - spirale di Baravelle
Figure Scheme per DR. GEO : - esempi: - spirale di Teodoro
Figure Scheme per DR. GEO : - introduzione -
Figure Scheme per DR. GEO : - nuova figura -
I
Inserire - Testo -
L
Luogo - -
Luogo: - script -
M
Macro-costruzione - -
Macro-costruzione: - apri -
Macro-costruzione: - crea -
Macro-costruzione: - esegui -
Macro-costruzione: - introduzione -
Macro-costruzione: - salva -
Modifica: - preferenze di default -
Modifica: - preferenze di default: - annulla/rifai
Modifica: - preferenze di default: - nomi
Modifica: - proprietà -
Modifica: - punto -
Modifica: - script -
Modifica: - stile -
Modifica: - stile di default -
Modifica: - valore -
N
Numero - -
Numero: - valore libero -
O
Oggetto geometrico: - cancella -
Oggetto geometrico: - nascondi -
Oggetto geometrico: - rinomina -
Oggetto geometrico: - spostamento di -
P
Poligono - -
Punto: - coordinate di -
Punto: - definito attraverso coordinate -
Punto: - di intersezione -
Punto: - libero -
Punto: - medio -
R
Retta - -
Retta - parallela -
Retta - perpendicolare -
Retta: - distanza da -
Retta: - pendenza -
S
Script - -
Script: - esempi -
Script: - intervallo -
Script: - introduzione -
Script: - numeri casuali -
Script: - parametri -
Script: - tangente a un grafico -
Script: - area trapezio -
Script: - getAbscissa -
Script: - getAngle -
Script: - getCenter -
Script: - getCoordinates -
Script: - getLength -
Script: - getLength -
Script: - getNorm -
Script: - getRadius -
Script: - getSlope -
Script: - getValue -
Script: - move -
Script: - perimetro -
Script: - radice quadrata -
Script: - segmento differenza -
Script: - setAbscissa -
Script: - setCoordinates -
Script: - setValue -
Script: - teorema di Pitagora -
Script: - teorema di Tolomeo -
Segmento - -
Segmento: - lunghezza -
Semiretta - -
Sessione: - apri -
Sessione: - salva -
Stampa: - figura -
Strumenti: - blocco -
Strumenti: - sblocco -
T
Tranformazioni del piano: - rotazione -
Trasformazioni del piano: - omotetia -
Trasformazioni del piano: - riflessione -
Trasformazioni del piano: - simmetria - centrale
Trasformazioni del piano: - traslazione -
Trasformazioni: - figure Scheme per DR. GEO-
V
Vettore - -
Vettore: - coordinate di -
Vettore: - norma -
Hai domande o commenti da fare?
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GNU Free Documentation LicenseIndiceApplicazioni didatticheIndice Analitico
drgeo-doc-1.5/it/drgenius_95.html0000644000175000017500000005637210117134567012364 Manuale di Dr. Geo -- GNU Free Documentation License
FootnotesIndiceIndice AnaliticoGNU Free Documentation License

GNU Free Documentation License


                GNU Free Documentation License
                  Version 1.2, November 2002


 Copyright (C) 2000,2001,2002  Free Software Foundation, Inc.
     59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 Everyone is permitted to copy and distribute verbatim copies
 of this license document, but changing it is not allowed.


0. PREAMBLE

The purpose of this License is to make a manual, textbook, or other
functional and useful document "free" in the sense of freedom: to
assure everyone the effective freedom to copy and redistribute it,
with or without modifying it, either commercially or noncommercially.
Secondarily, this License preserves for the author and publisher a way
to get credit for their work, while not being considered responsible
for modifications made by others.

This License is a kind of "copyleft", which means that derivative
works of the document must themselves be free in the same sense.  It
complements the GNU General Public License, which is a copyleft
license designed for free software.

We have designed this License in order to use it for manuals for free
software, because free software needs free documentation: a free
program should come with manuals providing the same freedoms that the
software does.  But this License is not limited to software manuals;
it can be used for any textual work, regardless of subject matter or
whether it is published as a printed book.  We recommend this License
principally for works whose purpose is instruction or reference.


1. APPLICABILITY AND DEFINITIONS

This License applies to any manual or other work, in any medium, that
contains a notice placed by the copyright holder saying it can be
distributed under the terms of this License.  Such a notice grants a
world-wide, royalty-free license, unlimited in duration, to use that
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A "Modified Version" of the Document means any work containing the
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A "Secondary Section" is a named appendix or a front-matter section of
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The "Invariant Sections" are certain Secondary Sections whose titles
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The "Cover Texts" are certain short passages of text that are listed,
as Front-Cover Texts or Back-Cover Texts, in the notice that says that
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A "Transparent" copy of the Document means a machine-readable copy,
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10. FUTURE REVISIONS OF THIS LICENSE

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ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of
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FootnotesIndiceIndice AnaliticoGNU Free Documentation License
drgeo-doc-1.5/it/drgenius_96.html0000644000175000017500000000543610117134567012360 Manuale di Dr. Geo -- Footnotes
IndiceGNU Free Documentation LicenseFootnotes

Footnotes

 (1)
Le macro costituiscono l'aspetto geometrico, gli script, quello numerico di un programma nato all'insegna di uno spirito "hacker"
 (2)
Se per errore sono stati selezionati oggetti indesiderati per annullare la selezione è sufficiente cliccare nuovamente sul comando per attivare uno script.
 (3)
Indipendentemente dal tipo di segmento di curva l'ascissa curvilinea è un numero reale appartenente all'intervallo [0;1]
 (4)
File che comprendono più documenti di DR. GEO (figure e/o testi)
 (5)
Da un punto di vista interno al linguaggio Scheme, i riferimenti sono dei simboli che puntano ad una struttura interna all'oggetto - un prototipo - nel momento in cui i nomi sono stringhe di caratteri.
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IndiceGNU Free Documentation LicenseFootnotes
drgeo-doc-1.5/it/drgenius_9.html0000644000175000017500000000453310117134567012267 Manuale di Dr. Geo -- Punti di intersezione
Punto definito attraverso coordinateCostruzione di punti Punto medioPunti di intersezione

Punti di intersezione

 

Selezionando questo comando si ottengono uno o più punti di intersezione tra due oggetti geometrici dati. Per creare i punti di intersezione è necessario cliccare con il mouse in sequenza sui due oggetti geometrici da intersecare.

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Punto definito attraverso coordinateCostruzione di punti Punto medioPunti di intersezione
drgeo-doc-1.5/it/drgenius_guile_script.html0000644000175000017500000000777110117134567014617 Manuale di Dr. Geo -- Script Guile per DR. GEO
Blocco di strumenti dell'interfacciaFunzioni AvanzateMacro-costruzioniScript Guile per DR. GEO

Script Guile per DR. GEO

Il software DR. GEO è compatible con Guile; ciò significa che con DR. GEO è possibile eseguire degli script Scheme che si appoggiano all'interprete Guile. Ma, che cos'è Guile? Se andiamo a leggere l'inizio del manuale di Guile troviamo scritto:

Guile è un interprete per il linguaggio di programmazione Scheme che può essere utilizzato in molti ambienti.

La citazione seguente descrive in modo più preciso come utilizzare Guile in DR. GEO:

Analogamente ad un terminale, Guile può essere lanciato in modo interattivo, può ricevere espressioni scritte dall'utilizzatore, elaborarle e restituire dei risultati. Alternativamente come interprete di script, Guile è in grado di leggere ed eseguire un codice Scheme contenuto in un file. In questo modo Guile è disponibile, sotto forma di biblioteca, per permettere ad applicazioni di vario tipo di incorporare facilmente e in modo completo un interprete Scheme. Una applicazione può utilizzare Guile come un languaggio potente di estensione o di autoconfigurazione, o come un adesivo universale per "incollare" funzioni primitive fornite dall'applicazione.

In DR. GEO, una API viene resa disponibile a partire dall'interprete Guile. L'utilizzatore di DR. GEO, attraverso gli script può manipolare opportunamente oggetti (geometrici o numerici) contenuti in una figura. Oltre a questo, dal momento che uno script viene considerato un oggetto come altri non vi è alcun bisogno di salvarlo separatamente dalla figura in cui è contenuto. D'ora in poi, per indicare uno script Guile, utilizzeremo sempre l'acronimo DGS ("DR. GEO Guile Script").

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Blocco di strumenti dell'interfacciaFunzioni AvanzateMacro-costruzioniScript Guile per DR. GEO
drgeo-doc-1.5/it/drgenius.html0000644000175000017500000000343510117134567012037 Manuale di Dr. Geo

Manuale di DR. GEO

Hilaire Fernandes
Andrea Centomo
OFSET
http://www.ofset.org

29 agosto 2004

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drgeo-doc-1.5/it/editing_object_styles.html0000644000175000017500000001032510117134567014567 Manuale di Dr. Geo -- Modificare lo stile di un oggetto
Modificare le proprietà di un oggettoAltre funzioniCancellazione di un oggetto geometricoModificare lo stile di un oggetto

Modificare lo stile di un oggetto

 

Selezionando questo comando si può modificare lo stile proprio di un oggetto che è definito dalle seguenti caratteristiche: colore, spessore, etichetta, dimensione e forma. Oltre a questo è possibile nascondere temporaneamente un oggetto presente in una costruzione senza tuttavia cancellarlo. Ciò può essere utile per gli oggetti geometrici che dopo essere stati usati in una costruzione geometrica non si desidera siano visibili. Quando, dopo aver selezionato questo comando, si clicca con il mouse su un oggetto, compare una finestra di dialogo che permette di modificare tutte le sue proprietà.

La finestra di dialogo ha preferenze leggermente diverse in relazione al particolare tipo di oggetto geometrico. La finestra di dialogo relativa ai punti è rappresentata in figura:

Finestra di dialogo stile Punto

e si nota che questa finestra è diversa da quella relativa alle linee (retta, semiretta, vettore, ecc...) rappresentata più in basso. Dal momento che questi oggetti vengono definiti specificando una coppia di punti essi non possono essere rinominati in quanto il loro nome viene riferito al nome della coppia di punti che li definisce.

Finestra di dialogo stile Linea

Una finestra del tutto analoga permette di modificare anche lo stile di una circonferenza, di un arco e di un luogo.

Una terza finestra di dialogo permette di modificare lo stile in cui vengono presentati i diversi valori numerici (direttamente editati dall'utente, generati da uno script Guile per DR. GEO o altro) e l'aspetto dei poligoni:

Finestra di dialogo stile Numeri e Poligoni

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Modificare le proprietà di un oggettoAltre funzioniCancellazione di un oggetto geometricoModificare lo stile di un oggetto
drgeo-doc-1.5/it/introduction.html0000644000175000017500000001116510117134567012737 Manuale di Dr. Geo -- Introduzione
Funzioni BaseIndiceCopyrightIntroduzione

Introduzione

DR. GEO è un programma Gnome per lo studio interattivo della geometria euclidea e della programmazione Scheme. Utilizzando DR. GEO è possibile creare costruzioni geometriche e manipolarle in modo da mantenere inalterate le loro proprietà geometriche fondamentali ed introdurre lo studente in modo graduale alla programmazione. DR. GEO rappresenta, in questo senso, un ottimo ausilio per la didattica della Matematica nel ciclo di istruzione primario e secondario.

La schermata iniziale di DR. GEO

La schermata iniziale evidenzia in alto due barre:
  1. la barra dei menu caratterizzata dalle voci File, Modifica, Aiuto;
  2. la barra delle azioni: aprire una nuova figura, aprire un nuovo foglio di testo, annullare o ripetere un comando.

Per creare una nuova figura geometrica è sufficiente cliccare sul primo bottone nella barra delle azioni. Alternativamente si può cliccare sull'opzione File -> Nuovo -> Figura della barra dei menu. Non appena creata una nuova figura geometrica, oltre ad un foglio da disegno bianco, comparirà la barra delle icone, che contiene sette icone fondamentali e che si conclude con un menu per l'aggiustamento della scala della figura geometrica corrente.

Schermata iniziale di una costruzione geometrica

Le prime sei icone della barra delle icone contengono dei sottomenu a tendina relativi alle funzioni base e avanzate di DR. GEO per la cui descrizione si rimanda al capitolo successivo.

Una figura geometrica in DR. GEO e la sua descrizione

Ogni figura è accompagnata da un albero sinottico che riassume le costruzioni eseguite. Inizialmente l'albero è coperto in modo che solo il foglio di lavoro risulti visibile. In ogni momento l'utilizzatore può aprirlo con la seguente procedura: si porta il mouse a sinistra del righello verticale che delimita il foglio di lavoro fino a quando, nella zona centrale, la freccia del puntatore assume la forma <->; si clicca quindi con il tasto sinistro del mouse e tenendo premuto ci si sposta verso destra quanto si desidera allargare l'albero. L'albero, che descrive la figura geometrica corrente, presenta dei nodi che possono essere espansi o compressi cliccando su linguette triangolari.
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Funzioni BaseIndiceCopyrightIntroduzione
drgeo-doc-1.5/it/line_tools.html0000644000175000017500000000463110117134567012365 Manuale di Dr. Geo -- Costruzione di linee
Trasformazioni del pianoStrumenti di CostruzioneCostruzione di punti Costruzione di linee

Costruzione di linee

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Trasformazioni del pianoStrumenti di CostruzioneCostruzione di punti Costruzione di linee
drgeo-doc-1.5/it/macroconstruction_tools.html0000644000175000017500000000450310117134567015210 Manuale di Dr. Geo -- Strumenti per la costruzione di macro
Strumenti di CostruzioneStrumenti numericiStrumenti per la costruzione di macro

Strumenti per la costruzione di macro

La costruzione di macro rappresenta uno degli aspetti essenziali di DR. GEO in quanto in questo modo possiamo ampliare indefinitamente il numero degli strumenti di costruzione in esso presenti.

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Strumenti di CostruzioneStrumenti numericiStrumenti per la costruzione di macro
drgeo-doc-1.5/it/numeric_tools.html0000644000175000017500000000460310117134567013077 Manuale di Dr. Geo -- Strumenti numerici
Strumenti per la costruzione di macroStrumenti di CostruzioneTrasformazioni del pianoStrumenti numerici

Strumenti numerici

Questo menu permette di editare e manipolare valori numerici.

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Strumenti per la costruzione di macroStrumenti di CostruzioneTrasformazioni del pianoStrumenti numerici
drgeo-doc-1.5/it/other_tools.html0000644000175000017500000000456210117134567012562 Manuale di Dr. Geo -- Altre funzioni
PreferenzeFunzioni BaseStrumenti di CostruzioneAltre funzioni

Altre funzioni

In questo capitolo si analizzano le funzioni per manipolare dinamicamente i diversi oggetti geometrici.

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PreferenzeFunzioni BaseStrumenti di CostruzioneAltre funzioni
drgeo-doc-1.5/it/point_tools.html0000644000175000017500000000417410117134567012571 Manuale di Dr. Geo -- Costruzione di punti
Costruzione di lineeStrumenti di CostruzioneCostruzione di punti

Costruzione di punti

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Costruzione di lineeStrumenti di CostruzioneCostruzione di punti
drgeo-doc-1.5/it/transformation_tools.html0000644000175000017500000000473410117134567014510 Manuale di Dr. Geo -- Trasformazioni del piano
Strumenti numericiStrumenti di CostruzioneCostruzione di lineeTrasformazioni del piano

Trasformazioni del piano

Questo menu permette di studiare le isometrie del piano euclideo e le trasformazioni omotetiche.

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Strumenti numericiStrumenti di CostruzioneCostruzione di lineeTrasformazioni del piano
drgeo-doc-1.5/it/using_macro.html0000644000175000017500000000775010117134567012531 Manuale di Dr. Geo -- Macro-costruzioni
Script Guile per DR. GEOFunzioni AvanzateMacro-costruzioni

Macro-costruzioni

La costruzione di una macro è una procedura attraverso la quale è possibile aggiungere a DR. GEO una nuova costruzione. Come in ogni costruzione geometrica si definiscono un certo numero di oggetti geometrici in ingresso e si ottengono alcuni oggetti geometrici in uscita. L'utilizzatore di DR. GEO stabilisce gli oggetti iniziali e finali della macro-costruzione, che poi verrà salvata in un file con estensione .mgeo.

La costruzione di una macro deve essere logicamente coerente: gli oggetti finali della macro devono dipendere in modo esclusivo dagli oggetti iniziali in modo che DR. GEO possa ricostruire senza ambiguità l'intera costruzione. Da questo punto di vista DR. GEO è in grado di memorizzare la sequenza della costruzione e di riprodurla ogni volta che l'utilizzatore, dopo aver azionato il comando di esecuzione di una macro, andrà a cliccare su oggetti geometrici che coincidono con gli oggetti in ingresso della macro.

(!) Quando si esegue una macro vengono ricostruiti tutti gli oggetti geometrici intermedi necessari per la costruzione degli oggetti finali della macro.

Per illustrare il modo in cui avviene la costruzione di una macro analizziamo in dettaglio, come esempio, la costruzione di una circonferenza passante per tre punti dati.

Figura iniziale

 

Prima di creare una macro-costruzione è necessario eseguire la costruzione che porta agli oggetti finali in modo da rendere disponibile a DR. GEO un modello. Nel nostro caso la costruzione è la seguente:

Figura finale

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Script Guile per DR. GEOFunzioni AvanzateMacro-costruzioni
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Other copyright apply to the respective owners of the modified documentations. See the section history for the complet list. \xname{inleiding} \chapter{Inleiding} \drgenius{} is het programma voor interactieve meetkunde van Gnome. Je kan er meetkundige figuren mee tekenen en deze interactief manipuleren, rekening houdende met hun meetkundige eigenschappen. Het programma is bruikbaar in lessituaties zowel in het lager als in het middelbaar onderwijs. De gebruikersinterface van \drgeo\ werd ontworpen om eenvoud in gebruik, ergonomie en gevorderde functies op een harmonische wijze met elkaar te verzoenen. Door de grote eenvoud van de \drgeo-interface raakt de beginner onmiddellijk uit de voeten met de basisfuncties. Naarmate hij de uithoeken van de interface en de werking van \drgeo\ verkent, dienen de voortgezette functies zich aan~: verschillende constructiewijzen van eenzelfde object\footnote{Met eenzelfde commando is het mogelijk een bepaald type object op verschillende wijzen te creëren. Wanneer je, bij voorbeeld, het commando `cirkel tekenen' gebruikt, kan je een cirkel definiëren aan de hand van het middelpunt enerzijds en een ander punt, een lengte (van de straal) of een lijnstuk (met de lengte van de straal) anderzijds.}, macro-constructies, sessies, aanpassing van de interface, scriptmogelijkheden en \drgeo{} Scheme figuren. De gevorderde functies blijken de interface niet te beladen, zodat men er aangenaam gebruik van kan maken in het lager onderwijs. Ook in het middelbaar onderwijs is het gebruik een makkie. In de gedeelten die volgen worden de basisfuncties uit de doeken gedaan. Vervolgens worden de voorgezette functies in detail behandeld. \drgeniusFigureSize{Opstartscherm van \drgenius}{fig1}{8} Om een meetkundige figuur te tekenen, kan je drukken op de eerste knop van de taakbalk. Een andere manier om dit te doen is via het menu \drgeniusMenu{Bestand->Nieuwe...->Figuur}. Wanneer je een nieuwe figuur hebt gecreëerd, verschijnt een nieuwe taakbalk met zes iconen. Op het einde van de balk staat een menu dat toelaat de schaal van de huidige meetkundige figuur aan te passen. \drgeniusFigureSize{Een lege meetkundige figuur}{fig2}{8} Via de zes iconen op de taakbalk krijg je toegang tot menu's voor specifieke functies. In het volgende hoofdstuk staan die functies beschreven. \drgeniusFigureSize{Een \drgenius-figuur en zijn beschrijving}{fig50}{8} Bij elke figuur hoort een beschrijving in een paneel. Dit paneel wordt standaard uiterst links geplaatst zodat aanvankelijk enkel de tekening van de figuur zichtbaar is. De gebruiker kan echter op elk moment het paneel naar rechts opschuiven en zo de beschrijving zichtbaar maken. Een beschrijving van een figuur is een boomstructuur waarin alle elementen van de figuur een plaats krijgen. Om de relaties tussen de elementen zichtbaar te maken, kan je op het `+'-teken klikken. Zo zie je de elementen waarmee een ander deel van de figuur werd opgebouwd. \chapter{Basisfuncties} Dit hoofdstuk beschrijft de instrumenten om een meetkundige figuur te construeren. Op het einde wordt getoond hoe de gebruiker zijn persoonlijke voorkeuren kan instellen. \section{Tekeninstrumenten} Deze instrumenten zijn in zes groepen onderverdeeld. Je krijgt toegang tot die groepen op de tweede taakbalk van \drgenius. \drgeniusFigureSize{De categorieën van de instrumenten van \drgenius{} en hun beschrijving}{fig3}{12} Wanneer je op een icoontje klikt waar een klein groen driehoekje opgetekend staat, komt ogenblikkelijk een nieuwe verticale taakbalk te voorschijn. Zo'n balk bevat alle functies van dezelfde familie. Van links naar rechts, hebben we toegang tot de verticale taakbalken om punten en lijnen te construeren, om transformaties in het vlak uit te voeren, om waarden te berekenen, macro-constructies te gebruiken en zaken aan te passen --~\emph{Verschillende instrumenten} op de figuur. Al deze functies zijn eveneens te selecteren via een contextueel menu dat verschijnt wanneer je met de rechtermuisknop klikt op de achtergrond van een figuur. \xname{point_tools} \subsection{Instrumenten die punten betreffen} \subsubsection{Willekeurig punt} \drgeniusIcon{fig4} \label{free_point} \drgeniusIndex{Punt}{Willekeurig}{}{} Tekent een willekeurig punt in het vlak of op een eendimensioneel object. In het eerste geval, kan men het punt achteraf overal verplaatsen in het vlak. Je tekent het punt door eenvoudigweg te klikken op gewenste plaats in het vlak. In het laatste geval kan het punt enkel vrij bewegen op het eendimensionele object (de rechte, etc.) waarop het punt oorspronkelijk werd getekend~; het punt plakt er als het ware aan vast. Om een dergelijk punt te tekenen, klik je op een drager (i.e.\ een rechte, een halfrechte, een lijnstuk, een cirkel, een cirkelboog, etc.). \subsubsection{Middelpunt} \drgeniusIcon{fig5} \drgeniusIndex{Punt}{Middelpunt}{}{} Tekent het middelpunt ofwel tussen twee punten ofwel van een lijnstuk. In het eerste geval, selecteert de gebruiker twee punten. In het laatste geval, selecteer je eenvoudigweg het gewenste lijnstuk. \subsubsection{Snijpunt} \drgeniusIcon{fig6} \drgeniusIndex{Punt}{Snijpunt}{}{} Tekent het of de snijpunten van twee lijnen (i.e.\ een rechte, halfrechte, lijnstuk, cirkelboog, cirkel). De gebruiker dient twee lijnen te selecteren. \subsubsection{Punt gedefinieerd door zijn coördinaten} \drgeniusIcon{fig7} \label{coordinate_point} \drgeniusIndex{Punt}{Gedefinieerd door coördinaten}{}{} Tekent een punt, gedefinieerd door zijn coördinaten. De gebruiker voert twee getallen in, waarbij het eerste als abscis, en het tweede als ordinaat van het punt geldt. \xname{line_tools} \subsection{Instrumenten die lijnen betreffen} \subsubsection{Rechte} \drgeniusIcon{fig8} \drgeniusIndex{Rechte}{}{}{} Tekent een rechte, door twee punten gedefinieerd. De gebruiker selecteert twee punten. \subsubsection{Halfrechte} \drgeniusIcon{fig9} \drgeniusIndex{Halfrechte}{}{}{} Tekent een halfrechte, bepaald door twee punten. De gebruiker selecteert twee punten. Het eerste punt vormt de oorsprong van de halfrechte, het tweede wordt een willekeurig punt op de halfrechte. \subsubsection{Lijnstuk} \drgeniusIcon{fig10} \drgeniusIndex{Lijnstuk}{}{}{} Tekent een lijnstuk, begrensd door twee punten. \subsubsection{Vector} \drgeniusIcon{fig11} \drgeniusIndex{Vector}{}{}{} Tekent een vector, bepaald door twee punten. De gebruiker selecteert twee punten, waarvan het eerste als aangrijpingspunt geldt en het tweede het grenspunt is. \subsubsection{Cirkel} \drgeniusIcon{fig12} \drgeniusIndex{Cirkel}{}{}{} Tekent een cirkel. Men kan op verschillende manieren een cirkel tekenen. Men maakt een van drie volgende selecties~: \begin{enumerate} \item het middelpunt en een punt op de cirkel~; \item het middelpunt en een getal (de straal van de cirkel)~; \item de cirkel en een lijnstuk, dat de lengte van de straal bepaalt. \end{enumerate} \subsubsection{Cirkelboog} \drgeniusIcon{fig13} \drgeniusIndex{Cirkelboog}{}{}{} Tekent een cirkelboog, bepaald door drie punten. Het eerste is het beginpunt van de boog, het derde is het eindpunt van de boog, en het tweede punt is een (willekeurig) punt op de boog. \subsubsection{Meetkundige plaats} \drgeniusIcon{fig14} \drgeniusIndex{Meetkundige plaats}{}{}{} Creëert een meetkundige plaats, bepaald door twee punten. De gebruiker selecteert twee punten. Het eerste punt is een punt op een lijn. Het tweede punt staat in een welbepaalde relatie tot het eerste punt, zodat het eerste punt voorwaarden stelt aan de bewegingsvrijheid van het tweede (i.e.{} wanneer het ene punt beweegt, beweegt het andere eveneens). \subsubsection{Veelhoek} \drgeniusIcon{fig15} \drgeniusIndex{Veelhoek}{}{}{} Tekent een veelhoek, bepaald door $n$ punten. De gebruiker selecteert $n+1$ punten die de hoeken van de veelhoek bepalen. Het eerst en laatst geselecteerde punt moeten hetzelfde zijn. Zo weet \drgenius{} dat de puntenselectie afgerond werd. Het object veelhoek is geen object dat zich gedraagt als de andere lijnen. Het is namelijk niet mogelijk om er een punt op te plaatsen of om een snijpunt te tekenen met een andere lijn. Het is daarentegen wel mogelijk om het beeld van een veelhoek te tekenen onder een meetkundige transformatie. \xname{transformation_tools} \subsection{Instrumenten die transformaties in het vlak betreffen} \subsubsection{Evenwijdige rechte} \drgeniusIcon{fig16} \drgeniusIndex{Rechte}{Evenwijdige}{}{} Tekent een rechte, evenwijdig aan een richting en door een punt. De gebruiker selecteert een punt en een richting (zoals die bepaald wordt door een rechte, een halfrechte, een lijnstuk of een vector). \subsubsection{Loodlijn} \drgeniusIcon{fig17} \drgeniusIndex{Rechte}{Loodlijn}{}{} Tekent een rechte, loodrecht op een richting en door een punt. De gebruiker selecteert een punt en een richting (i.e.\ een rechte, een halfrechte, een lijnstuk of een vector). \subsubsection{Spiegeling (om een as)} \drgeniusIcon{fig18} \drgeniusIndex{Transformatie}{Spiegeling}{om een as}{} Tekent het beeld van een object onder een spiegeling. De gebruiker selecteert het te spiegelen object en de spiegelas (een rechte). Wanneer je een rechte wil spiegelen, geldt de eerste rechte als de te spiegelen rechte. \subsubsection{Puntspiegeling} \drgeniusIcon{fig19} \drgeniusIndex{Transformatie}{Spiegeling}{Puntspiegeling}{} Tekent het beeld van een object onder een puntspiegeling. De gebruiker selecteert het te spiegelen object en het centrum van de spiegeling (een punt). Wanneer de gebruiker een punt wil spiegelen, geldt het eerste punt als het te spiegelen punt. \subsubsection{Verschuiving} \drgeniusIcon{fig20} \drgeniusIndex{Transformatie}{Verschuiving}{}{} Tekent het beeld van een object onder een verschuiving. Wanneer de gebruiker het beeld van een vector wenst te tekenen, geldt de eerste vector als de te verschuiven vector. \subsubsection{Draaiing} \drgeniusIcon{fig21} \drgeniusIndex{Transformatie}{Draaiing}{}{} Tekent het beeld van een object onder een draaiing. De gebruiker selecteert het te draaien object, het centrum van de draaiing en de hoek van de draaiing. Wanneer men het beeld van een punt onder een draaiing wil tekenen, geldt het eerst gekozen punt als het te draaien punt. Aan de hoek kan men op drie verschillende manieren een waarde toekennen~: \begin{itemize} \item \textbf{getalwaarde}~: de hoek wordt in dit geval uitgedrukt in radialen. Voorbeelden van getalwaarden zijn~: een willekeurige waarde, een afstand tussen twee punten, de lengte van een lijnstuk, een coördinaat, een waarde die de uitkomst is van een \drgenius-Guile-script, etc.~; \item \textbf{de grootte van een meetkundige hoek, gevormd door drie punten}~: hier wordt de hoekgrootte uitgedrukt in graden. Opgelet, de grootte kan in dit geval enkel vallen in het interval [0~;~180]~; \item \textbf{de grootte van een georiënteerde hoek tussen twee vectoren}~: hier wordt de hoekgrootte uitgedrukt in graden. De grootte van de hoek kan vallen in het interval ]-180~;~180]. \end{itemize} \subsubsection{Homothetie} \drgeniusIcon{fig22} \drgeniusIndex{Transformatie}{Homothetie}{}{} Tekent het beeld van een object onder een homothetie. De gebruiker selecteert een te transformeren object, het centrum en de factor (i.e.\ een getal). Wanneer je het beeld van een punt wil tekenen, geldt het eerste punt als het te transformeren punt. \xname{numeric_tools} \subsection{Numerieke instrumenten} \subsubsection{Afstand, lengte \& getal} \drgeniusIcon{fig23} \label{numeric_tool} \drgeniusIndex{Getal}{}{}{} \drgeniusIndex{Rechte}{Richtingscoëfficiënt}{}{} \drgeniusIndex{Rechte}{Afstand}{}{} \drgeniusIndex{Cirkel}{Omtrek}{}{} \drgeniusIndex{Lijnstuk}{Lengte}{}{} \drgeniusIndex{Vector}{Norm}{}{} \drgeniusIndex{Cirkelboog}{Lengte}{}{} \drgeniusIndex{Getal}{Willekeurige waarde}{}{} Creëert een getalwaarde. De getalwaarde kan naar keuze ofwel berekend ofwel ingebracht worden~: \begin{enumerate} \item twee punten~: de afstand tussen deze twee punten~; \item een lijnstuk~: de lengte van het lijnstuk~; \item een vector~: de norm van deze vector~; \item een cirkel~: de omtrek van de cirkel~; \item een cirkelboog~: de lengte van de cirkelboog~; \item een rechte~: de richtingscoëfficiënt van de rechte~; \item een rechte en een punt~: de afstand tussen van het punt tot de rechte~; \item wanneer je op het tekenvlak klikt, kan je een nieuwe getalwaarde invoeren (i.e.\ een willekeurige waarde). \end{enumerate} \subsubsection{Hoek} \drgeniusIcon{fig24} \drgeniusIndex{Hoek}{Meetkundige}{}{}{} \drgeniusIndex{Hoek}{Georiënteerde}{}{}{} Berekent de grootte van een hoek, gedefinieerd door hetzij drie punten hetzij twee vectoren. In het eerste geval wordt de hoek als niet-georiënteerd beschouwd (i.e.{} als een hoek waarvan de grootte binnen het interval [0~;~180] graden valt). In het tweede geval wordt de hoek als een georiënteerde hoek beschouwt en valt de hoekgrootte dus binnen het interval ]-180~;~180]. \subsubsection{Coördinaten} \drgeniusIcon{fig25} \drgeniusIndex{Punt}{Coördinaten}{}{} \drgeniusIndex{Vector}{Coördinaten}{}{} Creëert de coördinaten (abscis en ordinaat) van een punt of van een vector. \subsubsection{\drgenius-Guile-script} \label{script-tool} \drgeniusIcon{fig49} \drgeniusIndex{Script}{}{}{} Maakt een \drgenius-Guile-script aan. Het script ontvangt \emph{n} objecten als invoergegevens. Het kan, wanneer daarom gevraagd wordt, een getalwaarde als uitkomst leveren, die dan wordt afgebeeld in de figuur. Een script kan gebruikt worden omwille van de neveneffecten of voor de uitkomst die het levert. De Guile-scripts van \drgenius{} worden in detail belicht in het \link{hoofdstuk voor gevorderde functies}[ (hoofdstuk \Ref)]{advancedFeatures} en met name in het \link{deel \drgenius-Guile-scripts}[ (deel \Ref, pagina \Pageref)]{script}. \xname{macroconstruction_tools} \subsection{Instrumenten voor macro-constructies} \drgeniusIndex{Macro-constructie}{}{}{} \subsubsection{Een macro-constructie aanmaken} \drgeniusIcon{fig26} Slaat de opeenvolgende stappen van de constructie van een meetkundige figuur op en vormt het geheel om tot één enkele macro-constructie. \subsubsection{Een macro-constructie uitvoeren} \drgeniusIcon{fig27} Voert een vooraf aangemaakte macro-constructie uit (i.e.\ ``lanceert ze'' of ``laat ze afspelen''). De macro-constructie kan nieuw zijn (pas geconstrueerd) of opgeroepen zijn uit een bestand (waar ze vooraf werd opgeslagen). \drgeniusNote{De macro-constructies worden voorgesteld in het \link{deel gewijd aan macro-constructie}[, deel \Ref, pagina \Pageref]{macroConstruction}.} \xname{other_tools} \section{Andere functies} \subsection{Boomstructuur van de constructie} \drgeniusIndex{Historiek}{Boomstructuur}{}{} Elke figuur is verbonden met een boomstructuur van de constructie. De boom is chronologisch, d.w.z. dat hij van boven naar beneden de verschillende stappen in de constructie van de figuur weergeeft. Bepaalde takken aan de boom kunnen worden uitgeklapt om de antecedenten --~ de samenstellende objecten~-- zichtbaar te maken die gebruikt werden om het (resulterende) object te definiëren. De boom wordt standaard verscholen. Hij is eigenlijk dichtgeklapt tegen de linkerboord van het venster. Om hem te voorschijn te toveren, moet je de boom ontvouwen met behulp van de muis. Beweeg hiertoe de muis naar de linkerrand van het \drgeo-venster. Wanneer de muiscursor verandert in een``<->'', druk dan de muisknop in en sleep de boom open (naar rechts). \subsection{Een figuur verplaatsen} \drgeniusIndex{Figuur}{Verplaatsen}{}{} Je kan een figuur verplaatsen door de Control-toets in te drukken samen met de eerste muisknop. \subsection{Een object verplaatsen} \drgeniusIcon{fig28} \drgeniusIndex{Object}{Verplaatsen}{}{} Je kan een object verplaatsen door het vast te nemen (eerste muisknop) en te verschuiven naar de gewenste plaats. De figuur wordt ogenblikkelijk opnieuw getekend, rekening houdende met haar eigenschappen. Omzeggens alle meetkundige objecten kunnen verplaatst worden. Als het nodig is verplaatst \drgenius\ eveneens de willekeurige punten die in verband staan tot het object. Wanneer je b.v.\ een rechte verplaatst, die gedefinieerd werd door twee punten, zal \drgenius\ in eenzelfde beweging deze punten meeverplaatsen. \subsection{Een object verwijderen} \drgeniusIcon{fig30} \drgeniusIndex{Object}{Verwijderen}{}{} Een object van een figuur kan verwijderd worden door dit menu te activeren. De gebruiker kan de verwijdering eventueel annuleren. Hij kan daartoe ofwel de functie `Ongedaan maken' gebruiken op de taakbalk, ofwel door dezelfde functie aan te klikken in het menu. % evt. verduidelijken Standaard zijn 10 opeenvolgende annulaties mogelijk, maar dit aantal kan worden aangepast in het dialoogvenster `Voorkeuren'. \xname{editing_object_styles} \subsection{Het uitzicht van een object aanpassen} \drgeniusIcon{fig29} \drgeniusIndex{Bewerken}{Uitzicht}{}{} \drgeniusIndex{Object}{Nieuwe naam geven}{}{} \drgeniusIndex{Nieuwe naam geven}{Object}{}{} \drgeniusIndex{Object}{Verbergen}{}{} Van elk meetkundig object kan je een aantal visuele eigenschappen (zoals zijn kleur, dikte, etiket, grootte en vorm) aanpassen. Bovendien is het mogelijk om tijdelijk een object te verbergen zonder het te verwijderen. Het kan bij voorbeeld nuttig zijn om voorbereidende constructies onzichtbaar te maken zonder ze daarom te verwijderen. Al deze eigenschappen kunnen worden aangepast via het dialoogvenster dat verschijnt wanneer de gebruiker op een object van de figuur klikt. Om dit te doen, activeert men eerst de modus die toelaat het uitzicht van een object aan te passen door \drgeniusMenu{Andere->Uitzicht} te selecteren op het contextuele menu van de figuur. Men kan enveneens op bovenstaand icoon klikken, dat deel uitmaakt van de zesde iconenschuif. \drgeniusIndex{Point}{Renommer}{}{} Het dialoogvenster Uitzicht van een punt aanpassen% veranderen in Stijl van een punt !!! betreft alle soorten punten. Het is mogelijk de kleur, de vorm, de grootte, de naam en de zichtbaarheid aan te passen. \drgeniusFigure{Dialoogvenster voor het uitzicht van een `punt'-object}{fig31}%TV objet weg tov. Fr. Het dialoogvenster Uitzicht van een lijn betreft rechten, halfrechten, lijnstukken, vectoren, cirkels, cirkelbogen en meetkundige plaatsen. Het is mogelijk de kleur, de stijl, %TV ?? de naam en de zichtbaarheid aan te passen. Wanneer een rechte, halfrechte, vector of lijnstuk door twee punten gedefinieerd zijn en die twee punten een naam werden toegekend, wordt de naam van de rechte, etc. automatisch afgeleid van de naam van de twee punten. In dit geval kan de gebruiker zelf aan de rechte, etc. geen nieuwe naam geven. \drgeniusFigure{Dialoogvenster voor het uitzicht van een object `lijn'}{fig32} Het dialoogvenster Uitzicht van een getal of van een veelhoek betreft allerlei getalwaarden (ingevoerd door de gebruiker, berekend door een \drgenius-Guile-script of een grootte afgeleid van een meetkundige figuur) en de verschillende veelhoeken. \drgeniusFigure{Dialoogvenster voor het uitzicht van getallen \& veelhoek-objecten}{fig33} \T \clearpage \subsection{De eigenschappen van een object aanpassen} \label{property-item} \drgeniusIcon{fig52} \drgeniusIndex{Editer}{Eigenschappen}{}{} \drgeniusIndex{Editer}{Punt}{}{} \drgeniusIndex{Editer}{Script}{}{} \drgeniusIndex{Editer}{Getalswaarde}{}{} Van bepaalde eigenschappen van objecten kan de gebruiker de parameters aanpassen. Wanneer je op een object klikt, verschijnt het geëigende dialoogvenster. Op dit moment gaat het over volgende objecten~: \begin{enumerate} \item willekeurig punt~: abscis et ordinaat kan men wijzigen~;\\ \drgeniusFigure{Aanpassingen voor de coördinaten van een willekeurig punt}{fig34} \item willekeurige getalwaarde~: de waarde kan aangepast worden~;\\ \drgeniusFigure{Wijzigiging van een willekeurige getalwaarde}{fig36} \item script~: de code kan aangepast worden.\\ \drgeniusFigure{Wijziging van een script}{fig35} \end{enumerate} \T \clearpage \subsection{Een rooster weergeven} \drgeniusIndex{Figuur}{Weergeven}{Rooster}{} \drgeniusIndex{Rooster}{Weergeven}{}{} Het is mogelijk een rooster met de eenheden weer te geven op elke \drgeo-figuur via het menu \drgeniusMenu{Editie->Rooster tonen of verbergen}. %FIXME Je kan een rooster eveneens oproepen met de sneltoets \drgeniusMenu{Ctrl-G}. Wanneer men de functie een tweede maal activeert, verdwijnt het rooster opnieuw. Het betreft een unitair rooster~: elke onderverdeling stelt een eenheid voor. Tenslotte, wanneer het rooster zichtbaar is bij het opslaan, wordt het mee opgeslagen. \section{Voorkeuren van de gebruiker} \xname{default_behaviour} \subsection{Standaardvoorkeuren} \label{default_behaviour} \drgeniusIndex{Bewerken}{Standaardvoorkeuren}{}{} De standaardinstellingen van \drgenius\ kunnen op verscheidene manieren worden bijgesteld. Om zijn voorkeuren in te stellen, gaat de gebruiker naar het menu \drgeniusMenu{Bewerken->Voorkeuren...} om het dialoogvenster van de voorkeuren te openen. \drgeniusFigureSize{Voorkeuren i.v.m. de meetkundige figuren}{fig38}{8} Het dialoogvenster bevat twee delen~: \begin{enumerate} \item Het eerste deel betreft de voorkeuren in verband met de meetkundige figuren. Met de oortjes kan men de standaardinstellingen van elk soort object (meetkundig of numeriek) aanpassen. Men kan er met name het uitzicht van de figuren regelen. \item Het tweede deel betreft de algemene voorkeuren~: \begin{itemize} \item Het aantal niveaus voor het Ongedaan maken/Herstellen~; \item De standaardnaam bij creatie van een nieuwe figuur. De \%d wordt vervangen door een geheel getal dat \drgenius\ bijhoudt. Bij elke nieuwe figuur wordt dit getal met een eenheid verhoogd~; \item De standaard internetbrowser --~bladeraar~-- om de on-line-hulp weer te geven~; \item De standaardnamen bij het opslaan van een figuur of een sessie~; \item De standaardnamen voor bestanden met figuren die naar een \LaTeX- of PostScript-formaat worden geëxporteerd~; \end{itemize} \end{enumerate} \drgeniusIndex{Wijzigen}{Standaarduitzicht}{}{} \drgeniusIndex{Wijzigen}{Standaardinstellingen}{Ongedaan maken/Herstellen}{} \drgeniusIndex{Wijzigen}{Standaardinstellingen}{Namen}{} \drgeniusIndex{Hulp}{Standaardvoorkeuren}{Bladeraar}{} \subsection{Andere voorkeuren} \drgeniusIndex{Figuur}{Nieuwe naam geven}{}{} Naast de standaardinstellingen van \drgenius, kan de gebruiker ook de naam van een figuur aanpassen via het menu \drgeniusMenu{Bewerken->Nieuwe naam geven}. \drgeniusFigure{Naam van een figuur wijzigen}{fig39} \chapter{Gevorderde functies}%? \label{advancedFeatures} In dit hoofdstuk stellen wij functies voor die toelaten de mogelijkheden van \drgenius{} uit te breiden of het programma aan te passen aan een gegeven lessituatie. De eerste functie is de macro-constructie. Hiermee kan je verschillende opeenvolgende stappen in een constructie opslaan. Achteraf kan je deze constructie (opname) automatisch opnieuw laten bouwen (laten afspelen) of ze bewaren in een bestand. De \drgenius{}-Guile-scripts --~DGS~-- vormen een andere uitbreidingsmogelijkheid voor \drgenius. Deze scripts zijn werkelijk onderdelen van een figuur net als de meetkundige onderdelen. Zo'n script krijgt een of meer meetkundige items als input, en geeft als output een getalwaarde die in de figuur wordt geplaatst. De Guile scripts in \drgenius\ zijn nuttig omdat ze een waarde berekenen en weergeven of omwille van hun `pedagogisch surplus'. Alles hangt af van wat de gebruiker wil realiseren. Tenslotte is er de aanpassing van de gebruikersinterface van \drgenius. Deze stelt een leraar in staat stelt een sessie voor te bereiden met documenten waarin bepaalde functies geblokkeerd zijn en beveiligd met een paswoord. \xname{using_macro} \section{Macro-constructie} \label{macroConstruction} \drgeniusIndex{Macro-constructie}{Inleiding}{}{} Een macro-constructie gelijkt een beetje op een procedure waarbij je zelf onderdelen van de figuur aangeeft, en de macro-constructie vervolgens op basis van die gegevens nieuwe elementen automatisch toevoegt aan de figuur. Macro-constructies verrichten hun bouwwerk volgens het model dat werd aangereikt door de gebruiker. Dit betekent dat hij de opeenvolgende stappen in het constructieproces zelf een eerste keer toepast op een bepaalde figuur, om \drgenius\ vervolgens te vragen die opeenvolgende stappen als één geheel op te slaan in een macro-constructie. Om een constructie-proces te kunnen opslaan moet \drgenius\ een beeld hebben van de items die van in het begin aanwezig zijn én van de items die op het einde van de rit zichtbaar moeten zijn. Het spreekt voor zich dat de items in de eindconstructie \textit{enkel en alleen} getekend kunnen worden %\/ ? aan de hand van de items die van bij de start aanwezig waren. Anders kan \drgenius\ de eindconstructie niet stap voor stap afleiden uit de elementen in de beginsituatie. Op die manier leidt \drgenius\ dus de logica van het constructie-proces af en slaat die op in een macro-constructie. Achteraf kan de gebruiker deze macro-constructie het werk laten doen. De macro-constructie vraagt dan enkel om de begingegevens (van het juiste type) aan te duiden en construeert zelf alle onderdelen van de eindfiguur. \drgeniusNote{De items van voorlopige of onzichtbare constructies worden eveneens geconstrueerd door de macro-constructie. Ze zijn noodzakelijk om het eindresultaat te bekomen.} % verduid. dat ze onzichtb. blijv. Als illustratie van een macro-constructie, vertrekken we van het voorbeeld waarbij een gebruiker de constructie van een cirkel door drie punten samen met zijn middelpunt wil opslaan. \drgeniusFigureSize{De beginfiguur}{fig40}{4} \drgeniusIndex{Macro-constructie}{Aanmaken}{}{} Om een macro-constructie aan te maken, moet de gebruiker eerst zelf de eindfiguur construeren~: deze figuur fungeert als model voor de macro-constructie. \drgeniusFigureSize{De figuur met de gewenste eindconstructie}{fig41}{4} \subsection{Aanmaken van de macro-constructie} Op dit moment, zijn de opeenvolgende stappen in de constructie doorlopen. De gebruiker dient nu \drgenius\ duidelijk te maken dat hij een macro-constructie wil maken, vertrekkende van deze voorbeeldconstructie. Daartoe moet hij beroep doen op de functie \drgeniusMenu{Een macro aanmaken} die men op de taakbalk vindt \drgeniusIcon{fig26} of via het contextueel %uitleg toevoeg. = recht. muiskn. voor cont. menu menu van het beeld in zijn geheel. Een dialoogvenster zal de gebruiker bijstaan tot op het einde. Je selecteert de invoerparameters en de uitvoerparameters. Vervolgens kies je de naam en voeg je eventueel een beschrijving van de macro-constructie toe. \drgeniusFigureSize{Eerste pagina van het dialoogvenster dat de aanmaak van een macro-constructie begeleidt}{fig42}{6} Op de tweede pagina van het dialoogvenster kan men de invoerparameters kiezen. In ons voorbeeld gaat het om de drie punten die de cirkel definiëren. Het enige wat de gebruiker moet doen is naar die tweede pagina gaan en de drie punten op de figuur aanklikken. Als items correct geselecteerd worden, flikkeren ze op het scherm. \drgeniusFigureSize{De tweede pagina, de drie punten zijn geselecteerd}{fig43}{6} Op de derde pagina kiest de gebruiker de uitvoerparameters. In ons voorbeeld willen we de cirkel en zijn middelpunt als resultaat van de macro-constructie. De uitvoerparameters worden op dezelfde manier gekozen als de invoerparameters. \drgeniusFigureSize{De derde pagina, de cirkel en zijn middelpunt zijn geselecteerd}{fig44}{6} Op de vierde pagina kan de gebruiker een naam en een beschrijving toekennen aan de macro-constructie. Die informatie zal weergegeven worden, telkens je de bewuste macro-constructie uitvoert. Op die manier zijn macro-constructies overigens makkelijk te onderscheiden van mekaar. \drgeniusFigureSize{De vierde pagina, de naam en de beschrijving van de macro-constructie}{fig45}{6} Op de vijfde en laatste pagina van het dialoogvenster wordt de aanmaak afgerond, zodra de gebruiker op de knop \texttt{Beëindigen} drukt. Als hij dat wil, kan hij ook op zijn stappen terugkeren en de parameters van de macro-constructie aanpassen. \drgeniusNote{Als de keuze van invoerparameters en van uitvoerparameters niet coherent is (\drgenius{} vindt geen logica in de constructie), kan de macro-constructie niet aangemaakt worden. In dat geval, bekijkt de gebruiker zijn selectie van invoer- en uitvoerparameters best nog eens van dichterbij. Hij kan altijd terug naar de tweede of derde pagina van het dialoogvenster om die keuze te veranderen.} In deze fase is de macro-constructie aangemaakt en steekt hij in het geheugen van \drgenius. In het volgende deel, zien we hoe er gebruik van te maken. \subsection{Uitvoeren van een macro-constructie} \drgeniusIndex{Macro-constructie}{Uitvoeren}{}{} Om een macro-constructie uit te voeren, doet de gebruiker beroep op de functie \drgeniusMenu{Een vooraf gebouwde macro uitvoeren} vanop de taakbalk \drgeniusIcon{fig27} of via het contextueel menu van het beeld in zijn geheel. In het dialoogvenster dat verschijnt, kiest de gebruiker de gewenste macro-constructie. Op de tweede pagina selecteert hij de macro-constructie uit de lijst bovenaan het dialoogvenster. Eens hij de macro gekozen heeft, kan hij onmiddellijk klikken op de invoerparameters op de figuur. Van zodra alle invoerparameters geselecteerd zijn, wordt de macro-constructie uitgevoerd en wordt het eindresultaat (de uitvoerparameters) zichtbaar. \drgeniusFigureSize{De gebruiker selecteert de invoerparameters op de figuur}{fig46}{6} In ons voorbeeld had de macro-constructie drie invoerparameters nodig (drie punten), waarna de cirkel door die punten en zijn middelpunt worden geconstrueerd. Om de macro-constructie te kunnen uitvoeren, moeten er dus al drie punten staan op de figuur (waar we op aan het werken zijn). \drgeniusFigureSize{Een figuur met drie punten}{fig47}{4} Wanneer we de macro-constructie toepassen op die drie punten, verschijnt de gewenste cirkel met zijn middelpunt. \drgeniusFigureSize{De eindfiguur, met de cirkel en zijn middelpunt}{fig48}{4} \T \clearpage \xname{drgenius_guile_script} \section{\drgenius{} Guile scripts} \label{script} \drgeniusIndex{Script}{Inleiding}{}{} \drgenius{} is compatibel met Guile. Dit betekent dat het mogelijk is Guile scripts uit te voeren met \drgenius. Maar wat is Guile~? Volgens het Guile-handboek~: \begin{quote}{\em Guile is een interpreter voor de programmeertaal Scheme, en werd ontworpen voor gebruik in een grote hoeveelheid omgevingen. } \end{quote} Volgende citaten beschrijven precies hoe Guile gebruikt wordt in \drgenius~: \begin{quote}{\em Net als een shell, kan Guile op interactieve manier gebruikt worden, expressies %alternatief ? ontvangen van de gebruiker, ze evalueren en de resultaten weergeven. Guile kan ook, net als een interpreter van scripts, code lezen en uitvoeren die in een bestand bewaard werd. Guile is eveneens beschikbaar als een bibliotheek die toelaat op eenvoudige wijze een volwaardige Scheme interpreter in te bouwen in andere toepassingen. Een toepassing kan Guile gebruiken als een uitbreidingstaal, als een krachtige taal voor de eigen configuratie of als een multifunctionele ``lijm'', die de primitieven % verklarende voetnoot toevoegen ? van de toepassing verbindt. } \end{quote} Een API is beschikbaar in \drgenius\ via de Guile interpreter. Het is een verzameling ``haakjes'' % niet gesnapt; nog aanpassen in de meetkundige motor. Dat is de reden waarom een gebruiker scripts kan schrijven om de (meetkundige of numerieke) items van een figuur te manipuleren. Omdat scripts onderdelen zijn van een figuur net als andere onderdelen, is het niet nodig ze in een afzonderlijk bestand op te slaan~: ze worden bewaard in het bestand van de figuur. In wat volgt gebruiken we de afkorting DGS om een ``\drgenius-Guile-script'' aan te duiden. \subsection{DGS a.d.h.v.\ voorbeelden} \drgeniusIndex{Script}{Voorbeelden}{}{} Het instrument om een DGS te schrijven is bereikbaar via het numerieke onderdeel van het contextueel menu of van de gereedschapskist. Een DGS kan tussen de 0 en \textit{n} invoerparameters te verwerken krijgen. Nadat men het instrument gekozen heeft, volstaat het de in te voeren objecten aan te klikken en vervolgens ergens op de achtergrond van de figuur. Op die laatst aangeklikte positie zal het script geplaatst worden. In wat volgt stellen wij voor op enkele DGS-voorbeelden te werken, zodat men er de kracht en functionaliteit makkelijker van kan inzien. Net als de macro-constructies, geven de DGS een speciale dimensie aan \drgenius. Ze laten je toe --~elk met een andere aanpak\footnote{Macro-constructies hebben een meetkundige invalshoek. DGS daarentegen werken vanuit een numerieke invalshoek maar laten vooral ook toe te prutsen en de dingen fijn te stellen (te ``hacken'' in het Engels).}~-- paden te bewandelen die de auteurs van het programma niet bewandeld hebben of niet wensen te bewandelen. Het is belangrijk bewust te zijn dat het leeuwendeel van de funtionaliteit van de GNU-Guile-interpreter aanspreekbaar is via de DGS. Dit is met name zo voor de functiebibliotheken\footnote{In het bijzonder, de wiskundige functies}, die we uiteraard intens zullen gebruiken. \paragraph{DGS zonder invoerparameters} Klik, na \link{het instrument voor scripts}[(Cf. deel \Ref, pagina \Pageref)]{script-tool} te hebben gekozen, direct op de achtergrond van de figuur, op de plaats waar je het script wil zetten. Klik vooral op geen enkel object van de figuur. Als je dat wel zou doen, denkt \drgenius\ dat je dit object als invoerparameter van het script aanklikt\footnote{Als je per toeval toch op een object zou klikken, selecteer dan opnieuw het instrument voor scripts. Dit zal de selectie van een object ongedaan maken.}. Als het script een plaats gekregen heeft, ziet u de tekens ``Dr.~Genius'' verschijnen. Elk nieuw script bevat standaard het commando om die tekenreeks af te beelden, maar dit kan je uiteraard aanpassen met behulp van \link{het instrument m.b.t.\ de eigenschappen van een object}[ Deel \Ref, pagina \Pageref]{property-item}. Klik na de selectie van voornoemd instrument op het script --~of preciezer~: op zijn waarde~-- dat u wil bijstellen op de figuur. Een dialoogvenster met het script zal verschijnen. In de rest van dit deel, zullen we de scripts in dit dialoogvenster invoeren. \subparagraph{Een generator van willekeurige en andere getallen} % niet al te vlot \drgeniusIndex{Script}{\texttt{random}}{}{} Niets is eenvoudiger dan willekeurige getallen genereren. Voer volgende code in~: \begin{verbatim} (random 10) \end{verbatim} Bij elke update van de figuur, zal het script een willekeurig geheel getal voortbrengen dat valt in het interval [0~;~10[. Wanneer u een reëel getal (float) wenst % is reëel precies in het interval [0~;~1[, % genoeg maak dan gebruik van volgend script~: \begin{verbatim} (random:uniform) \end{verbatim} \drgeniusNote{Enkele precizeringen~: \begin{itemize} \item De uitkomst van het script is de waarde die op de laatste regel berekend werd. In dit voorbeeld, gaat het om een waarde die de uitkomst is van een functie waar we beroep op deden~; \item De laatste regel van het script moet een reëel getal als uitkomst hebben. Anders zal \drgenius{} de boodschap ``Niet af te drukken resultaat'' weergeven~; % checken interface adhv vb. \item Wanneer men de waarde van een veranderlijke wenst als uitkomst, volstaat het om de naam van de variabele op de laatste regel te plaatsen. \end{itemize} } \subparagraph{Veelgebruikte waarden berekenen} Om een benaderde waarde van $\pi$ te berekenen~: \begin{verbatim} (acos -1) \end{verbatim} of van $e$~: \begin{verbatim} (exp 1) \end{verbatim} De uitkomst van een DGS kan vervolgens gebruikt worden op dezelfde manier als alle andere getalwaarden die \drgenius\ kan voortbrengen. Voor dit soort kleine zaken, zijn de DGS dus uw bondgenoten. Maar ze kunnen veel interessanter dingen wanneer je hen laat werken met invoerparameters. \paragraph{DGS met minstens een invoerparameter} \drgeniusIndex{Script}{Parameters}{}{} De procedure om een DGS met invoerparameters te creëren is bijna identiek. Het volstaat om, onmiddellijk na het instrument voor scripts te hebben geselecteerd, het object aan te klikken dat je als invoerparameter wenst te gebruiken. Klik vervolgens op de achtergrond van de figuur, op de plaats waar je het script zetten wil. In het script wordt verwezen naar de invoerparameter met de veranderlijke $a1$. Hadden we twee invoerparameters gedefinieerd, dan zou de volgorde van selectie van die parameters weerspiegeld zijn in de naamgeving van de veranderlijken~: $a1$ en $a2$. Hetzelfde gaat op voor drie, vier of meer invoerparameters. Naargelang het type object waarnaar men verwijst, zijn er verschillende methoden om de getalwaarde te bekomen, om de coördinaten te bekomen, etc. Het overzicht van de methoden kan men nalezen in het deel \link{Verwijzingsmethoden van de DGS}[(Deel \Ref, pagina \Pageref)]{api-dgs}. In wat volgt, zullen we stapsgewijs de constructie uiteenzetten van een (deel van een) kromme en zijn tangens in een punt dat we zullen kunnen bewegen over dat deel van de kromme. De eindfiguur wordt meegeleverd met \drgenius. Zij heet \xlink{/usr/share/drgeo/examples/figures/slope.fgeo}{/usr/share/drgeo/examples/figures/slope.fgeo}. \drgeniusFigureSize{De figuur die we zullen bekomen}{fig55}{8} \subparagraph{Een waarde definiëren in een gegeven interval} \drgeniusIndex{Script}{Interval}{}{} Om te beginnen plaatsen we twee punten in een nieuwe figuur, en tekenen we het lijnstuk dat begrensd wordt door deze twee punten. Op dit lijnstuk plaatsen we een punt dat we ``Move me!'' noemen. Dit punt zal als ijkpunt fungeren~; de juiste afmetingen zal het script ons leveren. We creëren nu een script met als enige invoerparameter dit bewuste punt. Als $a1$ verwijst naar het punt ``Move me!'', dan geeft het script dat volgt als uitkomst een reëel getal binnen het interval [-10~;~10]~: \begin{verbatim} (define x (getAbscissa a1)) (* 20 (- x 0.5)) \end{verbatim} Wat uitleg is nodig. In de eerste regel, laat de aanroep \texttt{(getAbscissa a1)} toe de abscis % ? op de kromme ? te bekomen van het object waarnaar $a1$ verwijst\footnote{Deze abscis ligt in het interval [0~;~1], en dit voor om het even welke soort lijn.} --~namelijk het punt ``Move me!''. De waarden van deze abscis worden toegekend aan een nieuwe veranderlijke $x$. Op de tweede regel passen we vervolgens de schaal aan. Deze uitdrukking zou in algebraïsche notatie overeenstemmen met $20 \times ( x - 0.5)$. Omdat dit de laatste regel is, is de uitkomst van het script de uitkomst van die regel en wordt die uitkomst afgebeeld in de figuur. Laat ons dit script, tenslotte, Xo noemen. \subparagraph{Een representatief gedeelte van een kromme afbeelden} \drgeniusIndex{Meetkundige plaats}{Script}{}{} We zullen ons bedienen van de uitkomst van het eerste script om met een tweede script de ordinaat te berekenen in een punt onder de functie $x \rightarrow cos(x)$~: \begin{verbatim} (define x (getValue a1)) (cos x) \end{verbatim} De aanroep \texttt{(getValue a1)} laat toe de getalwaarde te bekomen van het object waarnaar we verwijzen met $a1$. Hier willen we de uitkomst van het vorige script gebruiken in een nieuw script. We zullen het Yo noemen. In een volgende stap creëren we het punt Mo met coördinaten (Xo~;~Yo). Het gaat om een willekeurig punt op de kromme $x \rightarrow cos(x)$. Om een representatief gedeelte van de kromme af te beelden dat zich b.v.\ uitstrekt over het interval [-10~;~10], creëren we de plaats van het punt Mo, wanneer het punt ``Move Me!'' het lijnstuk beschrijft. Zo, nu hebben we een kromme~! \subparagraph{De raaklijn aan een kromme berekenen en afbeelden} \drgeniusIndex{Script}{Raaklijn}{}{} Om de raaklijn in het punt Mo te tekenen, hebben we vooreerst de richtingscoëfficiënt in dat punt nodig, waarvoor we dus zowel de afgeleide functie $x \rightarrow -sin(x)$ nodig hebben als Xo. We schrijven dus een script met als invoerparameter het script Xo~: \begin{verbatim} (- 0 (sin (getValue a1))) \end{verbatim} De prefixnotatie die Scheme/Guile gebruikt kan verwarrend werken, maar is een kwestie van gewoonte. Laat ons dit script ``richtingscoëfficiënt in Mo'' noemen. Op die manier zal, telkens wanneer Mo verplaatst wordt, de richtingscoëfficiënt opnieuw berekend worden. Er rest ons nog de raaklijn te tekenen. Daartoe berekenen we eerst de coördinaten van een tweede punt --~M1~-- van deze rechte. Laat ons beginnen met de abscis, b.v.\ $X1 = Xo + 2$. Om die te berekenen, schrijven we een script met als invoerparameter het script Xo~: \begin{verbatim} (define x1 (getValue a1)) (+ x1 2) \end{verbatim} Dit script noemen we X1. Nu nog de ordinaat van M1 te pakken krijgen. Hiervoor hebben we hetvolgende nodig~: \begin{itemize} \item Mo (waarnaar we verwijzen met $a1$)~; \item de richtingscoëfficiënt in Mo ($a2$)~; \item de abscis van X1 ($a3$). \end{itemize} In dit script berekenen we de ordinaat van M1 op de volgende manier $Yo + m \times (X1 - X0)$~: \begin{verbatim} (define x0 (car (getCoordinates a1))) (define y0 (cadr (getCoordinates a1))) (define m (getValue a2)) (define x1 (getValue a3)) (+ (* m (- x1 x0)) y0) \end{verbatim} Enkele woorden commentaar bij de aanroep \texttt{(getCoordinates a1)}. Bij deze aanroep moet $a1$ verwijzen naar een object van het type `punt'. Deze methode geeft als output een lijst met de coördinaten van het punt --~hier Mo. Met \texttt{car} kan men het eerste element uit de lijst nemen, en met \texttt{cadr} het tweede. De rest van het script zou geen problemen mogen stellen. Laat ons dit script Y1 noemen. Nu kunnen we het punt M1 construeren, met coördinaten (X1~;~Y1) en tenslotte de raaklijn (MoM1). Het was natuurlijk mogelijk om maar twee of drie scripts te schrijven in plaats van deze panoplie. Maar we hopen dat u met deze kleine voorbeelden de smaak te pakken krijgt en zelf met DGS aan de slag gaat. \subsection{Methodes van verwijzen voor \drgeo-scripts} \label{api-dgs} % DGS API is exposed here De volgende delen beschrijven de methodes die beschikbaar zijn voor de \drgeo-scripts. % FIXME aangep. >< FR!! Ze zijn geordend naar het type meetkundig of numeriek object. \subsubsection{Punt} \drgeniusIndex{Script}{\texttt{getAbscissa}}{}{}{} \begin{drgeoApi}{waarde (getAbscissa punt)} \drgeoApiIn{punt}{Verwijzing naar een willekeurig punt op een lijn} \drgeoApiOut{De abscis van dit punt op de lijn. De waarde ligt in het interval [0~;~1]} \drgeoApiExample{(define x (getValue a1))\\ (* x 10)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{setAbscissa}}{}{}{} \begin{drgeoApi}{(setAbscissa punt x)} \drgeoApiIn{punt}{Verwijzing naar een willekeurig punt op een lijn} \drgeoApiIn{x}{De decimale waarde binnen het interval [0~;~1], die de nieuwe abscis voorstelt} \drgeoApiExample{(setAbscissa a1 0.5)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getCoordinates}}{}{} \begin{drgeoApi}{lijst (getCoordinates punt|vector)} Geeft als output de coördinaten van een punt of een vector.