pax_global_header00006660000000000000000000000064142666102750014523gustar00rootroot0000000000000052 comment=0a9bab0975a223651fee77a011844da4afd918fe msh-1.0.12/000077500000000000000000000000001426661027500123735ustar00rootroot00000000000000msh-1.0.12/.hgignore000066400000000000000000000014231426661027500141760ustar00rootroot00000000000000syntax: regexp # The recurrent (^|/) idiom in the regexps below should be understood # to mean "at any directory" while the ^ idiom means "from the # project's top-level directory". (^|/).*\.dvi$ (^|/).*\.pdf$ (^|/).*\.o$ (^|/).*\.oct$ (^|/).*\.octlink$ (^|/)octave-core$ (^|/)octave-workspace$ (^|/).*\.tar\.gz$ ## Our Makefile target ^target/ ## Files generated automatically by autoconf and the configure script ^src/aclocal\.m4$ ^src/configure$ ^src/autom4te\.cache($|/) ^src/config\.log$ ^src/config\.status$ ^src/Makefile$ ^src/.*\.m$ # e.g. doc/faq/OctaveFAQ.info # doc/interpreter/octave.info-4 ^doc/.*\.info(-\d)?$ ^doc/\w*/stamp-vti$ ^doc/\w*/version\.texi$ # Emacs tools create these (^|/)TAGS$ (^|/)semantic.cache$ # Other text editors often create these (^|/)~.* msh-1.0.12/COPYING000066400000000000000000000430771426661027500134410ustar00rootroot00000000000000 GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things. To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it. For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software. Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations. Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all. The precise terms and conditions for copying, distribution and modification follow. GNU GENERAL PUBLIC LICENSE TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION 0. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The "Program", below, refers to any such program or work, and a "work based on the Program" means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term "modification".) Each licensee is addressed as "you". Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program). Whether that is true depends on what the Program does. 1. You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and give any other recipients of the Program a copy of this License along with the Program. You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee. 2. You may modify your copy or copies of the Program or any portion of it, thus forming a work based on the Program, and copy and distribute such modifications or work under the terms of Section 1 above, provided that you also meet all of these conditions: a) You must cause the modified files to carry prominent notices stating that you changed the files and the date of any change. b) You must cause any work that you distribute or publish, that in whole or in part contains or is derived from the Program or any part thereof, to be licensed as a whole at no charge to all third parties under the terms of this License. c) If the modified program normally reads commands interactively when run, you must cause it, when started running for such interactive use in the most ordinary way, to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty (or else, saying that you provide a warranty) and that users may redistribute the program under these conditions, and telling the user how to view a copy of this License. (Exception: if the Program itself is interactive but does not normally print such an announcement, your work based on the Program is not required to print an announcement.) These requirements apply to the modified work as a whole. If identifiable sections of that work are not derived from the Program, and can be reasonably considered independent and separate works in themselves, then this License, and its terms, do not apply to those sections when you distribute them as separate works. But when you distribute the same sections as part of a whole which is a work based on the Program, the distribution of the whole must be on the terms of this License, whose permissions for other licensees extend to the entire whole, and thus to each and every part regardless of who wrote it. Thus, it is not the intent of this section to claim rights or contest your rights to work written entirely by you; rather, the intent is to exercise the right to control the distribution of derivative or collective works based on the Program. In addition, mere aggregation of another work not based on the Program with the Program (or with a work based on the Program) on a volume of a storage or distribution medium does not bring the other work under the scope of this License. 3. You may copy and distribute the Program (or a work based on it, under Section 2) in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following: a) Accompany it with the complete corresponding machine-readable source code, which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, b) Accompany it with a written offer, valid for at least three years, to give any third party, for a charge no more than your cost of physically performing source distribution, a complete machine-readable copy of the corresponding source code, to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, c) Accompany it with the information you received as to the offer to distribute corresponding source code. (This alternative is allowed only for noncommercial distribution and only if you received the program in object code or executable form with such an offer, in accord with Subsection b above.) The source code for a work means the preferred form of the work for making modifications to it. For an executable work, complete source code means all the source code for all modules it contains, plus any associated interface definition files, plus the scripts used to control compilation and installation of the executable. However, as a special exception, the source code distributed need not include anything that is normally distributed (in either source or binary form) with the major components (compiler, kernel, and so on) of the operating system on which the executable runs, unless that component itself accompanies the executable. If distribution of executable or object code is made by offering access to copy from a designated place, then offering equivalent access to copy the source code from the same place counts as distribution of the source code, even though third parties are not compelled to copy the source along with the object code. 4. You may not copy, modify, sublicense, or distribute the Program except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense or distribute the Program 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. 5. You are not required to accept this License, since you have not signed it. However, nothing else grants you permission to modify or distribute the Program or its derivative works. These actions are prohibited by law if you do not accept this License. Therefore, by modifying or distributing the Program (or any work based on the Program), you indicate your acceptance of this License to do so, and all its terms and conditions for copying, distributing or modifying the Program or works based on it. 6. Each time you redistribute the Program (or any work based on the Program), the recipient automatically receives a license from the original licensor to copy, distribute or modify the Program subject to these terms and conditions. You may not impose any further restrictions on the recipients' exercise of the rights granted herein. You are not responsible for enforcing compliance by third parties to this License. 7. If, as a consequence of a court judgment or allegation of patent infringement or for any other reason (not limited to patent issues), conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not distribute the Program at all. For example, if a patent license would not permit royalty-free redistribution of the Program by all those who receive copies directly or indirectly through you, then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program. If any portion of this section is held invalid or unenforceable under any particular circumstance, the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances. It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims; this section has the sole purpose of protecting the integrity of the free software distribution system, which is implemented by public license practices. Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system; it is up to the author/donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice. This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License. 8. If the distribution and/or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces, the original copyright holder who places the Program under this License may add an explicit geographical distribution limitation excluding those countries, so that distribution is permitted only in or among countries not thus excluded. In such case, this License incorporates the limitation as if written in the body of this License. 9. The Free Software Foundation may publish revised and/or new versions of the General Public 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. Each version is given a distinguishing version number. If the Program specifies a version number of this License which applies to it and "any later version", you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation. 10. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally. NO WARRANTY 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. END OF TERMS AND CONDITIONS How to Apply These Terms to Your New Programs If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. Copyright (C) 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 of the License, 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, see . Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. msh-1.0.12/DESCRIPTION000066400000000000000000000007441426661027500141060ustar00rootroot00000000000000Name: msh Version: 1.0.12 Date: 2022-07-22 Author: Carlo de Falco, Massimiliano Culpo Maintainer: Carlo de Falco Title: MeSHing software package for octave Description: Create and manage triangular and tetrahedral meshes for Finite Element or Finite Volume PDE solvers. Use a mesh data structure compatible with PDEtool. Rely on gmsh for unstructured mesh generation. Depends: octave (>= 3.0), splines SystemRequirements: gmsh (optional), awk (optional) Autoload: no License: GPLv2+ msh-1.0.12/INDEX000066400000000000000000000012431426661027500131650ustar00rootroot00000000000000MSH >> MSH - MeSHing software package for octave Structured mesh creation msh2m_structured_mesh msh3m_structured_mesh msh2m_mesh_along_spline Unstructured mesh creation msh2m_gmsh msh3m_gmsh Mesh manipulation msh2m_join_structured_mesh msh3m_join_structured_mesh Mesh properties msh2m_geometrical_properties msh3m_geometrical_properties msh2m_topological_properties msh2m_nodes_on_sides msh3m_nodes_on_faces Mesh adaptation msh2m_equalize_mesh msh2m_displacement_smoothing msh2m_jiggle_mesh Mesh extraction msh3e_surface_mesh msh2m_submesh msh3m_submesh Mesh plotting msh2p_mesh Mesh export to gmsh msh2m_gmsh_write msh3m_gmsh_writemsh-1.0.12/NEWS000066400000000000000000000030201426661027500130650ustar00rootroot00000000000000Summary of important user-visible changes for msh 1.0.11: ------------------------------------------------------------------- ** The functions which use FEniCS are now disabled by default ** Fixed Gmsh import functions Summary of important user-visible changes for msh 1.0.10: ------------------------------------------------------------------- ** The functions which use FEniCS are now complint with FEniCS 1.3 Summary of important user-visible changes for msh 1.0.9: ------------------------------------------------------------------- ** Added functions to write meshes to file in gmsh format ** Added option to compute center of mass for tetrahedral elements Summary of important user-visible changes for msh 1.0.8: ------------------------------------------------------------------- ** 1.0.8 is just a bugfix relases that solves some issues arising during the installation. Summary of important user-visible changes for msh 1.0.8: ------------------------------------------------------------------- ** 1.0.8 is just a bugfix relases that solves some issues arising during the installation. ------------------------------------------------------------------- Summary of important user-visible changes for msh 1.0.7: ------------------------------------------------------------------- ** Added new functions mshm_dolfin_read and mshm_dolfin_write for importing/exportinf DOLFIN mesh ** Added the function mshm_refine for refining a mesh (depends on dolfin) ------------------------------------------------------------------- msh-1.0.12/cruft/000077500000000000000000000000001426661027500135165ustar00rootroot00000000000000msh-1.0.12/cruft/src/000077500000000000000000000000001426661027500143055ustar00rootroot00000000000000msh-1.0.12/cruft/src/Makefile.in000066400000000000000000000004351426661027500163540ustar00rootroot00000000000000MKOCTFILE ?