\\ \drgeoApiIn{punt|vector}{Verwijzing naar een punt of een vector} \drgeoApiOut{Lijst die de coördinaten van het punt of van de vector bevat} \drgeoApiExample{(define c (getCoordinates a1))\\ (define x (car c))\\ (define y (cadr c))\\ (+ (* x x) (* y y))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{setCoordinates}}{}{} \begin{drgeoApi}{(setCoordinates punt coörd)} Legt de coördinaten van een punt vast\\ \drgeoApiIn{punt}{Verwijzing naar een willekeurig punt in het vlak} \drgeoApiIn{coörd}{Lijst van twee decimale getallen} \drgeoApiExample{(define l (list 1.4 (random 5)))\\ (setCoordinate a1 l)} \end{drgeoApi} \subsubsection{Rechte, Halfrechte, Lijnstuk, Vector} \drgeniusIndex{Script}{\texttt{getSlope}}{}{}{} \begin{drgeoApi}{waarde (getSlope richting)} \drgeoApiIn{richting}{Verwijzing naar een object van het type rechte, halfrechte, lijnstuk of vector} \drgeoApiOut{De richtingscoëfficiënt van deze richting} \drgeoApiExample{(define p (getSlope a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getNorm}}{}{} \begin{drgeoApi}{waarde (getNorm vector)} \drgeoApiIn{vector}{Verwijzing naar een vector} \drgeoApiOut{De norm van deze vector} \drgeoApiExample{(define n (getNorm a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getLength}}{}{} \begin{drgeoApi}{waarde (getLength lijnstuk)} \drgeoApiIn{lijnstuk}{Verwijzing naar een lijnstuk} \drgeoApiOut{De lengte van dit lijnstuk} \drgeoApiExample{(define l (getLength a1))} \end{drgeoApi} \subsubsection{Cirkel, Cirkelboog} \drgeniusIndex{Script}{\texttt{getCenter}}{}{} \begin{drgeoApi}{lijst (getCenter cirkel|cirkelboog)} \drgeoApiIn{cirkel|cirkelboog}{Verwijzing naar een cirkel of naar een cirkelboog} \drgeoApiOut{Lijst die de coördinaten van het middelpunt van de cirkel of van de cirkelboog bevat} \drgeoApiExample{(define c (getCenter a1))\\ (car c)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getRadius}}{}{} \begin{drgeoApi}{waarde (getRadius cirkel|cirkelboog)} \drgeoApiIn{cirkel|cirkelboog}{Verwijzing naar een cirkel of naar een cirkelboog} \drgeoApiOut{Straal van de cirkel of van de cirkelboog} \drgeoApiExample{(define r (getRadius a1))} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{getLength}}{}{} \begin{drgeoApi}{waarde (getLength cirkel|cirkelboog)} \drgeoApiIn{cirkel|cirkelboog}{Verwijzing naar een cirkel of naar een cirkelboog} \drgeoApiOut{Omtrek van de cirkel of lengte van de cirkelboog} \drgeoApiExample{(define l (getLength a1))} \end{drgeoApi} \subsubsection{Getal} \drgeniusIndex{Script}{\texttt{getValue}}{}{} \begin{drgeoApi}{waarde (getValue getal)} \drgeoApiIn{getal}{Verwijzing naar een getal} \drgeoApiOut{Waarde van dit getal} \drgeoApiExample{(define a (getValue a1))\\ (define b (getValue a2))\\ (+ a b)} \end{drgeoApi} \drgeniusIndex{Script}{\texttt{setValue}}{}{} \begin{drgeoApi}{(setValue getal v)} \drgeoApiIn{getal}{Verwijzing naar een getal} \drgeoApiIn{v}{Decimale getalwaarde} \drgeoApiExample{(define v (getValue a1))\\ (setValue a2 v)} \end{drgeoApi} \subsubsection{Hoek} \drgeniusIndex{Script}{\texttt{getAngle}}{}{} \begin{drgeoApi}{waarde (getAngle hoek)} \drgeoApiIn{hoek}{Verwijzing naar een meetkundige of georiënteerde hoek} \drgeoApiOut{De hoek uitgedrukt in graden. Om de hoek in radialen te bekomen, dient men de methode \texttt{getValue} te gebruiken} \drgeoApiExample{(define angle1 (getAngle a1))\\ (define angle2 (getAngle a2))\\ %FIXME in het FR (define angle3 (getAngle a3))\\ (+ angle1 angle2 angle3)} \end{drgeoApi} \subsubsection{Overige} \drgeniusIndex{Script}{\texttt{move}}{}{} \begin{drgeoApi}{(move item t)} \drgeoApiIn{item}{Verwijzing naar een object van de figuur} \drgeoApiIn{t}{Vector met twee dimensies} \drgeoApiExample{(define v (vector .1 0))\\ (move a1 v)} \end{drgeoApi} \section{De instrumenten in de gebruikersinterface aanpassen} \label{ui-lock} \drgenius\ biedt de mogelijkheid sessies\footnote{Sessies zijn bestanden die verschillende \drgeo-documenten (i.e.\ figuren en/of teksten) bevatten.} voor te bereiden waarbij de leraar voor bepaalde figuren kan beslissen de toegang tot bepaalde instrumenten te blokkeren. De beveiliging gebeurt per figuur afzonderlijk, en dit telkens met een verschillend paswoord. Op die manier heeft een leraar de volle vrijheid om een activiteit met verschillende figuren voor te bereiden en die op gepaste wijze te beveiligen. \subsection{Instrumenten vergrendelen} \drgeniusIndex{Instrumenten}{Vergrendelen}{}{} De beveiliging gebeurt figuur per figuur. Om een figuur te beveiligen, ga je naar het menu \drgeniusMenu{Bewerken->Gebruikersinterface aanpassen}. Er verschijnt een groot dialoogvenster waarin de gebruiker de verschillende icoontjes herkent, die men op de tweede taakbalk van \drgenius{} terugvindt. Om een instrument te activeren of vergrendelen, volstaat het op het gepaste icoontje te drukken. Als een instrument vergrendeld werd, ziet het overeenkomstige icoontje er iets grijzer uit. Het is eveneens mogelijk een hele reeks instrumenten in één keer uit te schakelen door te klikken op het icoontje van de hele groep (i.e.\ met een groen driehoekje) \drgeniusFigureSize{Het dialoogvenster om instrumenten te vergrendelen.}{fig53}{8} Wanneer de gebruiker de te beveiligen instrumenten geselecteerd heeft, kan hij overgaan tot de eigenlijke vergrendeling door in het dialoogvenster op de knop \drgeniusMenu{Vergrendelen} te drukken. \drgenius{} vraagt dan om een paswoord. \drgeniusNote{Bij het opslaan van een figuur of een sessie met vergrendelingen in de gebruikersinterface worden de paswoorden mee opgeslagen in het bestand. Ze zijn weliswaar gecrypteerd.} \subsection{Instrumenten ontgrendelen} \drgeniusIndex{Instrumenten}{Ontgrendelen}{}{} Het spreekt vanzelf dat je een interface daarna ook kan ontgrendelen, hetzij om geleidelijk aan toegang te verschaffen aan instrumenten --~wanneer leerlingen op een sessie werken b.v.~-- of om een figuur bij te werken. Om dit te doen moet je naar het menu \drgeniusMenu{Bewerken->Gebruikersinterface aanpassen} gaan en in het dialoogvenster de knop \drgeniusMenu{Ontgrendelen} aanklikken. \drgenius{} vraagt dan het correcte paswoord opnieuw in te voeren. \drgeniusFigure{Het dialoogvenster om de interface van een figuur te ontgrendelen.}{fig54} \chapter{\drgeo-Scheme-figuren} \drgeniusIndex{\drgeo-Scheme-figuren}{Inleiding}{}{} De \emph{\drgeo-Scheme-figuren} -- (DSF) -- zijn figuren die in een relatief natuurlijke taal beschreven worden. Het gaat er dan niet langer om een figuur te construeren via de grafische interface van \drgeo, maar veeleer om de figuur te beschrijven in de taal Scheme. Wij hebben gepoogd om de syntaxis zo licht en gemakkelijk mogelijk te maken. Alle sleutelwoorden om een eenvoudige figuur te tekenen kunnen in verschillende talen gesteld zijn. Zo kan men een figuur beschrijven in het Frans, in het Engels, in het Spaans, in het Nederlands, etc. % Ndl. toegevoegd (Een mengeling van talen is ook mogelijk, maar niet aan te raden). \section{Enkele voorbeelden} \drgeniusIndex{\drgeo-Scheme-figuren}{Voorbeelden}{}{} Scheme is als dusdanig een taal op hoog niveau. Wanneer we een figuur definiëren, kunnen we bijgevolg van zijn kracht gebruikmaken om dit of dat deel van de figuur op recursieve wijze te definiëren, of om bepaalde objecten op toevallige wijze op de figuur te plaatsen zodat de figuur er telkens lichtjes anders uitziet wanneer men ze opnieuw opent. De DSF zijn kortom bevrijd uit het kader van de grafische interface en winnen aan kracht dankzij Scheme. Een DSF is dus een bestand dat met een tekst-\emph{editor} wordt aangemaakt en dat in \drgeo{} wordt geopend met de opdracht \drgeniusMenu{Bestand->Evalueren}. \drgeniusIndex{\drgeo-Scheme-figuren}{Evalueren}{}{} Laat ons een eenvoudig voorbeeld van de DSF bestuderen~: \drgeniusIndex{\drgeo-Scheme-figuur}{Nieuwe figuur}{}{} \begin{verbatim} (nieuwe-figuur "Mijn figuur") \end{verbatim} Dit is de kleinste DSF die we konden definiëren. Wanneer we het bestand laden in \drgeo, wordt er louter een nieuwe, lege figuur gecreërd onder de naam ``Mijn figuur''. Hadden we verschillende commando's in de lijn van \texttt{(nieuwe-figuur "Mijn figuur")} ingebracht, dan zouden er evenveel nieuwe figuren gecreëerd zijn. Laat ons een tweede voorbeeld bekijken~: \begin{verbatim} (nieuwe-figuur "Mijn figuur") (weze Punt "A" willekeurig 1.2 -2) \end{verbatim} Deze DSF definiëert een figuur met een willekeurig punt $A$ met coördinaten $(1,2~;~-2)$. De syntaxis is kennelijk relatief aangenaam, te meer omdat zij in de moedertaal gesteld is. Laat ons dieper ingaan op de tweede regel. De syntaxis is immers dezelfde voor alle commando's die objecten definiëren. Een dergelijk commando kan als volgt worden opgesplitst~: \begin{enumerate} \item We beginnen steeds met het sleutelwoord \texttt{weze}, dat aangeeft dat we een nieuw object in het leven willen roepen. \item Onmiddellijk daarop volgt de categorie van het object, \texttt{Punt} in dit geval \texttt{Punt}. \item Vervolgens volgt de naam van het object, $A$, die we steeds tussen aanhalingstekens plaatsen. Zelfs als we geen naam willen geven aan het object, moet men een lege naam "" geven. \item Daarna geven we het type object aan --~het type punt in ons voorbeeld~-- hier \texttt{willekeurig}. Het punt $A$ is dus een willekeurig punt. \item Na het type object volgt een lijst met specifieke argumenten. Die lijst bestaat in ons voorbeeld uit twee getallen, de coördinaten van het willekeurige punt $A$. \end{enumerate} Laat ons verder gaan met een derde voorbeeld~: \begin{verbatim} (define (driehoek p1 p2 p3) (Lijnstuk "" uiteinden p1 p2) (Lijnstuk "" uiteinden p2 p3) (Lijnstuk "" uiteinden p1 p3)) (define (toeval) (- 8 (* 16 (random:uniform)))) (nieuwe-figuur "Mijn figuur") (weze Punt "A" willekeurig (toeval) 0) (weze Punt "B" willekeurig 5 0) (weze Punt "C" willekeurig (toeval) 5) (driehoek A B C) \end{verbatim} Dit voorbeeld is bijzonder interessant omdat het drie belangrijke zaken demonstreert~: \begin{enumerate} \item Het gebruik van constructies op hoog niveau. We definiëren een functie \texttt{driehoek} die aan de hand van drie gegeven punten, een driehoek door die punten construeert. Deze manier van handelen is vergelijkbaar met de macro-constructies, maar we hebben een veel grotere vrijheid van beweging. \item De definitie van bijkomende functies. Hier hebben we de functie \texttt{toeval} gecreëerd, die ons een decimaal getal bezorgt dat tussen -8 en 8 ligt. We gebruiken de functie om bepaalde punten van onze figuur op toevallige wijze te positioneren. Op die manier zal een figuur lichtjes anders zijn telkens zij geopend wordt. \item Het gebruik van het sleutelwoord \texttt{weze} is eigenlijk niet verplicht. Enkel als we een verwijzing (een naam) van een object willen bewaren, maken we er gebruik van. Bij de functie \texttt{driehoek} kozen we er bij voorbeeld voor om de lijnstukken geen namen te geven. De punten $A$, $B$ en $C$ daarentegen kregen verwijzingen met dezelfde naam. \end{enumerate} Merk op dat als we geen naam geven bij het definiëren van de lijnstukken, \drgeo\ zelf een standaardnaam toekent aan de hand van de uiteinden. De drie lijnstukken zullen dus in ons geval de namen $[AB]$, $[BC]$ en $[AC]$ dragen. Laat ons dit gedeelte met een laatste voorbeeld beëindigen~: \begin{verbatim} (weze Punt "A" willekeurig 1 0) (weze Punt "B" willekeurig 5 0) (weze Rechte "r1" 2punten A B) (zend A kleur geel) (zend A vorm rond) (zend A grootte groot) (zend B verbergen) (zend d1 dikte streepje) \end{verbatim} De drie eerste commando's creëren twee punten en een rechte. Hier belangt ons vooral de reeks \texttt{geef}-commando's aan. Met dit commando kunnen we communiceren met een object waarvan we een symbool hebben opgeslagen. In ons geval hebben we de symbolen \texttt{A}, \texttt{B} en \texttt{r1}. We zenden telkens een boodschap aan een object. In het eerste argument geven we aan met welk object we communiceren en in het tweede argument de boodschap die we willen meegeven. Het derde en de volgende argumenten hangen af van de aard van de boodschap in het tweede argument. Met de zin \texttt{(zend A kleur geel)} stuur je het punt A de boodschap kleur met als parameter \texttt{geel}. De andere \texttt{geef}-commando's zijn zo gemakkelijk te begrijpen. Ze zullen uitgelegd worden in het volgende gedeelte. Wij hebben onze kleine begeleide wandeling doorheen de \emph{Dr. Geo Scheme Figuren} afgerond. In wat volgt, zullen wij alle beschikbare commando's om DSF'en te definiëren uit de doeken doen. \section{Verwijzingsmethoden voor de \drgeo\ Scheme Figuren} Het definiëren van objecten in een DSF-document gebeurt via prototypes. Prototypes zijn om zo te zeggen objecten die wij kunnen bevragen en aanpassen zoals zal blijken. Vooraleer echter objecten te definiëren binnen een figuur moeten wij die figuur zelf tot leven wekken met het commando \texttt{nieuwe-figuur}. \subsection{Algemene commando's} \begin{drgeoApi}{(nieuwe-figuur naam)} \drgeoApiIn{naam}{Tekenreeks} \drgeoApiOut{Geeft geen waarde als resultaat. De functie-aanroep heeft enkel een zijdelings effect, namelijk het creëren van een nieuwe figuur. Alle objecten die volgen worden in deze figuur gecreëerd, tot we de functie-aanroep opnieuw gebruiken} \drgeoApiExample{(nieuwe-figuur "Mijn 1ste figuur")} \end{drgeoApi} \subsection{Definitie van nieuwe objecten van een figuur} \drgeniusIndex{\drgeo\ Scheme figuur}{Creatie van objecten}{}{} Een object kan op syntactisch verschillende wijzen worden gedefiniëerd. \begin{itemize} \item \texttt{(weze Punt "p1" type args)} Het punt wordt aangemaakt en zijn verwijzing wordt opgeslagen in de variabele \texttt{p1}. Deze syntaxis gebruikt een Scheme-macro. \item \texttt{(Punt "Naam" type args)} Het punt wordt aangemaakt maar geen enkele verwijzing naar het punt wordt bewaard. \item \texttt{(set! p1 (Punt "Naam" type args))} Het punt wordt aangemaakt en zijn verwijzing wordt gekopiëerd naar de reeds bestaande variabele \texttt{p1}. \end{itemize} Wanneer objecten worden gecreëerd vanuit een functie, gebruik dan ofwel de vorm \texttt{set!} ofwel de speciale Scheme-vorm \texttt{let}. Het is belangrijk op te merken dat de basisaanroep een functie is die een verwijzing naar het aangemaakte object als uitkomst geeft. \subsubsection{Punt} \drgeniusIndex{\drgeo\ Scheme figuur}{Creatie van objecten}{Punt}{} \begin{drgeoApi}{prototype (Punt naam willekeurig x y)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{x}{De abscis van het punt} \drgeoApiIn{y}{De ordinaat van het punt} \drgeoApiOut{Verwijzing naar een willekeurig punt in het vlak met coördinaten \texttt{x} en \texttt{y}.} \drgeoApiExample{(define p1 (Punt "A" willekeurig 1.2 (acos -1)))} \end{drgeoApi} \begin{drgeoApi}{prototype (Punt naam op-kromme lijn x)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{lijn}{Verwijzing naar een lijn (rechte, halfrechte, lijnstuk, etc.)} \drgeoApiIn{x}{Kromme-abscis van het willekeurig punt, de waarde behoort tot het interval [0~;~1]} % FIXME \drgeoApiOut{Verwijzing van een willekeurig punt op een lijn.} \drgeoApiExample{(Punt "M" op-kromme s1 0.5 )} \end{drgeoApi} \begin{drgeoApi}{prototype (Punt naam midden-2ptn p1 p2)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{p1}{Verwijzing naar een punt} \drgeoApiIn{p2}{Verwijzing naar een punt} \drgeoApiOut{Verwijzing naar het midden van twee punten.} \drgeoApiExample{(weze Punt "A" willekeurig 1 1)\\ (weze Punt "B" willekeurig 4 4)\\ (Punt "I" midden-2ptn A B)} \end{drgeoApi} \begin{drgeoApi}{prototype (Punt naam midden-lijnstuk s)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{s}{Verwijzing naar een lijnstuk} \drgeoApiOut{Verwijzing naar het midden van twee punten.} \drgeoApiExample{(weze Punt "L" midden-lijnstuk s)} \end{drgeoApi} \begin{drgeoApi}{prototype (Punt naam snijpunt l1 l2)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{l1}{Verwijzing naar een lijn} \drgeoApiIn{l2}{Verwijzing naar een lijn} \drgeoApiOut{Verwijzing naar het snijpunt van twee lijnen.} \drgeoApiExample{(Punt "I" snijpunt rechte lijnstuk)} \end{drgeoApi} \begin{drgeoApi}{prototype (Punt naam snijpunt2 l1 l2)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{l1}{Verwijzing naar een lijn} \drgeoApiIn{l2}{Verwijzing naar een lijn} \drgeoApiOut{Verwijzing naar het tweede snijpunt van twee lijnen als een van de twee een cirkelboog of een cirkel is.} \drgeoApiExample{(Punt "I" snijpunt2 rechte cirkel)} \end{drgeoApi} \subsubsection{Rechte} \drgeniusIndex{\drgeo{} Scheme Figuur}{Creatie van objecten}{Rechte}{} \begin{drgeoApi}{prototype (Rechte naam 2punten p1 p2)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{p1}{Verwijzing naar een punt} \drgeoApiIn{p2}{Verwijzing naar een punt} \drgeoApiOut{Verwijzing naar een rechte door twee punten} \drgeoApiExample{(weze Punt "A" willekeurig 0 0)\\ (weze Punt "M" willekeurig 1 2)\\ (Rechte "" 2punten A M)} \end{drgeoApi} \begin{drgeoApi}{prototype (Rechte naam evenwijdig p r)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{p}{Verwijzing naar een punt} \drgeoApiIn{r}{Verwijzing naar een richting (rechte, lijnstuk, vector, ...)} \drgeoApiOut{Verwijzing naar een rechte evenwijdig met de richting \texttt{r} en door het punt \texttt{p}.} \drgeoApiExample{(weze Punt "A" willekeurig 1 5)\\ (weze Rechte "r1" evenwijdig A r)} \end{drgeoApi} \begin{drgeoApi}{prototype (Rechte naam loodrecht p r)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{p}{Verwijzing naar een punt} \drgeoApiIn{r}{Verwijzing naar een richting (rechte, lijnstuk, vector, ...)} \drgeoApiOut{Verwijzing naar een rechte loodrecht op de richting \texttt{r} en door het punt \texttt{p}.} \drgeoApiExample{(weze Punt "A" willekeurig 1 5)\\ (weze Rechte "r1" loodrecht A r)} \end{drgeoApi} \subsubsection{Halfrechte} \drgeniusIndex{\drgeo\ Scheme-figuur}{Creatie van objecten}{Halfrechte}{} \begin{drgeoApi}{prototype (Halfrechte naam 2punten o p)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{o}{Verwijzing naar een punt, grenspunt van de halfrechte} \drgeoApiIn{p}{Verwijzing naar een ander punt, op de halfrechte} \drgeoApiOut{Verwijzing naar een halfrechte gedefiniëerd door zijn grenspunt en een tweede punt.} \drgeoApiExample{(weze Punt "A" willekeurig 1 5)\\ (weze Punt "O" willekeurig 0 0)\\ (weze Halfrechte "dd1" 2punten A O)} \end{drgeoApi} \subsubsection{Lijnstuk} \drgeniusIndex{\drgeo\ Scheme-figuur}{Creatie van objecten}{Lijnstuk}{} \begin{drgeoApi}{prototype (Lijnstuk naam grenspunten p1 p2)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{p1}{Verwijzing naar een punt} \drgeoApiIn{p2}{Verwijzing naar een punt} \drgeoApiOut{Verwijzing naar een lijnstuk gedefiniëerd door zijn grenspunten.} \drgeoApiExample{(weze Punt "A" willekeurig 1 5)\\ (weze Punt "B" willekeurig 10 4)\\ (weze Lijnstuk "" grenspunten A B)} \end{drgeoApi} \subsubsection{Cirkel} \drgeniusIndex{\drgeo\ Scheme-figuur}{Creatie van objecten}{Cirkel}{} \begin{drgeoApi}{prototype (Cirkel naam 2punten m p)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{m}{Verwijzing naar een punt, middelpunt van de cirkel} \drgeoApiIn{p}{Verwijzing naar een punt op de cirkel} \drgeoApiOut{Verwijzing naar een cirkel gedefiniëerd door zijn middelpunt en een punt} \drgeoApiExample{(weze Punt "A" willekeurig 1 5)\\ (weze Punt "B" willekeurig 10 4)\\ (weze Cirkel "C1" 2punten A B)} \end{drgeoApi} \begin{drgeoApi}{prototype (Cirkel naam middelpunt-straal m r)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{m}{Verwijzing naar een punt, middelpunt van de cirkel} \drgeoApiIn{r}{Verwijzing naar een lijnstuk, de straal van de cirkel} \drgeoApiOut{Verwijzing naar een cirkel bepaald door zijn middelpunt en straal} \drgeoApiExample{(weze Punt "A" willekeurig 1 5)\\ (weze Getal "r" willekeurig 10)\\ (weze Cirkel "C1" middelpunt-straal A r)} \end{drgeoApi} \subsubsection{Cirkelboog} \drgeniusIndex{\drgeo\ Scheme-figuur}{Creatie van objecten}{Cirkelboog}{} \begin{drgeoApi}{prototype (Cirkel naam 3punten p1 p2 p3)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{p1}{Verwijzing naar een punt, 1$^{e}$ grenspunt van de boog} \drgeoApiIn{p2}{Verwijzing naar een punt op de boog} \drgeoApiIn{p3}{Verwijzing naar een punt, 2$^{de}$ grenspunt van de boog} \drgeoApiOut{Verwijzing naar een cirkelboog gedefiniëerd door zijn grenspunten en een punt.} \drgeoApiExample{(weze Punt "A" willekeurig 1 5)\\ (weze Punt "B" willekeurig 0 5)\\ (weze Punt "C" willekeurig -1 -2)\\ (weze Cirkelboog "boog" 3punten A B C)} \end{drgeoApi} \subsubsection{Veelhoek} \drgeniusIndex{\drgeo\ Scheme-figuur}{Creatie van objecten}{Veelhoek}{} \begin{drgeoApi}{prototype (Veelhoek naam npunten args)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{args}{Een lijst met verwijzingen naar punten, hoekpunten van de veelhoek} \drgeoApiOut{Verwijzing naar een veelhoek gedefiniëerd door zijn hoekpunten} \drgeoApiExample{(weze Veelhoek "quad" npunten A B C D)} \end{drgeoApi} \subsubsection{Meetkundige transformaties} \drgeniusIndex{\drgeo\ Scheme-figuur}{Creatie van objecten}{Meetkundige transformaties}{} De prototypes van meetkundige transformaties laten toe objecten te tekenen onder een transformatie. Men kan transformaties toepassen op verwijzingen naar objecten van het type punt, lijnstuk, rechte, halfrechte, vector, cirkel, cirkelboog en veelhoek. \begin{drgeoApi}{prototype (ObjectType naam draaiing object middelpunt hoek)} \drgeoApiIn{ObjectType}{Punt, Lijnstuk, Rechte, Halfrechte, Vector, Cirkel, Cirkelboog, Veelhoek} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{object}{Verwijzing naar het te transformeren object} \drgeoApiIn{middelpunt}{Verwijzing naar een punt, middelpunt van de draaiing} \drgeoApiIn{hoek}{Verwijzing naar een getalwaarde, hoek van de draaiing} \drgeoApiOut{Verwijzing naar een getransformeerd object} \drgeoApiExample{(weze Punt "I1" draaiing I C a)} \end{drgeoApi} \begin{drgeoApi}{prototype (ObjectType naam homothetie object middelpunt k)} \drgeoApiIn{ObjectType}{Punt, Lijnstuk, Rechte, Halfrechte, Vector, Cirkel, Cirkelboog, Veelhoek} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{object}{Verwijzing naar het te transformeren object} \drgeoApiIn{middelpunt}{Verwijzing naar een punt, middelpunt van de homothetie} \drgeoApiIn{k}{Verwijzing naar een getalwaarde, factor van de homothetie} \drgeoApiOut{Verwijzing naar een getransformeerd object} \drgeoApiExample{(weze Veelhoek "P1" homothetie P C k1)} \end{drgeoApi} \begin{drgeoApi}{prototype (ObjectType naam puntspiegeling object middelpunt)} \drgeoApiIn{ObjectType}{Punt, Lijnstuk, Rechte, Halfrechte, Vector, Cirkel, Cirkelboog, Veelhoek} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{object}{Verwijzing naar het te transformeren object} \drgeoApiIn{middelpunt}{Verwijzing naar een punt, middelpunt van de puntspiegeling} \drgeoApiOut{Verwijzing naar het getransformeerde object} \drgeoApiExample{(weze Lijnstuk "L1" puntspiegeling L m)} \end{drgeoApi} \begin{drgeoApi}{prototype (ObjectType naam spiegeling object spiegelas)} \drgeoApiIn{ObjectType}{Punt, Lijnstuk, Rechte, Halfrechte, Vector, Cirkel, Cirkelboog, Veelhoek} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{object}{Verwijzing naar het te transformeren object} \drgeoApiIn{spiegelas}{Verwijzing naar een rechte, de spiegelas} \drgeoApiOut{Verwijzing naar het getransformeerde object} \drgeoApiExample{(weze Veelhoek "V1" spiegeling V r1)} \end{drgeoApi} \begin{drgeoApi}{prototype (ObjectType naam verschuiving object vector)} \drgeoApiIn{ObjectType}{Punt, Lijnstuk, Rechte, Halfrechte, Vector, Cirkel, Cirkelboog, Veelhoek} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{object}{Verwijzing naar het te transformeren object} \drgeoApiIn{vector}{Verwijzing naar een vector} \drgeoApiOut{Verwijzing naar het getransformeerde object.} \drgeoApiExample{(weze Cirkel "C1" verschuiving C v)} \end{drgeoApi} \subsubsection{Meetkundige plaats} \drgeniusIndex{\drgeo\ Scheme-figuur}{Creatie van een object}{Plaats}{} \begin{drgeoApi}{prototype (Plaats naam 2punten m c)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{m}{Verwijzing naar een beweeglijk punt op een lijn} \drgeoApiIn{c}{Verwijzing naar een vast punt dat afhangt van het punt \texttt{m}} \drgeoApiOut{Verwijzing naar een plaats.} \drgeoApiExample{(Plaats "plaats1" 2punten M I)} \end{drgeoApi} \subsubsection{Vector} \drgeniusIndex{\drgeo\ Scheme-figuur}{Creatie van objecten}{Vector}{} \begin{drgeoApi}{prototype (Vector naam 2punten o g)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{o}{Verwijzing naar een punt, oorsprong van de vector} \drgeoApiIn{g}{Verwijzing naar een punt, grenspunt van de vector} \drgeoApiOut{Verwijzing naar een vector.} \drgeoApiExample{(weze Punt "B" willekeurig 0 5)\\ (weze Punt "C" willekeurig -1 -2)\\ (Vector "" 2punten C B)} \end{drgeoApi} \subsubsection{Getal} \drgeniusIndex{\drgeo\ Scheme-figuur}{Creatie van objecten}{Getal}{} \begin{drgeoApi}{prototype (Getal naam vrij x y v)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{x,y}{De coördinaten voor de plaatsing van het getal} \drgeoApiIn{v}{De beginwaarde van het getal} \drgeoApiOut{Verwijzing naar een willekeurig getal.} \drgeoApiExample{(weze Getal "pi" willekeurig 5 5 (acos -1))} \end{drgeoApi} \begin{drgeoApi}{prototype (Getal naam lengte-lijnstuk x y l)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{x,y}{De coördinaten voor de plaatsing van het getal} \drgeoApiOut{l}{Verwijzing naar een lijnstuk.} \drgeoApiExample{(weze Getal "l" lengte-lijnstuk 5 5 S)} \end{drgeoApi} \begin{drgeoApi}{prototype (Getal naam norm-vector x y v)} \drgeoApiIn{naam}{Tekensreeks die de naam van het object aangeeft} \drgeoApiIn{x,y}{De coördinaten voor de plaatsing van het getal} \drgeoApiIn{v}{Verwijzing naar een vector} \drgeoApiOut{Verwijzing naar een getal, norm van de vector.} \drgeoApiExample{(weze Getal "l" norm-vector 5 5 V)} \end{drgeoApi} \begin{drgeoApi}{prototype (Getal naam norm-vector x y p c)} \drgeoApiIn{naam}{Tekensreeks die de naam van het object aangeeft} \drgeoApiIn{x,y}{De coördinaten voor de plaatsing van het getal} \drgeoApiIn{p}{Verwijzing naar een punt} \drgeoApiIn{c}{Verwijzing naar een cirkel} \drgeoApiOut{Verwijzing naar een getal, afstand tussen het punt en de cirkel} \drgeoApiExample{(weze Getal "l" punt-cirkel 5 5 P C)} \end{drgeoApi} \begin{drgeoApi}{prototype (Getal naam punt-rechte x y p r)} \drgeoApiIn{naam}{Tekensreeks die de naam van het object aangeeft} \drgeoApiIn{x,y}{De coördinaten voor de plaatsing van het getal} \drgeoApiIn{p}{Verwijzing naar een punt} \drgeoApiIn{r}{Verwijzing naar een rechte} \drgeoApiOut{Verwijzing naar een getal, afstand tussen het punt en de rechte} \drgeoApiExample{(weze Getal "a" punt-rechte 5 5 M D1)} \end{drgeoApi} \begin{drgeoApi}{prototype (Getal naam punt-punt x y p1 p2)} \drgeoApiIn{naam}{Tekensreeks die de naam van het object aangeeft} \drgeoApiIn{x,y}{De coördinaten voor de plaatsing van het getal} \drgeoApiIn{p1}{Verwijzing naar een punt} \drgeoApiIn{p2}{Verwijzing naar een punt} \drgeoApiOut{Verwijzing naar een getal, afstand tussen de twee punten.} \drgeoApiExample{(weze Getal "a" punt-punt A B)} \end{drgeoApi} \subsubsection{Hoek} \drgeniusIndex{\drgeo-Scheme-figuren}{Creatie van objecten}{Hoek}{} \begin{drgeoApi}{prototype (Hoek naam meetkundig A B C)} \drgeoApiIn{naam}{Tekensreeks die de naam van het object aangeeft} \drgeoApiIn{A}{Verwijzing naar een punt} \drgeoApiIn{B}{Verwijzing naar een punt, het hoekpunt} %FIXME \drgeoApiIn{C}{Verwijzing naar een punt} \drgeoApiOut{Verwijzing naar een meetkundige hoek.} \drgeoApiExample{(weze hoek "h" meetkundig A B C)} \end{drgeoApi} \begin{drgeoApi}{prototype (Hoek naam georiënteerd x y v1 v2)} \drgeoApiIn{naam}{Tekenreeks die de naam van het object aangeeft} \drgeoApiIn{x,y}{De coördinaten voor de plaatsing van de hoek} \drgeoApiIn{v1}{Verwijzing naar een vector} \drgeoApiIn{v2}{Verwijzing naar een vector} \drgeoApiOut{Verwijzing naar een georiënteerde hoek, gevormd door twee vectoren} \drgeoApiExample{(define v1 (Vector "" 2punten A B))\\ (define v2 (Vector "" 2punten A C))\\ (Hoek "a" georiënteerd 1 1 v1 v2)} \end{drgeoApi} \subsubsection{Attributen van objecten aanpassen} \drgeniusIndex{\drgeo\ Scheme-figuur}{Creatie van objecten}{Attributen van objecten}{} Om attributen aan te passen van een reeds gecreëerd object, gebruiken we een systeem dat direct boodschappen zendt aan het prototype dat het object in kwestie vertegenwoordigt. De aanpassing van attributen gebeurt dus steeds a posteriori. \begin{drgeoApi}{(zend object kleur waarde)} \drgeoApiIn{object}{Verwijzing naar een object} \drgeoApiIn{waarde}{De kleur~; mogelijke waarden zijn \texttt{zwart, donkergrijs, grijs, wit, donkergroen, groen, donkerblauw, blauw, rood, bordeaux, geel, oranje}} \drgeoApiExample{(weze Punt "A" willekeurig 1 2)\\ (zend A kleur groen)} \end{drgeoApi} \begin{drgeoApi}{(zend lijn dikte waarde)} \drgeoApiIn{lijn}{Verwijzing naar een lijn (rechte, halfrechte, cirkel, plaats, etc.)} \drgeoApiIn{waarde}{De dikte~; mogelijke waarden zijn \texttt{streepje, normaal, dik}} \drgeoApiExample{(weze Punt "A" willekeurig 1 2)\\ (weze punt "B" willekeurig 0 0)\\ (weze Rechte "r" 2 punten A B)\\ (zend d dikte streepje)} \end{drgeoApi} \begin{drgeoApi}{(zend punt grootte waarde)} \drgeoApiIn{punt}{Verwijzing naar een punt} \drgeoApiIn{waarde}{De grootte van het punt~; mogelijke waarden zijn \texttt{klein, normaal, groot}} \drgeoApiExample{(weze Punt "A" willekeurig 1 2)\\ (zend A grootte klein)} \end{drgeoApi} \begin{drgeoApi}{(zend punt vorm waarde)} \drgeoApiIn{punt}{Verwijzing naar een punt} \drgeoApiIn{waarde}{De vorm van het punt~; mogelijke waarden zijn \texttt{rond, kruisje, rond-leeg, rec, rec-leeg}} \drgeoApiExample{(weze Punt "A" willekeurig 1 2)\\ (zend A vorm rond)} \end{drgeoApi} \begin{drgeoApi}{(zend object verbergen)} \drgeoApiIn{object}{Verwijzing naar een te verbergen object} \drgeoApiExample{(weze Punt "A" willekeurig 1 2)\\ (zend A verbergen)} \end{drgeoApi} \section{Galerij met voorbeelden} \drgeniusIndex{\drgeo-Scheme-figuren}{Voorbeelden}{}{} Om het gebruik van de \drgeo-Scheme-figuren te illustreren, stellen we een kleine voorbeeldenreeks voor. Deze voorbeelden tonen belangrijke voorbeelden en wij hopen dat ze inspirerend werken. Voor elk voorbeeld geven wij de Scheme-broncode, gevolgd door het resultaat. De broncode kan in een tekst-\emph{editor} gekopiëerd en opgeslagen worden om ze vervolgens te evalueren met \drgeo. \subsection{Regelmatige veelhoek} \drgeniusIndex{\drgeo-Scheme-figuren}{Voorbeelden}{Regelmatige veelhoek}{} Een regelmatige veelhoek met een willekeurig aantal zijden kan men met behulp van een recursieve Scheme-functie construeren. % moet dit niet vertaald worden in het Frans ? \begin{verbatim} (define pi (acos -1)) (define n 15) (define x0 0) (define y0 0) (define p1 0) (define (polygon center p a n) (if (> n 0) (begin (set! p1 (Point "" rotation p center a)) (send p1 masked) (Segment "" extremities p p1) (polygon center p1 a (- n 1))))) (new-figure "Regular Polygon!") (lets Point "C" free x0 y0) (lets Numeric "a" free 0 0 (* 2 (/ pi n))) (send a masked) (set! p1 (Point "I" free 5 0)) (lets Segment "S" extremities C p1) (Segment "" rotation S C a) (polygon C p1 a n) \end{verbatim} \drgeniusFigureSize{Een regelmatige veelhoek met 15 zijden}{fig59}{6} \subsection{Fractaal} \drgeniusIndex{\drgeo-Scheme-figuren}{Voorbeelden}{Fractaal}{} De constructie van een fractaal in boomvorm is erg eenvoudig. De broncode van de figuur is wonderlijk compact, vooral wanneer men ze vergelijkt met een ``handmatige'' constructie via de grafische interface. % moet nog vertaald worden \begin{verbatim} (new-figure "Baum") (lets Numeric "A1" free 2 2 +3.4) (lets Numeric "A2" free 2 3 -3.7) (lets Numeric "S1" free 2 4 +0.5) (lets Numeric "S2" free 2 5 +0.9) (define (dec n) (- n 1)) (define (inc n) (+ n 1)) (define (invisible p) (send p masked) p) (define (scalerot oP C a s) (let* ((sP (invisible (Point "" scale oP C s))) (rP (invisible (Point "" rotation sP C a))) ) rP)) (define (Zweig p0 p1 n) (Segment "" extremities p0 p1) (let* ((left-scale (if (odd? n) S1 S2)) (left-angle A1) (right-scale (if (odd? n) S2 S1)) (right-angle A2) ) (if (> n 0) (begin (Zweig p1 (scalerot p0 p1 left-angle left-scale) (dec n)) (Zweig p1 (scalerot p0 p1 right-angle right-scale) (dec n)))))) (lets Point "A" free -3 0) (lets Point "B" free -3 2) (Zweig A B 6) \end{verbatim} \drgeniusFigureSize{Een fractaal die een boomvorm simuleert}{fig60}{8} \chapter{Bestanden en documenten} Constructies kunnen op twee manieren worden opgeslagen. Ofwel sla je één constructie op in één bestand, ofwel sla je een verzameling constructies op in één bestand (i.e.\ een zgn.\ \drgenius-sessie). \section{Opslaan van een constructie} \drgeniusIndex{Figuur}{Opslaan}{}{} Via het menu \drgeniusMenu{Bestand->Opslaan} of \drgeniusMenu{Bestand->Opslaan als...}, wordt de figuur die op dat moment zichtbaar is opgeslagen. \drgeniusNote{\drgenius\ kan met verschillende figuren tegelijkertijd werken. Je kan van figuur veranderen door op het overeenkomstige oortje te klikken.} Via het tweede menu kan de gebruiker de naam wijzigen van het document dat men opslaat. \drgeniusNote{De standaard bestandsnaam kan je veranderen via het menu \drgeniusMenu{Bewerken->Voorkeuren...}. Meer informatie vindt men in het \link{deel over standaardinstellingen}[ (Deel \Ref, pagina \Pageref)]{default_behaviour}.} \section{Opslaan van een sessie} \drgeniusIndex{Macro-constructie}{Opslaan}{}{} \drgeniusIndex{Sessie}{Opslaan}{}{} Een sessie is een verzameling \drgenius-gegevens die de gebruiker in een keer verlangt op te slaan in een bestand. Zo kan een leraar een verzameling gegevens (figuren, macro-constructies, aantekeningen) organiseren in een enkel bestand, zodat hij het geheel gemakkelijk opnieuw kan gebruiken. Via het menu \drgeniusMenu{Bestand->Samenvoegen en opslaan}, opent de gebruiker het dialoogvenster in verband met een sessie. \drgeniusFigureSize{Het dialoogvenster i.v.m.\ een \drgenius-sessie}{fig51}{8} In dit dialoogvenster verschijnt een tabel met alle actieve gegevens. In de eerste kolom staat de respectieve soort aangeduid van de gegevens die in \drgenius{} actief zijn. In de tweede kolom staan de namen van die gegevens. \drgeniusNote{Op dit moment kan een sessie drie soorten gegevens bevatten~: een interactieve 2D-figuur, een macro-constructie of een tekst.} De gebruiker kan de gewenste gegevens één voor één selecteren in de lijst en ze dan opslaan door op de knop \drgeniusMenu{Selectie opslaan} te drukken. Hij kan ook alle gegevens in een klap opslaan door de knop \drgeniusMenu{Alles opslaan} in te drukken. \drgeniusNote{Het menu \drgeniusMenu{Bestand->Samenvoegen en opslaan} is de enige manier om een macro-constructie op te slaan in een bestand.} \section{Een bestand openen} \drgeniusIndex{Macro-constructie}{Openen}{}{} \drgeniusIndex{Sessie}{Openen}{}{} \drgeniusIndex{Figuur}{Openen}{}{} Of de gebruiker nu een enkele figuur of een sessie met verschillende soorten documenten heeft opgeslagen, de procedure om een bestand te openen blijft dezelfde~: via het menu \drgeniusMenu{Bestand->Openen...}. Als de geopende sessie macro-constructies bevat, kunnen die onmiddellijk worden uitgevoerd door het gepaste instrument aan te klikken. Macro-constructies zijn beschikbaar vanop elke geopende figuur. \section{Een figuur exporteren} \drgeo\ biedt de mogelijkheid om een meetkundige figuur te exporteren naar een \LaTeX- of PostScript-document. Beide formaten zijn van het vectoriële type. Dit betekent dat ze een betere afdrukkwaliteit zullen hebben dan beelden die in een bitmap-formaat worden opgeslagen. Men kan een figuur exporteren via het sub-menu \drgeniusMenu{Figuur->Exporteren naar...} % FIXME ldots ? \subsection{Exporteren naar \LaTeX} \drgeniusIndex{Figuur}{Exporteren}{\LaTeX}{} Wanneer men naar \LaTeX\ wil exporteren, heeft men het \texttt{pstricks}-pakket nodig. Over het algemeen wordt dit pakket verspreid samen met \LaTeX\ zelf. Een figuur die men naar \LaTeX exporteerde kan je vanzelfsprekend in een \LaTeX-document opnemen, maar je kan het ook direct als een op zich staand document compileren~: \begin{verbatim} latex figure.tex dvips figure.dvi \end{verbatim} Als men deze twee commando's invoert, bekomt men het document figure.ps. Dit kan dan op het scherm weergegeven worden met het programma GhostView\footnote{GhostView is een programma dat zowel PostScript-documenten (.ps of .eps) als PDF's op het scherm kan weergeven} \texttt{gv}. \subsection{Exporteren naar PostScript} \label{exporter-ps} \drgeniusIndex{Figuur}{Exporteren}{PostScript}{} Exporteren naar het PostScript-formaat biedt het voordeel dat je de documenten makkelijk kan gebruiken in andere programma's\footnote{Het formaat wordt herkend door TeXmacs, OpenOffice.org, LyX, \LaTeX, Xfig, The Gimp en vele andere programma's}. Het EPS-formaat is de facto eigenlijk min of meer de standaard waar het vectoriële beelden aangaat. Om dit soort beelden snel weer te geven gebruiken we het programma GhostView. Zijn commando is \texttt{gv}. \subsection{De zone bepalen die men exporteert} \drgeniusIndex{Figuur}{Exporteren}{Zone bepalen die men exporteert}{} \drgeo\ zal standaard de zichtbare zone van de figuur exporteren. Om dus een precieze zone van een figuur te exporteren, kunnen we de grootte van het \drgeo-venster aanpassen, tot we de gewenste zone bekomen\footnote{Men kan eventueel het zijpaneel met de boomstructuur openvouwen om de zone die men wil exporteren nog kleiner te krijgen.}. Hoewel die methode snel en eenvoudig kan werken, is ze niet altijd even soepel. Bovendien wordt de zone die men exporteert niet automatisch mee opgeslagen met de figuur zelf. Een andere manier van werken bestaat erin het commando \drgeniusMenu{De te exporteren zone afbakenen} te gebruiken. Gebruik hiervoor het menu \drgeniusMenu{Bestand->Instellingen m.b.t. exporteren}. Eens dit commando actief is, kan je op de figuur een rechthoek afbakenen, die dan kan worden geëxporteerd. Die rechthoekige zone kan men nadien zoveel bijstellen als men wil. Hij zal in het lichtgrijs getekend worden. Wanneer men achteraf de figuur opslaat, zal de afgebakende zone nu wel mee worden opgeslagen. Tenslotte kan men de bewuste zone altijd verwijderen via het commando \drgeniusMenu{De te exporteren zone verwijderen}. \drgeniusFigureSize{Een figuur waarin een te exporteren zone werd afgebakend}{fig56}{7} \drgeniusFigureSize{De zone werd geëxporteerd naar een PostScript-document en weergegeven met GhostView}{fig57}{7} \chapter{Receptenboek} Dit hoofdstuk is een steuntje in de rug voor wie meetkundige figuren wenst te tekenen met \drgenius. In tegenstelling tot de vorige hoofdstukken, is de aanpak hier concreet en op precieze situaties toegespitst. De inhoud van dit hoofdstuk werd tot stand gebracht aan de hand van de reacties van de gebruikers van \drgenius. \section{Constructies} \subsection{Een punt plaatsen met gegeven coördinaten} De meest eenvoudige manier bestaat erin een willekeurig punt te plaatsen --~via het instrument \link{Willekeurig Punt}[(Deel \Ref, pagina \Pageref)]{free_point}~-- en dan de eigenschappen van het punt aan te passen --~via het instrument \link{Eigenschap}[ (Deel \Ref, pagina \Pageref)]{property-item}~-- en met name de gewenste coördinaten in te voeren. Een andere mogelijkheid --~minder soepel voor dit voorbeeld~-- is om twee willekeurige getalwaarden in de figuur te plaatsen --~via het instrument \link{Getal}[ (Deel \Ref, pagina \Pageref)]{numeric_tool}~-- en dan een punt te construeren met beide waarden als coördinaten~-- instrument \link{Punt gedefinieerd door zijn coördinaten}[ (Deel \Ref, pagina \Pageref)]{coordinate_point}. Een voordeel echter, ten opzichte van de vorige methode is dat een punt dat zo werd geconstrueerd niet direct met de muis kan worden verplaatst. Het is als het ware vastgeketend aan zijn positie. \subsection{Een punt plaatsen a.d.h.v.\ zijn coördinaten} Deze functie wordt veelvuldig gebruikt wanneer men b.v. de meetkundige plaats van een punt wil construeren. Deze constructie veronderstelt het bestaan van twee waarden. Het punt wordt geplaatst met het instrument \link{Punt bepaald door zijn coördinaten}[ (Deel \Ref, pagina \Pageref)]{coordinate_point}. \section{Andere truken} \subsection{Een figuur afdrukken} \drgeniusIndex{Figuur}{Afdrukken}{}{} \drgeniusIndex{Afdrukken}{Figuur}{}{} De meest eenvoudige manier is om de figuur naar het PostScript-formaat te exporteren -- \link{Exporteren naar PostScript}[ Section \Ref, page \Pageref]{exporter-ps}. Gebruik vervolgens een programma dat PostScript-documenten kan weergeven en afdrukken. Zo'n document zal met vectoriële kwaliteit worden afgedrukt. De programma's GhostView, Gnome GhostView of K GhostView zijn daar perfect geschikt voor. \subsection{Een paragraaf met tekst in een figuur plaatsen} \drgeniusIndex{Weergeven}{Tekst}{}{} \drgeniusIndex{Figuur}{Weergeven}{Tekst}{} Hiervoor kan je voordelig gebruik maken van scripts, zij het op een wat afwijkende manier. Activeer de modus om een script te schrijven -- \link{het instrument voor scripts}[ (Deel \Ref, pagina \Pageref)]{script-tool} -- en klik onmiddellijk op de achtergrond van het scherm. Zo maak je een script aan zonder invoerparameter. Daarna dien je de eigenschappen van het script -- \link{eigenschappen van een object}[ (Deel \Ref, pagina \Pageref)]{property-item} -- aan te passen. In de tekstzone waar de Scheme-code normaal wordt geschreven kan je nu de tekst plaatsen. De tekst moet tussen aanhalingstekens staan en worden voorafgegaan door een apostrof. Bij voorbeeld~: \begin{verbatim} '"Animatie en waarnemingen ================ Verplaats de punten op de figuur en beantwoord volgende vragen. 1. Waar moet men het punt A' plaatsen zodat men het niet meer kan onderscheiden van A ? 2. Waar moet men het punt A plaatsen zodat men het punt A' niet meer kan onderscheiden van het punt B ? 3. Hoe moet men het punt I plaatsen zodat de punten B', C' en I op dezelfde lijn liggen ? 4. Wat is het spiegelpunt van I ? Wat is het spiegelpunt van A' ?" \end{verbatim} \drgeniusFigureSize{Voorbeeld van een paragraaf met tekst in een figuur}{fig58}{10} Zoals dat geldt voor elk script, kan men ook hier het kleur van de tekst aanpassen. \W \chapter*{Index} \W \htmlprintindex \W \begin{iftex} \appendix \listoffigures \printindex \W \end{iftex} \chapter{GNU Free Documentation License} \input{../fdl} \end{document} % LocalWords: Guile Homothétie homothétie macro-construction glisser-déposer % LocalWords: redessinée drgeo-doc-1.5/nl/figures/0002777000175000017500000000000010117134567011053 5drgeo-doc-1.5/nl/default_behaviour.html0000644000175000017500000000667110117134567013711 Gebruikershandleiding van Dr. Geo -- Standaardvoorkeuren
Andere voorkeurenVoorkeuren van de gebruikeralt=""Standaardvoorkeuren

Standaardvoorkeuren

De standaardinstellingen van DR. GEO kunnen op verscheidene manieren worden bijgesteld. Om zijn voorkeuren in te stellen, gaat de gebruiker naar het menu Bewerken->Voorkeuren... om het dialoogvenster van de voorkeuren te openen.

Voorkeuren i.v.m. de meetkundige figuren

Het dialoogvenster bevat twee delen :
  1. Het eerste deel betreft de voorkeuren in verband met de meetkundige figuren. Met de oortjes kan men de standaardinstellingen van elk soort object (meetkundig of numeriek) aanpassen. Men kan er met name het uitzicht van de figuren regelen.
  2. Het tweede deel betreft de algemene voorkeuren :
    • Het aantal niveaus voor het Ongedaan maken/Herstellen ;
    • De standaardnaam bij creatie van een nieuwe figuur. De %d wordt vervangen door een geheel getal dat DR. GEO bijhoudt. Bij elke nieuwe figuur wordt dit getal met een eenheid verhoogd ;
    • De standaard internetbrowser - bladeraar - om de on-line-hulp weer te geven ;
    • De standaardnamen bij het opslaan van een figuur of een sessie ;
    • De standaardnamen voor bestanden met figuren die naar een LaTeX- of PostScript-formaat worden geëxporteerd ;

 

Commentaar of opmerkingen ?
Bent u vrijwilliger om delen van de handleiding te schrijven ?
-> Contacteer Hilaire Fernandes op OFSET of word lid van de mailing list van DR. GEO.

Andere voorkeurenVoorkeuren van de gebruikeralt=""Standaardvoorkeuren
drgeo-doc-1.5/nl/drgenius_100.html0000644000175000017500000005652410117134567012423 Gebruikershandleiding van Dr. Geo -- GNU Free Documentation License
FootnotesTopIndexGNU Free Documentation License

GNU Free Documentation License


                GNU Free Documentation License
                  Version 1.2, November 2002


 Copyright (C) 2000,2001,2002  Free Software Foundation, Inc.
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The "Title Page" means, for a printed book, the title page itself,
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The Document may include Warranty Disclaimers next to the notice which
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Disclaimers are considered to be included by reference in this
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no effect on the meaning of this License.


2. VERBATIM COPYING

You may copy and distribute the Document in any medium, either
commercially or noncommercially, provided that this License, the
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You may also lend copies, under the same conditions stated above, and
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If you publish printed copies (or copies in media that commonly have
printed covers) of the Document, numbering more than 100, and the
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If the required texts for either cover are too voluminous to fit
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If you publish or distribute Opaque copies of the Document numbering
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It is requested, but not required, that you contact the authors of the
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4. MODIFICATIONS

You may copy and distribute a Modified Version of the Document under
the conditions of sections 2 and 3 above, provided that you release
the Modified Version under precisely this License, with the Modified
Version filling the role of the Document, thus licensing distribution
and modification of the Modified Version to whoever possesses a copy
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A. Use in the Title Page (and on the covers, if any) a title distinct
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B. List on the Title Page, as authors, one or more persons or entities
   responsible for authorship of the modifications in the Modified
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   Document (all of its principal authors, if it has fewer than five),
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C. State on the Title page the name of the publisher of the
   Modified Version, as the publisher.
D. Preserve all the copyright notices of the Document.
E. Add an appropriate copyright notice for your modifications
   adjacent to the other copyright notices.
F. Include, immediately after the copyright notices, a license notice
   giving the public permission to use the Modified Version under the
   terms of this License, in the form shown in the Addendum below.
G. Preserve in that license notice the full lists of Invariant Sections
   and required Cover Texts given in the Document's license notice.
H. Include an unaltered copy of this License.
I. Preserve the section Entitled "History", Preserve its Title, and add
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J. Preserve the network location, if any, given in the Document for
   public access to a Transparent copy of the Document, and likewise
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   You may omit a network location for a work that was published at
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   publisher of the version it refers to gives permission.
K. For any section Entitled "Acknowledgements" or "Dedications",
   Preserve the Title of the section, and preserve in the section all
   the substance and tone of each of the contributor acknowledgements
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L. Preserve all the Invariant Sections of the Document,
   unaltered in their text and in their titles.  Section numbers
   or the equivalent are not considered part of the section titles.
M. Delete any section Entitled "Endorsements".  Such a section
   may not be included in the Modified Version.
N. Do not retitle any existing section to be Entitled "Endorsements"
   or to conflict in title with any Invariant Section.
O. Preserve any Warranty Disclaimers.

If the Modified Version includes new front-matter sections or
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of these sections as invariant.  To do this, add their titles to the
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These titles must be distinct from any other section titles.

You may add a section Entitled "Endorsements", provided it contains
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You may add a passage of up to five words as a Front-Cover Text, and a
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includes a cover text for the same cover, previously added by you or
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you may not add another; but you may replace the old one, on explicit
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The author(s) and publisher(s) of the Document do not by this License
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imply endorsement of any Modified Version.


5. COMBINING DOCUMENTS

You may combine the Document with other documents released under this
License, under the terms defined in section 4 above for modified
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The combined work need only contain one copy of this License, and
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Make the same adjustment to the section titles in the list of
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In the combination, you must combine any sections Entitled "History"
in the various original documents, forming one section Entitled
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Entitled "Endorsements".


6. COLLECTIONS OF DOCUMENTS

You may make a collection consisting of the Document and other documents
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License in the various documents with a single copy that is included in
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verbatim copying of each of the documents in all other respects.

You may extract a single document from such a collection, and distribute
it individually under this License, provided you insert a copy of this
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other respects regarding verbatim copying of that document.


7. AGGREGATION WITH INDEPENDENT WORKS

A compilation of the Document or its derivatives with other separate
and independent documents or works, in or on a volume of a storage or
distribution medium, is called an "aggregate" if the copyright
resulting from the compilation is not used to limit the legal rights
of the compilation's users beyond what the individual works permit.
When the Document is included in an aggregate, this License does not
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If the Cover Text requirement of section 3 is applicable to these
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the entire aggregate, the Document's Cover Texts may be placed on
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8. TRANSLATION

Translation is considered a kind of modification, so you may
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Replacing Invariant Sections with translations requires special
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or disclaimer, the original version will prevail.

If a section in the Document is Entitled "Acknowledgements",
"Dedications", or "History", the requirement (section 4) to Preserve
its Title (section 1) will typically require changing the actual
title.


9. TERMINATION

You may not copy, modify, sublicense, or distribute the Document except
as expressly provided for under this License.  Any other attempt to
copy, modify, sublicense or distribute the Document is void, and will
automatically terminate your rights under this License.  However,
parties who have received copies, or rights, from you under this
License will not have their licenses terminated so long as such
parties remain in full compliance.


10. FUTURE REVISIONS OF THIS LICENSE

The Free Software Foundation may publish new, revised versions
of the GNU Free Documentation License from time to time.  Such new
versions will be similar in spirit to the present version, but may
differ in detail to address new problems or concerns.  See
http://www.gnu.org/copyleft/.

Each version of the License is given a distinguishing version number.
If the Document specifies that a particular numbered version of this
License "or any later version" applies to it, you have the option of
following the terms and conditions either of that specified version or
of any later version that has been published (not as a draft) by the
Free Software Foundation.  If the Document does not specify a version
number of this License, you may choose any version ever published (not
as a draft) by the Free Software Foundation.


ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of
the License in the document and put the following copyright and
license notices just after the title page:

    Copyright (c)  YEAR  YOUR NAME.
    Permission is granted to copy, distribute and/or modify this document
    under the terms of the GNU Free Documentation License, Version 1.2
    or any later version published by the Free Software Foundation;
    with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
    A copy of the license is included in the section entitled "GNU
    Free Documentation License".

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
replace the "with...Texts." line with this:

    with the Invariant Sections being LIST THEIR TITLES, with the
    Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.

If you have Invariant Sections without Cover Texts, or some other
combination of the three, merge those two alternatives to suit the
situation.

If your document contains nontrivial examples of program code, we
recommend releasing these examples in parallel under your choice of
free software license, such as the GNU General Public License,
to permit their use in free software.

Commentaar of opmerkingen ?
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FootnotesTopIndexGNU Free Documentation License
drgeo-doc-1.5/nl/drgenius_101.html0000644000175000017500000000706710117134567012422 Gebruikershandleiding van Dr. Geo -- Footnotes
alt=""TopGNU Free Documentation LicenseFootnotes

Footnotes

 (1)
Met eenzelfde commando is het mogelijk een bepaald type object op verschillende wijzen te creëren. Wanneer je, bij voorbeeld, het commando `cirkel tekenen' gebruikt, kan je een cirkel definiëren aan de hand van het middelpunt enerzijds en een ander punt, een lengte (van de straal) of een lijnstuk (met de lengte van de straal) anderzijds.
 (2)
Macro-constructies hebben een meetkundige invalshoek. DGS daarentegen werken vanuit een numerieke invalshoek maar laten vooral ook toe te prutsen en de dingen fijn te stellen (te "hacken" in het Engels).
 (3)
In het bijzonder, de wiskundige functies
 (4)
Als je per toeval toch op een object zou klikken, selecteer dan opnieuw het instrument voor scripts. Dit zal de selectie van een object ongedaan maken.
 (5)
Deze abscis ligt in het interval [0 ; 1], en dit voor om het even welke soort lijn.
 (6)
Sessies zijn bestanden die verschillende DR. GEO-documenten (i.e. figuren en/of teksten) bevatten.
 (7)
GhostView is een programma dat zowel PostScript-documenten (.ps of .eps) als PDF's op het scherm kan weergeven
 (8)
Het formaat wordt herkend door TeXmacs, OpenOffice.org, LyX, LaTeX, Xfig, The Gimp en vele andere programma's
 (9)
Men kan eventueel het zijpaneel met de boomstructuur openvouwen om de zone die men wil exporteren nog kleiner te krijgen.
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alt=""TopGNU Free Documentation LicenseFootnotes
drgeo-doc-1.5/nl/drgenius_10.html0000644000175000017500000000444610117134567012337 Gebruikershandleiding van Dr. Geo -- Punt gedefinieerd door zijn coördinaten
alt=""Instrumenten die punten betreffenSnijpuntPunt gedefinieerd door zijn coördinaten

Punt gedefinieerd door zijn coördinaten

 

Tekent een punt, gedefinieerd door zijn coördinaten. De gebruiker voert twee getallen in, waarbij het eerste als abscis, en het tweede als ordinaat van het punt geldt.

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alt=""Instrumenten die punten betreffenSnijpuntPunt gedefinieerd door zijn coördinaten
drgeo-doc-1.5/nl/drgenius_11.html0000644000175000017500000000377510117134567012344 Gebruikershandleiding van Dr. Geo -- Rechte
HalfrechteInstrumenten die lijnen betreffenalt=""Rechte

Rechte

Tekent een rechte, door twee punten gedefinieerd. De gebruiker selecteert twee punten.

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HalfrechteInstrumenten die lijnen betreffenalt=""Rechte
drgeo-doc-1.5/nl/drgenius_12.html0000644000175000017500000000405110117134567012331 Gebruikershandleiding van Dr. Geo -- Rechte
HalfrechteInstrumenten die lijnen betreffenalt=""Rechte

Rechte

Tekent een rechte, door twee punten gedefinieerd. De gebruiker selecteert twee punten.

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HalfrechteInstrumenten die lijnen betreffenalt=""Rechte
drgeo-doc-1.5/nl/drgenius_13.html0000644000175000017500000000440410117134567012334 Gebruikershandleiding van Dr. Geo -- Halfrechte
LijnstukInstrumenten die lijnen betreffenRechteHalfrechte

Halfrechte

 

Tekent een halfrechte, bepaald door twee punten. De gebruiker selecteert twee punten. Het eerste punt vormt de oorsprong van de halfrechte, het tweede wordt een willekeurig punt op de halfrechte.

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LijnstukInstrumenten die lijnen betreffenRechteHalfrechte
drgeo-doc-1.5/nl/drgenius_14.html0000644000175000017500000000415310117134567012336 Gebruikershandleiding van Dr. Geo -- Lijnstuk
VectorInstrumenten die lijnen betreffenHalfrechteLijnstuk

Lijnstuk

 

Tekent een lijnstuk, begrensd door twee punten.

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VectorInstrumenten die lijnen betreffenHalfrechteLijnstuk
drgeo-doc-1.5/nl/drgenius_15.html0000644000175000017500000000431710117134567012341 Gebruikershandleiding van Dr. Geo -- Vector
CirkelInstrumenten die lijnen betreffenLijnstukVector

Vector

 

Tekent een vector, bepaald door twee punten. De gebruiker selecteert twee punten, waarvan het eerste als aangrijpingspunt geldt en het tweede het grenspunt is.

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CirkelInstrumenten die lijnen betreffenLijnstukVector
drgeo-doc-1.5/nl/drgenius_16.html0000644000175000017500000000456210117134567012344 Gebruikershandleiding van Dr. Geo -- Cirkel
CirkelboogInstrumenten die lijnen betreffenVectorCirkel

Cirkel

 

Tekent een cirkel. Men kan op verschillende manieren een cirkel tekenen. Men maakt een van drie volgende selecties :

  1. het middelpunt en een punt op de cirkel ;
  2. het middelpunt en een getal (de straal van de cirkel) ;
  3. de cirkel en een lijnstuk, dat de lengte van de straal bepaalt.
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CirkelboogInstrumenten die lijnen betreffenVectorCirkel
drgeo-doc-1.5/nl/drgenius_17.html0000644000175000017500000000441510117134567012342 Gebruikershandleiding van Dr. Geo -- Cirkelboog
Meetkundige plaatsInstrumenten die lijnen betreffenCirkelCirkelboog

Cirkelboog

 

Tekent een cirkelboog, bepaald door drie punten. Het eerste is het beginpunt van de boog, het derde is het eindpunt van de boog, en het tweede punt is een (willekeurig) punt op de boog.

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Meetkundige plaatsInstrumenten die lijnen betreffenCirkelCirkelboog
drgeo-doc-1.5/nl/drgenius_18.html0000644000175000017500000000471610117134567012347 Gebruikershandleiding van Dr. Geo -- Meetkundige plaats
VeelhoekInstrumenten die lijnen betreffenCirkelboogMeetkundige plaats

Meetkundige plaats

 

Creëert een meetkundige plaats, bepaald door twee punten. De gebruiker selecteert twee punten. Het eerste punt is een punt op een lijn. Het tweede punt staat in een welbepaalde relatie tot het eerste punt, zodat het eerste punt voorwaarden stelt aan de bewegingsvrijheid van het tweede (i.e. wanneer het ene punt beweegt, beweegt het andere eveneens).