= mkoctfile OCTFILES= mshm_refine.oct mshm_dolfin_read.oct mshm_dolfin_write.oct CPPFLAGS += @ac_dolfin_cpp_flags@ LDFLAGS += @ac_dolfin_ld_flags@ all: $(OCTFILES) %.oct: %.cc $(MKOCTFILE) $(CPPFLAGS) $< $(LDFLAGS) clean: -rm -f *.o core octave-core *.oct *~ *.xml msh-1.0.12/cruft/src/bootstrap000077500000000000000000000001131426661027500162430ustar00rootroot00000000000000#!/bin/bash ## Octave-Forge: msh package bootstrap script set -e autoconf msh-1.0.12/cruft/src/configure.ac000066400000000000000000000010421426661027500165700ustar00rootroot00000000000000AC_PREREQ([2.67]) AC_INIT([Msh Package], [1.0]) AC_PROG_CXX AC_LANG(C++) AC_CHECK_PROG([HAVE_MKOCTFILE], [mkoctfile], [yes], [no]) if [test $HAVE_MKOCTFILE = "no"]; then AC_MSG_ERROR([mkoctfile required to install $PACKAGE_NAME]) fi AC_CHECK_HEADER([dolfin.h], [AC_SUBST(ac_dolfin_cpp_flags,-DHAVE_DOLFIN_H) AC_SUBST(ac_dolfin_ld_flags,-ldolfin)], [AC_MSG_WARN([dolfin headers could not be found, som functionalities will be disabled, don't worry your package will still be working, though.])] ) AC_CONFIG_FILES([Makefile]) AC_OUTPUT msh-1.0.12/cruft/src/mshm_dolfin_read.cc000066400000000000000000000140531426661027500201110ustar00rootroot00000000000000/* Copyright (C) 2013-14 Marco Vassallo This file is part of: MSH - Meshing Software Package for Octave MSH 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 of the License, or (at your option) any later version. MSH 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, see . */ #ifdef HAVE_DOLFIN_H #include #endif #include #include #include DEFUN_DLD (mshm_dolfin_read, args, ,"-*- texinfo -*-\n\ @deftypefn {Function File} {[@var{mesh}]} = \ mshm_dolfin_read (@var{mesh_to_read}) \n\ Read a mesh from a dolfin .xml.gz file.\n\ The string @var{mesh_to_read} should be the name of the \ mesh file to be read.\n\ The output @var{mesh} is a PDE-tool like structure\n\ with matrix fields (p,e,t).\n\ @seealso{msh3m_structured_mesh, msh2m_structured_mesh, mshm_dolfin_write}\n\ @end deftypefn") { octave_value_list retval; #ifndef HAVE_DOLFIN_H error("mshm_dolfin_read: the msh package was built without support for dolfin (dolfin.h required)"); #else int nargin = args.length (); dim_vector dims; dims.resize (2); if (nargin != 1) print_usage (); else { std::string mesh_to_read = args(0).string_value (); if (! error_state) { boost::shared_ptr mesh (new dolfin::Mesh (mesh_to_read)); uint D = mesh->topology ().dim (); if (D < 2 || D > 3) error ("mshm_dolfin_read: only 2D or 3D meshes are supported"); else { // matrix p std::size_t num_v = mesh->num_vertices (); Matrix p (D, num_v); std::copy (mesh->coordinates ().begin (), mesh->coordinates ().end (), p.fortran_vec ()); // e has 7 rows in 2d, 10 rows in 3d mesh->init (D - 1, D); std::size_t num_f = mesh->num_facets (); dims(0) = D == 2 ? 7 : 10; dims(1) = num_f; Array e (dims, 0); octave_idx_type *evec = e.fortran_vec (); uint D2 = D * D; octave_idx_type l = 0, m = 0; dolfin::MeshFunction facet_domains (mesh, D - 1); bool empty = true; if (! mesh->domains ().is_empty ()) if (mesh->domains ().num_marked (D-1) != 0) { empty = false; dolfin::MeshFunction facet_domains_tmp (mesh, D - 1, mesh->domains ()); facet_domains = facet_domains_tmp; } for (dolfin::FacetIterator f (*mesh); ! f.end (); ++f) { if ((*f).exterior () == true) { l = 0; for (dolfin::VertexIterator v (*f); ! v.end (); ++v, ++l) e.xelem (l, m) = (*v).index () + 1; if (! empty) e.xelem (D2, m) = facet_domains[*f]; ++m; } } dims(1) = m; e.resize (dims); for (octave_idx_type j = e.rows () - 2; j < e.numel () - 2; j += e.rows ()) evec[j] = 1; // t matrix dims(0) = D + 2; dims(1) = mesh->num_cells (); Array t (dims, 1); std::vector my_cells = mesh->cells (); std::size_t n = 0; empty = true; boost::shared_ptr msh; dolfin::MeshFunction cell_domains; if (! mesh->domains ().is_empty ()) if (mesh->domains ().num_marked (D) != 0) { empty = false; dolfin::MeshFunction cell_domains_tmp (mesh, D, mesh->domains ()); cell_domains = cell_domains_tmp; } for (octave_idx_type j = 0; j < t.cols (); ++j) { for (octave_idx_type i = 0; i < D + 1; ++i, ++n) t.xelem (i, j) += my_cells[n]; if (! empty) t.xelem (D + 1, j) = cell_domains[j]; } octave_scalar_map a; a.setfield ("p", p); a.setfield ("e", e); a.setfield ("t", t); retval = octave_value (a); } } } #endif return retval; } /* %!test %! x = y = z = linspace (0, 1, 2); %! msh = msh3m_structured_mesh (x, y, z, 1, [1 : 6]); %! mshm_dolfin_write (msh, "msh"); %! msh = mshm_dolfin_read ("msh.xml"); %! p = [ 0 0 1 1 0 0 1 1 %! 0 1 0 1 0 1 0 1 %! 0 0 0 0 1 1 1 1]; %! assert (msh.p, p) %! t = [ 1 3 1 2 3 3 %! 2 5 3 3 6 4 %! 3 6 5 4 7 6 %! 6 7 6 6 8 8 %! 1 1 1 1 1 1]; %! assert (msh.t, t) %! e = [1 1 5 3 1 1 2 2 6 3 4 3 %! 2 2 6 5 5 3 4 3 7 7 6 4 %! 6 3 7 7 6 5 6 4 8 8 8 8 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 1 5 6 3 1 3 4 5 6 2 4 2]; %! assert (msh.e, e) */ msh-1.0.12/cruft/src/mshm_dolfin_write.cc000066400000000000000000000426541426661027500203400ustar00rootroot00000000000000/* Copyright (C) 2013-14 Marco Vassallo This file is part of: MSH - Meshing Software Package for Octave MSH 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 of the License, or (at your option) any later version. MSH 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, see . */ #ifdef HAVE_DOLFIN_H #include #endif #include #include DEFUN_DLD (mshm_dolfin_write, args, ,"-*- texinfo -*-\n\ @deftypefn {Function File}\ mshm_dolfin_write (@var{mesh}, @var{mesh_name})\n\ Write a mesh to a dolfin .xml file.\n\ @itemize @bullet\n\ @item @var{mesh} is a PDE-tool like structure\n\ with matrix fields (p,e,t).\n\ @item The string @var{mesh_name} is an optional value specifying the output name.\n\ @end itemize\n\ @seealso{msh3m_structured_mesh, msh2m_structured_mesh, mshm_dolfin_read}\n\ @end deftypefn") { int nargin = args.length (); octave_value_list retval; #ifndef HAVE_DOLFIN_H error("mshm_dolfn_write: the msh package was built without support for dolfin (dolfin.h required)"); #else if (nargin < 1 || nargin > 2) print_usage (); else { octave_scalar_map a = args(0).scalar_map_value (); std::string output_mesh; output_mesh = "mesh"; if (nargin == 2) output_mesh = args(1).string_value (); Array p = a.contents ("p").matrix_value (); Array t = a.contents ("t").matrix_value (); Array e = a.contents ("e").matrix_value (); if (! error_state) { boost::shared_ptr mesh (new dolfin::Mesh ()); std::size_t D = p.rows (); if (D < 2 || D > 3) error ("mshm_dolfin_write: only 2D or 3D meshes are supported"); else { dolfin::MeshEditor editor; editor.open (*mesh, D, D); editor.init_vertices (p.cols ()); editor.init_cells (t.cols ()); if (D == 2) { for (uint i = 0; i < p.cols (); ++i) editor.add_vertex (i, p.xelem (0, i), p.xelem (1, i)); for (uint i = 0; i < t.cols (); ++i) editor.add_cell (i, t.xelem (0, i) - 1, t.xelem (1, i) - 1, t.xelem (2, i) - 1); } if (D == 3) { for (uint i = 0; i < p.cols (); ++i) editor.add_vertex (i, p.xelem (0, i), p.xelem (1, i), p.xelem (2, i)); for (uint i = 0; i < t.cols (); ++i) editor.add_cell (i, t.xelem (0, i) - 1, t.xelem (1, i) - 1, t.xelem (2, i) - 1, t.xelem (3, i) - 1); } editor.close (); // store information associated with e mesh->init (D - 1); dolfin::MeshValueCollection facet(*mesh, D - 1); std::size_t num_side_edges = e.cols (); if (D == 2) { for (uint i = 0; i < num_side_edges; ++i) { dolfin::Vertex v (*mesh, e.xelem (0, i) - 1); for (dolfin::FacetIterator f (v); ! f.end (); ++f) { if ((*f).entities(0)[0] == e.xelem (0, i) - 1 && (*f).entities(0)[1] == e.xelem (1, i) - 1 || (*f).entities(0)[0] == e.xelem (1, i) - 1 && (*f).entities(0)[1] == e.xelem (0, i) - 1) { std::pair idxvl ((*f).index (), e.xelem (4, i)); mesh->domains ().set_marker (idxvl, D - 1); break; } } } } if (D == 3) { for (uint i = 0; i < num_side_edges; ++i) { dolfin::Vertex v (*mesh, e.xelem (0, i) - 1); for (dolfin::FacetIterator f (v); ! f.end (); ++f) { if ((*f).entities(0)[0] == e(0, i) - 1 && (*f).entities(0)[1] == e.xelem (1, i) - 1 && (*f).entities(0)[2] == e.xelem (2, i) - 1 || (*f).entities(0)[0] == e.xelem (0, i) - 1 && (*f).entities(0)[1] == e.xelem (2, i) - 1 && (*f).entities(0)[2] == e.xelem (1, i) - 1 || (*f).entities(0)[0] == e.xelem (1, i) - 1 && (*f).entities(0)[1] == e.xelem (0, i) - 1 && (*f).entities(0)[2] == e.xelem (2, i) - 1 || (*f).entities(0)[0] == e.xelem (1, i) - 1 && (*f).entities(0)[1] == e.xelem (2, i) - 1 && (*f).entities(0)[2] == e.xelem (0, i) - 1 || (*f).entities(0)[0] == e.xelem (2, i) - 1 && (*f).entities(0)[1] == e.xelem (0, i) - 1 && (*f).entities(0)[2] == e.xelem (1, i) - 1 || (*f).entities(0)[0] == e.xelem (2, i) - 1 && (*f).entities(0)[1] == e.xelem (1, i) - 1 && (*f).entities(0)[2] == e.xelem (0, i) - 1) { std::pair idxvl ((*f).index (), e.xelem (9, i)); mesh->domains ().set_marker (idxvl, D - 1); break; } } } } // store information associated with t dolfin::MeshValueCollection cell (*mesh, D); std::size_t num_cells = t.cols (); if (D == 2) { for (uint i = 0; i < num_cells; ++i) { dolfin::Vertex v (*mesh, t.xelem (0, i) - 1); for (dolfin::CellIterator f (v); ! f.end (); ++f) { if ((*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1) { std::pair idxvl ((*f).index (), t.xelem (3, i)); mesh->domains ().set_marker (idxvl, D); break; } } } } if (D == 3) { for (uint i = 0; i < num_cells; ++i) { dolfin::Vertex v (*mesh, t.xelem (0, i) - 1); for (dolfin::CellIterator f (v); ! f.end (); ++f) { if ((*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1) { std::pair idxvl ((*f).index (), t.xelem (4, i)); mesh->domains ().set_marker (idxvl, D); break; } } } } dolfin::File mesh_file (output_mesh + ".xml"); mesh_file << *mesh; } } } #endif return retval; } /* %!test %! x = y = z = linspace (0, 1, 2); %! msh = msh3m_structured_mesh (x, y, z, 1, [1 : 6]); %! mshm_dolfin_write (msh, "msh"); %! msh = mshm_dolfin_read ("msh.xml"); %! p = [ 0 0 1 1 0 0 1 1 %! 0 1 0 1 0 1 0 1 %! 0 0 0 0 1 1 1 1]; %! assert (msh.p, p) %! t = [ 1 3 1 2 3 3 %! 2 5 3 3 6 4 %! 3 6 5 4 7 6 %! 6 7 6 6 8 8 %! 1 1 1 1 1 1]; %! assert (msh.t, t) %! e = [1 1 5 3 1 1 2 2 6 3 4 3 %! 2 2 6 5 5 3 4 3 7 7 6 4 %! 6 3 7 7 6 5 6 4 8 8 8 8 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 0 0 0 0 %! 