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VeelhoekInstrumenten die lijnen betreffenCirkelboogMeetkundige plaats
drgeo-doc-1.5/nl/drgenius_19.html0000644000175000017500000000504010117134567012337 Gebruikershandleiding van Dr. Geo -- Veelhoek
alt=""Instrumenten die lijnen betreffenMeetkundige plaatsVeelhoek

Veelhoek

 

Tekent een veelhoek, bepaald door n punten. De gebruiker selecteert n+1 punten die de hoeken van de veelhoek bepalen. Het eerst en laatst geselecteerde punt moeten hetzelfde zijn. Zo weet DR. GEO dat de puntenselectie afgerond werd. Het object veelhoek is geen object dat zich gedraagt als de andere lijnen. Het is namelijk niet mogelijk om er een punt op te plaatsen of om een snijpunt te tekenen met een andere lijn. Het is daarentegen wel mogelijk om het beeld van een veelhoek te tekenen onder een meetkundige transformatie.

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alt=""Instrumenten die lijnen betreffenMeetkundige plaatsVeelhoek
drgeo-doc-1.5/nl/drgenius_20.html0000644000175000017500000000434010117134567012331 Gebruikershandleiding van Dr. Geo -- Evenwijdige rechte
LoodlijnInstrumenten die transformaties in het vlak betreffenalt=""Evenwijdige rechte

Evenwijdige rechte

 

Tekent een rechte, evenwijdig aan een richting en door een punt. De gebruiker selecteert een punt en een richting (zoals die bepaald wordt door een rechte, een halfrechte, een lijnstuk of een vector).

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LoodlijnInstrumenten die transformaties in het vlak betreffenalt=""Evenwijdige rechte
drgeo-doc-1.5/nl/drgenius_21.html0000644000175000017500000000441410117134567012334 Gebruikershandleiding van Dr. Geo -- Evenwijdige rechte
LoodlijnInstrumenten die transformaties in het vlak betreffenalt=""Evenwijdige rechte

Evenwijdige rechte

 

Tekent een rechte, evenwijdig aan een richting en door een punt. De gebruiker selecteert een punt en een richting (zoals die bepaald wordt door een rechte, een halfrechte, een lijnstuk of een vector).

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LoodlijnInstrumenten die transformaties in het vlak betreffenalt=""Evenwijdige rechte
drgeo-doc-1.5/nl/drgenius_22.html0000644000175000017500000000455610117134567012344 Gebruikershandleiding van Dr. Geo -- Loodlijn
Spiegeling (om een as)Instrumenten die transformaties in het vlak betreffenEvenwijdige rechteLoodlijn

Loodlijn

 

Tekent een rechte, loodrecht op een richting en door een punt. De gebruiker selecteert een punt en een richting (i.e. een rechte, een halfrechte, een lijnstuk of een vector).

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Spiegeling (om een as)Instrumenten die transformaties in het vlak betreffenEvenwijdige rechteLoodlijn
drgeo-doc-1.5/nl/drgenius_23.html0000644000175000017500000000463210117134567012340 Gebruikershandleiding van Dr. Geo -- Spiegeling (om een as)
PuntspiegelingInstrumenten die transformaties in het vlak betreffenLoodlijnSpiegeling (om een as)

Spiegeling (om een as)

 

Tekent het beeld van een object onder een spiegeling. De gebruiker selecteert het te spiegelen object en de spiegelas (een rechte). Wanneer je een rechte wil spiegelen, geldt de eerste rechte als de te spiegelen rechte.

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PuntspiegelingInstrumenten die transformaties in het vlak betreffenLoodlijnSpiegeling (om een as)
drgeo-doc-1.5/nl/drgenius_24.html0000644000175000017500000000465410117134567012345 Gebruikershandleiding van Dr. Geo -- Puntspiegeling
VerschuivingInstrumenten die transformaties in het vlak betreffenSpiegeling (om een as)Puntspiegeling

Puntspiegeling

 

Tekent het beeld van een object onder een puntspiegeling. De gebruiker selecteert het te spiegelen object en het centrum van de spiegeling (een punt). Wanneer de gebruiker een punt wil spiegelen, geldt het eerste punt als het te spiegelen punt.

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VerschuivingInstrumenten die transformaties in het vlak betreffenSpiegeling (om een as)Puntspiegeling
drgeo-doc-1.5/nl/drgenius_25.html0000644000175000017500000000450210117134567012336 Gebruikershandleiding van Dr. Geo -- Verschuiving
DraaiingInstrumenten die transformaties in het vlak betreffenPuntspiegelingVerschuiving

Verschuiving

 

Tekent het beeld van een object onder een verschuiving. Wanneer de gebruiker het beeld van een vector wenst te tekenen, geldt de eerste vector als de te verschuiven vector.

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DraaiingInstrumenten die transformaties in het vlak betreffenPuntspiegelingVerschuiving
drgeo-doc-1.5/nl/drgenius_26.html0000644000175000017500000000634210117134567012343 Gebruikershandleiding van Dr. Geo -- Draaiing
HomothetieInstrumenten die transformaties in het vlak betreffenVerschuivingDraaiing

Draaiing

 

Tekent het beeld van een object onder een draaiing. De gebruiker selecteert het te draaien object, het centrum van de draaiing en de hoek van de draaiing. Wanneer men het beeld van een punt onder een draaiing wil tekenen, geldt het eerst gekozen punt als het te draaien punt.

Aan de hoek kan men op drie verschillende manieren een waarde toekennen :

  • getalwaarde : de hoek wordt in dit geval uitgedrukt in radialen. Voorbeelden van getalwaarden zijn : een willekeurige waarde, een afstand tussen twee punten, de lengte van een lijnstuk, een coördinaat, een waarde die de uitkomst is van een DR. GEO-Guile-script, etc. ;
  • de grootte van een meetkundige hoek, gevormd door drie punten : hier wordt de hoekgrootte uitgedrukt in graden. Opgelet, de grootte kan in dit geval enkel vallen in het interval [0 ; 180] ;
  • de grootte van een georiënteerde hoek tussen twee vectoren : hier wordt de hoekgrootte uitgedrukt in graden. De grootte van de hoek kan vallen in het interval ]-180 ; 180].
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HomothetieInstrumenten die transformaties in het vlak betreffenVerschuivingDraaiing
drgeo-doc-1.5/nl/drgenius_27.html0000644000175000017500000000446310117134567012346 Gebruikershandleiding van Dr. Geo -- Homothetie
alt=""Instrumenten die transformaties in het vlak betreffenDraaiingHomothetie

Homothetie

 

Tekent het beeld van een object onder een homothetie. De gebruiker selecteert een te transformeren object, het centrum en de factor (i.e. een getal). Wanneer je het beeld van een punt wil tekenen, geldt het eerste punt als het te transformeren punt.

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alt=""Instrumenten die transformaties in het vlak betreffenDraaiingHomothetie
drgeo-doc-1.5/nl/drgenius_28.html0000644000175000017500000000527210117134567012346 Gebruikershandleiding van Dr. Geo -- Afstand, lengte & getal
HoekNumerieke instrumentenalt=""Afstand, lengte & getal

Afstand, lengte & getal

 

Creëert een getalwaarde. De getalwaarde kan naar keuze ofwel berekend ofwel ingebracht worden :

  1. twee punten : de afstand tussen deze twee punten ;
  2. een lijnstuk : de lengte van het lijnstuk ;
  3. een vector : de norm van deze vector ;
  4. un cirkel : de omtrek van de cirkel ;
  5. un cirkelboog : de lengte van de cirkelboog ;
  6. een rechte : de richtingscoëfficiënt van de rechte ;
  7. een rechte en een punt : de afstand tussen van het punt tot de rechte ;
  8. wanneer je op het tekenvlak klikt, kan je een nieuwe getalwaarde invoeren (i.e. een willekeurige waarde).
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HoekNumerieke instrumentenalt=""Afstand, lengte & getal
drgeo-doc-1.5/nl/drgenius_29.html0000644000175000017500000000535010117134567012344 Gebruikershandleiding van Dr. Geo -- Afstand, lengte & getal
HoekNumerieke instrumentenalt=""Afstand, lengte & getal

Afstand, lengte & getal

 

Creëert een getalwaarde. De getalwaarde kan naar keuze ofwel berekend ofwel ingebracht worden :

  1. twee punten : de afstand tussen deze twee punten ;
  2. een lijnstuk : de lengte van het lijnstuk ;
  3. een vector : de norm van deze vector ;
  4. een cirkel : de omtrek van de cirkel ;
  5. een cirkelboog : de lengte van de cirkelboog ;
  6. een rechte : de richtingscoëfficiënt van de rechte ;
  7. een rechte en een punt : de afstand tussen van het punt tot de rechte ;
  8. wanneer je op het tekenvlak klikt, kan je een nieuwe getalwaarde invoeren (i.e. een willekeurige waarde).
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HoekNumerieke instrumentenalt=""Afstand, lengte & getal
drgeo-doc-1.5/nl/drgenius_2.html0000644000175000017500000000471010117134567012252 Gebruikershandleiding van Dr. Geo -- Copyright
InleidingTopInhoudsopgaveCopyright

Copyright

Copyright (c) 2000-2003 OFSET.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.

Other copyright apply to the respective owners of the modified documentations. See the section history for the complet list.

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InleidingTopInhoudsopgaveCopyright
drgeo-doc-1.5/nl/drgenius_30.html0000644000175000017500000000475510117134567012344 Gebruikershandleiding van Dr. Geo -- Hoek
CoördinatenNumerieke instrumentenAfstand, lengte & getalHoek

Hoek

 

Berekent de grootte van een hoek, gedefinieerd door hetzij drie punten hetzij twee vectoren. In het eerste geval wordt de hoek als niet-georiënteerd

beschouwd (i.e. als een hoek waarvan de grootte binnen het interval [0 ; 180] graden valt). In het tweede geval wordt de hoek als een georiënteerde hoek beschouwt en valt de hoekgrootte dus binnen het interval ]-180 ; 180].

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CoördinatenNumerieke instrumentenAfstand, lengte & getalHoek
drgeo-doc-1.5/nl/drgenius_31.html0000644000175000017500000000430010117134567012327 Gebruikershandleiding van Dr. Geo -- Coördinaten
DR. GEO-Guile-scriptNumerieke instrumentenHoekCoördinaten

Coördinaten

 

Creëert de coördinaten (abscis en ordinaat) van een punt of van een vector.

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DR. GEO-Guile-scriptNumerieke instrumentenHoekCoördinaten
drgeo-doc-1.5/nl/drgenius_32.html0000644000175000017500000000511610117134567012336 Gebruikershandleiding van Dr. Geo -- DR. GEO-Guile-script
alt=""Numerieke instrumentenCoördinatenDR. GEO-Guile-script

DR. GEO-Guile-script

 

Maakt een DR. GEO-Guile-script aan. Het script ontvangt n objecten als invoergegevens. Het kan, wanneer daarom gevraagd wordt, een getalwaarde als uitkomst leveren, die dan wordt afgebeeld in de figuur. Een script kan gebruikt worden omwille van de neveneffecten of voor de uitkomst die het levert. De Guile-scripts van DR. GEO worden in detail belicht in het hoofdstuk voor gevorderde functies en met name in het deel DR. GEO-Guile-scripts.

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alt=""Numerieke instrumentenCoördinatenDR. GEO-Guile-script
drgeo-doc-1.5/nl/drgenius_33.html0000644000175000017500000000432310117134567012336 Gebruikershandleiding van Dr. Geo -- Een macro-constructie aanmaken
Een macro-constructie uitvoerenInstrumenten voor macro-constructiesalt=""Een macro-constructie aanmaken

Een macro-constructie aanmaken

Slaat de opeenvolgende stappen van de constructie van een meetkundige figuur op en vormt het geheel om tot één enkele macro-constructie.

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Een macro-constructie uitvoerenInstrumenten voor macro-constructiesalt=""Een macro-constructie aanmaken
drgeo-doc-1.5/nl/drgenius_34.html0000644000175000017500000000437710117134567012350 Gebruikershandleiding van Dr. Geo -- Een macro-constructie aanmaken
Een macro-constructie uitvoerenInstrumenten voor macro-constructiesalt=""Een macro-constructie aanmaken

Een macro-constructie aanmaken

Slaat de opeenvolgende stappen van de constructie van een meetkundige figuur op en vormt het geheel om tot één enkele macro-constructie.

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Een macro-constructie uitvoerenInstrumenten voor macro-constructiesalt=""Een macro-constructie aanmaken
drgeo-doc-1.5/nl/drgenius_35.html0000644000175000017500000000477210117134567012350 Gebruikershandleiding van Dr. Geo -- Een macro-constructie uitvoeren
alt=""Instrumenten voor macro-constructiesEen macro-constructie aanmakenEen macro-constructie uitvoeren

Een macro-constructie uitvoeren

Voert een vooraf aangemaakte macro-constructie uit (i.e. "lanceert ze" of "laat ze afspelen"). De macro-constructie kan nieuw zijn (pas geconstrueerd) of opgeroepen zijn uit een bestand (waar ze vooraf werd opgeslagen).

(!) De macro-constructies worden voorgesteld in het deel gewijd aan macro-constructie.
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alt=""Instrumenten voor macro-constructiesEen macro-constructie aanmakenEen macro-constructie uitvoeren
drgeo-doc-1.5/nl/drgenius_36.html0000644000175000017500000000531710117134567012345 Gebruikershandleiding van Dr. Geo -- Boomstructuur van de constructie
Een figuur verplaatsenAndere functiesalt=""Boomstructuur van de constructie

Boomstructuur van de constructie

Elke figuur is verbonden met een boomstructuur van de constructie. De boom is chronologisch, d.w.z. dat hij van boven naar beneden de verschillende stappen in de constructie van de figuur weergeeft. Bepaalde takken aan de boom kunnen worden uitgeklapt om de antecedenten -  de samenstellende objecten - zichtbaar te maken die gebruikt werden om het (resulterende) object te definiëren.

De boom wordt standaard verscholen. Hij is eigenlijk dichtgeklapt tegen de linkerboord van het venster. Om hem te voorschijn te toveren, moet je de boom ontvouwen met behulp van de muis. Beweeg hiertoe de muis naar de linkerrand van het DR. GEO-venster. Wanneer de muiscursor verandert in een"<->", druk dan de muisknop in en sleep de boom open (naar rechts).

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Een figuur verplaatsenAndere functiesalt=""Boomstructuur van de constructie
drgeo-doc-1.5/nl/drgenius_37.html0000644000175000017500000000537310117134567012350 Gebruikershandleiding van Dr. Geo -- Boomstructuur van de constructie
Een figuur verplaatsenAndere functiesalt=""Boomstructuur van de constructie

Boomstructuur van de constructie

Elke figuur is verbonden met een boomstructuur van de constructie. De boom is chronologisch, d.w.z. dat hij van boven naar beneden de verschillende stappen in de constructie van de figuur weergeeft. Bepaalde takken aan de boom kunnen worden uitgeklapt om de antecedenten -  de samenstellende objecten - zichtbaar te maken die gebruikt werden om het (resulterende) object te definiëren.

De boom wordt standaard verscholen. Hij is eigenlijk dichtgeklapt tegen de linkerboord van het venster. Om hem te voorschijn te toveren, moet je de boom ontvouwen met behulp van de muis. Beweeg hiertoe de muis naar de linkerrand van het DR. GEO-venster. Wanneer de muiscursor verandert in een"<->", druk dan de muisknop in en sleep de boom open (naar rechts).

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Een figuur verplaatsenAndere functiesalt=""Boomstructuur van de constructie
drgeo-doc-1.5/nl/drgenius_38.html0000644000175000017500000000426310117134567012346 Gebruikershandleiding van Dr. Geo -- Een figuur verplaatsen
Een object verplaatsenAndere functiesBoomstructuur van de constructieEen figuur verplaatsen

Een figuur verplaatsen

Je kan een figuur verplaatsen door de Control-toets in te drukken samen met de eerste muisknop.

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Een object verplaatsenAndere functiesBoomstructuur van de constructieEen figuur verplaatsen
drgeo-doc-1.5/nl/drgenius_39.html0000644000175000017500000000524110117134567012344 Gebruikershandleiding van Dr. Geo -- Een object verplaatsen
Een object verwijderenAndere functiesEen figuur verplaatsenEen object verplaatsen

Een object verplaatsen

 

Je kan een object verplaatsen door het vast te nemen (eerste muisknop) en te verschuiven naar de gewenste plaats. De figuur wordt ogenblikkelijk opnieuw getekend, rekening houdende met haar eigenschappen. Omzeggens alle meetkundige objecten kunnen verplaatst worden. Als het nodig is verplaatst DR. GEO eveneens de willekeurige punten die in verband staan tot het object. Wanneer je b.v. een rechte verplaatst, die gedefinieerd werd door twee punten, zal DR. GEO in eenzelfde beweging deze punten meeverplaatsen.

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Een object verwijderenAndere functiesEen figuur verplaatsenEen object verplaatsen
drgeo-doc-1.5/nl/drgenius_3.html0000644000175000017500000000440110117134567012250 Gebruikershandleiding van Dr. Geo -- Basisfuncties
Gevorderde functiesTopInleidingBasisfuncties

Basisfuncties

Dit hoofdstuk beschrijft de instrumenten om een meetkundige figuur te construeren. Op het einde wordt getoond hoe de gebruiker zijn persoonlijke voorkeuren kan instellen.

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Gevorderde functiesTopInleidingBasisfuncties
drgeo-doc-1.5/nl/drgenius_40.html0000644000175000017500000000507710117134567012343 Gebruikershandleiding van Dr. Geo -- Een object verwijderen
Het uitzicht van een object aanpassenAndere functiesEen object verplaatsenEen object verwijderen

Een object verwijderen

 

Een object van een figuur kan verwijderd worden door dit menu te activeren. De gebruiker kan de verwijdering eventueel annuleren. Hij kan daartoe ofwel de functie `Ongedaan maken' gebruiken op de taakbalk, ofwel door dezelfde functie aan te klikken in het menu. Standaard zijn 10 opeenvolgende annulaties mogelijk, maar dit aantal kan worden aangepast in het dialoogvenster `Voorkeuren'.

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Het uitzicht van een object aanpassenAndere functiesEen object verplaatsenEen object verwijderen
drgeo-doc-1.5/nl/drgenius_41.html0000644000175000017500000000623510117134567012341 Gebruikershandleiding van Dr. Geo -- De eigenschappen van een object aanpassen
Een rooster weergevenAndere functiesHet uitzicht van een object aanpassenDe eigenschappen van een object aanpassen

De eigenschappen van een object aanpassen

 

Van bepaalde eigenschappen van objecten kan de gebruiker de parameters aanpassen. Wanneer je op een object klikt, verschijnt het geëigende dialoogvenster. Op dit moment gaat het over volgende objecten :

  1. willekeurig punt : abscis et ordinaat kan men wijzigen ;

    Aanpassingen voor de coördinaten van een willekeurig punt

  2. willekeurige getalwaarde : de waarde kan aangepast worden ;

    Wijzigiging van een willekeurige getalwaarde

  3. script : de code kan aangepast worden.

    Wijziging van een script

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Een rooster weergevenAndere functiesHet uitzicht van een object aanpassenDe eigenschappen van een object aanpassen
drgeo-doc-1.5/nl/drgenius_42.html0000644000175000017500000000631110117134567012335 Gebruikershandleiding van Dr. Geo -- De eigenschappen van een object aanpassen
Een rooster weergevenAndere functiesHet uitzicht van een object aanpassenDe eigenschappen van een object aanpassen

De eigenschappen van een object aanpassen

 

Van bepaalde eigenschappen van objecten kan de gebruiker de parameters aanpassen. Wanneer je op een object klikt, verschijnt het geëigende dialoogvenster. Op dit moment gaat het over volgende objecten :

  1. willekeurig punt : abscis et ordinaat kan men wijzigen ;

    Aanpassingen voor de coördinaten van een willekeurig punt

  2. willekeurige getalwaarde : de waarde kan aangepast worden ;

    Wijzigiging van een willekeurige getalwaarde

  3. script : de code kan aangepast worden.

    Wijziging van een script

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Een rooster weergevenAndere functiesHet uitzicht van een object aanpassenDe eigenschappen van een object aanpassen
drgeo-doc-1.5/nl/drgenius_43.html0000644000175000017500000000471410117134567012343 Gebruikershandleiding van Dr. Geo -- Een rooster weergeven
alt=""Andere functiesDe eigenschappen van een object aanpassenEen rooster weergeven

Een rooster weergeven

Het is mogelijk een rooster met de eenheden weer te geven op elke DR. GEO-figuur via het menu Editie->Rooster tonen of verbergen. Je kan een rooster eveneens oproepen met de sneltoets Ctrl-G. Wanneer men de functie een tweede maal activeert, verdwijnt het rooster opnieuw. Het betreft een unitair rooster : elke onderverdeling stelt een eenheid voor. Tenslotte, wanneer het rooster zichtbaar is bij het opslaan, wordt het mee opgeslagen.

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alt=""Andere functiesDe eigenschappen van een object aanpassenEen rooster weergeven
drgeo-doc-1.5/nl/drgenius_44.html0000644000175000017500000000410210117134567012333 Gebruikershandleiding van Dr. Geo -- Voorkeuren van de gebruiker
alt=""BasisfunctiesAndere functiesVoorkeuren van de gebruiker

Voorkeuren van de gebruiker

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alt=""BasisfunctiesAndere functiesVoorkeuren van de gebruiker
drgeo-doc-1.5/nl/drgenius_45.html0000644000175000017500000000435010117134567012341 Gebruikershandleiding van Dr. Geo -- Andere voorkeuren
alt=""Voorkeuren van de gebruikerStandaardvoorkeurenAndere voorkeuren

Andere voorkeuren

Naast de standaardinstellingen van DR. GEO, kan de gebruiker ook de naam van een figuur aanpassen via het menu Bewerken->Nieuwe naam geven.

Naam van een figuur wijzigen

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alt=""Voorkeuren van de gebruikerStandaardvoorkeurenAndere voorkeuren
drgeo-doc-1.5/nl/drgenius_46.html0000644000175000017500000000442410117134567012344 Gebruikershandleiding van Dr. Geo -- Andere voorkeuren
alt=""Voorkeuren van de gebruikerStandaardvoorkeurenAndere voorkeuren

Andere voorkeuren

Naast de standaardinstellingen van DR. GEO, kan de gebruiker ook de naam van een figuur aanpassen via het menu Bewerken->Nieuwe naam geven.

Naam van een figuur wijzigen

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alt=""Voorkeuren van de gebruikerStandaardvoorkeurenAndere voorkeuren
drgeo-doc-1.5/nl/drgenius_47.html0000644000175000017500000000656610117134567012356 Gebruikershandleiding van Dr. Geo -- Gevorderde functies
DR. GEO-Scheme-figurenTopBasisfunctiesGevorderde functies

Gevorderde functies

In dit hoofdstuk stellen wij functies voor die toelaten de mogelijkheden van DR. GEO uit te breiden of het programma aan te passen aan een gegeven lessituatie.

De eerste functie is de macro-constructie. Hiermee kan je verschillende opeenvolgende stappen in een constructie opslaan. Achteraf kan je deze constructie (opname) automatisch opnieuw laten bouwen (laten afspelen) of ze bewaren in een bestand.

De DR. GEO-Guile-scripts - DGS - vormen een andere uitbreidingsmogelijkheid voor DR. GEO. Deze scripts zijn werkelijk onderdelen van een figuur net als de meetkundige onderdelen. Zo'n script krijgt een of meer meetkundige items als input, en geeft als output een getalwaarde die in de figuur wordt geplaatst.

De Guile scripts in DR. GEO zijn nuttig omdat ze een waarde berekenen en weergeven of omwille van hun `pedagogisch surplus'. Alles hangt af van wat de gebruiker wil realiseren.

Tenslotte is er de aanpassing van de gebruikersinterface van DR. GEO. Deze stelt een leraar in staat stelt een sessie voor te bereiden met documenten waarin bepaalde functies geblokkeerd zijn en beveiligd met een paswoord.

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DR. GEO-Scheme-figurenTopBasisfunctiesGevorderde functies
drgeo-doc-1.5/nl/drgenius_48.html0000644000175000017500000001210110117134567012335 Gebruikershandleiding van Dr. Geo -- Aanmaken van de macro-constructie
Uitvoeren van een macro-constructieMacro-constructiealt=""Aanmaken van de macro-constructie

Aanmaken van de macro-constructie

Op dit moment, zijn de opeenvolgende stappen in de constructie doorlopen. De gebruiker dient nu DR. GEO duidelijk te maken dat hij een macro-constructie wil maken, vertrekkende van deze voorbeeldconstructie. Daartoe moet hij beroep doen op de functie Een macro aanmaken die men op de taakbalk vindt of via het contextueel menu van het beeld in zijn geheel.

Een dialoogvenster zal de gebruiker bijstaan tot op het einde. Je selecteert de invoerparameters en de uitvoerparameters. Vervolgens kies je de naam en voeg je eventueel een beschrijving van de macro-constructie toe.

Eerste pagina van het dialoogvenster dat de aanmaak van een macro-constructie begeleidt

Op de tweede pagina van het dialoogvenster kan men de invoerparameters kiezen. In ons voorbeeld gaat het om de drie punten die de cirkel definiëren. Het enige wat de gebruiker moet doen is naar die tweede pagina gaan en de drie punten op de figuur aanklikken. Als items correct geselecteerd worden, flikkeren ze op het scherm.

De tweede pagina, de drie punten zijn geselecteerd

Op de derde pagina kiest de gebruiker de uitvoerparameters. In ons voorbeeld willen we de cirkel en zijn middelpunt als resultaat van de macro-constructie. De uitvoerparameters worden op dezelfde manier gekozen als de invoerparameters.

De derde pagina, de cirkel en zijn middelpunt zijn geselecteerd

Op de vierde pagina kan de gebruiker een naam en een beschrijving toekennen aan de macro-constructie. Die informatie zal weergegeven worden, telkens je de bewuste macro-constructie uitvoert. Op die manier zijn macro-constructies overigens makkelijk te onderscheiden van mekaar.

De vierde pagina, de naam en de beschrijving van de macro-constructie

Op de vijfde en laatste pagina van het dialoogvenster wordt de aanmaak afgerond, zodra de gebruiker op de knop Beëindigen drukt. Als hij dat wil, kan hij ook op zijn stappen terugkeren en de parameters van de macro-constructie aanpassen.

(!) Als de keuze van invoerparameters en van uitvoerparameters niet coherent is (DR. GEO vindt geen logica in de constructie), kan de macro-constructie niet aangemaakt worden. In dat geval, bekijkt de gebruiker zijn selectie van invoer- en uitvoerparameters best nog eens van dichterbij. Hij kan altijd terug naar de tweede of derde pagina van het dialoogvenster om die keuze te veranderen.

In deze fase is de macro-constructie aangemaakt en steekt hij in het geheugen van DR. GEO. In het volgende deel, zien we hoe er gebruik van te maken.

Commentaar of opmerkingen ?
Bent u vrijwilliger om delen van de handleiding te schrijven ?
-> Contacteer Hilaire Fernandes op OFSET (hilaire@ofset.org) of word lid van de mailing list van DR. GEO.

Uitvoeren van een macro-constructieMacro-constructiealt=""Aanmaken van de macro-constructie
drgeo-doc-1.5/nl/drgenius_49.html0000644000175000017500000001215510117134567012347 Gebruikershandleiding van Dr. Geo -- Aanmaken van de macro-constructie
Uitvoeren van een macro-constructieMacro-constructiealt=""Aanmaken van de macro-constructie

Aanmaken van de macro-constructie

Op dit moment, zijn de opeenvolgende stappen in de constructie doorlopen. De gebruiker dient nu DR. GEO duidelijk te maken dat hij een macro-constructie wil maken, vertrekkende van deze voorbeeldconstructie. Daartoe moet hij beroep doen op de functie Een macro aanmaken die men op de taakbalk vindt of via het contextueel menu van het beeld in zijn geheel.

Een dialoogvenster zal de gebruiker bijstaan tot op het einde. Je selecteert de invoerparameters en de uitvoerparameters. Vervolgens kies je de naam en voeg je eventueel een beschrijving van de macro-constructie toe.

Eerste pagina van het dialoogvenster dat de aanmaak van een macro-constructie begeleidt

Op de tweede pagina van het dialoogvenster kan men de invoerparameters kiezen. In ons voorbeeld gaat het om de drie punten die de cirkel definiëren. Het enige wat de gebruiker moet doen is naar die tweede pagina gaan en de drie punten op de figuur aanklikken. Als items correct geselecteerd worden, flikkeren ze op het scherm.

De tweede pagina, de drie punten zijn geselecteerd

Op de derde pagina kiest de gebruiker de uitvoerparameters. In ons voorbeeld willen we de cirkel en zijn middelpunt als resultaat van de macro-constructie. De uitvoerparameters worden op dezelfde manier gekozen als de invoerparameters.

De derde pagina, de cirkel en zijn middelpunt zijn geselecteerd

Op de vierde pagina kan de gebruiker een naam en een beschrijving toekennen aan de macro-constructie. Die informatie zal weergegeven worden, telkens je de bewuste macro-constructie uitvoert. Op die manier zijn macro-constructies overigens makkelijk te onderscheiden van mekaar.

De vierde pagina, de naam en de beschrijving van de macro-constructie

Op de vijfde en laatste pagina van het dialoogvenster wordt de aanmaak afgerond, zodra de gebruiker op de knop Beëindigen drukt. Als hij dat wil, kan hij ook op zijn stappen terugkeren en de parameters van de macro-constructie aanpassen.

(!) Als de keuze van invoerparameters en van uitvoerparameters niet coherent is (DR. GEO vindt geen logica in de constructie), kan de macro-constructie niet aangemaakt worden. In dat geval, bekijkt de gebruiker zijn selectie van invoer- en uitvoerparameters best nog eens van dichterbij. Hij kan altijd terug naar de tweede of derde pagina van het dialoogvenster om die keuze te veranderen.

In deze fase is de macro-constructie aangemaakt en steekt hij in het geheugen van DR. GEO. In het volgende deel, zien we hoe er gebruik van te maken.

Commentaar of opmerkingen ?
Bent u vrijwilliger om delen van de handleiding te schrijven ?
-> Contacteer Hilaire Fernandes op OFSET of word lid van de mailing list van DR. GEO.

Uitvoeren van een macro-constructieMacro-constructiealt=""Aanmaken van de macro-constructie
drgeo-doc-1.5/nl/drgenius_4.html0000644000175000017500000000445510117134567012262 Gebruikershandleiding van Dr. Geo -- Basisfuncties
Gevorderde functiesTopInleidingBasisfuncties

Basisfuncties

Dit hoofdstuk beschrijft de instrumenten om een meetkundige figuur te construeren. Op het einde wordt getoond hoe de gebruiker zijn persoonlijke voorkeuren kan instellen.

Commentaar of opmerkingen ?
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Gevorderde functiesTopInleidingBasisfuncties
drgeo-doc-1.5/nl/drgenius_50.html0000644000175000017500000000720110117134567012333 Gebruikershandleiding van Dr. Geo -- Uitvoeren van een macro-constructie
alt=""Macro-constructieAanmaken van de macro-constructieUitvoeren van een macro-constructie

Uitvoeren van een macro-constructie

Om een macro-constructie uit te voeren, doet de gebruiker beroep op de functie Een vooraf gebouwde macro uitvoeren vanop de taakbalk of via het contextueel menu van het beeld in zijn geheel.

In het dialoogvenster dat verschijnt, kiest de gebruiker de gewenste macro-constructie. Op de tweede pagina selecteert hij de macro-constructie uit de lijst bovenaan het dialoogvenster. Eens hij de macro gekozen heeft, kan hij onmiddellijk klikken op de invoerparameters op de figuur. Van zodra alle invoerparameters geselecteerd zijn, wordt de macro-constructie uitgevoerd en wordt het eindresultaat (de uitvoerparameters) zichtbaar.

De gebruiker selecteert de invoerparameters op de figuur

In ons voorbeeld had de macro-constructie drie invoerparameters nodig (drie punten), waarna de cirkel door die punten en zijn middelpunt worden geconstrueerd. Om de macro-constructie te kunnen uitvoeren, moeten er dus al drie punten staan op de figuur (waar we op aan het werken zijn).

Een figuur met drie punten

Wanneer we de macro-constructie toepassen op die drie punten, verschijnt de gewenste cirkel met zijn middelpunt.

De eindfiguur, met de cirkel en zijn middelpunt

Commentaar of opmerkingen ?
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-> Contacteer Hilaire Fernandes op OFSET of word lid van de mailing list van DR. GEO.

alt=""Macro-constructieAanmaken van de macro-constructieUitvoeren van een macro-constructie
drgeo-doc-1.5/nl/drgenius_51.html0000644000175000017500000002736610117134567012352 Gebruikershandleiding van Dr. Geo -- DGS a.d.h.v. voorbeelden
Methodes van verwijzen voor DR. GEO-scriptsDR. GEO Guile scriptsalt=""DGS a.d.h.v. voorbeelden

DGS a.d.h.v. voorbeelden

Het instrument om een DGS te schrijven is bereikbaar via het numerieke onderdeel van het contextueel menu of van de gereedschapskist. Een DGS kan tussen de 0 en n invoerparameters te verwerken krijgen.

Nadat men het instrument gekozen heeft, volstaat het de in te voeren objecten aan te klikken en vervolgens ergens op de achtergrond van de figuur. Op die laatst aangeklikte positie zal het script geplaatst worden.

In wat volgt stellen wij voor op enkele DGS-voorbeelden te werken, zodat men er de kracht en functionaliteit makkelijker van kan inzien. Net als de macro-constructies, geven de DGS een speciale dimensie aan DR. GEO. Ze laten je toe - elk met een andere aanpak2 - paden te bewandelen die de auteurs van het programma niet bewandeld hebben of niet wensen te bewandelen.

Het is belangrijk bewust te zijn dat het leeuwendeel van de funtionaliteit van de GNU-Guile-interpreter aanspreekbaar is via de DGS. Dit is met name zo voor de functiebibliotheken3, die we uiteraard intens zullen gebruiken.

DGS zonder invoerparameters

Klik, na het instrument voor scripts te hebben gekozen, direct op de achtergrond van de figuur, op de plaats waar je het script wil zetten. Klik vooral op geen enkel object van de figuur. Als je dat wel zou doen, denkt DR. GEO dat je dit object als invoerparameter van het script aanklikt4. Als het script een plaats gekregen heeft, ziet u de tekens "Dr. Genius" verschijnen. Elk nieuw script bevat standaard het commando om die tekenreeks af te beelden, maar dit kan je uiteraard aanpassen met behulp van het instrument m.b.t. de eigenschappen van een object. Klik na de selectie van voornoemd instrument op het script - of preciezer : op zijn waarde - dat u wil bijstellen op de figuur. Een dialoogvenster met het script zal verschijnen. In de rest van dit deel, zullen we de scripts in dit dialoogvenster invoeren.

Een generator van willekeurige en andere getallen

Niets is eenvoudiger dan willekeurige getallen genereren. Voer volgende code in : 

(random 10)

Bij elke update van de figuur, zal het script een willekeurig geheel getal voortbrengen dat valt in het interval [0 ; 10[.

Wanneer u een reëel getal (float) wenst in het interval [0 ; 1[, maak dan gebruik van volgend script : 

(random:uniform)

(!) Enkele precizeringen :
  • De uitkomst van het script is de waarde die op de laatste regel berekend werd. In dit voorbeeld, gaat het om een waarde die de uitkomst is van een functie waar we beroep op deden ;
  • De laatste regel van het script moet een reëel getal als uitkomst hebben. Anders zal DR. GEO de boodschap "Niet af te drukken resultaat" weergeven ;
  • Wanneer men de waarde van een veranderlijke wenst als uitkomst, volstaat het om de naam van de variabele op de laatste regel te plaatsen.

Veelgebruikte waarden berekenen

Om een benaderde waarde van pi te berekenen : 

(acos -1)

of van e : 

(exp 1)

De uitkomst van een DGS kan vervolgens gebruikt worden op dezelfde manier als alle andere getalwaarden die DR. GEO kan voortbrengen. Voor dit soort kleine zaken, zijn de DGS dus uw bondgenoten. Maar ze kunnen veel interessanter dingen wanneer je hen laat werken met invoerparameters.

DGS met minstens een invoerparameter

De procedure om een DGS met invoerparameters te creëren is bijna identiek. Het volstaat om, onmiddellijk na het instrument voor scripts te hebben geselecteerd, het object aan te klikken dat je als invoerparameter wenst te gebruiken. Klik vervolgens op de achtergrond van de figuur, op de plaats waar je het script zetten wil.

In het script wordt verwezen naar de invoerparameter met de veranderlijke a1. Hadden we twee invoerparameters gedefinieerd, dan zou de volgorde van selectie van die parameters weerspiegeld zijn in de naamgeving van de veranderlijken : a1 en a2. Hetzelfde gaat op voor drie, vier of meer invoerparameters.

Naargelang het type object waarnaar men verwijst, zijn er verschillende methoden om de getalwaarde te bekomen, om de coördinaten te bekomen, etc. Het overzicht van de methoden kan men nalezen in het deel Verwijzingsmethoden van de DGS.

In wat volgt, zullen we stapsgewijs de constructie uiteenzetten van een (deel van een) kromme en zijn tangens in een punt dat we zullen kunnen bewegen over dat deel van de kromme.

De eindfiguur wordt meegeleverd met DR. GEO. Zij heet slope.fgeo

De figuur die we zullen bekomen

Een waarde definiëren in een gegeven interval

Om te beginnen plaatsen we twee punten in een nieuwe figuur, en tekenen we het lijnstuk dat begrensd wordt door deze twee punten. Op dit lijnstuk plaatsen we een punt dat we "Move me!" noemen. Dit punt zal als ijkpunt fungeren ; de juiste afmetingen zal het script ons leveren. We creëren nu een script met als enige invoerparameter dit bewuste punt.

Als a1 verwijst naar het punt "Move me!", dan geeft het script dat volgt als uitkomst een reëel getal binnen het interval [-10 ; 10] : 

(define x (getAbscissa a1))
(* 20  (- x 0.5))

Wat uitleg is nodig. In de eerste regel, laat de aanroep (getAbscissa a1) toe de abscis te bekomen van het object waarnaar a1 verwijst5 - namelijk het punt "Move me!". De waarden van deze abscis worden toegekend aan een nieuwe veranderlijke x. Op de tweede regel passen we vervolgens de schaal aan. Deze uitdrukking zou in algebraïsche notatie overeenstemmen met 20 ×( x - 0.5). Omdat dit de laatste regel is, is de uitkomst van het script de uitkomst van die regel en wordt die uitkomst afgebeeld in de figuur.

Laat ons dit script, tenslotte, Xo noemen.

Een representatief gedeelte van een kromme afbeelden

We zullen ons bedienen van de uitkomst van het eerste script om met een tweede script de ordinaat te berekenen in een punt onder de functie x -> cos(x) : 

(define x (getValue a1))
(cos x)

De aanroep (getValue a1) laat toe de getalwaarde te bekomen van het object waarnaar we verwijzen met a1. Hier willen we de uitkomst van het vorige script gebruiken in een nieuw script. We zullen het Yo noemen.

In een volgende stap creëren we het punt Mo met coördinaten (Xo ; Yo). Het gaat om een willekeurig punt op de kromme x -> cos(x). Om een representatief gedeelte van de kromme af te beelden dat zich b.v. uitstrekt over het interval [-10 ; 10], creëren we de plaats van het punt Mo, wanneer het punt "Move Me!" het lijnstuk beschrijft. Zo, nu hebben we een kromme !

De raaklijn aan een kromme berekenen en afbeelden

Om de raaklijn in het punt Mo te tekenen, hebben we vooreerst de richtingscoëfficiënt in dat punt nodig, waarvoor we dus zowel de afgeleide functie x -> -sin(x) nodig hebben als Xo. We schrijven dus een script met als invoerparameter het script Xo : 

(- 0 (sin (getValue a1)))

De prefixnotatie die Scheme/Guile gebruikt kan verwarrend werken, maar is een kwestie van gewoonte. Laat ons dit script "richtingscoëfficiënt in Mo" noemen. Op die manier zal, telkens wanneer Mo verplaatst wordt, de richtingscoëfficiënt opnieuw berekend worden.

Er rest ons nog de raaklijn te tekenen. Daartoe berekenen we eerst de coördinaten van een tweede punt - M1 - van deze rechte.

Laat ons beginnen met de abscis, b.v. X1 = Xo + 2. Om die te berekenen, schrijven we een script met als invoerparameter het script Xo : 

(define x1 (getValue a1))
(+ x1 2)

Dit script noemen we X1.

Nu nog de ordinaat van M1 te pakken krijgen. Hiervoor hebben we hetvolgende nodig :

  • Mo (waarnaar we verwijzen met a1) ;
  • de richtingscoëfficiënt in Mo (a2) ;
  • de abscis van X1 (a3).

In dit script berekenen we de ordinaat van M1 op de volgende manier Yo + m ×(X1 - X0) : 

(define x0 (car (getCoordinates a1)))
(define y0 (cadr (getCoordinates a1)))
(define m (getValue a2))
(define x1 (getValue a3))
(+ (* m (- x1 x0)) y0)

Enkele woorden commentaar bij de aanroep (getCoordinates a1). Bij deze aanroep moet a1 verwijzen naar een object van het type `punt'. Deze methode geeft als output een lijst met de coördinaten van het punt - hier Mo. Met car kan men het eerste element uit de lijst nemen, en met cadr het tweede. De rest van het script zou geen problemen mogen stellen.

Laat ons dit script Y1 noemen. Nu kunnen we het punt M1 construeren, met coördinaten (X1 ; Y1) en tenslotte de raaklijn (MoM1).

Het was natuurlijk mogelijk om maar twee of drie scripts te schrijven in plaats van deze panoplie. Maar we hopen dat u met deze kleine voorbeelden de smaak te pakken krijgt en zelf met DGS aan de slag gaat.

Commentaar of opmerkingen ?
Bent u vrijwilliger om delen van de handleiding te schrijven ?
-> Contacteer Hilaire Fernandes op OFSET (hilaire@ofset.org) of word lid van de mailing list van DR. GEO.

Methodes van verwijzen voor DR. GEO-scriptsDR. GEO Guile scriptsalt=""DGS a.d.h.v. voorbeelden
drgeo-doc-1.5/nl/drgenius_52.html0000644000175000017500000002751410117134567012346 Gebruikershandleiding van Dr. Geo -- DGS a.d.h.v. voorbeelden
Methodes van verwijzen voor DR. GEO-scriptsDR. GEO Guile scriptsalt=""DGS a.d.h.v. voorbeelden

DGS a.d.h.v. voorbeelden

Het instrument om een DGS te schrijven is bereikbaar via het numerieke onderdeel van het contextueel menu of van de gereedschapskist. Een DGS kan tussen de 0 en n invoerparameters te verwerken krijgen.

Nadat men het instrument gekozen heeft, volstaat het de in te voeren objecten aan te klikken en vervolgens ergens op de achtergrond van de figuur. Op die laatst aangeklikte positie zal het script geplaatst worden.

In wat volgt stellen wij voor op enkele DGS-voorbeelden te werken, zodat men er de kracht en functionaliteit makkelijker van kan inzien. Net als de macro-constructies, geven de DGS een speciale dimensie aan DR. GEO. Ze laten je toe - elk met een andere aanpak2 - paden te bewandelen die de auteurs van het programma niet bewandeld hebben of niet wensen te bewandelen.

Het is belangrijk bewust te zijn dat het leeuwendeel van de funtionaliteit van de GNU-Guile-interpreter aanspreekbaar is via de DGS. Dit is met name zo voor de functiebibliotheken3, die we uiteraard intens zullen gebruiken.

DGS zonder invoerparameters

Klik, na het instrument voor scripts te hebben gekozen, direct op de achtergrond van de figuur, op de plaats waar je het script wil zetten. Klik vooral op geen enkel object van de figuur. Als je dat wel zou doen, denkt DR. GEO dat je dit object als invoerparameter van het script aanklikt4. Als het script een plaats gekregen heeft, ziet u de tekens "Dr. Genius" verschijnen. Elk nieuw script bevat standaard het commando om die tekenreeks af te beelden, maar dit kan je uiteraard aanpassen met behulp van het instrument m.b.t. de eigenschappen van een object. Klik na de selectie van voornoemd instrument op het script - of preciezer : op zijn waarde - dat u wil bijstellen op de figuur. Een dialoogvenster met het script zal verschijnen. In de rest van dit deel, zullen we de scripts in dit dialoogvenster invoeren.

Een generator van willekeurige en andere getallen

Niets is eenvoudiger dan willekeurige getallen genereren. Voer volgende code in : 

(random 10)

Bij elke update van de figuur, zal het script een willekeurig geheel getal voortbrengen dat valt in het interval [0 ; 10[.

Wanneer u een reëel getal (float) wenst in het interval [0 ; 1[, maak dan gebruik van volgend script : 

(random:uniform)

(!) Enkele precizeringen :
  • De uitkomst van het script is de waarde die op de laatste regel berekend werd. In dit voorbeeld, gaat het om een waarde die de uitkomst is van een functie waar we beroep op deden ;
  • De laatste regel van het script moet een reëel getal als uitkomst hebben. Anders zal DR. GEO de boodschap "Niet af te drukken resultaat" weergeven ;
  • Wanneer men de waarde van een veranderlijke wenst als uitkomst, volstaat het om de naam van de variabele op de laatste regel te plaatsen.

Veelgebruikte waarden berekenen

Om een benaderde waarde van pi te berekenen : 

(acos -1)

of van e : 

(exp 1)

De uitkomst van een DGS kan vervolgens gebruikt worden op dezelfde manier als alle andere getalwaarden die DR. GEO kan voortbrengen. Voor dit soort kleine zaken, zijn de DGS dus uw bondgenoten. Maar ze kunnen veel interessanter dingen wanneer je hen laat werken met invoerparameters.

DGS met minstens een invoerparameter

De procedure om een DGS met invoerparameters te creëren is bijna identiek. Het volstaat om, onmiddellijk na het instrument voor scripts te hebben geselecteerd, het object aan te klikken dat je als invoerparameter wenst te gebruiken. Klik vervolgens op de achtergrond van de figuur, op de plaats waar je het script zetten wil.

In het script wordt verwezen naar de invoerparameter met de veranderlijke a1. Hadden we twee invoerparameters gedefinieerd, dan zou de volgorde van selectie van die parameters weerspiegeld zijn in de naamgeving van de veranderlijken : a1 en a2. Hetzelfde gaat op voor drie, vier of meer invoerparameters.

Naargelang het type object waarnaar men verwijst, zijn er verschillende methoden om de getalwaarde te bekomen, om de coördinaten te bekomen, etc. Het overzicht van de methoden kan men nalezen in het deel Verwijzingsmethoden van de DGS.

In wat volgt, zullen we stapsgewijs de constructie uiteenzetten van een (deel van een) kromme en zijn tangens in een punt dat we zullen kunnen bewegen over dat deel van de kromme.

De eindfiguur wordt meegeleverd met DR. GEO. Zij heet /usr/share/drgeo/examples/figures/slope.fgeo.

De figuur die we zullen bekomen

Een waarde definiëren in een gegeven interval

Om te beginnen plaatsen we twee punten in een nieuwe figuur, en tekenen we het lijnstuk dat begrensd wordt door deze twee punten. Op dit lijnstuk plaatsen we een punt dat we "Move me!" noemen. Dit punt zal als ijkpunt fungeren ; de juiste afmetingen zal het script ons leveren. We creëren nu een script met als enige invoerparameter dit bewuste punt.

Als a1 verwijst naar het punt "Move me!", dan geeft het script dat volgt als uitkomst een reëel getal binnen het interval [-10 ; 10] : 

(define x (getAbscissa a1))
(* 20  (- x 0.5))

Wat uitleg is nodig. In de eerste regel, laat de aanroep (getAbscissa a1) toe de abscis te bekomen van het object waarnaar a1 verwijst5 - namelijk het punt "Move me!". De waarden van deze abscis worden toegekend aan een nieuwe veranderlijke x. Op de tweede regel passen we vervolgens de schaal aan. Deze uitdrukking zou in algebraïsche notatie overeenstemmen met 20 ×( x - 0.5). Omdat dit de laatste regel is, is de uitkomst van het script de uitkomst van die regel en wordt die uitkomst afgebeeld in de figuur.

Laat ons dit script, tenslotte, Xo noemen.

Een representatief gedeelte van een kromme afbeelden

We zullen ons bedienen van de uitkomst van het eerste script om met een tweede script de ordinaat te berekenen in een punt onder de functie x -> cos(x) : 

(define x (getValue a1))
(cos x)

De aanroep (getValue a1) laat toe de getalwaarde te bekomen van het object waarnaar we verwijzen met a1. Hier willen we de uitkomst van het vorige script gebruiken in een nieuw script. We zullen het Yo noemen.

In een volgende stap creëren we het punt Mo met coördinaten (Xo ; Yo). Het gaat om een willekeurig punt op de kromme x -> cos(x). Om een representatief gedeelte van de kromme af te beelden dat zich b.v. uitstrekt over het interval [-10 ; 10], creëren we de plaats van het punt Mo, wanneer het punt "Move Me!" het lijnstuk beschrijft. Zo, nu hebben we een kromme !

De raaklijn aan een kromme berekenen en afbeelden

Om de raaklijn in het punt Mo te tekenen, hebben we vooreerst de richtingscoëfficiënt in dat punt nodig, waarvoor we dus zowel de afgeleide functie x -> -sin(x) nodig hebben als Xo. We schrijven dus een script met als invoerparameter het script Xo : 

(- 0 (sin (getValue a1)))

De prefixnotatie die Scheme/Guile gebruikt kan verwarrend werken, maar is een kwestie van gewoonte. Laat ons dit script "richtingscoëfficiënt in Mo" noemen. Op die manier zal, telkens wanneer Mo verplaatst wordt, de richtingscoëfficiënt opnieuw berekend worden.

Er rest ons nog de raaklijn te tekenen. Daartoe berekenen we eerst de coördinaten van een tweede punt - M1 - van deze rechte.

Laat ons beginnen met de abscis, b.v. X1 = Xo + 2. Om die te berekenen, schrijven we een script met als invoerparameter het script Xo : 

(define x1 (getValue a1))
(+ x1 2)

Dit script noemen we X1.

Nu nog de ordinaat van M1 te pakken krijgen. Hiervoor hebben we hetvolgende nodig :

  • Mo (waarnaar we verwijzen met a1) ;
  • de richtingscoëfficiënt in Mo (a2) ;
  • de abscis van X1 (a3).

In dit script berekenen we de ordinaat van M1 op de volgende manier Yo + m ×(X1 - X0) : 

(define x0 (car (getCoordinates a1)))
(define y0 (cadr (getCoordinates a1)))
(define m (getValue a2))
(define x1 (getValue a3))
(+ (* m (- x1 x0)) y0)

Enkele woorden commentaar bij de aanroep (getCoordinates a1). Bij deze aanroep moet a1 verwijzen naar een object van het type `punt'. Deze methode geeft als output een lijst met de coördinaten van het punt - hier Mo. Met car kan men het eerste element uit de lijst nemen, en met cadr het tweede. De rest van het script zou geen problemen mogen stellen.

Laat ons dit script Y1 noemen. Nu kunnen we het punt M1 construeren, met coördinaten (X1 ; Y1) en tenslotte de raaklijn (MoM1).

Het was natuurlijk mogelijk om maar twee of drie scripts te schrijven in plaats van deze panoplie. Maar we hopen dat u met deze kleine voorbeelden de smaak te pakken krijgt en zelf met DGS aan de slag gaat.

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Methodes van verwijzen voor DR. GEO-scriptsDR. GEO Guile scriptsalt=""DGS a.d.h.v. voorbeelden
drgeo-doc-1.5/nl/drgenius_53.html0000644000175000017500000000505410117134567012342 Gebruikershandleiding van Dr. Geo -- Methodes van verwijzen voor DR. GEO-scripts
alt=""DR. GEO Guile scriptsDGS a.d.h.v. voorbeeldenMethodes van verwijzen voor DR. GEO-scripts

Methodes van verwijzen voor DR. GEO-scripts

De volgende delen beschrijven de methodes die beschikbaar zijn voor de DR. GEO-scripts. Ze zijn geordend naar het type meetkundig of numeriek object.
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alt=""DR. GEO Guile scriptsDGS a.d.h.v. voorbeeldenMethodes van verwijzen voor DR. GEO-scripts
drgeo-doc-1.5/nl/drgenius_54.html0000644000175000017500000000703110117134567012340 Gebruikershandleiding van Dr. Geo -- Punt
Rechte, Halfrechte, Lijnstuk, VectorMethodes van verwijzen voor DR. GEO-scriptsalt=""Punt

Punt

waarde (getAbscissa punt)
punt: Verwijzing naar een willekeurig punt op een lijn
Uitkomst: De abscis van dit punt op de lijn. De waarde ligt in het interval [0 ; 1]
Voorbeeld:
(define x (getValue a1))
(* x 10)

  (setAbscissa punt x)
punt: Verwijzing naar een willekeurig punt op een lijn
x: De decimale waarde binnen het interval [0 ; 1], die de nieuwe abscis voorstelt
Voorbeeld:
(setAbscissa a1 0.5)

 

lijst (getCoordinates punt|vector)
Geeft als output de coördinaten van een punt of een vector.
punt|vector: Verwijzing naar een punt of een vector
Uitkomst: Lijst die de coördinaten van het punt of van de vector bevat
Voorbeeld:
(define c (getCoordinates a1))
(define x (car c))
(define y (cadr c))
(+ (* x x) (* y y))

  (setCoordinates punt coörd)
Legt de coördinaten van een punt vast
punt: Verwijzing naar een willekeurig punt in het vlak
coörd: Lijst van twee decimale getallen
Voorbeeld:
(define l (list 1.4 (random 5)))
(setCoordinate a1 l)

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Rechte, Halfrechte, Lijnstuk, VectorMethodes van verwijzen voor DR. GEO-scriptsalt=""Punt
drgeo-doc-1.5/nl/drgenius_55.html0000644000175000017500000000574710117134567012355 Gebruikershandleiding van Dr. Geo -- Rechte, Halfrechte, Lijnstuk, Vector
Cirkel, CirkelboogMethodes van verwijzen voor DR. GEO-scriptsPuntRechte, Halfrechte, Lijnstuk, Vector

Rechte, Halfrechte, Lijnstuk, Vector

waarde (getSlope richting)
richting: Verwijzing naar een object van het type rechte, halfrechte, lijnstuk of vector
Uitkomst: De richtingscoëfficiënt van deze richting
Voorbeeld:
(define p (getSlope a1))

  waarde (getNorm vector)
vector: Verwijzing naar een vector
Uitkomst: De norm van deze vector
Voorbeeld:
(define n (getNorm a1))

  waarde (getLength lijnstuk)
lijnstuk: Verwijzing naar een lijnstuk
Uitkomst: De lengte van dit lijnstuk
Voorbeeld:
(define l (getLength a1))

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Cirkel, CirkelboogMethodes van verwijzen voor DR. GEO-scriptsPuntRechte, Halfrechte, Lijnstuk, Vector
drgeo-doc-1.5/nl/drgenius_56.html0000644000175000017500000000616010117134567012344 Gebruikershandleiding van Dr. Geo -- Cirkel, Cirkelboog
GetalMethodes van verwijzen voor DR. GEO-scriptsRechte, Halfrechte, Lijnstuk, VectorCirkel, Cirkelboog

Cirkel, Cirkelboog

lijst (getCenter cirkel|cirkelboog)
cirkel|cirkelboog: Verwijzing naar een cirkel of naar een cirkelboog
Uitkomst: Lijst die de coördinaten van het middelpunt van de cirkel of van de cirkelboog bevat
Voorbeeld:
(define c (getCenter a1))
(car c)

  waarde (getRadius cirkel|cirkelboog)
cirkel|cirkelboog: Verwijzing naar een cirkel of naar een cirkelboog
Uitkomst: Straal van de cirkel of van de cirkelboog
Voorbeeld:
(define r (getRadius a1))

  waarde (getLength cirkel|cirkelboog)
cirkel|cirkelboog: Verwijzing naar een cirkel of naar een cirkelboog
Uitkomst: Omtrek van de cirkel of lengte van de cirkelboog
Voorbeeld:
(define l (getLength a1))

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GetalMethodes van verwijzen voor DR. GEO-scriptsRechte, Halfrechte, Lijnstuk, VectorCirkel, Cirkelboog
drgeo-doc-1.5/nl/drgenius_57.html0000644000175000017500000000506410117134567012347 Gebruikershandleiding van Dr. Geo -- Getal
HoekMethodes van verwijzen voor DR. GEO-scriptsCirkel, CirkelboogGetal

Getal

waarde (getValue getal)
getal: Verwijzing naar een getal
Uitkomst: Waarde van dit getal
Voorbeeld:
(define a (getValue a1))
(define b (getValue a2))
(+ a b)

  (setValue getal v)
getal: Verwijzing naar een getal
v: Decimale getalwaarde
Voorbeeld:
(define v (getValue a1))
(setValue a2 v)

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HoekMethodes van verwijzen voor DR. GEO-scriptsCirkel, CirkelboogGetal
drgeo-doc-1.5/nl/drgenius_58.html0000644000175000017500000000476510117134567012357 Gebruikershandleiding van Dr. Geo -- Hoek
OverigeMethodes van verwijzen voor DR. GEO-scriptsGetalHoek

Hoek

waarde (getAngle hoek)
hoek: Verwijzing naar een meetkundige of georiënteerde hoek
Uitkomst: De hoek uitgedrukt in graden. Om de hoek in radialen te bekomen, dient men de methode getValue te gebruiken
Voorbeeld:
(define angle1 (getAngle a1))
(define angle2 (getAngle a2))
(define angle3 (getAngle a3))
(+ angle1 angle2 angle3)

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OverigeMethodes van verwijzen voor DR. GEO-scriptsGetalHoek
drgeo-doc-1.5/nl/drgenius_59.html0000644000175000017500000000426210117134567012350 Gebruikershandleiding van Dr. Geo -- Overige
alt=""Methodes van verwijzen voor DR. GEO-scriptsHoekOverige

Overige

(move item t)
item: Verwijzing naar een object van de figuur
t: Vector met twee dimensies
Voorbeeld:
(define v (vector .1 0))
(move a1 v)

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alt=""Methodes van verwijzen voor DR. GEO-scriptsHoekOverige
drgeo-doc-1.5/nl/drgenius_5.html0000644000175000017500000000637710117134567012270 Gebruikershandleiding van Dr. Geo -- Tekeninstrumenten
Andere functiesBasisfunctiesalt=""Tekeninstrumenten

Tekeninstrumenten

Deze instrumenten zijn in zes groepen onderverdeeld. Je krijgt toegang tot die groepen op de tweede taakbalk van DR. GEO.

De categorieën van de instrumenten van DR. GEO en hun beschrijving

Wanneer je op een icoontje klikt waar een klein groen driehoekje opgetekend staat, komt ogenblikkelijk een nieuwe verticale taakbalk te voorschijn. Zo'n balk bevat alle functies van dezelfde familie.

Van links naar rechts, hebben we toegang tot de verticale taakbalken om punten en lijnen te construeren, om transformaties in het vlak uit te voeren, om waarden te berekenen, macro-constructies te gebruiken en zaken aan te passen - Verschillende instrumenten op de figuur.

Al deze functies zijn eveneens te selecteren via een contextueel menu dat verschijnt wanneer je met de rechtermuisknop klikt op de achtergrond van een figuur.

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Andere functiesBasisfunctiesalt=""Tekeninstrumenten
drgeo-doc-1.5/nl/drgenius_60.html0000644000175000017500000000526310117134567012342 Gebruikershandleiding van Dr. Geo -- De instrumenten in de gebruikersinterface aanpassen
alt=""Gevorderde functiesDR. GEO Guile scriptsDe instrumenten in de gebruikersinterface aanpassen

De instrumenten in de gebruikersinterface aanpassen

DR. GEO biedt de mogelijkheid sessies6 voor te bereiden waarbij de leraar voor bepaalde figuren kan beslissen de toegang tot bepaalde instrumenten te blokkeren. De beveiliging gebeurt per figuur afzonderlijk, en dit telkens met een verschillend paswoord. Op die manier heeft een leraar de volle vrijheid om een activiteit met verschillende figuren voor te bereiden en die op gepaste wijze te beveiligen.

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alt=""Gevorderde functiesDR. GEO Guile scriptsDe instrumenten in de gebruikersinterface aanpassen
drgeo-doc-1.5/nl/drgenius_61.html0000644000175000017500000000651610117134567012345 Gebruikershandleiding van Dr. Geo -- Instrumenten vergrendelen
Instrumenten ontgrendelenDe instrumenten in de gebruikersinterface aanpassenalt=""Instrumenten vergrendelen

Instrumenten vergrendelen

De beveiliging gebeurt figuur per figuur. Om een figuur te beveiligen, ga je naar het menu Bewerken->Gebruikersinterface aanpassen. Er verschijnt een groot dialoogvenster waarin de gebruiker de verschillende icoontjes herkent, die men op de tweede taakbalk van DR. GEO terugvindt. Om een instrument te activeren of vergrendelen, volstaat het op het gepaste icoontje te drukken. Als een instrument vergrendeld werd, ziet het overeenkomstige icoontje er iets grijzer uit. Het is eveneens mogelijk een hele reeks instrumenten in één keer uit te schakelen door te klikken op het icoontje van de hele groep (i.e. met een groen driehoekje)

Het dialoogvenster om instrumenten te vergrendelen.

Wanneer de gebruiker de te beveiligen instrumenten geselecteerd heeft, kan hij overgaan tot de eigenlijke vergrendeling door in het dialoogvenster op de knop Vergrendelen te drukken. DR. GEO vraagt dan om een paswoord.

(!) Bij het opslaan van een figuur of een sessie met vergrendelingen in de gebruikersinterface worden de paswoorden mee opgeslagen in het bestand. Ze zijn weliswaar gecrypteerd.
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Instrumenten ontgrendelenDe instrumenten in de gebruikersinterface aanpassenalt=""Instrumenten vergrendelen
drgeo-doc-1.5/nl/drgenius_62.html0000644000175000017500000000527310117134567012345 Gebruikershandleiding van Dr. Geo -- Instrumenten ontgrendelen
alt=""De instrumenten in de gebruikersinterface aanpassenInstrumenten vergrendelenInstrumenten ontgrendelen

Instrumenten ontgrendelen

Het spreekt vanzelf dat je een interface daarna ook kan ontgrendelen, hetzij om geleidelijk aan toegang te verschaffen aan instrumenten - wanneer leerlingen op een sessie werken b.v. - of om een figuur bij te werken. Om dit te doen moet je naar het menu Bewerken->Gebruikersinterface aanpassen gaan en in het dialoogvenster de knop Ontgrendelen aanklikken. DR. GEO vraagt dan het correcte paswoord opnieuw in te voeren.

Het dialoogvenster om de interface van een figuur te ontgrendelen.

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alt=""De instrumenten in de gebruikersinterface aanpassenInstrumenten vergrendelenInstrumenten ontgrendelen
drgeo-doc-1.5/nl/drgenius_63.html0000644000175000017500000000560110117134567012341 Gebruikershandleiding van Dr. Geo -- DR. GEO-Scheme-figuren
Bestanden en documentenTopGevorderde functiesDR. GEO-Scheme-figuren

DR. GEO-Scheme-figuren

De DR. GEO-Scheme-figuren - (DSF) - zijn figuren die in een relatief natuurlijke taal beschreven worden. Het gaat er dan niet langer om een figuur te construeren via de grafische interface van DR. GEO, maar veeleer om de figuur te beschrijven in de taal Scheme. Wij hebben gepoogd om de syntaxis zo licht en gemakkelijk mogelijk te maken. Alle sleutelwoorden om een eenvoudige figuur te tekenen kunnen in verschillende talen gesteld zijn. Zo kan men een figuur beschrijven in het Frans, in het Engels, in het Spaans, in het Nederlands, etc. (Een mengeling van talen is ook mogelijk, maar niet aan te raden).

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Bestanden en documentenTopGevorderde functiesDR. GEO-Scheme-figuren
drgeo-doc-1.5/nl/drgenius_64.html0000644000175000017500000001715010117134567012344 Gebruikershandleiding van Dr. Geo -- Enkele voorbeelden
Verwijzingsmethoden voor de DR. GEO Scheme FigurenDR. GEO-Scheme-figurenalt=""Enkele voorbeelden

Enkele voorbeelden

Scheme is als dusdanig een taal op hoog niveau. Wanneer we een figuur definiëren, kunnen we bijgevolg van zijn kracht gebruikmaken om dit of dat deel van de figuur op recursieve wijze te definiëren, of om bepaalde objecten op toevallige wijze op de figuur te plaatsen zodat de figuur er telkens lichtjes anders uitziet wanneer men ze opnieuw opent. De DSF zijn kortom bevrijd uit het kader van de grafische interface en winnen aan kracht dankzij Scheme. Een DSF is dus een bestand dat met een tekst-editor wordt aangemaakt en dat in DR. GEO wordt geopend met de opdracht Bestand->Evalueren.