1 5 6 3 1 3 4 5 6 2 4 2]; %! assert (msh.e, e) */ msh-1.0.12/cruft/src/mshm_refine.cc000066400000000000000000000554201426661027500171160ustar00rootroot00000000000000/* Copyright (C) 2013-14 Marco Vassallo This file is part of: MSH - Meshing Software Package for Octave MSH 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 of the License, or (at your option) any later version. MSH 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, see . */ #ifdef HAVE_DOLFIN_H #include #endif #include #include #include DEFUN_DLD (mshm_refine, args, ,"-*- texinfo -*-\n\ @deftypefn {Function File} {[@var{refined_mesh}]} = \ mshm_refine (@var{mesh},@var{cell_marker}) \n\ Refine a mesh\n\ @itemize @bullet \n\ @item The @var{mesh} is a PDE-tool like structures with matrix field (p,e,t).\n\ @item The optional argument @var{cell_marker} is a list\n\ containing the number of the cells you want to refine.\n\ By default a uniform refinement is applied.\n\ @end itemize\n\ The output @var{refined_mesh} is a refined mesh with\n\ the same structure as @var{mesh}\n\ @seealso{msh3m_structured_mesh, msh2m_structured_mesh}\n\ @end deftypefn") { int nargin = args.length (); octave_value_list retval; #ifndef HAVE_DOLFIN_H error("mshm_refine: the msh package was built without support for dolfin (dolfin.h required)"); #else dim_vector dims; dims.resize (2); if (nargin < 1 || nargin > 2) print_usage (); else { octave_scalar_map a = args(0).scalar_map_value (); Array p = a.contents ("p").matrix_value (); Array t = a.contents ("t").matrix_value (); Array e = a.contents ("e").matrix_value (); Array cell_idx; if (nargin == 2) cell_idx = args(1).array_value (); if (! error_state) { int min = *std::min_element (cell_idx.fortran_vec (), cell_idx.fortran_vec () + cell_idx.length ()); int max = *std::max_element (cell_idx.fortran_vec (), cell_idx.fortran_vec () + cell_idx.length ()); if (nargin == 2 && (min < 1 || max > t.cols ())) error ("mshm_refine: cell index out of bounds"); else { boost::shared_ptr mesh (new dolfin::Mesh ()); std::size_t D = p.rows (); if (D < 2 || D > 3) error ("mshm_refine: only 2D or 3D meshes are supported"); else { dolfin::MeshEditor editor; editor.open (*mesh, D, D); editor.init_vertices (p.cols ()); editor.init_cells (t.cols ()); if (D == 2) { for (uint i = 0; i < p.cols (); ++i) editor.add_vertex (i, p.xelem (0, i), p.xelem (1, i)); for (uint i = 0; i < t.cols (); ++i) editor.add_cell (i, t.xelem (0, i) - 1, t.xelem (1, i) - 1, t.xelem (2, i) - 1); } if (D == 3) { for (unsigned int i = 0; i < p.cols (); ++i) editor.add_vertex (i, p.xelem (0, i), p.xelem (1, i), p.xelem (2, i)); for (unsigned int i = 0; i < t.cols (); ++i) editor.add_cell (i, t.xelem (0, i) - 1, t.xelem (1, i) - 1, t.xelem (2, i) - 1, t.xelem (3, i) - 1); } editor.close (); // store information associated with e mesh->init (D - 1); std::size_t num_side_edges = e.cols (); if (D == 2) { for (uint i = 0; i < num_side_edges; ++i) { dolfin::Vertex v (*mesh, e.xelem (0, i) - 1); for (dolfin::FacetIterator f (v); ! f.end (); ++f) { if ((*f).entities(0)[0] == e.xelem (0, i) - 1 && (*f).entities(0)[1] == e.xelem (1, i) - 1 || (*f).entities(0)[0] == e.xelem (1, i) - 1 && (*f).entities(0)[1] == e.xelem (0, i) - 1) { std::pair idxvl ((*f).index (), e.xelem (4, i)); mesh->domains ().set_marker (idxvl, D - 1); break; } } } } if (D == 3) { for (uint i = 0; i < num_side_edges; ++i) { dolfin::Vertex v (*mesh, e.xelem (0, i) - 1); for (dolfin::FacetIterator f (v); ! f.end (); ++f) { if ((*f).entities(0)[0] == e(0, i) - 1 && (*f).entities(0)[1] == e.xelem (1, i) - 1 && (*f).entities(0)[2] == e.xelem (2, i) - 1 || (*f).entities(0)[0] == e.xelem (0, i) - 1 && (*f).entities(0)[1] == e.xelem (2, i) - 1 && (*f).entities(0)[2] == e.xelem (1, i) - 1 || (*f).entities(0)[0] == e.xelem (1, i) - 1 && (*f).entities(0)[1] == e.xelem (0, i) - 1 && (*f).entities(0)[2] == e.xelem (2, i) - 1 || (*f).entities(0)[0] == e.xelem (1, i) - 1 && (*f).entities(0)[1] == e.xelem (2, i) - 1 && (*f).entities(0)[2] == e.xelem (0, i) - 1 || (*f).entities(0)[0] == e.xelem (2, i) - 1 && (*f).entities(0)[1] == e.xelem (0, i) - 1 && (*f).entities(0)[2] == e.xelem (1, i) - 1 || (*f).entities(0)[0] == e.xelem (2, i) - 1 && (*f).entities(0)[1] == e.xelem (1, i) - 1 && (*f).entities(0)[2] == e.xelem (0, i) - 1) { std::pair idxvl ((*f).index (), e.xelem (9, i)); mesh->domains ().set_marker (idxvl, D - 1); break; } } } } // store information associated with t std::size_t num_cells = t.cols (); if (D == 2) { for (uint i = 0; i < num_cells; ++i) { dolfin::Vertex v (*mesh, t.xelem (0, i) - 1); for (dolfin::CellIterator f (v); ! f.end (); ++f) { if ((*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1) { std::pair idxvl ((*f).index (), t.xelem (3, i)); mesh->domains ().set_marker (idxvl, D); break; } } } } if (D == 3) { for (uint i = 0; i < num_cells; ++i) { dolfin::Vertex v (*mesh, t.xelem (0, i) - 1); for (dolfin::CellIterator f (v); ! f.end (); ++f) { if ((*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (0, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (1, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (3, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (3, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (2, i) - 1 && (*f).entities(0)[1] == t.xelem (3, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (0, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (2, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (1, i) - 1 && (*f).entities(0)[2] == t.xelem (2, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (0, i) - 1 && (*f).entities(0)[3] == t.xelem (1, i) - 1 || (*f).entities(0)[0] == t.xelem (3, i) - 1 && (*f).entities(0)[1] == t.xelem (2, i) - 1 && (*f).entities(0)[2] == t.xelem (1, i) - 1 && (*f).entities(0)[3] == t.xelem (0, i) - 1) { std::pair idxvl ((*f).index (), t.xelem (4, i)); mesh->domains ().set_marker (idxvl, D); break; } } } } dolfin::MeshFunction cell (mesh, D, mesh->domains ()); dolfin::MeshFunction facet (mesh, D - 1, mesh->domains ()); dolfin::CellFunction cell_markers (*mesh); if (nargin == 2) { cell_markers.set_all (false); for (octave_idx_type i = 0; i < cell_idx.length (); ++i) cell_markers.set_value (cell_idx.xelem (i) - 1, true); } else cell_markers.set_all (true); boost::shared_ptr r_mesh(new dolfin::Mesh ()); dolfin::refine (*r_mesh, *mesh, cell_markers); std::size_t num_v = (*r_mesh).num_vertices (); dims(0) = D; dims(1) = num_v; p.resize (dims); std::copy ((*r_mesh).coordinates ().begin (), (*r_mesh).coordinates ().end (), p.fortran_vec ()); // e has 7 rows in 2d, 10 rows in 3d (*r_mesh).init (D - 1, D); std::size_t num_f = (*r_mesh).num_facets (); dims(0) = D == 2 ? 7 : 10; dims(1) = num_f; e.clear (); e.resize (dims, 0); octave_idx_type *evec = e.fortran_vec (); uint D2 = D * D; octave_idx_type l = 0, m = 0; dolfin::MeshFunction r_facet (*r_mesh, D - 1); r_facet = dolfin::adapt (facet, r_mesh); for (dolfin::FacetIterator f (*r_mesh); ! f.end (); ++f) { if ((*f).exterior () == true) { l = 0; for (dolfin::VertexIterator v (*f); ! v.end (); ++v, ++l) e.xelem (l, m) = (*v).index () + 1 ; e.xelem (D2, m) = r_facet[*f]; ++m; } } dims(1) = m; e.resize (dims); for (octave_idx_type j = e.rows () - 2; j < e.numel () - 2; j += e.rows ()) evec[j] = 1; dims(0) = D + 2; dims(1) = (*r_mesh).num_cells (); t.clear (); t.resize (dims, 1); std::vector my_cells = (*r_mesh).cells (); std::size_t n = 0; dolfin::MeshFunction r_cell (*r_mesh, D); r_cell = dolfin::adapt (cell, r_mesh); for (octave_idx_type j = 0; j < t.cols (); ++j) { for (octave_idx_type i = 0; i < D + 1; ++i, ++n) t.xelem (i, j) += my_cells[n]; t.xelem (D + 1, j) = r_cell[j]; } a.setfield ("p", p); a.setfield ("e", e); a.setfield ("t", t); retval = octave_value (a); } } } } #endif return retval; } /* %!demo %! # Create a uniform mesh %! msh = msh2m_structured_mesh (linspace (0, 1, 4), linspace (0, 1, 4), 1, [1 : 4]); %! # Refine it only on cells from 1 to 3 %! partially_refined_mesh = mshm_refine (msh,[1:3]); %! # Refine the original mesh uniformly %! uniformly_refined_mesh = mshm_refine (msh); %! %! # plot the result %! clf; %! subplot (1, 3, 1); %! msh2p_mesh (msh); %! title ('original mesh'); %! subplot (1, 3, 2); %! msh2p_mesh (partially_refined_mesh); %! title ('partially refined mesh'); %! subplot (1, 3, 3); %! msh2p_mesh (uniformly_refined_mesh); %! title ('uniformly refined mesh'); */ /* %!test %! x = y = linspace (0, 1, 2); %! msh = msh2m_structured_mesh (x, y, 1, [1 : 4]); %! msh.t (4, 2) = 2; %! msh_r = mshm_refine (msh); %! msh_rr = mshm_refine (msh_r); %! p = [ 0.00000 0.00000 1.00000 1.00000 0.50000 0.50000 1.00000 0.00000 0.50000 %! 0.00000 1.00000 0.00000 1.00000 0.50000 0.00000 0.50000 0.50000 1.00000]; %! assert (msh_rr.p, p) %! t = [ 1 3 3 4 1 2 2 4 %! 5 5 5 5 5 5 5 5 %! 6 6 7 7 8 8 9 9 %! 1 1 1 1 2 2 2 2]; %! assert (msh_rr.t, t) %! e =[ 1 3 3 4 1 2 2 4 %! 6 6 7 7 8 8 9 9 %! 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 %! 1 1 2 2 4 4 3 3 %! 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0]; %! assert (msh_rr.e, e) */ msh-1.0.12/inst/000077500000000000000000000000001426661027500133505ustar00rootroot00000000000000msh-1.0.12/inst/msh2m_displacement_smoothing.m000066400000000000000000000111101426661027500213650ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{Ax},@var{Ay}]} = @ ## msh2m_displacement_smoothing(@var{msh},@var{k}) ## ## Displace the boundary of a 2D mesh setting a spring with force/length ## constant @var{k} along each edge and enforcing equilibrium. ## ## This function builds matrices containing the resulting (linearized) ## equation for x and y coordinates of each mesh node. Boundary ## conditions enforcing the displacement (Dirichlet type problem) or the ## force (Neumann type) at the boundary must be added to make the system ## solvable, e.g.: ## ## @example ## msh = msh2m_structured_mesh(linspace(0,1,10),@ ## linspace(0,1,10),@ ## 1,1:4,"left"); ## ## dnodes = msh2m_nodes_on_sides(msh,1:4); ## varnodes = setdiff([1:columns(msh.p)],dnodes); ## xd = msh.p(1,dnodes)'; ## yd = msh.p(2,dnodes)'; ## dx = dy = zeros(columns(msh.p),1); ## dxtot = dytot = -.5*sin(xd.*yd*pi/2); ## Nsteps = 10; ## ## for ii = 1:Nsteps ## dx(dnodes) = dxtot; ## dy(dnodes) = dytot; ## [Ax,Ay] = msh2m_displacement_smoothing(msh,1); ## dx(varnodes) = Ax(varnodes,varnodes) \ ... ## (-Ax(varnodes,dnodes)*dx(dnodes)); ## dy(varnodes) = Ay(varnodes,varnodes) \ ... ## (-Ay(varnodes,dnodes)*dy(dnodes)); ## msh.p += [ dx'/Nsteps; dy'/Nsteps ] ; ## triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)'); ## pause(.01) ## endfor ## @end example ## ## @seealso{msh2m_jiggle_mesh} ## ## @end deftypefn function [Ax,Ay] = msh2m_displacement_smoothing(msh, k) ## Check input if nargin != 2 # Number of input parameters error("msh2m_displacement_smoothing: wrong number of input parameters."); elseif !(isstruct(msh) && isfield(msh,"p") && isfield(msh,"t") && isfield(msh,"e")) error("msh2m_displacement_smoothing: first input is not a valid mesh structure."); elseif !isscalar(k) error("msh2m_displacement_smoothing: k must be a valid scalar"); endif ## Construct matrices x = msh.p(1,:); y = msh.p(2,:); dx2 = (x(msh.t([1 2 3],:))-x(msh.t([2 3 1],:))).^2; dy2 = (y(msh.t([1 2 3],:))-y(msh.t([2 3 1],:))).^2; l2 = dx2 + dy2; Ax = spalloc(length(x),length(x),1); Ay = spalloc(length(x),length(x),1); ax = zeros(3,3,columns(msh.t)); ay = zeros(3,3,columns(msh.t)); for inode=1:3 for jnode=1:3 ginode(inode,jnode,:)=msh.t(inode,:); gjnode(inode,jnode,:)=msh.t(jnode,:); endfor endfor for ii=1:3 for jj=ii+1:3 ax(ii,jj,:) = ax(jj,ii,:) = reshape(-k * dx2(ii,:)./l2(ii,:),1,1,[]); ay(ii,jj,:) = ay(jj,ii,:) = reshape(-k * dy2(ii,:)./l2(ii,:),1,1,[]); ax(ii,ii,:) -= ax(ii,jj,:); ax(jj,jj,:) -= ax(ii,jj,:); ay(ii,ii,:) -= ay(ii,jj,:); ay(jj,jj,:) -= ay(ii,jj,:); endfor endfor Ax = sparse(ginode(:),gjnode(:),ax(:)); Ay = sparse(ginode(:),gjnode(:),ay(:)); endfunction %!demo %! msh = msh2m_structured_mesh(linspace(0,1,10), %! linspace(0,1,10), %! 