 

Laat ons een eenvoudig voorbeeld van de DSF bestuderen :

  

(nieuwe-figuur "Mijn figuur")

Dit is de kleinste DSF die we konden definiëren. Wanneer we het bestand laden in DR. GEO, wordt er louter een nieuwe, lege figuur gecreërd onder de naam "Mijn figuur". Hadden we verschillende commando's in de lijn van (nieuwe-figuur Mijn figuur) ingebracht, dan zouden er evenveel nieuwe figuren gecreëerd zijn.

Laat ons een tweede voorbeeld bekijken : 

(nieuwe-figuur "Mijn figuur")
(weze Punt "A" willekeurig 1.2 -2)

Deze DSF definiëert een figuur met een willekeurig punt A met coördinaten (1,2 ; -2). De syntaxis is kennelijk relatief aangenaam, te meer omdat zij in de moedertaal gesteld is. Laat ons dieper ingaan op de tweede regel. De syntaxis is immers dezelfde voor alle commando's die objecten definiëren. Een dergelijk commando kan als volgt worden opgesplitst :

  1. We beginnen steeds met het sleutelwoord weze, dat aangeeft dat we een nieuw object in het leven willen roepen.
  2. Onmiddellijk daarop volgt de categorie van het object, Punt in dit geval Punt.
  3. Vervolgens volgt de naam van het object, A, die we steeds tussen aanhalingstekens plaatsen. Zelfs als we geen naam willen geven aan het object, moet men een lege naam geven.
  4. Daarna geven we het type object aan - het type punt in ons voorbeeld - hier willekeurig. Het punt A is dus een willekeurig punt.
  5. Na het type object volgt een lijst met specifieke argumenten. Die lijst bestaat in ons voorbeeld uit twee getallen, de coördinaten van het willekeurige punt A.

Laat ons verder gaan met een derde voorbeeld : 

 (define (driehoek p1 p2 p3)
   (Lijnstuk "" uiteinden p1 p2)
   (Lijnstuk "" uiteinden p2 p3)
   (Lijnstuk "" uiteinden p1 p3))

(define (toeval)
  (- 8 (* 16 (random:uniform))))

(nieuwe-figuur "Mijn figuur")

(weze Punt "A" willekeurig (toeval) 0)
(weze Punt "B" willekeurig 5 0)
(weze Punt "C" willekeurig (toeval) 5)

(driehoek A B C)

Dit voorbeeld is bijzonder interessant omdat het drie belangrijke zaken demonstreert :

  1. Het gebruik van constructies op hoog niveau. We definiëren een functie driehoek die aan de hand van drie gegeven punten, een driehoek door die punten construeert. Deze manier van handelen is vergelijkbaar met de macro-constructies, maar we hebben een veel grotere vrijheid van beweging.
  2. De definitie van bijkomende functies. Hier hebben we de functie toeval gecreëerd, die ons een decimaal getal bezorgt dat tussen -8 en 8 ligt. We gebruiken de functie om bepaalde punten van onze figuur op toevallige wijze te positioneren. Op die manier zal een figuur lichtjes anders zijn telkens zij geopend wordt.
  3. Het gebruik van het sleutelwoord weze is eigenlijk niet verplicht. Enkel als we een verwijzing (een naam) van een object willen bewaren, maken we er gebruik van. Bij de functie driehoek kozen we er bij voorbeeld voor om de lijnstukken geen namen te geven. De punten A, B en C daarentegen kregen verwijzingen met dezelfde naam.

Merk op dat als we geen naam geven bij het definiëren van de lijnstukken, DR. GEO zelf een standaardnaam toekent aan de hand van de uiteinden. De drie lijnstukken zullen dus in ons geval de namen [AB], [BC] en [AC] dragen.

Laat ons dit gedeelte met een laatste voorbeeld beëindigen : 

(weze Punt "A" willekeurig 1 0)
(weze Punt "B" willekeurig 5 0)
(weze Rechte "r1" 2punten A B)

(zend A kleur geel)
(zend A vorm rond)
(zend A grootte groot)
(zend B verbergen)
(zend d1 dikte streepje)

De drie eerste commando's creëren twee punten en een rechte. Hier belangt ons vooral de reeks geef-commando's aan. Met dit commando kunnen we communiceren met een object waarvan we een symbool hebben opgeslagen. In ons geval hebben we de symbolen A, B en r1. We zenden telkens een boodschap aan een object. In het eerste argument geven we aan met welk object we communiceren en in het tweede argument de boodschap die we willen meegeven. Het derde en de volgende argumenten hangen af van de aard van de boodschap in het tweede argument. Met de zin (zend A kleur geel) stuur je het punt A de boodschap kleur met als parameter geel. De andere geef-commando's zijn zo gemakkelijk te begrijpen. Ze zullen uitgelegd worden in het volgende gedeelte.

Wij hebben onze kleine begeleide wandeling doorheen de Dr. Geo Scheme Figuren afgerond. In wat volgt, zullen wij alle beschikbare commando's om DSF'en te definiëren uit de doeken doen.

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Verwijzingsmethoden voor de DR. GEO Scheme FigurenDR. GEO-Scheme-figurenalt=""Enkele voorbeelden
drgeo-doc-1.5/nl/drgenius_65.html0000644000175000017500000000526410117134567012350 Gebruikershandleiding van Dr. Geo -- Verwijzingsmethoden voor de DR. GEO Scheme Figuren
Galerij met voorbeeldenDR. GEO-Scheme-figurenEnkele voorbeeldenVerwijzingsmethoden voor de DR. GEO Scheme Figuren

Verwijzingsmethoden voor de DR. GEO Scheme Figuren

Het definiëren van objecten in een DSF-document gebeurt via prototypes. Prototypes zijn om zo te zeggen objecten die wij kunnen bevragen en aanpassen zoals zal blijken.

Vooraleer echter objecten te definiëren binnen een figuur moeten wij die figuur zelf tot leven wekken met het commando nieuwe-figuur.

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Galerij met voorbeeldenDR. GEO-Scheme-figurenEnkele voorbeeldenVerwijzingsmethoden voor de DR. GEO Scheme Figuren
drgeo-doc-1.5/nl/drgenius_66.html0000644000175000017500000000500010117134567012335 Gebruikershandleiding van Dr. Geo -- Algemene commando's
Definitie van nieuwe objecten van een figuurVerwijzingsmethoden voor de DR. GEO Scheme Figurenalt=""Algemene commando's

Algemene commando's

(nieuwe-figuur naam)
naam: Tekenreeks
Uitkomst: Geeft geen waarde als resultaat. De functie-aanroep heeft enkel een zijdelings effect, namelijk het creëren van een nieuwe figuur. Alle objecten die volgen worden in deze figuur gecreëerd, tot we de functie-aanroep opnieuw gebruiken
Voorbeeld:
(nieuwe-figuur Mijn 1ste figuur)

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Definitie van nieuwe objecten van een figuurVerwijzingsmethoden voor de DR. GEO Scheme Figurenalt=""Algemene commando's
drgeo-doc-1.5/nl/drgenius_67.html0000644000175000017500000000705510117134567012352 Gebruikershandleiding van Dr. Geo -- Definitie van nieuwe objecten van een figuur
alt=""Verwijzingsmethoden voor de DR. GEO Scheme FigurenAlgemene commando'sDefinitie van nieuwe objecten van een figuur

Definitie van nieuwe objecten van een figuur

Een object kan op syntactisch verschillende wijzen worden gedefiniëerd.

  • (weze Punt p1 type args)

    Het punt wordt aangemaakt en zijn verwijzing wordt opgeslagen in de variabele p1. Deze syntaxis gebruikt een Scheme-macro.

  • (Punt Naam type args)

    Het punt wordt aangemaakt maar geen enkele verwijzing naar het punt wordt bewaard.

  • (set! p1 (Punt Naam type args))

    Het punt wordt aangemaakt en zijn verwijzing wordt gekopiëerd naar de reeds bestaande variabele p1.

Wanneer objecten worden gecreëerd vanuit een functie, gebruik dan ofwel de vorm set! ofwel de speciale Scheme-vorm let. Het is belangrijk op te merken dat de basisaanroep een functie is die een verwijzing naar het aangemaakte object als uitkomst geeft.

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alt=""Verwijzingsmethoden voor de DR. GEO Scheme FigurenAlgemene commando'sDefinitie van nieuwe objecten van een figuur
drgeo-doc-1.5/nl/drgenius_68.html0000644000175000017500000001102110117134567012337 Gebruikershandleiding van Dr. Geo -- Punt
RechteDefinitie van nieuwe objecten van een figuuralt=""Punt

Punt

prototype (Punt naam willekeurig x y)
naam: Tekenreeks die de naam van het object aangeeft
x: De abscis van het punt
y: De ordinaat van het punt
Uitkomst: Verwijzing naar een willekeurig punt in het vlak met coördinaten x en y.
Voorbeeld:
(define p1 (Punt Ä willekeurig 1.2 (acos -1)))

prototype (Punt naam op-kromme lijn x)
naam: Tekenreeks die de naam van het object aangeeft
lijn: Verwijzing naar een lijn (rechte, halfrechte, lijnstuk, etc.)
x: Kromme-abscis van het willekeurig punt, de waarde behoort tot het interval [0 ; 1]
Uitkomst: Verwijzing van een willekeurig punt op een lijn.
Voorbeeld:
(Punt M op-kromme s1 0.5 )

prototype (Punt naam midden-2ptn p1 p2)
naam: Tekenreeks die de naam van het object aangeeft
p1: Verwijzing naar een punt
p2: Verwijzing naar een punt
Uitkomst: Verwijzing naar het midden van twee punten.
Voorbeeld:
(weze Punt Ä willekeurig 1 1)
(weze Punt B willekeurig 4 4)
(Punt Ï midden-2ptn A B)

prototype (Punt naam midden-lijnstuk s)
naam: Tekenreeks die de naam van het object aangeeft
s: Verwijzing naar een lijnstuk
Uitkomst: Verwijzing naar het midden van twee punten.
Voorbeeld:
(weze Punt L midden-lijnstuk s)

prototype (Punt naam snijpunt l1 l2)
naam: Tekenreeks die de naam van het object aangeeft
l1: Verwijzing naar een lijn
l2: Verwijzing naar een lijn
Uitkomst: Verwijzing naar het snijpunt van twee lijnen.
Voorbeeld:
(Punt Ï snijpunt rechte lijnstuk)

prototype (Punt naam snijpunt2 l1 l2)
naam: Tekenreeks die de naam van het object aangeeft
l1: Verwijzing naar een lijn
l2: Verwijzing naar een lijn
Uitkomst: Verwijzing naar het tweede snijpunt van twee lijnen als een van de twee een cirkelboog of een cirkel is.
Voorbeeld:
(Punt Ï snijpunt2 rechte cirkel)

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RechteDefinitie van nieuwe objecten van een figuuralt=""Punt
drgeo-doc-1.5/nl/drgenius_69.html0000644000175000017500000000675610117134567012363 Gebruikershandleiding van Dr. Geo -- Rechte
HalfrechteDefinitie van nieuwe objecten van een figuurPuntRechte

Rechte

prototype (Rechte naam 2punten p1 p2)
naam: Tekenreeks die de naam van het object aangeeft
p1: Verwijzing naar een punt
p2: Verwijzing naar een punt
Uitkomst: Verwijzing naar een rechte door twee punten
Voorbeeld:
(weze Punt Ä willekeurig 0 0)
(weze Punt M willekeurig 1 2)
(Rechte 2punten A M)

prototype (Rechte naam evenwijdig p r)
naam: Tekenreeks die de naam van het object aangeeft
p: Verwijzing naar een punt
r: Verwijzing naar een richting (rechte, lijnstuk, vector, ...)
Uitkomst: Verwijzing naar een rechte evenwijdig met de richting r en door het punt p.
Voorbeeld:
(weze Punt Ä willekeurig 1 5)
(weze Rechte r1 evenwijdig A r)

prototype (Rechte naam loodrecht p r)
naam: Tekenreeks die de naam van het object aangeeft
p: Verwijzing naar een punt
r: Verwijzing naar een richting (rechte, lijnstuk, vector, ...)
Uitkomst: Verwijzing naar een rechte loodrecht op de richting r en door het punt p.
Voorbeeld:
(weze Punt Ä willekeurig 1 5)
(weze Rechte r1 loodrecht A r)

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HalfrechteDefinitie van nieuwe objecten van een figuurPuntRechte
drgeo-doc-1.5/nl/drgenius_6.html0000644000175000017500000000502510117134567012256 Gebruikershandleiding van Dr. Geo -- Willekeurig punt
MiddelpuntInstrumenten die punten betreffenalt=""Willekeurig punt

Willekeurig punt

 

Tekent een willekeurig punt in het vlak of op een eendimensioneel object. In het eerste geval, kan men het punt achteraf overal verplaatsen in het vlak. Je tekent het punt door eenvoudigweg te klikken op gewenste plaats in het vlak. In het laatste geval kan het punt enkel vrij bewegen op het eendimensionele object (de rechte, etc.) waarop het punt oorspronkelijk werd getekend ; het punt plakt er als het ware aan vast. Om een dergelijk punt te tekenen, klik je op een drager (i.e. een rechte, een halfrechte, een lijnstuk, een cirkel, een cirkelboog, etc.).

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MiddelpuntInstrumenten die punten betreffenalt=""Willekeurig punt
drgeo-doc-1.5/nl/drgenius_70.html0000644000175000017500000000513310117134567012337 Gebruikershandleiding van Dr. Geo -- Halfrechte
LijnstukDefinitie van nieuwe objecten van een figuurRechteHalfrechte

Halfrechte

prototype (Halfrechte naam 2punten o p)
naam: Tekenreeks die de naam van het object aangeeft
o: Verwijzing naar een punt, grenspunt van de halfrechte
p: Verwijzing naar een ander punt, op de halfrechte
Uitkomst: Verwijzing naar een halfrechte gedefiniëerd door zijn grenspunt en een tweede punt.
Voorbeeld:
(weze Punt Ä willekeurig 1 5)
(weze Punt Ö willekeurig 0 0)
(weze Halfrechte dd1 2punten A O)

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LijnstukDefinitie van nieuwe objecten van een figuurRechteHalfrechte
drgeo-doc-1.5/nl/drgenius_71.html0000644000175000017500000000502010117134567012333 Gebruikershandleiding van Dr. Geo -- Lijnstuk
CirkelDefinitie van nieuwe objecten van een figuurHalfrechteLijnstuk

Lijnstuk

prototype (Lijnstuk naam grenspunten p1 p2)
naam: Tekenreeks die de naam van het object aangeeft
p1: Verwijzing naar een punt
p2: Verwijzing naar een punt
Uitkomst: Verwijzing naar een lijnstuk gedefiniëerd door zijn grenspunten.
Voorbeeld:
(weze Punt Ä willekeurig 1 5)
(weze Punt B willekeurig 10 4)
(weze Lijnstuk grenspunten A B)

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CirkelDefinitie van nieuwe objecten van een figuurHalfrechteLijnstuk
drgeo-doc-1.5/nl/drgenius_72.html0000644000175000017500000000620310117134567012340 Gebruikershandleiding van Dr. Geo -- Cirkel
CirkelboogDefinitie van nieuwe objecten van een figuurLijnstukCirkel

Cirkel

prototype (Cirkel naam 2punten m p)
naam: Tekenreeks die de naam van het object aangeeft
m: Verwijzing naar een punt, middelpunt van de cirkel
p: Verwijzing naar een punt op de cirkel
Uitkomst: Verwijzing naar een cirkel gedefiniëerd door zijn middelpunt en een punt
Voorbeeld:
(weze Punt Ä willekeurig 1 5)
(weze Punt B willekeurig 10 4)
(weze Cirkel C1 2punten A B)

prototype (Cirkel naam middelpunt-straal m r)
naam: Tekenreeks die de naam van het object aangeeft
m: Verwijzing naar een punt, middelpunt van de cirkel
r: Verwijzing naar een lijnstuk, de straal van de cirkel
Uitkomst: Verwijzing naar een cirkel bepaald door zijn middelpunt en straal
Voorbeeld:
(weze Punt Ä willekeurig 1 5)
(weze Getal r willekeurig 10)
(weze Cirkel C1 middelpunt-straal A r)

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CirkelboogDefinitie van nieuwe objecten van een figuurLijnstukCirkel
drgeo-doc-1.5/nl/drgenius_73.html0000644000175000017500000000540210117134567012341 Gebruikershandleiding van Dr. Geo -- Cirkelboog
VeelhoekDefinitie van nieuwe objecten van een figuurCirkelCirkelboog

Cirkelboog

prototype (Cirkel naam 3punten p1 p2 p3)
naam: Tekenreeks die de naam van het object aangeeft
p1: Verwijzing naar een punt, 1e grenspunt van de boog
p2: Verwijzing naar een punt op de boog
p3: Verwijzing naar een punt, 2de grenspunt van de boog
Uitkomst: Verwijzing naar een cirkelboog gedefiniëerd door zijn grenspunten en een punt.
Voorbeeld:
(weze Punt Ä willekeurig 1 5)
(weze Punt B willekeurig 0 5)
(weze Punt C willekeurig -1 -2)
(weze Cirkelboog boog 3punten A B C)

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VeelhoekDefinitie van nieuwe objecten van een figuurCirkelCirkelboog
drgeo-doc-1.5/nl/drgenius_74.html0000644000175000017500000000476010117134567012350 Gebruikershandleiding van Dr. Geo -- Veelhoek
Meetkundige transformatiesDefinitie van nieuwe objecten van een figuurCirkelboogVeelhoek

Veelhoek

prototype (Veelhoek naam npunten args)
naam: Tekenreeks die de naam van het object aangeeft
args: Een lijst met verwijzingen naar punten, hoekpunten van de veelhoek
Uitkomst: Verwijzing naar een veelhoek gedefiniëerd door zijn hoekpunten
Voorbeeld:
(weze Veelhoek quad npunten A B C D)

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Meetkundige transformatiesDefinitie van nieuwe objecten van een figuurCirkelboogVeelhoek
drgeo-doc-1.5/nl/drgenius_75.html0000644000175000017500000001312210117134567012341 Gebruikershandleiding van Dr. Geo -- Meetkundige transformaties
Meetkundige plaatsDefinitie van nieuwe objecten van een figuurVeelhoekMeetkundige transformaties

Meetkundige transformaties

De prototypes van meetkundige transformaties laten toe objecten te tekenen onder een transformatie. Men kan transformaties toepassen op verwijzingen naar objecten van het type punt, lijnstuk, rechte, halfrechte, vector, cirkel, cirkelboog en veelhoek.

prototype (ObjectType naam draaiing object middelpunt hoek)
ObjectType: Punt, Lijnstuk, Rechte, Halfrechte, Vector, Cirkel, Cirkelboog, Veelhoek
naam: Tekenreeks die de naam van het object aangeeft
object: Verwijzing naar het te transformeren object
middelpunt: Verwijzing naar een punt, middelpunt van de draaiing
hoek: Verwijzing naar een getalwaarde, hoek van de draaiing
Uitkomst: Verwijzing naar een getransformeerd object
Voorbeeld:
(weze Punt Ï1 draaiing I C a)

prototype (ObjectType naam homothetie object middelpunt k)
ObjectType: Punt, Lijnstuk, Rechte, Halfrechte, Vector, Cirkel, Cirkelboog, Veelhoek
naam: Tekenreeks die de naam van het object aangeeft
object: Verwijzing naar het te transformeren object
middelpunt: Verwijzing naar een punt, middelpunt van de homothetie
k: Verwijzing naar een getalwaarde, factor van de homothetie
Uitkomst: Verwijzing naar een getransformeerd object
Voorbeeld:
(weze Veelhoek P1 homothetie P C k1)

prototype (ObjectType naam puntspiegeling object middelpunt)
ObjectType: Punt, Lijnstuk, Rechte, Halfrechte, Vector, Cirkel, Cirkelboog, Veelhoek
naam: Tekenreeks die de naam van het object aangeeft
object: Verwijzing naar het te transformeren object
middelpunt: Verwijzing naar een punt, middelpunt van de puntspiegeling
Uitkomst: Verwijzing naar het getransformeerde object
Voorbeeld:
(weze Lijnstuk L1 puntspiegeling L m)

prototype (ObjectType naam spiegeling object spiegelas)
ObjectType: Punt, Lijnstuk, Rechte, Halfrechte, Vector, Cirkel, Cirkelboog, Veelhoek
naam: Tekenreeks die de naam van het object aangeeft
object: Verwijzing naar het te transformeren object
spiegelas: Verwijzing naar een rechte, de spiegelas
Uitkomst: Verwijzing naar het getransformeerde object
Voorbeeld:
(weze Veelhoek V1 spiegeling V r1)

prototype (ObjectType naam verschuiving object vector)
ObjectType: Punt, Lijnstuk, Rechte, Halfrechte, Vector, Cirkel, Cirkelboog, Veelhoek
naam: Tekenreeks die de naam van het object aangeeft
object: Verwijzing naar het te transformeren object
vector: Verwijzing naar een vector
Uitkomst: Verwijzing naar het getransformeerde object.
Voorbeeld:
(weze Cirkel C1 verschuiving C v)

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Meetkundige plaatsDefinitie van nieuwe objecten van een figuurVeelhoekMeetkundige transformaties
drgeo-doc-1.5/nl/drgenius_76.html0000644000175000017500000000502710117134567012347 Gebruikershandleiding van Dr. Geo -- Meetkundige plaats
VectorDefinitie van nieuwe objecten van een figuurMeetkundige transformatiesMeetkundige plaats

Meetkundige plaats

prototype (Plaats naam 2punten m c)
naam: Tekenreeks die de naam van het object aangeeft
m: Verwijzing naar een beweeglijk punt op een lijn
c: Verwijzing naar een vast punt dat afhangt van het punt m
Uitkomst: Verwijzing naar een plaats.
Voorbeeld:
(Plaats plaats1 2punten M I)

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VectorDefinitie van nieuwe objecten van een figuurMeetkundige transformatiesMeetkundige plaats
drgeo-doc-1.5/nl/drgenius_77.html0000644000175000017500000000477010117134567012354 Gebruikershandleiding van Dr. Geo -- Vector
GetalDefinitie van nieuwe objecten van een figuurMeetkundige plaatsVector

Vector

prototype (Vector naam 2punten o g)
naam: Tekenreeks die de naam van het object aangeeft
o: Verwijzing naar een punt, oorsprong van de vector
g: Verwijzing naar een punt, grenspunt van de vector
Uitkomst: Verwijzing naar een vector.
Voorbeeld:
(weze Punt B willekeurig 0 5)
(weze Punt C willekeurig -1 -2)
(Vector 2punten C B)

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GetalDefinitie van nieuwe objecten van een figuurMeetkundige plaatsVector
drgeo-doc-1.5/nl/drgenius_78.html0000644000175000017500000001134310117134567012347 Gebruikershandleiding van Dr. Geo -- Getal
HoekDefinitie van nieuwe objecten van een figuurVectorGetal

Getal

prototype (Getal naam vrij x y v)
naam: Tekenreeks die de naam van het object aangeeft
x,y: De coördinaten voor de plaatsing van het getal
v: De beginwaarde van het getal
Uitkomst: Verwijzing naar een willekeurig getal.
Voorbeeld:
(weze Getal pi willekeurig 5 5 (acos -1))

prototype (Getal naam lengte-lijnstuk x y l)
naam: Tekenreeks die de naam van het object aangeeft
x,y: De coördinaten voor de plaatsing van het getal
Uitkomst: l
Verwijzing naar een lijnstuk. Voorbeeld:
(weze Getal l lengte-lijnstuk 5 5 S)

prototype (Getal naam norm-vector x y v)
naam: Tekensreeks die de naam van het object aangeeft
x,y: De coördinaten voor de plaatsing van het getal
v: Verwijzing naar een vector
Uitkomst: Verwijzing naar een getal, norm van de vector.
Voorbeeld:
(weze Getal l norm-vector 5 5 V)

prototype (Getal naam norm-vector x y p c)
naam: Tekensreeks die de naam van het object aangeeft
x,y: De coördinaten voor de plaatsing van het getal
p: Verwijzing naar een punt
c: Verwijzing naar een cirkel
Uitkomst: Verwijzing naar een getal, afstand tussen het punt en de cirkel
Voorbeeld:
(weze Getal l punt-cirkel 5 5 P C)

prototype (Getal naam punt-rechte x y p r)
naam: Tekensreeks die de naam van het object aangeeft
x,y: De coördinaten voor de plaatsing van het getal
p: Verwijzing naar een punt
r: Verwijzing naar een rechte
Uitkomst: Verwijzing naar een getal, afstand tussen het punt en de rechte
Voorbeeld:
(weze Getal ä punt-rechte 5 5 M D1)

prototype (Getal naam punt-punt x y p1 p2)
naam: Tekensreeks die de naam van het object aangeeft
x,y: De coördinaten voor de plaatsing van het getal
p1: Verwijzing naar een punt
p2: Verwijzing naar een punt
Uitkomst: Verwijzing naar een getal, afstand tussen de twee punten.
Voorbeeld:
(weze Getal ä punt-punt A B)

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HoekDefinitie van nieuwe objecten van een figuurVectorGetal
drgeo-doc-1.5/nl/drgenius_79.html0000644000175000017500000000613110117134567012347 Gebruikershandleiding van Dr. Geo -- Hoek
Attributen van objecten aanpassenDefinitie van nieuwe objecten van een figuurGetalHoek

Hoek

prototype (Hoek naam meetkundig A B C)
naam: Tekensreeks die de naam van het object aangeeft
A: Verwijzing naar een punt
B: Verwijzing naar een punt, het hoekpunt
C: Verwijzing naar een punt
Uitkomst: Verwijzing naar een meetkundige hoek.
Voorbeeld:
(weze hoek h meetkundig A B C)

prototype (Hoek naam georiënteerd x y v1 v2)
naam: Tekenreeks die de naam van het object aangeeft
x,y: De coördinaten voor de plaatsing van de hoek
v1: Verwijzing naar een vector
v2: Verwijzing naar een vector
Uitkomst: Verwijzing naar een georiënteerde hoek, gevormd door twee vectoren
Voorbeeld:
(define v1 (Vector 2punten A B))
(define v2 (Vector 2punten A C))
(Hoek ä georiënteerd 1 1 v1 v2)

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Attributen van objecten aanpassenDefinitie van nieuwe objecten van een figuurGetalHoek
drgeo-doc-1.5/nl/drgenius_7.html0000644000175000017500000000510110117134567012252 Gebruikershandleiding van Dr. Geo -- Willekeurig punt
MiddelpuntInstrumenten die punten betreffenalt=""Willekeurig punt

Willekeurig punt

 

Tekent een willekeurig punt in het vlak of op een eendimensioneel object. In het eerste geval, kan men het punt achteraf overal verplaatsen in het vlak. Je tekent het punt door eenvoudigweg te klikken op gewenste plaats in het vlak. In het laatste geval kan het punt enkel vrij bewegen op het eendimensionele object (de rechte, etc.) waarop het punt oorspronkelijk werd getekend ; het punt plakt er als het ware aan vast. Om een dergelijk punt te tekenen, klik je op een drager (i.e. een rechte, een halfrechte, een lijnstuk, een cirkel, een cirkelboog, etc.).

Commentaar of opmerkingen ?
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MiddelpuntInstrumenten die punten betreffenalt=""Willekeurig punt
drgeo-doc-1.5/nl/drgenius_80.html0000644000175000017500000001012410117134567012334 Gebruikershandleiding van Dr. Geo -- Attributen van objecten aanpassen
alt=""Definitie van nieuwe objecten van een figuurHoekAttributen van objecten aanpassen

Attributen van objecten aanpassen

Om attributen aan te passen van een reeds gecreëerd object, gebruiken we een systeem dat direct boodschappen zendt aan het prototype dat het object in kwestie vertegenwoordigt. De aanpassing van attributen gebeurt dus steeds a posteriori.

(zend object kleur waarde)
object: Verwijzing naar een object
waarde: De kleur ; mogelijke waarden zijn zwart, donkergrijs, grijs, wit, donkergroen, groen, donkerblauw, blauw, rood, bordeaux, geel, oranje
Voorbeeld:
(weze Punt Ä willekeurig 1 2)
(zend A kleur groen)

(zend lijn dikte waarde)
lijn: Verwijzing naar een lijn (rechte, halfrechte, cirkel, plaats, etc.)
waarde: De dikte ; mogelijke waarden zijn streepje, normaal, dik
Voorbeeld:
(weze Punt Ä willekeurig 1 2)
(weze punt B willekeurig 0 0)
(weze Rechte r 2 punten A B)
(zend d dikte streepje)

(zend punt grootte waarde)
punt: Verwijzing naar een punt
waarde: De grootte van het punt ; mogelijke waarden zijn klein, normaal, groot
Voorbeeld:
(weze Punt Ä willekeurig 1 2)
(zend A grootte klein)

(zend punt vorm waarde)
punt: Verwijzing naar een punt
waarde: De vorm van het punt ; mogelijke waarden zijn rond, kruisje, rond-leeg, rec, rec-leeg
Voorbeeld:
(weze Punt Ä willekeurig 1 2)
(zend A vorm rond)

(zend object verbergen)
object: Verwijzing naar een te verbergen object
Voorbeeld:
(weze Punt Ä willekeurig 1 2)
(zend A verbergen)

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alt=""Definitie van nieuwe objecten van een figuurHoekAttributen van objecten aanpassen
drgeo-doc-1.5/nl/drgenius_81.html0000644000175000017500000000506610117134567012346 Gebruikershandleiding van Dr. Geo -- Galerij met voorbeelden
alt=""DR. GEO-Scheme-figurenVerwijzingsmethoden voor de DR. GEO Scheme FigurenGalerij met voorbeelden

Galerij met voorbeelden

Om het gebruik van de DR. GEO-Scheme-figuren te illustreren, stellen we een kleine voorbeeldenreeks voor. Deze voorbeelden tonen belangrijke voorbeelden en wij hopen dat ze inspirerend werken. Voor elk voorbeeld geven wij de Scheme-broncode, gevolgd door het resultaat. De broncode kan in een tekst-editor gekopiëerd en opgeslagen worden om ze vervolgens te evalueren met DR. GEO.

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alt=""DR. GEO-Scheme-figurenVerwijzingsmethoden voor de DR. GEO Scheme FigurenGalerij met voorbeelden
drgeo-doc-1.5/nl/drgenius_82.html0000644000175000017500000000537510117134567012352 Gebruikershandleiding van Dr. Geo -- Regelmatige veelhoek
FractaalGalerij met voorbeeldenalt=""Regelmatige veelhoek

Regelmatige veelhoek

Een regelmatige veelhoek met een willekeurig aantal zijden kan men met behulp van een recursieve Scheme-functie construeren. 

(define pi (acos -1))
(define n 15)
(define x0 0)
(define y0 0)
(define p1 0)

(define (polygon center p a n)
  (if (> n 0)
      (begin
        (set! p1 (Point "" rotation p center a))
        (send p1 masked)
        (Segment "" extremities p p1)
        (polygon center p1 a (- n 1)))))

(new-figure "Regular Polygon!")
(lets Point "C" free x0 y0)
(lets Numeric "a" free 0 0 (* 2 (/ pi n)))
(send a masked)

(set! p1 (Point "I" free 5 0))

(lets Segment "S" extremities C p1)
(Segment ""  rotation S C a)

(polygon C p1 a n)

Een regelmatige veelhoek met 15 zijden

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FractaalGalerij met voorbeeldenalt=""Regelmatige veelhoek
drgeo-doc-1.5/nl/drgenius_83.html0000644000175000017500000000616310117134567012347 Gebruikershandleiding van Dr. Geo -- Fractaal
alt=""Galerij met voorbeeldenRegelmatige veelhoekFractaal

Fractaal

De constructie van een fractaal in boomvorm is erg eenvoudig. De broncode van de figuur is wonderlijk compact, vooral wanneer men ze vergelijkt met een "handmatige" constructie via de grafische interface. 