1,1:4,"left"); %! dnodes = msh2m_nodes_on_sides(msh,1:4); %! varnodes = setdiff([1:columns(msh.p)],dnodes); %! %! xd = msh.p(1,dnodes)'; %! yd = msh.p(2,dnodes)'; %! %! dy = zeros(columns(msh.p),1); %! dx = dy; %! %! dxtot = -.5*sin(xd.*yd*pi/2); %! dytot = -.5*sin(xd.*yd*pi/2); %! %! Nsteps = 5; %! for ii=1:Nsteps %! %! dx(dnodes) = dxtot; %! dy(dnodes) = dytot; %! %! [Ax,Ay] = msh2m_displacement_smoothing(msh,1); %! %! dx(varnodes) = Ax(varnodes,varnodes) \ ... %! (-Ax(varnodes,dnodes)*dx(dnodes)); %! dy(varnodes) = Ay(varnodes,varnodes) \ ... %! (-Ay(varnodes,dnodes)*dy(dnodes)); %! %! msh.p(1,:) += dx'/Nsteps; %! msh.p(2,:) += dy'/Nsteps; %! %! if mod(ii,2)==0 %! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)'); %! pause(.01) %! endif %! endfor msh-1.0.12/inst/msh2m_equalize_mesh.m000066400000000000000000000101201426661027500174610ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mesh}]} = @ ## msh2m_equalize_mesh(@var{mesh}) ## ## Apply a baricentric regularization to equalize the size of triangle ## edges, i.e. move each node to the center of mass of the patch of ## triangles to which it belongs. ## ## May be useful when distorting a mesh. ## Type @code{demo msh2m_equalize_mesh} to see some examples. ## ## @seealso{msh2m_displacement_smoothing} ## ## @end deftypefn function [msh] = msh2m_equalize_mesh(msh) ## Check input if nargin != 1 # Number of input parameters error("msh2m_equalize_mesh: wrong number of input parameters."); elseif !(isstruct(msh) && isfield(msh,"p") && isfield(msh,"t") && isfield(msh,"e")) error("msh2m_equalize_mesh: first input is not a valid mesh structure."); endif ## Apply regularization nel= columns(msh.t); x = msh.p(1,:)'; y = msh.p(2,:)'; dnodes = unique(msh.e(1:2,:)(:)); varnodes = setdiff([1:columns(msh.p)],dnodes); Ax = spalloc(length(x),length(x),1); Ay = spalloc(length(x),length(x),1); ax = zeros(3,3,nel); ay = zeros(3,3,nel); for inode=1:3 giinode(inode,:)=msh.t(inode,:); for jnode=1:3 ginode(inode,jnode,:)=msh.t(inode,:); gjnode(inode,jnode,:)=msh.t(jnode,:); endfor endfor for ii=1:3 for jj=ii+1:3 ax(ii,jj,:) = ax(jj,ii,:) = -ones(1,1,nel); ay(ii,jj,:) = ay(jj,ii,:) = -ones(1,1,nel); ax(ii,ii,:) -= ax(ii,jj,:); ax(jj,jj,:) -= ax(ii,jj,:); ay(ii,ii,:) -= ay(ii,jj,:); ay(jj,jj,:) -= ay(ii,jj,:); endfor endfor Ax = sparse(ginode(:),gjnode(:),ax(:)); Ay = sparse(ginode(:),gjnode(:),ay(:)); x(varnodes) = Ax(varnodes,varnodes) \ (-Ax(varnodes,dnodes)*x(dnodes)); y(varnodes) = Ay(varnodes,varnodes) \ (-Ay(varnodes,dnodes)*y(dnodes)); msh.p(1,:) = x'; msh.p(2,:) = y'; endfunction %!demo %! ### equalize a structured mesh without moving boundary nodes %! msh = msh2m_structured_mesh(linspace(0,1,10),linspace(0,1,10),1,1:4,"random"); %! dnodes = msh2m_nodes_on_sides(msh,1:4); %! varnodes = setdiff([1:columns(msh.p)],dnodes); %! x = msh.p(1,:)'; %! y = msh.p(2,:)'; %! msh = msh2m_equalize_mesh(msh); %! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)'); %! pause(.01) %!demo %! ### distort a mesh on a square equalizing at each step %! msh = msh2m_structured_mesh(linspace(0,1,10),linspace(0,1,10),1,1:4,"random"); %! dnodes = msh2m_nodes_on_sides(msh,1:4); %! varnodes = setdiff([1:columns(msh.p)],dnodes); %! x = msh.p(1,:)'; %! y = msh.p(2,:)'; %! dx = dy = zeros(columns(msh.p),1); %! dytot = dxtot = -.7*sin(x(dnodes).*y(dnodes)*pi/2); %! Nsteps = 10; %! for ii=1:Nsteps %! dx(dnodes) = dxtot; %! dy(dnodes) = dytot; %! [Ax,Ay] = msh2m_displacement_smoothing(msh,1); %! dx(varnodes) = Ax(varnodes,varnodes) \ ... %! (-Ax(varnodes,dnodes)*dx(dnodes)); %! dy(varnodes) = Ay(varnodes,varnodes) \ ... %! (-Ay(varnodes,dnodes)*dy(dnodes)); %! msh.p(1,:) += dx'/Nsteps; %! msh.p(2,:) += dy'/Nsteps; %! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)','r'); %! pause(.5) %! x = msh.p(1,:)'; %! y = msh.p(2,:)'; %! msh = msh2m_equalize_mesh(msh); %! hold on;triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)');hold off %! pause(.5) %! endformsh-1.0.12/inst/msh2m_geometrical_properties.m000066400000000000000000000415031426661027500214060ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{varargout}]} = @ ## msh2m_geometrical_properties(@var{mesh},[@var{string1},@var{string2},...]) ## ## Compute @var{mesh} geometrical properties identified by input strings. ## ## Valid properties are: ## @itemize @bullet ## @item @code{"bar"}: return a matrix with size 2 times the number of mesh ## elements containing the center of mass coordinates. ## @item @code{"cir"}: return a matrix with size 2 times the number of ## mesh elements containing the circumcenter coordinates. ## @item @code{"emidp"}: return a matrix with size 2 times the number of ## side edges containing their midpoint coordinates. ## @item @code{"slength"}: return a matrix with size 3 times the number ## of mesh elements containing the length of each element side. ## @item @code{"cdist"}: return a matrix of size 3 times the number of ## mesh elements containing the distance among circumcenters of ## neighbouring elements. If the corresponding side lies on the edge, ## the distance between circumcenter and border edge is returned in the ## matrix. ## @item @code{"wjacdet"}: return the weigthed Jacobian determinant used ## for the numerical integration with trapezoidal rule over an element. ## @item @code{"shg"}: return a matrix of size 3 times the number of ## elements matrix containing the gradient of P1 shape functions. ## @item @code{"area"}: return a row vector containing the area of every ## element. ## @item @code{"midedge"}: return a multi-dimensional array with size 2 ## times 3 times the number of elements containing the coordinates of ## the midpoint of every edge. ## @end itemize ## ## The output will contain the geometrical properties requested in the ## input in the same order specified in the function call. ## ## If an unexpected string is given as input, an empty vector is ## returned in output. ## ## @seealso{msh2m_topological_properties, msh3m_geometrical_properties} ## @end deftypefn function varargout = msh2m_geometrical_properties (mesh, varargin) ## Check input if (nargin < 2) # Number of input parameters error (["msh2m_geometrical_properties: ", ... "wrong number of input parameters."]); elseif (! (isstruct (mesh) && isfield (mesh, "p") && isfield (mesh, "t") && isfield (mesh, "e"))) error (["msh2m_geometrical_properties: ", ... "first input is not a valid mesh structure."]); elseif (! iscellstr (varargin)) error (["msh2m_geometrical_properties: ", ... "only string value admitted for properties."]); endif ## Compute properties p = mesh.p; e = mesh.e; t = mesh.t; nelem = columns (t); [k,j,w] = coeflines (p, t, nelem); # Edge coefficients for nn = 1:length (varargin) request = varargin{nn}; switch request case "bar" # Center of mass coordinates if (isfield (mesh, "bar")) varargout{nn} = mesh.bar; else [b] = coordinates (p, t, nelem, j, w, k, "bar"); varargout{nn} = b; clear b; endif case "cir" # Circum-center coordinates if (isfield (mesh, "cir")) varargout{nn} = mesh.cir; else [b] = coordinates(p,t,nelem,j,w,k,"cir"); varargout{nn} = b; clear b; endif case "emidp" # Boundary edges midpoint coordinates if (isfield (mesh, "emidp")) varargout{nn} = mesh.emidp; else b = midpoint (p, e); varargout{nn} = b; clear b; endif case "slength" # Length of every side if (isfield (mesh, "slength")) varargout{nn} = mesh.slength; else b = sidelength (p, t, nelem); varargout{nn} = b; clear b; endif case "cdist" # Distance among circumcenters of neighbouring elements if (isfield (mesh, "cdist")) varargout{nn} = mesh.cdist; else if (isfield (mesh,"cir")) cir = mesh.cir; else cir = coordinates (p, t, nelem, j, w, k, "cir"); endif if (isfield (mesh, "n")) n = mesh.n; else n = msh2m_topological_properties (mesh, "n"); endif b = distance (cir, n, nelem); semib = semidistance (cir, nelem, j, w, k); border = isnan (n); index1 = find (border(1,:)); index2 = find (border(2,:)); index3 = find (border(3,:)); b(1,index1) = semib (1,index1); b(2,index2) = semib (2,index2); b(3,index3) = semib (3,index3); varargout{nn} = b; clear b semib index1 index2 index3 border; endif case "wjacdet" # Weighted Jacobian determinant if (isfield (mesh, "wjacdet")) varargout{nn} = mesh.wjacdet; else b = computearea (p, e, t, "wjac"); varargout{nn} = b; clear b endif case "area" # Area of the elements if (isfield (mesh, "area")) varargout{nn} = mesh.area; else b = computearea (p, e, t, "area"); varargout{nn} = b; clear b endif case "shg" # Gradient of hat functions if (isfield (mesh, "shg")) varargout{nn} = mesh.shg; else b = shapegrad (p, t); varargout{nn} = b; clear b endif case "midedge" # Mid-edge coordinates if (isfield (mesh, "midedge")) varargout{nn} = mesh.midedge; else b = midedge (p, t, nelem); varargout{nn} = b; clear b; endif otherwise warning (["msh2m_geometrical_properties: ", ... "unexpected value in property string. ", ... "Empty vector passed as output."]) varargout{nn} = []; endswitch endfor endfunction function [k, j, w] = coeflines (p, t, nelem) ## Edges are described by the analytical expression: ## ## k*x + j*y + w = 0 ## ## Coefficients k,j,w are stored in matrixes ## i-th edge list, i =1,2,3 s1 = sort (t(2:3,:),1); s2 = sort (t([3,1],:),1); s3 = sort (t(1:2,:),1); ## Initialization of the matrix data-structure k = ones(3,nelem); j = ones(3,nelem); w = ones(3,nelem); ## Searching for lines parallel to x axis [i1] = find ((p(2,s1(2,:)) - p(2,s1(1,:))) != 0); noti1 = setdiff([1:nelem], i1); [i2] = find ((p(2,s2(2,:)) - p(2,s2(1,:))) != 0); noti2 = setdiff([1:nelem], i2); [i3] = find ((p(2,s3(2,:)) - p(2,s3(1,:))) != 0); noti3 = setdiff([1:nelem], i3); ## Computation of the coefficients ## Edge 1 j(1,i1) = (p(1,s1(1,i1)) - p(1,s1(2,i1))) ./ ... (p(2,s1(2,i1)) - p(2,s1(1,i1))); w(1,i1) = -(p(1,s1(1,i1)) + p(2,s1(1,i1)).*j(1,i1)); k(1,noti1) = 0; j(1,noti1) = 1; w(1,noti1) = - p(2,s1(1,noti1)); ## Edge 2 j(2,i2) = (p(1,s2(1,i2)) - p(1,s2(2,i2))) ./ ... (p(2,s2(2,i2)) - p(2,s2(1,i2))); w(2,i2) = -(p(1,s2(1,i2)) + p(2,s2(1,i2)).*j(2,i2)); k(2,noti2) = 0; j(2,noti2) = 1; w(2,noti2) = - p(2,s2(1,noti2)); ## Edge 3 j(3,i3) = (p(1,s3(1,i3)) - p(1,s3(2,i3))) ./ ... (p(2,s3(2,i3)) - p(2,s3(1,i3))); w(3,i3) = -(p(1,s3(1,i3)) + p(2,s3(1,i3)).*j(3,i3)); k(3,noti3) = 0; j(3,noti3) = 1; w(3,noti3) = - p(2,s3(1,noti3)); endfunction function b = coordinates (p, t, nelem, j, w, k, string) ## Compute the coordinates of the geometrical entity specified by string ## Initialization of the output vectors b = zeros (2, nelem); switch string case "bar" b(1,:) = (p(1,t(1,:)) + p(1,t(2,:)) + p(1,t(3,:))) / 3; b(2,:) = (p(2,t(1,:)) + p(2,t(2,:)) + p(2,t(3,:))) / 3; case "cir" ## Computation of the midpoint of the first two edges mid1 = zeros (2, nelem); mid2 = zeros (2, nelem); ## X coordinate mid1(1,:) = (p(1,t(2,:)) + p(1,t(3,:))) / 2; mid2(1,:) = (p(1,t(3,:)) + p(1,t(1,:))) / 2; ## Y coordinate mid1(2,:) = (p(2,t(2,:)) + p(2,t(3,:))) / 2; mid2(2,:) = (p(2,t(3,:)) + p(2,t(1,:))) / 2; ## Computation of the intersect between axis 1 and axis 2 ## Searching for element with edge 1 parallel to x-axes parx = find (j(1,:) == 0); notparx = setdiff (1:nelem, parx); coefy = zeros (1, nelem); ## If it is not parallel coefy(notparx) = ((j(2,notparx)./j(1,notparx)) .* k(1,notparx) - k(2,notparx)).^(-1); b(2,notparx) = coefy(1,notparx) .* ... (j(2,notparx) .* mid2(1,notparx) - k(2,notparx) .* mid2(2,notparx) + k(1,notparx) ./ j(1,notparx) .* j(2,notparx) .* mid1(2,notparx) - j(2,notparx) .* mid1(1,notparx)); b(1,notparx) = (k(1,notparx) .* b(2,notparx) + j(1,notparx) .* mid1(1,notparx) - k(1,notparx) .* mid1(2,notparx)) ./ ... j(1,notparx); ## If it is parallel b(2,parx) = mid1(2,parx); b(1,parx) = k(2,parx) ./ j(2,parx) .* ... (b(2,parx) - mid2(2,parx)) + ... mid2(1,parx); endswitch endfunction function [b] = midpoint(p,e) ## Compute the coordinates of the midpoint on the boundary edges b = zeros(2,columns(e)); b(1,:) = (p(1,e(1,:)) + p(1,e(2,:)))./2; b(2,:) = (p(2,e(1,:)) + p(2,e(2,:)))./2; endfunction function [l] = sidelength(p,t,nelem) ## Compute the length of every side l = zeros(3, nelem); ## i-th edge list, i =1,2,3 s1 = sort (t(2:3,:),1); s2 = sort (t([3,1],:),1); s3 = sort (t(1:2,:),1); ## First side length l(1,:) = sqrt ((p(1,s1(1,:)) - p(1,s1(2,:))).^2 + (p(2,s1(1,:)) - p(2,s1(2,:))).^2); ## Second side length l(2,:) = sqrt ((p(1,s2(1,:)) - p(1,s2(2,:))).^2 + (p(2,s2(1,:)) - p(2,s2(2,:))).^2); ## Third side length l(3,:) = sqrt ((p(1,s3(1,:)) - p(1,s3(2,:))).^2 + (p(2,s3(1,:)) - p(2,s3(2,:))).^2); endfunction function [d] = semidistance(b,nelem,j,w,k) ## Compute the distance to the sides of the nodes with coordinates b ## The edges are described by the analytical expression: ## ## k*x + j*y + w = 0 ## ## The coefficients k,j,w are stored in matrixes ## Initialization of the distance output vector d = zeros(3, nelem); ## Computation of the distances from the geometrical entity to the edges d(1,:) = abs (k(1,:).*b(1,:) + j(1,:).*b(2,:) + w(1,:)) ./ ... (sqrt (k(1,:).^2 + j(1,:).^2)); d(2,:) = abs (k(2,:).*b(1,:) + j(2,:).*b(2,:) + w(2,:)) ./ ... (sqrt (k(2,:).^2 + j(2,:).^2)); d(3,:) = abs (k(3,:).*b(1,:) + j(3,:).*b(2,:) + w(3,:)) ./ ... (sqrt (k(3,:).^2 + j(3,:).^2)); endfunction function [d] = distance(b,n,nelem) ## Compute the distance between two neighbouring entities ## Initialization of the distance output vector d = NaN(3, nelem); ## Trg not on the geometrical border border = isnan(n); [index1] = find (border(1,:) == 0); [index2] = find (border(2,:) == 0); [index3] = find (border(3,:) == 0); ## Computation of the distances between two neighboring geometrical entities d(1,index1) = sqrt ((b(1,index1) - b(1,n(1,index1))).^2 + (b(2,index1) - b(2,n(1,index1))).^2); d(2,index2) = sqrt ((b(1,index2) - b(1,n(2,index2))).^2 + (b(2,index2) - b(2,n(2,index2))).^2); d(3,index3) = sqrt ((b(1,index3) - b(1,n(3,index3))).^2 + (b(2,index3) - b(2,n(3,index3))).^2); endfunction function [b] = computearea(p,e,t,string) ## Compute the area of every element in the mesh weight = [1/3 1/3 1/3]; areakk = 1/2; Nelements = columns(t); jac([1,2],:) = [p(1,t(2,:))-p(1,t(1,:)); p(1,t(3,:))-p(1,t(1,:))]; jac([3,4],:) = [p(2,t(2,:))-p(2,t(1,:)); p(2,t(3,:))-p(2,t(1,:))]; jacdet = jac(1,:).*jac(4,:)-jac(2,:).*jac(3,:); degen = find (jacdet <= 0); if ~isempty(degen) ## XXX FIXME: there should be a -verbose option to allow to see this ## fprintf(1,"invalid mesh element: %d fixing...\n",degen); t(1:3,degen) = t([2,1,3],degen); jac([1,2],degen) = [p(1,t(2,degen))-p(1,t(1,degen)); p(1,t(3,degen))-p(1,t(1,degen))]; jac([3,4],degen) = [p(2,t(2,degen))-p(2,t(1,degen)); p(2,t(3,degen))-p(2,t(1,degen))]; jacdet(degen) = jac(1,degen) .* jac(4,degen) - ... jac(2,degen) .* jac(3,degen); endif for inode = 1:3 wjacdet(inode,:) = areakk .* jacdet .* weight(inode); endfor if string == "wjac" b = wjacdet; elseif string == "area" b = sum(wjacdet)'; endif endfunction function [d] = midedge(p,t,nelem) ## Compute the midpoint coordinates for every edge s1 = t(2:3,:); s2 = t([3,1],:); s3 = t(1:2,:); edge = cell(3,1); edge(1) = s1; edge(2) = s2; edge(3) = s3; d = zeros(2,3,nelem); #Lati * Coordinate * Elementi for jj = 1:3 tempx = (p(1,edge{jj}(1,:)) + p(1,edge{jj}(2,:)))/2; tempy = (p(2,edge{jj}(1,:)) + p(2,edge{jj}(2,:)))/2; temp = [tempx; tempy]; d(:,jj,:) = temp; endfor endfunction function [shg] = shapegrad(p,t) ## Compute the gradient of the hat functions x0 = p(1,t(1,:)); y0 = p(2,t(1,:)); x1 = p(1,t(2,:)); y1 = p(2,t(2,:)); x2 = p(1,t(3,:)); y2 = p(2,t(3,:)); denom = (-(x1.*y0) + x2.*y0 + x0.*y1 - x2.*y1 - x0.*y2 + x1.*y2); shg(1,1,:) = (y1 - y2)./denom; shg(2,1,:) = -(x1 - x2)./denom; shg(1,2,:) = -(y0 - y2)./denom; shg(2,2,:) = (x0 - x2)./denom; shg(1,3,:) = (y0 - y1)./denom; shg(2,3,:) = -(x0 - x1)./denom; endfunction %!test %! [mesh] = msh2m_structured_mesh(0:.5:1, 0:.5:1, 1, 1:4, "left"); %! [mesh.bar, mesh.cir, mesh.emidp, mesh.slength, mesh.cdist, mesh.area,mesh.midedge] = msh2m_geometrical_properties(mesh,"bar","cir","emidp","slength","cdist","area","midedge"); %! bar = [0.16667 0.16667 0.66667 0.66667 0.33333 0.33333 0.83333 0.83333 %! 0.16667 0.66667 0.16667 0.66667 0.33333 0.83333 0.33333 0.83333]; %! cir = [0.25000 0.25000 0.75000 0.75000 0.25000 0.25000 0.75000 0.75000 %! 0.25000 0.75000 0.25000 0.75000 0.25000 0.75000 0.25000 0.75000]; %! emidp =[0.25000 0.75000 1.00000 1.00000 0.25000 0.75000 0.00000 0.00000 %! 0.00000 0.00000 0.25000 0.75000 1.00000 1.00000 0.25000 0.75000]; %! slength =[0.70711 0.70711 0.70711 0.70711 0.50000 0.50000 0.50000 0.50000 %! 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000 0.50000 %! 0.50000 0.50000 0.50000 0.50000 0.70711 0.70711 0.70711 0.70711]; %! cdist = [0.00000 0.00000 0.00000 0.00000 0.50000 0.50000 0.25000 0.25000 %! 0.25000 0.25000 0.50000 0.50000 0.50000 0.25000 0.50000 0.25000 %! 0.25000 0.50000 0.25000 0.50000 0.00000 0.00000 0.00000 0.00000]; %! area = [ 0.12500 ; 0.12500 ; 0.12500 ; 0.12500 ; 0.12500 ; 0.12500 ; 0.12500 ; 0.12500]; %! midedge = zeros(2,3,8); %! midedge(:,:,1) = [0.25000 0.00000 0.25000 %! 0.25000 0.25000 0.00000]; %! midedge(:,:,2) = [0.25000 0.00000 0.25000 %! 0.75000 0.75000 0.50000]; %! midedge(:,:,3) = [0.75000 0.50000 0.75000 %! 0.25000 0.25000 0.00000]; %! midedge(:,:,4) = [0.75000 0.50000 0.75000 %! 0.75000 0.75000 0.50000]; %! midedge(:,:,5) = [0.50000 0.25000 0.25000 %! 0.25000 0.50000 0.25000]; %! midedge(:,:,6) = [0.50000 0.25000 0.25000 %! 0.75000 1.00000 0.75000]; %! midedge(:,:,7) = [1.00000 0.75000 0.75000 %! 0.25000 0.50000 0.25000]; %! midedge(:,:,8) = [1.00000 0.75000 0.75000 %! 0.75000 1.00000 0.75000]; %! toll = 1e-4; %! assert(mesh.bar,bar,toll); %! assert(mesh.cir,cir,toll); %! assert(mesh.emidp,emidp,toll); %! assert(mesh.slength,slength,toll); %! assert(mesh.cdist,cdist,toll); %! assert(mesh.area,area,toll); %! assert(mesh.midedge,midedge,toll); msh-1.0.12/inst/msh2m_gmsh.m000066400000000000000000000153001426661027500155710ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010,2012 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mesh}]} = @ ## msh2m_gmsh(@var{geometry},@var{option},@var{value},...) ## @deftypefnx {Function File}{[@var{mesh}, @var{gmsh_out}]} = msh2m_gmsh(...) ## ## Construct an unstructured triangular 2D mesh making use of the free ## software gmsh. ## ## The compulsory argument @var{geometry} is the basename of the ## @code{*.geo} file to be meshed. ## ## The optional arguments @var{option} and @var{value} identify ## respectively a gmsh option and its value. For more information ## regarding the possible option to pass, refer to gmsh manual or gmsh ## site @url{http://www.geuz.org/gmsh/}. ## ## The returned value @var{mesh} is a PDE-tool like mesh structure. ## If the function is called with two outputs @var{gmsh_out} is the verbose output ## of the gmsh subprocess. ## ## @seealso{msh2m_structured_mesh, msh3m_gmsh, msh2m_mesh_along_spline} ## @end deftypefn function [mesh, gmsh_output] = msh2m_gmsh (geometry, varargin) ## Check input if !mod(nargin,2) # Number of input parameters error("msh2m_gmsh: wrong number of input parameters."); endif ## FIXME: add input type check? ## Build mesh noptions = (nargin - 1) / 2; # Number of passed options ## Construct system command string verbose = 1; optstring = ""; for ii = 1:noptions option = varargin{2*(ii)-1}; value = varargin{2*ii}; ## Check for verbose option if strcmp(option,"v") verbose = value; endif if !ischar(value) value = num2str(value); endif optstring = [optstring," -",option," ",value]; endfor ## Invoke gmsh if (verbose) printf("\n"); printf("Generating mesh...\n"); endif msh_name = strcat (tempname (), ".msh"); fclose (fopen (msh_name, "w")); [status, gmsh_output] = system (["gmsh -format msh2 -2 -o " msh_name optstring " " geometry ".geo 2>&1 "]); if (status) error ("msh2m_gmsh: the gmesh subprocess exited abnormally"); endif fname = tempname (); fclose (fopen (strcat (fname, "_e.txt"), "w")); e_filename = canonicalize_file_name (strcat (fname, "_e.txt")); fclose (fopen (strcat (fname, "_p.txt"), "w")); p_filename = canonicalize_file_name (strcat (fname, "_p.txt")); fclose (fopen (strcat (fname, "_t.txt"), "w")); t_filename = canonicalize_file_name (strcat (fname, "_t.txt")); ## Build structure fields if (verbose) printf("Processing gmsh data...\n"); endif ## Points com_p = sprintf ("awk '/\\$Nodes/,/\\$EndNodes/ {print $2, $3 > ""%s""}' ", p_filename); ## Side edges com_e = sprintf ("awk '/\\$Elements/,/\\$EndElements/ {n=3+$3; if ($2 == ""1"") print $(n+1), $(n+2), $5 > ""%s""}' ", e_filename); ## Triangles com_t = sprintf ("awk '/\\$Elements/,/\\$EndElements/ {n=3+$3; if ($2 == ""2"") print $(n+1), $(n+2), $(n+3), $5 > ""%s""}' ", t_filename); command = [com_p, msh_name, ";"]; command = [command, com_e, msh_name, ";"]; command = [command, com_t, msh_name]; system (command); ## Create PDE-tool like structure if (verbose) printf("Creating PDE-tool like mesh...\n"); endif p = load(p_filename)'; # Mesh-points tmp = load(e_filename)'; # Mesh surface-edges be = zeros(7,columns(tmp)); be([1,2,5],:) = tmp; t = load(t_filename)'; # Mesh tetrahedra ## Remove hanging nodes if (verbose) printf("Check for hanging nodes...\n"); endif nnodes = columns(p); in_msh = intersect( 1:nnodes , t(1:3,:) ); if length(in_msh) != nnodes new_num(in_msh) = [1:length(in_msh)]; t(1:3,:) = new_num(t(1:3,:)); be(1:2,:) = new_num(be(1:2,:)); p = p(:,in_msh); endif ## Set region numbers in edge structure if (verbose) printf("Setting region number in edge structure...\n"); endif mesh = struct("p",p,"t",t,"e",be); tmp = msh2m_topological_properties (mesh, "boundary"); mesh.e(6,:) = t(4,tmp(1,:)); jj = find (sum(tmp>0)==4); mesh.e(7,jj) = t(4,tmp(3,jj)); ## Delete temporary files if (verbose) printf("Deleting temporary files...\n"); endif unlink (p_filename); unlink (e_filename); unlink (t_filename); unlink (msh_name); endfunction %!test %! fid = fopen("circle.geo","w"); %! fprintf(fid,"Point(1) = {0, 0, 0, 1};\n"); %! fprintf(fid,"Point(2) = {1, 0, 0, 1};\n"); %! fprintf(fid,"Point(3) = {-1, 0, 0, 1};\n"); %! fprintf(fid,"Circle(1) = {3, 1, 2};\n"); %! fprintf(fid,"Circle(2) = {2, 1, 3};\n"); %! fprintf(fid,"Line Loop(4) = {2, 1};\n"); %! fprintf(fid,"Plane Surface(4) = {4};"); %! fclose(fid); %! mesh = msh2m_gmsh("circle","v",0); %! system("rm circle.geo"); %! nnodest = length(unique(mesh.t)); %! nnodesp = columns(mesh.p); %! assert(nnodest,nnodesp); %!demo %! name = [tempname() ".geo"]; %! fid = fopen (name, "w"); %! fputs (fid, "Point(1) = {0, 0, 0, .1};\n"); %! fputs (fid, "Point(2) = {1, 0, 0, .1};\n"); %! fputs (fid, "Point(3) = {1, 0.5, 0, .1};\n"); %! fputs (fid, "Point(4) = {1, 1, 0, .1};\n"); %! fputs (fid, "Point(5) = {0, 1, 0, .1};\n"); %! fputs (fid, "Point(6) = {0, 0.5, 0, .1};\n"); %! fputs (fid, "Line(1) = {1, 2};\n"); %! fputs (fid, "Line(2) = {2, 3};\n"); %! fputs (fid, "Line(3) = {3, 4};\n"); %! fputs (fid, "Line(4) = {4, 5};\n"); %! fputs (fid, "Line(5) = {5, 6};\n"); %! fputs (fid, "Line(6) = {6, 1};\n"); %! fputs (fid, "Point(7) = {0.2, 0.6, 0};\n"); %! fputs (fid, "Point(8) = {0.5, 0.4, 0};\n"); %! fputs (fid, "Point(9) = {0.7, 0.6, 0};\n"); %! fputs (fid, "BSpline(7) = {6, 7, 8, 9, 3};\n"); %! fputs (fid, "Line Loop(8) = {6, 1, 2, -7};\n"); %! fputs (fid, "Plane Surface(9) = {8};\n"); %! fputs (fid, "Line Loop(10) = {7, 3, 4, 5};\n"); %! fputs (fid, "Plane Surface(11) = {10};\n"); %! fclose (fid); %! mesh = msh2m_gmsh (canonicalize_file_name (name)(1:end-4), "clscale", ".5"); %! trimesh (mesh.t(1:3,:)', mesh.p(1,:)', mesh.p(2,:)'); %! unlink (canonicalize_file_name (name)); msh-1.0.12/inst/msh2m_gmsh_write.m000066400000000000000000000066321426661027500170130ustar00rootroot00000000000000## Copyright (C) 2013 Carlo de Falco ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## -*- texinfo -*- ## @deftypefn {Function File} {} = msh2m_gmsh_write (@var{filename}, @var{msh}) ## @seealso{msh3m_gmsh_write} ## @end deftypefn function msh2m_gmsh_write (filename, msh, node_data, cell_data) if (! ((fid = fopen (filename, "w")) >= 0)); error ("msh3m_gmsh_write: unable to open file %s for writing", filename); else ## file format string fprintf (fid, "$MeshFormat\n2.0 0 8\n$EndMeshFormat\n"); ## node coordinates nnodes = columns (msh.p); fprintf (fid, "$Nodes\n%d\n", nnodes); p = [1:nnodes; msh.p]; p(4, :) = 0.0; fprintf (fid, "%d %17.17g %17.17g %17.17g\n", p); fprintf (fid, "$EndNodes\n"); ## elements number_of_tets = columns (msh.t); number_of_tri = columns (msh.e); fprintf (fid, "$Elements\n%d\n", number_of_tets + number_of_tri); ## 2-node lines e = [1:number_of_tri; ## element number 1*ones(1, number_of_tri); ## element type, 1 = line 3*ones(1, number_of_tri); ## number of tags zeros(1, number_of_tri); ## first tag, physical entity: 0 = unspecified msh.e(6, :); ## second tag, geometrical entity zeros(1, number_of_tri); ## third tag, partition: 0 = unspecified msh.e(1:2, :)]; ## node number list fprintf (fid, "%d %d %d %d %d %d %d %d\n", e); ## 3-node triangles t = [[(number_of_tri+1):(number_of_tets+number_of_tri)]; ## element number 2*ones(1, number_of_tets); ## element type, 2 = triangle 3*ones(1, number_of_tets); ## number of tags zeros(1, number_of_tets); ## first tag, physical entity: 0 = unspecified msh.t(4, :); ## first tag, geometrical entity zeros(1, number_of_tets); ## third tag, partition: 0 = unspecified msh.t(1:3, :)]; ## node number list fprintf (fid, "%d %d %d %d %d %d %d %d %d\n", t); fprintf(fid, "$EndElements\n"); ## node data if (! isempty (node_data)) for ii = 1:rows (node_data) fprintf (fid, "$NodeData\n") fprintf (fid, "%d\n", 1) ## number of string tags fprintf (fid, """%s""\n", node_data{ii, 1}) ## name of view fprintf (fid, "%d\n", 1) ## number of real tags fprintf (fid, "%g\n", 0.0) ## time fprintf (fid, "%d\n", 4) ## number of int tags fprintf (fid, "%d\n", [1, 1, nnodes, 0]) v = [1:nnodes; node_data{ii, 2}(:)']; fprintf (fid, "%d %g\n", v); fprintf (fid, "$EndNodeData\n"); endfor endif fclose (fid); endif endfunction msh-1.0.12/inst/msh2m_jiggle_mesh.m000066400000000000000000000075561426661027500171260ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{newmsh}]} = @ ## msh2m_jiggle_mesh(@var{msh},@var{steps}) ## ## Equalize the size of triangle edges setting a spring of rest length ## @var{factor}*@var{area} along each edge of the mesh and solving for ## static equilibrium. ## ## The non-linear eqautions of the system obtained are solved via a ## non-linear Gauss-Seidel method. @var{step} is the number of steps of ## the method to be applied. ## ## May be useful when distorting a mesh, type @code{demo ## msh2m_jiggle_mesh} to see some examples. ## ## @seealso{msh2m_displacement_smoothing, msh2m_equalize_mesh} ## ## @end deftypefn function [msh] = msh2m_jiggle_mesh(msh,steps) ## Check input if nargin != 2 # Number of input parameters error("msh2m_jiggle_mesh: wrong number of input parameters."); elseif !(isstruct(msh) && isfield(msh,"p") && isfield(msh,"t") && isfield(msh,"e")) error("msh2m_jiggle_mesh: first input is not a valid mesh structure."); elseif !isscalar(steps) error("msh2m_jiggle_mesh: second argument is not a valid scalar"); endif ## Solve for static equilibrium nel= columns(msh.t); nnodes = columns(msh.p); x = msh.p(1,:)'; y = msh.p(2,:)'; dnodes = unique(msh.e(1:2,:)(:)); vnodes = setdiff(1:nnodes,dnodes); ## Find node neighbours ## FIXME: should this go into msh2m_topological_properties ? sides = msh2m_topological_properties(msh,"sides"); for inode = 1:nnodes neig{inode} = (sides(:, sides(1,:) == inode | sides(2,:) == inode))(:); neig{inode} (neig{inode} == inode) = []; endfor for istep = 1:steps for inode =vnodes xx = x(neig{inode}) * ones(size(neig{inode}))'; lx = abs ( xx - xx' )(:); mx = ( xx + xx' )(:)/2; x(inode) = sum(mx.*lx)/sum(lx); yy = y(neig{inode}) * ones(size(neig{inode}))'; ly = abs ( yy - yy' )(:); my = (yy + yy')(:)/2; y(inode) = sum(my.*ly)/sum(ly); endfor endfor msh.p = [x';y']; endfunction %!demo %! ### distort a mesh on a square equalizing at each step %! msh = msh2m_structured_mesh(linspace(0,1,10),linspace(0,1,10),1,1:4,"right"); %! dnodes = msh2m_nodes_on_sides(msh,1:4); %! varnodes = setdiff([1:columns(msh.p)],dnodes); %! x = msh.p(1,:)'; %! y = msh.p(2,:)'; %! dx = dy = zeros(columns(msh.p),1); %! dytot = dxtot = -.4*sin(x(dnodes).*y(dnodes)*pi/2); %! Nsteps = 30; %! for ii=1:Nsteps %! dx(dnodes) = dxtot; %! dy(dnodes) = dytot; %! [Ax,Ay] = msh2m_displacement_smoothing(msh,1); %! dx(varnodes) = Ax(varnodes,varnodes) \ ... %! (-Ax(varnodes,dnodes)*dx(dnodes)); %! dy(varnodes) = Ay(varnodes,varnodes) \ ... %! (-Ay(varnodes,dnodes)*dy(dnodes)); %! msh.p(1,:) += dx'/Nsteps; %! msh.p(2,:) += dy'/Nsteps; %! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)','r'); %! pause(.5) %! x = msh.p(1,:)'; %! y = msh.p(2,:)'; %! msh = msh2m_jiggle_mesh(msh,10); %! hold on; %! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)'); %! hold off; %! pause(.5) %! endformsh-1.0.12/inst/msh2m_join_structured_mesh.m000066400000000000000000000140721426661027500210770ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mesh}]} = @ ## msh2m_join_structured_mesh(@var{mesh1},@var{mesh2},@var{s1},@var{s2}) ## ## Join the two structured meshes @var{mesh1} and @var{mesh2} into one ## single mesh. ## ## The two meshes must share a common edge identified by @var{s1} and ## @var{s2}. ## ## @strong{WARNING}: the two meshes must share the same vertexes on the ## common edge. ## ## @seealso{msh2m_structured_mesh, msh2m_gmsh, msh2m_submesh, ## msh3m_join_structured_mesh} ## @end deftypefn function [mesh] = msh2m_join_structured_mesh(mesh1,mesh2,s1,s2) ## Check input if nargin != 4 # Number of input parameters error("msh2m_join_structured_mesh: wrong number of input parameters."); elseif !(isstruct(mesh1) && isfield(mesh1,"p") && isfield (mesh1,"e") && isfield(mesh1,"t") && isstruct(mesh2) && isfield(mesh2,"p") && isfield (mesh2,"e") && isfield(mesh2,"t") ) error("msh2m_join_structured_mesh: invalid mesh structure passed as input."); elseif !(isvector(s1) && isvector(s2)) error("msh2m_join_structured_mesh: shared geometrical sides are not vectors."); elseif (length(s1) != length(s2)) error("msh2m_join_structured_mesh: vectors containing shared geometrical sides are not of the same length."); endif ## Join meshes ## Make sure that the outside world is always on the same side of the ## boundary of mesh1 [mesh1.e(6:7,:),I] = sort(mesh1.e(6:7,:)); for ic=1:size(mesh1.e,2) mesh1.e(1:2,ic) = mesh1.e(I(:,ic),ic); endfor ## FIXME: here a check could be added to see whether ## the coordinate points of the two meshes coincide on the ## side edges intnodes1=[]; intnodes2=[]; ## FIXME: Can the following cycle be replaced by ## msh2m_nodes_on_sides? j1=[];j2=[]; for is=1:length(s1) side1 = s1(is); side2 = s2(is); [i,j] = find(mesh1.e(5,:)==side1); j1=[j1 j]; [i,j] = find(mesh2.e(5,:)==side2); oldregion(side1) = max(max(mesh2.e(6:7,j))); j2=[j2 j]; endfor intnodes1=[mesh1.e(1,j1),mesh1.e(2,j1)]; intnodes2=[mesh2.e(1,j2),mesh2.e(2,j2)]; intnodes1 = unique(intnodes1); [tmp,I] = sort(mesh1.p(1,intnodes1)); intnodes1 = intnodes1(I); [tmp,I] = sort(mesh1.p(2,intnodes1)); intnodes1 = intnodes1(I); intnodes2 = unique(intnodes2); [tmp,I] = sort(mesh2.p(1,intnodes2)); intnodes2 = intnodes2(I); [tmp,I] = sort(mesh2.p(2,intnodes2)); intnodes2 = intnodes2(I); ## Delete redundant edges mesh2.e(:,j2) = []; ## Change edge numbers indici=[]; consecutivi=[]; indici = unique(mesh2.e(5,:)); consecutivi (indici) = [1:length(indici)]+max(mesh1.e(5,:)); mesh2.e(5,:)=consecutivi(mesh2.e(5,:)); ## Change node indices in connectivity matrix and edge list indici=[]; consecutivi=[]; indici = 1:size(mesh2.p,2); offint = setdiff(indici,intnodes2); consecutivi (offint) = [1:length(offint)]+size(mesh1.p,2); consecutivi (intnodes2) = intnodes1; mesh2.e(1:2,:)=consecutivi(mesh2.e(1:2,:)); mesh2.t(1:3,:)=consecutivi(mesh2.t(1:3,:)); ## Delete redundant points mesh2.p(:,intnodes2) = []; ## Set region numbers regions = unique(mesh1.t(4,:)); # Mesh 1 newregions(regions) = 1:length(regions); mesh1.t(4,:) = newregions(mesh1.t(4,:)); regions = unique(mesh2.t(4,:)); # Mesh 2 newregions(regions) = [1:length(regions)]+max(mesh1.t(4,:)); mesh2.t(4,:) = newregions(mesh2.t(4,:)); ## Set adjacent region numbers in edge structure 2 [i,j] = find(mesh2.e(6:7,:)); i = i+5; mesh2.e(i,j) = newregions(mesh2.e(i,j)); ## Set adjacent region numbers in edge structure 1 mesh1.e(6,j1) = newregions(oldregion(mesh1.e(5,j1))); ## Make the new p structure mesh.p = [mesh1.p mesh2.p]; mesh.e = [mesh1.e mesh2.e]; mesh.t = [mesh1.t mesh2.t]; endfunction %!test %! [mesh1] = msh2m_structured_mesh(0:.5:1, 0:.5:1, 1, 1:4, 'left'); %! [mesh2] = msh2m_structured_mesh(1:.5:2, 0:.5:1, 1, 1:4, 'left'); %! [mesh] = msh2m_join_structured_mesh(mesh1,mesh2,2,4); %! p = [0.00000 0.00000 0.00000 0.50000 0.50000 0.50000 1.00000 1.00000 1.00000 1.50000 1.50000 1.50000 2.00000 2.00000 2.00000 %! 0.00000 0.50000 1.00000 0.00000 0.50000 1.00000 0.00000 0.50000 1.00000 0.00000 0.50000 1.00000 0.00000 0.50000 1.00000]; %! e = [1 4 7 8 3 6 1 2 7 10 13 14 9 12 %! 4 7 8 9 6 9 2 3 10 13 14 15 12 15 %! 0 0 0 0 0 0 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 0 0 0 0 0 0 %! 1 1 2 2 3 3 4 4 5 5 6 6 7 7 %! 0 0 2 2 0 0 0 0 0 0 0 0 0 0 %! 1 1 1 1 1 1 1 1 2 2 2 2 2 2]; %! t = [1 2 4 5 2 3 5 6 7 8 10 11 8 9 11 12 %! 4 5 7 8 4 5 7 8 10 11 13 14 10 11 13 14 %! 2 3 5 6 5 6 8 9 8 9 11 12 11 12 14 15 %! 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2]; %! toll = 1e-4; %! assert(mesh.p,p,toll); %! assert(mesh.e,e,toll); %! assert(mesh.t,t,toll);msh-1.0.12/inst/msh2m_mesh_along_spline.m000066400000000000000000000055001426661027500203220ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mesh}]} = @ ## msh2m_mesh_along_spline(@var{xc},@var{yc},@var{Nnx},@var{Nny},@var{sigma}) ## ## Generate a structured mesh in a thin layer of size @var{sigma} ## sitting on a natural Catmull-Rom type cubic spline with control ## points @var{xc}, @var{yc}. ## ## If @var{Nnx} and @var{Nny} are scalars, the mesh has @var{Nnx} nodes ## in the direction along the spline and @var{Nny} in the normal ## direction. ## ## If @var{Nnx} and @var{Nny} are vectors they indicate the curvilinear ## coordinates of the mesh nodes. ## ## The returned value @var{mesh} is a PDE-tool like mesh structure. ## ## Be aware that if @var{sigma} is not much smaller than the curvature ## of the line the resulting mesh may be invalid. ## ## @seealso{msh2m_structured_mesh, msh2m_gmsh, msh3m_structured_mesh} ## @end deftypefn function msh2 = msh2m_mesh_along_spline(xc,yc,Nnx,Nny,sigma) ## Check input ## FIXME: input type not checked for the first 4 arguments if (nargin != 5) # Number of input parameters error("msh2m_mesh_along_spline: wrong number of input parameters."); elseif (!isscalar(sigma)) error("msh2m_mesh_along_spline: sigma must be a valid scalar value."); endif ## Construct mesh s = [0:length(xc)-1]; xsPP = catmullrom ( s, xc ); ysPP = catmullrom ( s, yc ); if (length(Nnx)>1) ss = Nnx(:).'; else ss = linspace(0,s(end),Nnx); endif xs = ppval(xsPP,ss); ys = ppval(ysPP,ss); dxsPP = fnder(xsPP,1); dysPP = fnder(ysPP,1); nx = -ppval(dysPP,ss)'; ny = ppval(dxsPP,ss)'; nx = nx ./ sqrt(nx.^2+ny.^2); ny = ny ./ sqrt(nx.^2+ny.^2); if (length(Nny)>1) ssy = Nny(:).'; else ssy = linspace(0,1,Nny); endif msh2 = msh2m_structured_mesh([1:length(ss)], ssy, 1, 1:4); jj = (msh2.p(1,:)); p(1,:) = xs(jj) + sigma*nx(jj)' .