(new-figure "Baum")
(lets Numeric "A1" free 2 2 +3.4)
(lets Numeric "A2" free 2 3 -3.7)
(lets Numeric "S1" free 2 4 +0.5)
(lets Numeric "S2" free 2 5 +0.9)

(define (dec n)
  (- n 1))
(define (inc n)
  (+ n 1))
(define (invisible p)
  (send p masked)
  p)
(define (scalerot oP C a s)
  (let* ((sP (invisible (Point "" scale oP C s)))
         (rP (invisible (Point "" rotation sP C a))) )
    rP))
(define (Zweig p0 p1 n)
  (Segment "" extremities p0 p1)
  (let* ((left-scale (if (odd? n) S1 S2))
         (left-angle A1)
         (right-scale (if (odd? n) S2 S1))
         (right-angle A2) )
    (if (> n 0)
      (begin
        (Zweig p1 (scalerot p0 p1  left-angle  left-scale) (dec n))
        (Zweig p1 (scalerot p0 p1 right-angle right-scale) (dec n))))))
        
(lets Point "A" free -3 0)
(lets Point "B" free -3 2)
(Zweig A B 6)

Een fractaal die een boomvorm simuleert

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alt=""Galerij met voorbeeldenRegelmatige veelhoekFractaal
drgeo-doc-1.5/nl/drgenius_84.html0000644000175000017500000000500310117134567012340 Gebruikershandleiding van Dr. Geo -- Bestanden en documenten
ReceptenboekTopDR. GEO-Scheme-figurenBestanden en documenten

Bestanden en documenten

Constructies kunnen op twee manieren worden opgeslagen. Ofwel sla je één constructie op in één bestand, ofwel sla je een verzameling constructies op in één bestand (i.e. een zgn. DR. GEO-sessie).

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ReceptenboekTopDR. GEO-Scheme-figurenBestanden en documenten
drgeo-doc-1.5/nl/drgenius_85.html0000644000175000017500000000523510117134567012350 Gebruikershandleiding van Dr. Geo -- Opslaan van een constructie
Opslaan van een sessieBestanden en documentenalt=""Opslaan van een constructie

Opslaan van een constructie

Via het menu Bestand->Opslaan of Bestand->Opslaan als..., wordt de figuur die op dat moment zichtbaar is opgeslagen.

(!) DR. GEO kan met verschillende figuren tegelijkertijd werken. Je kan van figuur veranderen door op het overeenkomstige oortje te klikken.

Via het tweede menu kan de gebruiker de naam wijzigen van het document dat men opslaat.

(!) De standaard bestandsnaam kan je veranderen via het menu Bewerken->Voorkeuren.... Meer informatie vindt men in het deel over standaardinstellingen.
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Opslaan van een sessieBestanden en documentenalt=""Opslaan van een constructie
drgeo-doc-1.5/nl/drgenius_86.html0000644000175000017500000000704210117134567012347 Gebruikershandleiding van Dr. Geo -- Opslaan van een sessie
Een bestand openenBestanden en documentenOpslaan van een constructieOpslaan van een sessie

Opslaan van een sessie

Een sessie is een verzameling DR. GEO-gegevens die de gebruiker in een keer verlangt op te slaan in een bestand. Zo kan een leraar een verzameling gegevens (figuren, macro-constructies, aantekeningen) organiseren in een enkel bestand, zodat hij het geheel gemakkelijk opnieuw kan gebruiken.

Via het menu Bestand->Samenvoegen en opslaan, opent de gebruiker het dialoogvenster in verband met een sessie.

Het dialoogvenster i.v.m. een DR. GEO-sessie

In dit dialoogvenster verschijnt een tabel met alle actieve gegevens. In de eerste kolom staat de respectieve soort aangeduid van de gegevens die in DR. GEO actief zijn. In de tweede kolom staan de namen van die gegevens.

(!) Op dit moment kan een sessie drie soorten gegevens bevatten : een interactieve 2D-figuur, een macro-constructie of een tekst.

De gebruiker kan de gewenste gegevens één voor één selecteren in de lijst en ze dan opslaan door op de knop Selectie opslaan te drukken. Hij kan ook alle gegevens in een klap opslaan door de knop Alles opslaan in te drukken.

(!) Het menu Bestand->Samenvoegen en opslaan is de enige manier om een macro-constructie op te slaan in een bestand.
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Een bestand openenBestanden en documentenOpslaan van een constructieOpslaan van een sessie
drgeo-doc-1.5/nl/drgenius_87.html0000644000175000017500000000474410117134567012356 Gebruikershandleiding van Dr. Geo -- Een bestand openen
Een figuur exporterenBestanden en documentenOpslaan van een sessieEen bestand openen

Een bestand openen

Of de gebruiker nu een enkele figuur of een sessie met verschillende soorten documenten heeft opgeslagen, de procedure om een bestand te openen blijft dezelfde : via het menu Bestand->Openen.... Als de geopende sessie macro-constructies bevat, kunnen die onmiddellijk worden uitgevoerd door het gepaste instrument aan te klikken. Macro-constructies zijn beschikbaar vanop elke geopende figuur.

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Een figuur exporterenBestanden en documentenOpslaan van een sessieEen bestand openen
drgeo-doc-1.5/nl/drgenius_88.html0000644000175000017500000000501010117134567012342 Gebruikershandleiding van Dr. Geo -- Een figuur exporteren
alt=""Bestanden en documentenEen bestand openenEen figuur exporteren

Een figuur exporteren

DR. GEO biedt de mogelijkheid om een meetkundige figuur te exporteren naar een LaTeX- of PostScript-document. Beide formaten zijn van het vectoriële type. Dit betekent dat ze een betere afdrukkwaliteit zullen hebben dan beelden die in een bitmap-formaat worden opgeslagen. Men kan een figuur exporteren via het sub-menu Figuur->Exporteren naar...

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alt=""Bestanden en documentenEen bestand openenEen figuur exporteren
drgeo-doc-1.5/nl/drgenius_89.html0000644000175000017500000000504310117134567012351 Gebruikershandleiding van Dr. Geo -- Exporteren naar LaTeX
Exporteren naar PostScriptEen figuur exporterenalt=""Exporteren naar LaTeX

Exporteren naar LaTeX

Wanneer men naar LaTeX wil exporteren, heeft men het pstricks-pakket nodig. Over het algemeen wordt dit pakket verspreid samen met LaTeX zelf. Een figuur die men naar LaTeXexporteerde kan je vanzelfsprekend in een LaTeX-document opnemen, maar je kan het ook direct als een op zich staand document compileren : 

latex figure.tex
dvips figure.dvi

Als men deze twee commando's invoert, bekomt men het document figure.ps. Dit kan dan op het scherm weergegeven worden met het programma GhostView7 gv.

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Exporteren naar PostScriptEen figuur exporterenalt=""Exporteren naar LaTeX
drgeo-doc-1.5/nl/drgenius_8.html0000644000175000017500000000443110117134567012260 Gebruikershandleiding van Dr. Geo -- Middelpunt
SnijpuntInstrumenten die punten betreffenWillekeurig puntMiddelpunt

Middelpunt

 

Tekent het middelpunt ofwel tussen twee punten ofwel van een lijnstuk. In het eerste geval, selecteert de gebruiker twee punten. In het laatste geval, selecteer je eenvoudigweg het gewenste lijnstuk.

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SnijpuntInstrumenten die punten betreffenWillekeurig puntMiddelpunt
drgeo-doc-1.5/nl/drgenius_90.html0000644000175000017500000000476510117134567012353 Gebruikershandleiding van Dr. Geo -- Exporteren naar PostScript
De zone bepalen die men exporteertEen figuur exporterenExporteren naar LaTeXExporteren naar PostScript

Exporteren naar PostScript

Exporteren naar het PostScript-formaat biedt het voordeel dat je de documenten makkelijk kan gebruiken in andere programma's8.

Het EPS-formaat is de facto eigenlijk min of meer de standaard waar het vectoriële beelden aangaat. Om dit soort beelden snel weer te geven gebruiken we het programma GhostView. Zijn commando is gv.

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De zone bepalen die men exporteertEen figuur exporterenExporteren naar LaTeXExporteren naar PostScript
drgeo-doc-1.5/nl/drgenius_91.html0000644000175000017500000000673510117134567012353 Gebruikershandleiding van Dr. Geo -- De zone bepalen die men exporteert
alt=""Een figuur exporterenExporteren naar PostScriptDe zone bepalen die men exporteert

De zone bepalen die men exporteert

DR. GEO zal standaard de zichtbare zone van de figuur exporteren. Om dus een precieze zone van een figuur te exporteren, kunnen we de grootte van het DR. GEO-venster aanpassen, tot we de gewenste zone bekomen9.

Hoewel die methode snel en eenvoudig kan werken, is ze niet altijd even soepel. Bovendien wordt de zone die men exporteert niet automatisch mee opgeslagen met de figuur zelf. Een andere manier van werken bestaat erin het commando De te exporteren zone afbakenen te gebruiken. Gebruik hiervoor het menu Bestand->Instellingen m.b.t. exporteren.

Eens dit commando actief is, kan je op de figuur een rechthoek afbakenen, die dan kan worden geëxporteerd. Die rechthoekige zone kan men nadien zoveel bijstellen als men wil. Hij zal in het lichtgrijs getekend worden. Wanneer men achteraf de figuur opslaat, zal de afgebakende zone nu wel mee worden opgeslagen. Tenslotte kan men de bewuste zone altijd verwijderen via het commando De te exporteren zone verwijderen.

Een figuur waarin een te exporteren zone werd afgebakend

De zone werd geëxporteerd naar een PostScript-document en weergegeven met GhostView

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alt=""Een figuur exporterenExporteren naar PostScriptDe zone bepalen die men exporteert
drgeo-doc-1.5/nl/drgenius_92.html0000644000175000017500000000461110117134567012343 Gebruikershandleiding van Dr. Geo -- Receptenboek
IndexTopBestanden en documentenReceptenboek

Receptenboek

Dit hoofdstuk is een steuntje in de rug voor wie meetkundige figuren wenst te tekenen met DR. GEO. In tegenstelling tot de vorige hoofdstukken, is de aanpak hier concreet en op precieze situaties toegespitst. De inhoud van dit hoofdstuk werd tot stand gebracht aan de hand van de reacties van de gebruikers van DR. GEO.

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IndexTopBestanden en documentenReceptenboek
drgeo-doc-1.5/nl/drgenius_93.html0000644000175000017500000000406210117134567012344 Gebruikershandleiding van Dr. Geo -- Constructies
Andere trukenReceptenboekalt=""Constructies

Constructies

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Andere trukenReceptenboekalt=""Constructies
drgeo-doc-1.5/nl/drgenius_94.html0000644000175000017500000000575710117134567012361 Gebruikershandleiding van Dr. Geo -- Een punt plaatsen met gegeven coördinaten
Een punt plaatsen a.d.h.v. zijn coördinatenConstructiesalt=""Een punt plaatsen met gegeven coördinaten

Een punt plaatsen met gegeven coördinaten

De meest eenvoudige manier bestaat erin een willekeurig punt te plaatsen - via het instrument Willekeurig Punt - en dan de eigenschappen van het punt aan te passen - via het instrument Eigenschap - en met name de gewenste coördinaten in te voeren.

Een andere mogelijkheid - minder soepel voor dit voorbeeld - is om twee willekeurige getalwaarden in de figuur te plaatsen - via het instrument Getal - en dan een punt te construeren met beide waarden als coördinaten - instrument Punt gedefinieerd door zijn coördinaten. Een voordeel echter, ten opzichte van de vorige methode is dat een punt dat zo werd geconstrueerd niet direct met de muis kan worden verplaatst. Het is als het ware vastgeketend aan zijn positie.

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Een punt plaatsen a.d.h.v. zijn coördinatenConstructiesalt=""Een punt plaatsen met gegeven coördinaten
drgeo-doc-1.5/nl/drgenius_95.html0000644000175000017500000000462110117134567012347 Gebruikershandleiding van Dr. Geo -- Een punt plaatsen a.d.h.v. zijn coördinaten
alt=""ConstructiesEen punt plaatsen met gegeven coördinatenEen punt plaatsen a.d.h.v. zijn coördinaten

Een punt plaatsen a.d.h.v. zijn coördinaten

Deze functie wordt veelvuldig gebruikt wanneer men b.v. de meetkundige plaats van een punt wil construeren. Deze constructie veronderstelt het bestaan van twee waarden. Het punt wordt geplaatst met het instrument Punt bepaald door zijn coördinaten.

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alt=""ConstructiesEen punt plaatsen met gegeven coördinatenEen punt plaatsen a.d.h.v. zijn coördinaten
drgeo-doc-1.5/nl/drgenius_96.html0000644000175000017500000000403310117134567012345 Gebruikershandleiding van Dr. Geo -- Andere truken
alt=""ReceptenboekConstructiesAndere truken

Andere truken

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alt=""ReceptenboekConstructiesAndere truken
drgeo-doc-1.5/nl/drgenius_97.html0000644000175000017500000000456710117134567012362 Gebruikershandleiding van Dr. Geo -- Een figuur afdrukken
Een paragraaf met tekst in een figuur plaatsenAndere trukenalt=""Een figuur afdrukken

Een figuur afdrukken

De meest eenvoudige manier is om de figuur naar het PostScript-formaat te exporteren - Exporteren naar PostScript. Gebruik vervolgens een programma dat PostScript-documenten kan weergeven en afdrukken. Zo'n document zal met vectoriële kwaliteit worden afgedrukt. De programma's GhostView, Gnome GhostView of K GhostView zijn daar perfect geschikt voor.

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Een paragraaf met tekst in een figuur plaatsenAndere trukenalt=""Een figuur afdrukken
drgeo-doc-1.5/nl/drgenius_98.html0000644000175000017500000000661410117134567012356 Gebruikershandleiding van Dr. Geo -- Een paragraaf met tekst in een figuur plaatsen
alt=""Andere trukenEen figuur afdrukkenEen paragraaf met tekst in een figuur plaatsen

Een paragraaf met tekst in een figuur plaatsen

Hiervoor kan je voordelig gebruik maken van scripts, zij het op een wat afwijkende manier. Activeer de modus om een script te schrijven - het instrument voor scripts - en klik onmiddellijk op de achtergrond van het scherm. Zo maak je een script aan zonder invoerparameter. Daarna dien je de eigenschappen van het script - eigenschappen van een object - aan te passen. In de tekstzone waar de Scheme-code normaal wordt geschreven kan je nu de tekst plaatsen. De tekst moet tussen aanhalingstekens staan en worden voorafgegaan door een apostrof. Bij voorbeeld : 

'"Animatie en waarnemingen
================
Verplaats de punten op de figuur en beantwoord volgende vragen.

 1. Waar moet men het punt A' plaatsen zodat men het niet meer kan onderscheiden van A ?
 2. Waar moet men het punt A plaatsen zodat men het punt A' niet meer kan onderscheiden van het punt B ?
 3. Hoe moet men het punt I plaatsen zodat de punten B', C' en I op dezelfde lijn liggen ?
 4. Wat is het spiegelpunt van I ? Wat is het spiegelpunt van A' ?"

Voorbeeld van een paragraaf met tekst in een figuur

Zoals dat geldt voor elk script, kan men ook hier het kleur van de tekst aanpassen.
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alt=""Andere trukenEen figuur afdrukkenEen paragraaf met tekst in een figuur plaatsen
drgeo-doc-1.5/nl/drgenius_99.html0000644000175000017500000002634710117134567012364 Gebruikershandleiding van Dr. Geo -- Index
GNU Free Documentation LicenseTopReceptenboekIndex

Index

Symbols A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Symbols
DR. GEO-Scheme-figuren - Creatie van objecten - Hoek
DR. GEO-Scheme-figuren - Evalueren -
DR. GEO-Scheme-figuren - Inleiding -
DR. GEO-Scheme-figuren - Voorbeelden -
DR. GEO-Scheme-figuren - Voorbeelden -
DR. GEO-Scheme-figuren - Voorbeelden - Fractaal
DR. GEO-Scheme-figuren - Voorbeelden - Regelmatige veelhoek
DR. GEO-Scheme-figuur - Nieuwe figuur -
DR. GEO Scheme figuur - Creatie van objecten -
DR. GEO Scheme figuur - Creatie van objecten - Punt
DR. GEO Scheme-figuur - Creatie van objecten - Attributen van objecten
DR. GEO Scheme-figuur - Creatie van objecten - Cirkelboog
DR. GEO Scheme-figuur - Creatie van objecten - Meetkundige transformaties
DR. GEO Scheme-figuur - Creatie van een object - Plaats
DR. GEO Scheme-figuur - Creatie van objecten - Cirkel
DR. GEO Scheme-figuur - Creatie van objecten - Getal
DR. GEO Scheme-figuur - Creatie van objecten - Halfrechte
DR. GEO Scheme-figuur - Creatie van objecten - Lijnstuk
DR. GEO Scheme-figuur - Creatie van objecten - Vector
DR. GEO Scheme-figuur - Creatie van objecten - Veelhoek
DR. GEO Scheme Figuur - Creatie van objecten - Rechte
A
Afdrukken - Figuur -
B
Bewerken - Standaardvoorkeuren -
Bewerken - Uitzicht -
C
Cirkel - -
Cirkel - Omtrek -
Cirkelboog - -
Cirkelboog - Lengte -
E
Editer - Eigenschappen -
Editer - Getalswaarde -
Editer - Punt -
Editer - Script -
F
Figuur - Afdrukken -
Figuur - Exporteren - PostScript
Figuur - Exporteren - Zone bepalen die men exporteert
Figuur - Exporteren - LaTeX
Figuur - Nieuwe naam geven -
Figuur - Openen -
Figuur - Opslaan -
Figuur - Verplaatsen -
Figuur - Weergeven - Rooster
Figuur - Weergeven - Tekst
G
Getal - -
Getal - Willekeurige waarde -
H
Halfrechte - -
Historiek - Boomstructuur -
Hoek - Georiënteerde -
Hoek - Meetkundige -
Hulp - Standaardvoorkeuren - Bladeraar
I
Instrumenten - Ontgrendelen -
Instrumenten - Vergrendelen -
L
Lijnstuk - -
Lijnstuk - Lengte -
M
Macro-constructie - -
Macro-constructie - Aanmaken -
Macro-constructie - Inleiding -
Macro-constructie - Openen -
Macro-constructie - Opslaan -
Macro-constructie - Uitvoeren -
Meetkundige plaats - -
Meetkundige plaats - Script -
N
Nieuwe naam geven - Object -
O
Object - Nieuwe naam geven -
Object - Verbergen -
Object - Verplaatsen -
Object - Verwijderen -
P
Point - Renommer -
Punt - Coördinaten -
Punt - Gedefinieerd door coördinaten -
Punt - Middelpunt -
Punt - Snijpunt -
Punt - Willekeurig -
R
Rechte - -
Rechte - Afstand -
Rechte - Evenwijdige -
Rechte - Loodlijn -
Rechte - Richtingscoëfficiënt -
Rooster - Weergeven -
S
Script - -
Script - Inleiding -
Script - Interval -
Script - Parameters -
Script - Raaklijn -
Script - Voorbeelden -
Script - getAbscissa -
Script - getAngle -
Script - getCenter -
Script - getCoordinates -
Script - getLength -
Script - getLength -
Script - getNorm -
Script - getRadius -
Script - getSlope -
Script - getValue -
Script - move -
Script - random -
Script - setAbscissa -
Script - setCoordinates -
Script - setValue -
Sessie - Openen -
Sessie - Opslaan -
T
Transformatie - Draaiing -
Transformatie - Homothetie -
Transformatie - Spiegeling - om een as
Transformatie - Spiegeling - Puntspiegeling
Transformatie - Verschuiving -
V
Vector - -
Vector - Coördinaten -
Vector - Norm -
Veelhoek - -
W
Weergeven - Tekst -
Wijzigen - Standaardinstellingen - Namen
Wijzigen - Standaardinstellingen - Ongedaan maken/Herstellen
Wijzigen - Standaarduitzicht -
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GNU Free Documentation LicenseTopReceptenboekIndex
drgeo-doc-1.5/nl/drgenius_9.html0000644000175000017500000000444110117134567012262 Gebruikershandleiding van Dr. Geo -- Snijpunt
Punt gedefinieerd door zijn coördinatenInstrumenten die punten betreffenMiddelpuntSnijpunt

Snijpunt

 

Tekent het of de snijpunten van twee lijnen (i.e. een rechte, halfrechte, lijnstuk, cirkelboog, cirkel). De gebruiker dient twee lijnen te selecteren.

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Punt gedefinieerd door zijn coördinatenInstrumenten die punten betreffenMiddelpuntSnijpunt
drgeo-doc-1.5/nl/drgenius_guile_script.html0000644000175000017500000000761110117134567014605 Gebruikershandleiding van Dr. Geo -- DR. GEO Guile scripts
De instrumenten in de gebruikersinterface aanpassenGevorderde functiesMacro-constructieDR. GEO Guile scripts

DR. GEO Guile scripts

DR. GEO is compatibel met Guile. Dit betekent dat het mogelijk is Guile scripts uit te voeren met DR. GEO. Maar wat is Guile ? Volgens het Guile-handboek :

Guile is een interpreter voor de programmeertaal Scheme, en werd ontworpen voor gebruik in een grote hoeveelheid omgevingen.

Volgende citaten beschrijven precies hoe Guile gebruikt wordt in DR. GEO :

Net als een shell, kan Guile op interactieve manier gebruikt worden, expressies ontvangen van de gebruiker, ze evalueren en de resultaten weergeven. Guile kan ook, net als een interpreter van scripts, code lezen en uitvoeren die in een bestand bewaard werd. Guile is eveneens beschikbaar als een bibliotheek die toelaat op eenvoudige wijze een volwaardige Scheme interpreter in te bouwen in andere toepassingen. Een toepassing kan Guile gebruiken als een uitbreidingstaal, als een krachtige taal voor de eigen configuratie of als een multifunctionele "lijm", die de primitieven van de toepassing verbindt.

Een API is beschikbaar in DR. GEO via de Guile interpreter. Het is een verzameling "haakjes" in de meetkundige motor. Dat is de reden waarom een gebruiker scripts kan schrijven om de (meetkundige of numerieke) items van een figuur te manipuleren. Omdat scripts onderdelen zijn van een figuur net als andere onderdelen, is het niet nodig ze in een afzonderlijk bestand op te slaan : ze worden bewaard in het bestand van de figuur. In wat volgt gebruiken we de afkorting DGS om een "DR. GEO-Guile-script" aan te duiden.

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De instrumenten in de gebruikersinterface aanpassenGevorderde functiesMacro-constructieDR. GEO Guile scripts
drgeo-doc-1.5/nl/drgenius.html0000644000175000017500000000353310117134567012033 Gebruikershandleiding van Dr. Geo

Gebruikershandleiding van DR. GEO

Hilaire Fernandes
Tobias Verbeke
OFSET
http://www.ofset.org

29 augustus 2004

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drgeo-doc-1.5/nl/editing_object_styles.html0000644000175000017500000001101210117134567014556 Gebruikershandleiding van Dr. Geo -- Het uitzicht van een object aanpassen
De eigenschappen van een object aanpassenAndere functiesEen object verwijderenHet uitzicht van een object aanpassen

Het uitzicht van een object aanpassen

 

Van elk meetkundig object kan je een aantal visuele eigenschappen (zoals zijn kleur, dikte, etiket, grootte en vorm) aanpassen. Bovendien is het mogelijk om tijdelijk een object te verbergen zonder het te verwijderen. Het kan bij voorbeeld nuttig zijn om voorbereidende constructies onzichtbaar te maken zonder ze daarom te verwijderen. Al deze eigenschappen kunnen worden aangepast via het dialoogvenster dat verschijnt wanneer de gebruiker op een object van de figuur klikt. Om dit te doen, activeert men eerst de modus die toelaat het uitzicht van een object aan te passen door Andere->Uitzicht te selecteren op het contextuele menu van de figuur. Men kan enveneens op bovenstaand icoon klikken, dat deel uitmaakt van de zesde iconenschuif.

 

Het dialoogvenster Uitzicht van een punt aanpassenbetreft alle soorten punten. Het is mogelijk de kleur, de vorm, de grootte, de naam en de zichtbaarheid aan te passen.

Dialoogvenster voor het uitzicht van een `punt'-object

Het dialoogvenster Uitzicht van een lijn betreft rechten, halfrechten, lijnstukken, vectoren, cirkels, cirkelbogen en meetkundige plaatsen. Het is mogelijk de kleur, de stijl, de naam en de zichtbaarheid aan te passen. Wanneer een rechte, halfrechte, vector of lijnstuk door twee punten gedefinieerd zijn en die twee punten een naam werden toegekend, wordt de naam van de rechte, etc. automatisch afgeleid van de naam van de twee punten. In dit geval kan de gebruiker zelf aan de rechte, etc. geen nieuwe naam geven.

Dialoogvenster voor het uitzicht van een object `lijn'

Het dialoogvenster Uitzicht van een getal of van een veelhoek betreft allerlei getalwaarden (ingevoerd door de gebruiker, berekend door een DR. GEO-Guile-script of een grootte afgeleid van een meetkundige figuur) en de verschillende veelhoeken.

Dialoogvenster voor het uitzicht van getallen & veelhoek-objecten

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De eigenschappen van een object aanpassenAndere functiesEen object verwijderenHet uitzicht van een object aanpassen
drgeo-doc-1.5/nl/inhoudstabel.html0000644000175000017500000002050610117134567012673 Gebruikershandleiding van Dr. Geo -- Inhoudsopgave
CopyrightTopalt=""Inhoudsopgave

Inhoudsopgave

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CopyrightTopalt=""Inhoudsopgave
drgeo-doc-1.5/nl/inleiding.html0000644000175000017500000001134510117134567012155 Gebruikershandleiding van Dr. Geo -- Inleiding
BasisfunctiesTopCopyrightInleiding

Inleiding

DR. GEO is het programma voor interactieve meetkunde van Gnome. Je kan er meetkundige figuren mee tekenen en deze interactief manipuleren, rekening houdende met hun meetkundige eigenschappen. Het programma is bruikbaar in lessituaties zowel in het lager als in het middelbaar onderwijs.

De gebruikersinterface van DR. GEO werd ontworpen om eenvoud in gebruik, ergonomie en gevorderde functies op een harmonische wijze met elkaar te verzoenen.

Door de grote eenvoud van de DR. GEO-interface raakt de beginner onmiddellijk uit de voeten met de basisfuncties. Naarmate hij de uithoeken van de interface en de werking van DR. GEO verkent, dienen de voortgezette functies zich aan : verschillende constructiewijzen van eenzelfde object1, macro-constructies, sessies, aanpassing van de interface, scriptmogelijkheden en DR. GEO Scheme figuren. De gevorderde functies blijken de interface niet te beladen, zodat men er aangenaam gebruik van kan maken in het lager onderwijs. Ook in het middelbaar onderwijs is het gebruik een makkie.

In de gedeelten die volgen worden de basisfuncties uit de doeken gedaan. Vervolgens worden de voorgezette functies in detail behandeld.

Opstartscherm van DR. GEO

Om een meetkundige figuur te tekenen, kan je drukken op de eerste knop van de taakbalk. Een andere manier om dit te doen is via het menu Bestand->Nieuwe...->Figuur. Wanneer je een nieuwe figuur hebt gecreëerd, verschijnt een nieuwe taakbalk met zes iconen. Op het einde van de balk staat een menu dat toelaat de schaal van de huidige meetkundige figuur aan te passen.

Een lege meetkundige figuur

Via de zes iconen op de taakbalk krijg je toegang tot menu's voor specifieke functies. In het volgende hoofdstuk staan die functies beschreven.

Een DR. GEO-figuur en zijn beschrijving

Bij elke figuur hoort een beschrijving in een paneel. Dit paneel wordt standaard uiterst links geplaatst zodat aanvankelijk enkel de tekening van de figuur zichtbaar is. De gebruiker kan echter op elk moment het paneel naar rechts opschuiven en zo de beschrijving zichtbaar maken. Een beschrijving van een figuur is een boomstructuur waarin alle elementen van de figuur een plaats krijgen. Om de relaties tussen de elementen zichtbaar te maken, kan je op het `+'-teken klikken. Zo zie je de elementen waarmee een ander deel van de figuur werd opgebouwd.
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BasisfunctiesTopCopyrightInleiding
drgeo-doc-1.5/nl/line_tools.html0000644000175000017500000000507310117134567012363 Gebruikershandleiding van Dr. Geo -- Instrumenten die lijnen betreffen
Instrumenten die transformaties in het vlak betreffenTekeninstrumentenInstrumenten die punten betreffenInstrumenten die lijnen betreffen

Instrumenten die lijnen betreffen

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Instrumenten die transformaties in het vlak betreffenTekeninstrumentenInstrumenten die punten betreffenInstrumenten die lijnen betreffen
drgeo-doc-1.5/nl/macroconstruction_tools.html0000644000175000017500000000422710117134567015210 Gebruikershandleiding van Dr. Geo -- Instrumenten voor macro-constructies
alt=""TekeninstrumentenNumerieke instrumentenInstrumenten voor macro-constructies

Instrumenten voor macro-constructies

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alt=""TekeninstrumentenNumerieke instrumentenInstrumenten voor macro-constructies
drgeo-doc-1.5/nl/numeric_tools.html0000644000175000017500000000463510117134567013101 Gebruikershandleiding van Dr. Geo -- Numerieke instrumenten
Instrumenten voor macro-constructiesTekeninstrumentenInstrumenten die transformaties in het vlak betreffenNumerieke instrumenten

Numerieke instrumenten

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Instrumenten voor macro-constructiesTekeninstrumentenInstrumenten die transformaties in het vlak betreffenNumerieke instrumenten
drgeo-doc-1.5/nl/other_tools.html0000644000175000017500000000474610117134567012563 Gebruikershandleiding van Dr. Geo -- Andere functies
Voorkeuren van de gebruikerBasisfunctiesTekeninstrumentenAndere functies

Andere functies

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Voorkeuren van de gebruikerBasisfunctiesTekeninstrumentenAndere functies
drgeo-doc-1.5/nl/point_tools.html0000644000175000017500000000434410117134567012565 Gebruikershandleiding van Dr. Geo -- Instrumenten die punten betreffen
Instrumenten die lijnen betreffenTekeninstrumentenalt=""Instrumenten die punten betreffen

Instrumenten die punten betreffen

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Instrumenten die lijnen betreffenTekeninstrumentenalt=""Instrumenten die punten betreffen
drgeo-doc-1.5/nl/transformation_tools.html0000644000175000017500000000505510117134567014502 Gebruikershandleiding van Dr. Geo -- Instrumenten die transformaties in het vlak betreffen
Numerieke instrumentenTekeninstrumentenInstrumenten die lijnen betreffenInstrumenten die transformaties in het vlak betreffen

Instrumenten die transformaties in het vlak betreffen

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Numerieke instrumentenTekeninstrumentenInstrumenten die lijnen betreffenInstrumenten die transformaties in het vlak betreffen
drgeo-doc-1.5/nl/using_macro.html0000644000175000017500000001062210117134567012516 Gebruikershandleiding van Dr. Geo -- Macro-constructie
DR. GEO Guile scriptsGevorderde functiesalt=""Macro-constructie

Macro-constructie

Een macro-constructie gelijkt een beetje op een procedure waarbij je zelf onderdelen van de figuur aangeeft, en de macro-constructie vervolgens op basis van die gegevens nieuwe elementen automatisch toevoegt aan de figuur. Macro-constructies verrichten hun bouwwerk volgens het model dat werd aangereikt door de gebruiker. Dit betekent dat hij de opeenvolgende stappen in het constructieproces zelf een eerste keer toepast op een bepaalde figuur, om DR. GEO vervolgens te vragen die opeenvolgende stappen als één geheel op te slaan in een macro-constructie. Om een constructie-proces te kunnen opslaan moet DR. GEO een beeld hebben van de items die van in het begin aanwezig zijn én van de items die op het einde van de rit zichtbaar moeten zijn. Het spreekt voor zich dat de items in de eindconstructie enkel en alleen getekend kunnen worden aan de hand van de items die van bij de start aanwezig waren. Anders kan DR. GEO de eindconstructie niet stap voor stap afleiden uit de elementen in de beginsituatie.

Op die manier leidt DR. GEO dus de logica van het constructie-proces af en slaat die op in een macro-constructie. Achteraf kan de gebruiker deze macro-constructie het werk laten doen. De macro-constructie vraagt dan enkel om de begingegevens (van het juiste type) aan te duiden en construeert zelf alle onderdelen van de eindfiguur.

(!) De items van voorlopige of onzichtbare constructies worden eveneens geconstrueerd door de macro-constructie. Ze zijn noodzakelijk om het eindresultaat te bekomen.
Als illustratie van een macro-constructie, vertrekken we van het voorbeeld waarbij een gebruiker de constructie van een cirkel door drie punten samen met zijn middelpunt wil opslaan.

De beginfiguur

 

Om een macro-constructie aan te maken, moet de gebruiker eerst zelf de eindfiguur construeren : deze figuur fungeert als model voor de macro-constructie.

De figuur met de gewenste eindconstructie

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DR. GEO Guile scriptsGevorderde functiesalt=""Macro-constructie