* msh2.p(2,:); p(2,:) = ys(jj) + sigma*ny(jj)' .* msh2.p(2,:); msh2.p = p; endfunctionmsh-1.0.12/inst/msh2m_nodes_on_sides.m000066400000000000000000000044111426661027500176270ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{nodelist}]} = @ ## msh2m_nodes_on_sides(@var{mesh},@var{sidelist}) ## ## Return a list of @var{mesh} nodes lying on the sides specified in ## @var{sidelist}. ## ## @seealso{msh2m_geometrical_properties, msh2m_topological_properties, ## msh3m_nodes_on_faces} ## @end deftypefn function [nodelist] = msh2m_nodes_on_sides(mesh,sidelist) ## Check input if nargin != 2 # Number of input parameters error("msh2m_nodes_on_sides: wrong number of input parameters."); elseif !(isstruct(mesh) && isfield(mesh,"p") && isfield(mesh,"t") && isfield(mesh,"e")) error("msh2m_nodes_on_sides: first input is not a valid mesh structure."); elseif !isnumeric(sidelist) error("msh2m_nodes_on_sides: only numeric value admitted as sidelist."); endif ## Search nodes edgelist = []; for ii = 1:length(sidelist) edgelist=[edgelist,find(mesh.e(5,:)==sidelist(ii))]; endfor nodelist = mesh.e(1:2,edgelist); nodelist = [nodelist(1,:) nodelist(2,:)]; nodelist = unique(nodelist); endfunction %!test %! [mesh1] = msh2m_structured_mesh(0:.5:1, 0:.5:1, 1, 1:4, 'left'); %! [mesh2] = msh2m_structured_mesh(1:.5:2, 0:.5:1, 1, 1:4, 'left'); %! [mesh] = msh2m_join_structured_mesh(mesh1,mesh2,2,4); %! [nodelist] = msh2m_nodes_on_sides(mesh,[1 2]); %! reallist = [1 4 7 8 9]; %! assert(nodelist,reallist); msh-1.0.12/inst/msh2m_structured_mesh.m000066400000000000000000000201571426661027500200610ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mesh}]} = @ ## msh2m_structured_mesh(@var{x},@var{y},@var{region},@var{sides},@var{string}) ## ## Construct a structured triangular 2D mesh on a rectangular domain. ## ## @itemize @bullet ## @item @var{x} and @var{y} are the one dimensional mesh vector of the ## corresponding Cartesian axis. ## @item @var{region} is a number identifying the geometrical surface ## region, while @var{sides} is a 4 components vector containing the ## numbers used to identify the geometrical side edges. ## @item @var{string} is an optional value specifying the orientation of ## the diagonal edge of the structured mesh. It may take the value ## @code{"right"} (default), @code{"left"}, @code{"random"}. ## @end itemize ## ## The returned value @var{mesh} is a PDE-tool like mesh structure ## composed of the following fields: ## @itemize @minus ## @item @var{p}: matrix with size 2 times number of mesh points. ## @itemize @bullet ## @item 1st row: x-coordinates of the points. ## @item 2nd row: y-coordinates of the points. ## @end itemize ## @item @var{e}: matrix with size 7 times number of mesh side edges. ## @itemize @bullet ## @item 1st row: number of the first vertex of the side edge. ## @item 2nd row: number of the second vertex of the side edge. ## @item 3rd row: set to 0, present for compatibility with MatLab PDE-tool. ## @item 4th row: set to 0, present for compatibility with MatLab PDE-tool. ## @item 5th row: number of the geometrical border containing the side ## edge. ## @item 6th row: number of the geometrical surface to the right of ## side edge. ## @item 7th row: number of the geometrical surface to the left of the ## side edge. ## @end itemize ## @item @var{t}: matrix with size 4 times number of mesh elements. ## @itemize @bullet ## @item 1st row: number of the first vertex of the element. ## @item 2nd row: number of the second vertex of the element. ## @item 3rd row: number of the third vertex of the element. ## @item 4th row: number of the geometrical surface containing the element. ## @end itemize ## @end itemize ## ## @seealso{msh3m_structured_mesh, msh2m_gmsh, msh2m_mesh_along_spline, ## msh2m_join_structured_mesh, msh2m_submesh} ## @end deftypefn function [mesh] = msh2m_structured_mesh(x,y,region,sides,varargin) ## Check input if ((nargin < 4) || (nargin > 5)) # Number of input parameters error("msh2m_structured_mesh: wrong number of input parameters."); elseif !(isvector(x) && isnumeric(x) && isvector(y) && isnumeric(y)) error("msh2m_structured_mesh: X and Y must be valid numeric vectors."); elseif !isscalar(region) error("msh2m_structured_mesh: REGION must be a valid scalar."); elseif !(isvector(sides) && (length(sides) == 4)) error("msh2m_structured_mesh: SIDES must be a 4 components vector."); endif ## Build mesh default = "right"; ## Check if any orientation is given if length(varargin)==0 string = default; else string = varargin{1}; endif ## Construct mesh switch string case "right" [mesh] = Ustructmesh_right(x, y, region, sides); case "left" [mesh] = Ustructmesh_left(x, y, region, sides); case "random" [mesh] = Ustructmesh_random(x, y, region, sides); otherwise error("msh2m_structured_mesh: STRING has not a valid value."); endswitch endfunction ## Right diagonal structured mesh function [mesh]=Ustructmesh_right(x,y,region,sides) x = sort(x); y = sort(y); nx = length(x); ny = length(y); [XX,YY] = meshgrid(x,y); p = [XX(:),YY(:)]'; iiv (ny,nx)=0; iiv(:)=1:nx*ny; iiv(end,:)=[]; iiv(:,end)=[]; iiv=iiv(:)'; t = [[iiv;iiv+ny;iiv+ny+1],[iiv;iiv+ny+1;iiv+1] ]; t (4,:)=region; l1 = 1+ny*([1:nx]-1); l4 = 1:ny; l2 = ny*(nx-1)+1:nx*ny; l3 = ny + l1 -1; e = [ l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1]) l1([2:end]) l2([2:end]) l3([2:end]) l4([2:end]) [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0 [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0 l1([1:end-1])*0+sides(1) l2([1:end-1])*0+sides(2) l3([1:end-1])*0+sides(3) l4([1:end-1])*0+sides(4) [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0 [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0+region ]; mesh.p = p; mesh.e = e; mesh.t = t; endfunction ## Left diagonal structured mesh function [mesh]=Ustructmesh_left(x,y,region,sides) x = sort(x); y = sort(y); nx = length(x); ny = length(y); [XX,YY] = meshgrid(x,y); p = [XX(:),YY(:)]'; iiv (ny,nx)=0; iiv(:)=1:nx*ny; iiv(end,:)=[]; iiv(:,end)=[]; iiv=iiv(:)'; t = [[iiv;iiv+ny;iiv+1],[iiv+1;iiv+ny;iiv+ny+1] ]; t (4,:)=region; l1 = 1+ny*([1:nx]-1); l4 = 1:ny; l2 = ny*(nx-1)+1:nx*ny; l3 = ny + l1 -1; e = [ l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1]) l1([2:end]) l2([2:end]) l3([2:end]) l4([2:end]) [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0 [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0 l1([1:end-1])*0+sides(1) l2([1:end-1])*0+sides(2) l3([1:end-1])*0+sides(3) l4([1:end-1])*0+sides(4) [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0 [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0+region ]; mesh.p = p; mesh.e = e; mesh.t = t; endfunction ## Random diagonal structured mesh function [mesh]=Ustructmesh_random(x,y,region,sides) x = sort(x); y = sort(y); nx = length(x); ny = length(y); [XX,YY] = meshgrid(x,y); p = [XX(:),YY(:)]'; iiv (ny,nx)=0; iiv(:)=1:nx*ny; iiv(end,:)=[]; iiv(:,end)=[]; iiv=iiv(:)'; niiv = length(iiv); theperm = iiv(randperm(niiv)); first = theperm(1:floor(niiv/2)); second = theperm(floor(niiv/2)+1:end); t = [[first;first+ny;first+ny+1],[first;first+ny+1;first+1] ]; t = [t,[second;second+ny;second+1],[second+ny;second+ny+1;second+1] ]; t (4,:)=region; l1 = 1+ny*([1:nx]-1); l4 = 1:ny; l2 = ny*(nx-1)+1:nx*ny; l3 = ny + l1 -1; e = [ l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1]) l1([2:end]) l2([2:end]) l3([2:end]) l4([2:end]) [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0 [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0 l1([1:end-1])*0+sides(1) l2([1:end-1])*0+sides(2) l3([1:end-1])*0+sides(3) l4([1:end-1])*0+sides(4) [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0 [l1([1:end-1]) l2([1:end-1]) l3([1:end-1]) l4([1:end-1])]*0+region ]; mesh.p = p; mesh.e = e; mesh.t = t; endfunction %!test %! x = y = linspace(0,1,3); %! msh = msh2m_structured_mesh(x,y,1,[1:4]); %! p = [0.00000 0.00000 0.00000 0.50000 0.50000 0.50000 \ %! 1.00000 1.00000 1.00000 %! 0.00000 0.50000 1.00000 0.00000 0.50000 1.00000 \ %! 0.00000 0.50000 1.00000]; %! assert(msh.p,p) %! e = [1 4 7 8 3 6 1 2 %! 4 7 8 9 6 9 2 3 %! 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 %! 1 1 2 2 3 3 4 4 %! 0 0 0 0 0 0 0 0 %! 1 1 1 1 1 1 1 1]; %! assert(msh.e,e) %! t =[1 2 4 5 1 2 4 5 %! 4 5 7 8 5 6 8 9 %! 5 6 8 9 2 3 5 6 %! 1 1 1 1 1 1 1 1]; %! assert(msh.t,t)msh-1.0.12/inst/msh2m_submesh.m000066400000000000000000000123651426661027500163110ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{omesh},@var{nodelist},@var{elementlist}]} = @ ## msh2m_submesh(@var{imesh},@var{intrfc},@var{sdl}) ## ## Extract the subdomain(s) in @var{sdl} from @var{imesh}. ## ## The row vector @var{intrfc} contains the internal interface sides to ## be maintained (field @code{mesh.e(5,:)}). It can be empty. ## ## Return the vectors @var{nodelist} and @var{elementlist} containing ## respectively the list of nodes and elements of the original mesh that ## are part of the selected subdomain(s). ## ## @seealso{msh2m_join_structured_mesh, msh3m_submesh, ## msh3e_surface_mesh} ## @end deftypefn function [omesh,nodelist,elementlist] = msh2m_submesh(imesh,intrfc,sdl) ## Check input if nargin != 3 error("msh2m_submesh: wrong number of input parameters."); endif if !isstruct(imesh) error("msh2m_submesh: first input is not a valid mesh structure."); endif if !isvector(sdl) error("msh2m_submesh: third input is not a valid vector."); endif ## Extract sub-mesh nsd = length(sdl); # number of subdomains ## Set list of output triangles elementlist=[]; for isd=1:nsd elementlist = [elementlist find(imesh.t(4,:) == sdl(isd))]; endfor omesh.t = imesh.t(:,elementlist); ## Set list of output nodes nodelist = unique(reshape(imesh.t(1:3,elementlist),1,[])); omesh.p = imesh.p(:,nodelist); ## Use new node numbering in connectivity matrix indx(nodelist) = [1:length(nodelist)]; iel = [1:length(elementlist)]; omesh.t(1:3,iel) = indx(omesh.t(1:3,iel)); ## Set list of output edges omesh.e =[]; for isd=1:nsd omesh.e = [omesh.e imesh.e(:,imesh.e(7,:)==sdl(isd))]; omesh.e = [omesh.e imesh.e(:,imesh.e(6,:)==sdl(isd))]; endfor omesh.e=unique(omesh.e',"rows")'; ## Use new node numbering in boundary segment list ied = [1:size(omesh.e,2)]; omesh.e(1:2,ied) = indx(omesh.e(1:2,ied)); endfunction %!test %! [mesh1] = msh2m_structured_mesh(0:.5:1, 0:.5:1, 1, 1:4, 'left'); %! [mesh2] = msh2m_structured_mesh(1:.5:2, 0:.5:1, 1, 1:4, 'left'); %! [mesh] = msh2m_join_structured_mesh(mesh1,mesh2,2,4); %! [omesh,nodelist,elementlist] = msh2m_submesh(mesh,[],2); %! p = [1.00000 1.00000 1.00000 1.50000 1.50000 1.50000 2.00000 2.00000 2.00000 %! 0.00000 0.50000 1.00000 0.00000 0.50000 1.00000 0.00000 0.50000 1.00000]; %! e = [1 1 2 3 4 6 7 8 %! 2 4 3 6 7 9 8 9 %! 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0 %! 2 5 2 7 5 7 6 6 %! 2 0 2 0 0 0 0 0 %! 1 2 1 2 2 2 2 2]; %! t = [1 2 4 5 2 3 5 6 %! 4 5 7 8 4 5 7 8 %! 2 3 5 6 5 6 8 9 %! 2 2 2 2 2 2 2 2]; %! nl = [7 8 9 10 11 12 13 14 15]; %! el = [9 10 11 12 13 14 15 16]; %! toll = 1e-4; %! assert(omesh.p,p,toll); %! assert(omesh.e,e); %! assert(omesh.t,t); %! assert(nodelist,nl); %! assert(elementlist,el); %!demo %! name = [tmpnam ".geo"]; %! fid = fopen (name, "w"); %! fputs (fid, "Point(1) = {0, 0, 0, .1};\n"); %! fputs (fid, "Point(2) = {1, 0, 0, .1};\n"); %! fputs (fid, "Point(3) = {1, 0.5, 0, .1};\n"); %! fputs (fid, "Point(4) = {1, 1, 0, .1};\n"); %! fputs (fid, "Point(5) = {0, 1, 0, .1};\n"); %! fputs (fid, "Point(6) = {0, 0.5, 0, .1};\n"); %! fputs (fid, "Line(1) = {1, 2};\n"); %! fputs (fid, "Line(2) = {2, 3};\n"); %! fputs (fid, "Line(3) = {3, 4};\n"); %! fputs (fid, "Line(4) = {4, 5};\n"); %! fputs (fid, "Line(5) = {5, 6};\n"); %! fputs (fid, "Line(6) = {6, 1};\n"); %! fputs (fid, "Point(7) = {0.2, 0.6, 0};\n"); %! fputs (fid, "Point(8) = {0.5, 0.4, 0};\n"); %! fputs (fid, "Point(9) = {0.7, 0.6, 0};\n"); %! fputs (fid, "BSpline(7) = {6, 7, 8, 9, 3};\n"); %! fputs (fid, "Line Loop(8) = {6, 1, 2, -7};\n"); %! fputs (fid, "Plane Surface(9) = {8};\n"); %! fputs (fid, "Line Loop(10) = {7, 3, 4, 5};\n"); %! fputs (fid, "Plane Surface(11) = {10};\n"); %! fclose (fid); %! mesh = msh2m_gmsh (canonicalize_file_name (name)(1:end-4), "clscale", ".5"); %! mesh1 = msh2m_submesh (mesh, 7, 9); %! subplot (1, 2, 1); %! trimesh (mesh.t(1:3,:)', mesh.p(1,:)', mesh.p(2,:)'); %! axis ("equal"); title ("full mesh") %! subplot (1, 2, 2); %! trimesh (mesh1.t(1:3,:)', mesh1.p(1,:)', mesh1.p(2,:)'); %! axis ("equal"); title ("sub-mesh") %! unlink (canonicalize_file_name (name))msh-1.0.12/inst/msh2m_topological_properties.m000066400000000000000000000231371426661027500214320ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{varargout}]} = @ ## msh2m_topological_properties(@var{mesh},[@var{string1},@var{string2},...]) ## ## Compute @var{mesh} topological properties identified by input strings. ## ## Valid properties are: ## @itemize @bullet ## @item @code{"n"}: return a matrix with size 3 times the number of ## mesh elements containing the list of its neighbours. The entry ## @code{M(i,j)} in this matrix is the mesh element sharing the side ## @code{i} of triangle @code{j}. If no such element exists (i.e. for ## boundary edges) a value of @code{NaN} is set. ## @item @code{"sides"}: return a matrix with size 2 times number of ## sides.The entry @code{M(i,j)} is the index of the i-th vertex of j-th ## side. ## @item @code{"ts"}: return a matrix with size 3 times the number of ## mesh elements containing the sides associated with each element. ## @item @code{"tws"}:return a matrix with size 2 times the number of ## mesh sides containing the elements associated with each side. For a ## side belonging to one triangle only a value of @code{NaN} is set. ## @item @code{"coinc"}: return a matrix with 2 rows. Each column ## contains the indices of two triangles sharing the same circumcenter. ## @item @code{"boundary"}: return a matrix with size 2 times the number ## of side edges. The first row contains the mesh element to which the ## side belongs, the second row is the local index of this edge. ## @end itemize ## ## The output will contain the geometrical properties requested in the ## input in the same order specified in the function call. ## ## If an unexpected string is given as input, an empty vector is ## returned in output. ## ## @seealso{mshm2m_geometrical_properties, msh3m_geometrical_properties} ## @end deftypefn function [varargout] = msh2m_topological_properties(mesh,varargin) ## Check input if nargin < 2 # Number of input parameters error("msh2m_topological_properties: wrong number of input parameters."); elseif !(isstruct(mesh) && isfield(mesh,"p") && isfield(mesh,"t") && isfield(mesh,"e")) error("msh2m_topological_properties: first input is not a valid mesh structure."); elseif !iscellstr(varargin) error("msh2m_topological_properties: only string value admitted for properties."); endif ## Compute properties p = mesh.p; e = mesh.e; t = mesh.t; nelem = columns(t); # Number of elements in the mesh [n,ts,tws,sides] = neigh(t,nelem); for nn = 1:length(varargin) request = varargin{nn}; switch request case "n" # Neighbouring triangles if isfield(mesh,"n") varargout{nn} = mesh.n; else varargout{nn} = n; endif case "sides" # Global edge matrix if isfield(mesh,"sides") varargout{nn} = mesh.sides; else varargout{nn} = sides; endif case "ts" # Triangle sides matrix if isfield(mesh,"ts") varargout{nn} = mesh.ts; else varargout{nn} = ts; endif case "tws" # Trg with sides matrix if isfield(mesh,"tws") varargout{nn} = mesh.tws; else varargout{nn} = tws; endif case "coinc" # Coincident circumcenter matrix if isfield(mesh,"coinc") varargout{nn} = mesh.coinc; else if isfield(mesh,"cdist") d = mesh.cdist; else [d] = msh2m_geometrical_properties(mesh,"cdist"); endif [b] = coinc(n,d); varargout{nn} = b; clear b endif case "boundary" # Boundary edge matrix if isfield(mesh,"boundary") varargout{nn} = mesh.boundary; else [b] = borderline(e,t); varargout{nn} = b; clear b endif otherwise warning("msh2m_topological_properties: unexpected value in property string. Empty vector passed as output.") varargout{nn} = []; endswitch endfor endfunction function [n,ts,triwside,sides] = neigh(t,nelem) n = nan*ones(3,nelem); t = t(1:3,:); s3 = sort(t(1:2,:),1); s1 = sort(t(2:3,:),1); s2 = sort(t([3,1],:),1); allsides = [s1 s2 s3]'; [sides, ii, jj] = unique( allsides,"rows"); sides = sides'; ts = reshape(jj,[],3)'; triwside = zeros(2,columns(sides)); for kk =1:3 triwside(1,ts(kk,1:end)) = 1:nelem; triwside(2,ts(4-kk,end:-1:1)) = nelem:-1:1; endfor triwside(2,triwside(1,:)==triwside(2,:)) = NaN; n(1,:) = triwside(1,ts(1,:)); n(1,n(1,:)==1:nelem) = triwside(2,ts(1,:))(n(1,:)==1:nelem); n(2,:) = triwside(1,ts(2,:)); n(2,n(2,:)==1:nelem) = triwside(2,ts(2,:))(n(2,:)==1:nelem); n(3,:) = triwside(1,ts(3,:)); n(3,n(3,:)==1:nelem) = triwside(2,ts(3,:))(n(3,:)==1:nelem); endfunction function [output] = coinc(n,d); ## Tolerance value for considering two point to be coincident toll = 1e-10; ## Check the presence of more than two trgs sharing the same circum centre degen = d < toll; res = sum(degen); [check] = find(res > 1); ## Index of the sharing pairs [ii, jj] = find(degen >= 1); if isempty(jj) == 0 temp = zeros(2,length(jj)); temp(1,:) = jj'; temp(2,:) = diag(n(ii,jj))'; temp = sort(temp); temp = temp'; [output] = unique(temp,"rows"); output = output'; if isempty(check) == 0 warning("More than two trgs sharing the same circum-centre.") ## FIXME if more than two trgs shares the same circen ---> construct a cell array endif else output = []; endif endfunction function [output] = borderline(e,t) nelem = columns(e); t = t(1:3,:); output = zeros(4,nelem); for ii = 1:nelem point = ( e(1,ii) == t ); point += ( e(2,ii) == t ); [jj1] = find( sum(point(2:3,:)) == 2); [jj2] = find( sum(point([3 1],:)) == 2); [jj3] = find( sum(point(1:2,:)) == 2); assert( (length(jj1) + length(jj2) + length(jj3)) <= 2 ); numtrg = 0; for jj=1:length(jj1) output(2*numtrg+1,ii) = jj1(jj); output(2*numtrg+2,ii) = 1; numtrg += 1; endfor for jj=1:length(jj2) output(2*numtrg+1,ii) = jj2(jj); output(2*numtrg+2,ii) = 2; numtrg += 1; endfor for jj=1:length(jj3) output(2*numtrg+1,ii) = jj3(jj); output(2*numtrg+2,ii) = 3; numtrg += 1; endfor endfor endfunction %!test %! [mesh] = msh2m_structured_mesh(0:.5:1, 0:.5:1, 1, 1:4, "left"); %! [mesh.n,mesh.sides,mesh.ts,mesh.tws,mesh.coinc,mesh.boundary] = msh2m_topological_properties(mesh,"n","sides","ts","tws","coinc","boundary"); %! n = [5 6 7 8 3 4 NaN NaN %! NaN NaN 5 6 2 NaN 4 NaN %! NaN 5 NaN 7 1 2 3 4]; %! sides = [1 1 2 2 2 3 3 4 4 5 5 5 6 6 7 8 %! 2 4 3 4 5 5 6 5 7 6 7 8 8 9 8 9]; %! ts = [4 6 11 13 8 10 15 16 %! 1 3 8 10 5 7 12 14 %! 2 5 9 12 4 6 11 13]; %! tws = [ 1 1 2 5 2 6 6 3 3 4 7 4 8 8 7 8 %! NaN NaN NaN 1 5 2 NaN 5 NaN 6 3 7 4 NaN NaN NaN]; %! coinc = [1 2 3 4 %! 5 6 7 8]; %! boundary =[ 1 3 7 8 6 8 1 2 %! 3 3 1 1 2 2 2 2 %! 0 0 0 0 0 0 0 0 %! 0 0 0 0 0 0 0 0]; %! assert(mesh.n,n); %! assert(mesh.sides,sides); %! assert(mesh.ts,ts); %! assert(mesh.tws,tws); %! assert(mesh.coinc,coinc); %! assert(mesh.boundary,boundary); %!test %! mesh.p = []; mesh.e = []; %! mesh.t = [3 9 10 1 6 9 10 9 8 9 %! 9 3 1 10 10 10 7 5 9 8 %! 6 5 7 8 2 6 2 4 4 10 %! 6 6 6 6 6 6 6 6 6 6]; %! [mesh.n] = msh2m_topological_properties(mesh,"n"); %! n = [6 NaN NaN 10 7 5 NaN NaN 8 4 %! NaN 8 7 NaN NaN 1 5 9 NaN 6 %! 2 1 4 3 6 10 3 2 10 9]; %! assert(mesh.n,n); %!test %! mesh.p = []; mesh.e = []; %! mesh.t =[ %! 10 3 6 11 10 3 6 11 1 7 5 9 2 5 11 9 13 6 %! 14 7 10 15 15 8 11 16 5 11 9 13 6 6 12 10 14 7 %! 15 8 11 16 11 4 7 12 2 8 6 10 3 2 8 6 10 3 %! 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]; %! [mesh.n] = msh2m_topological_properties(mesh,"n"); %! n =[ %! NaN 10 5 NaN 4 NaN 10 NaN 14 15 16 17 18 13 NaN 3 1 2 %! 5 6 7 8 3 NaN 18 15 NaN 2 14 16 NaN 9 10 11 12 13 %! 17 18 16 5 1 2 3 4 NaN 7 NaN NaN 14 11 8 12 NaN 7]; %! assert(mesh.n,n); msh-1.0.12/inst/msh2p_mesh.m000066400000000000000000000031241426661027500155730ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} msh2p_mesh(@var{mesh}, @var{linespec}) ## ## Plot @var{mesh} with the line specification in @var{linespec} using ## @code{triplot}. ## ## @seealso{triplot} ## ## @end deftypefn function msh2p_mesh(mesh,linespec) ## Check input if nargin > 2 error("msh2p_mesh: wrong number of input parameters."); elseif !(isstruct(mesh) && isfield(mesh,"p") && isfield (mesh,"t") && isfield(mesh,"e")) error("msh2p_mesh: first input is not a valid mesh structure."); endif tri = mesh.t(1:3,:)'; x = mesh.p(1,:)'; y = mesh.p(2,:)'; if ~exist("linespec") linespec = "r"; endif triplot(tri,x,y,linespec); endfunctionmsh-1.0.12/inst/msh3e_surface_mesh.m000066400000000000000000000067711426661027500173040ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{emesh},@var{snodes},@var{ssides},@var{striangles}]} = @ ## msh3e_surface_mesh(@var{mesh},@var{nsrf},@var{nsides}) ## ## Extract the plane surface @var{nsrf} delimited by @var{nsides} from ## @var{mesh}. ## ## Return the vector @var{snodes} containing the references to input ## mesh nodes (field @code{mesh.p}), the vector @var{ssides} containing ## the references to input mesh side (field @code{mesh.s}) and the ## vector @var{striangles} containing the references to input mesh side ## edges (field @code{mesh.e}). ## ## @strong{WARNING}: the suface MUST be ortogonal to either X, Y or Z ## axis. This should be changed to account for generic 2D surface. ## ## @end deftypefn function [emesh,snodes,ssides,striangles] = msh3e_surface_mesh(mesh,nsrf,nsides) ## Check input if nargin != 3 error("msh3e_surface_mesh: wrong number of input parameters."); elseif !(isstruct(mesh) && isfield(mesh,"p") && isfield (mesh,"t") && isfield(mesh,"e")) error("msh3e_surface_mesh: first input is not a valid mesh structure."); elseif !isscalar(nsrf) error("msh3e_surface_mesh: second input is not a valid scalar."); elseif !(isvector(nsides) && isnumeric(nsides)) error("msh3e_surface_mesh: third input is not a valid numeric vector."); endif ## Surface extraction ## Extraction of 2D surface elements striangles = find( mesh.e(10,:) == nsrf ); t = mesh.e(1:3,striangles); tmp = reshape(t,[],1); ## Renumbering [snodes,ii,jj] = unique(tmp); nds = 1:length(snodes); emesh.t = reshape(nds(jj),3,[]); ## Extraction of 2D mesh points points = mesh.p(:,snodes); ## Test for normals ## FIXME: this should disappear as soon as 2D mesh are not supposed to ## lie on a plane. if length(unique(points(1,:))) == 1 xyz = [2,3]; # normal to X coordinate elseif length(unique(points(2,:))) == 1 xyz = [1,3]; # normal to Y coordinate else xyz = [1,2]; # normal to Z coordinate endif emesh.p = points(xyz,:); ## Extraction of 1D side edges ssides = []; for ll = nsides tmp = find ( mesh.s(3,:) == ll ); ssides = [ssides,tmp]; endfor nedges = length(ssides); emesh.e = zeros(7,nedges); emesh.e(5,:) = mesh.s(3,ssides); tmp = reshape(mesh.s(1:2,ssides),[],1); [enodes,nn,mm] = unique(tmp); [tmp1, nds, tmp2] = intersect(snodes,enodes); emesh.e(1:2,:) = reshape(nds(mm),2,[]); ## Compute mesh properties ## FIXME: this has to be removed. MSH should not depend on BIM. emesh = bim2c_mesh_properties(emesh); endfunctionmsh-1.0.12/inst/msh3m_geometrical_properties.m000066400000000000000000000164341426661027500214140ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{varargout}]} = @ ## msh3m_geometrical_properties(@var{mesh},[@var{string1},@var{string2},...]) ## ## ## Compute @var{mesh} geometrical properties identified by input strings. ## ## Valid properties are: ## @itemize @bullet ## @item @code{"bar"}: return a matrix with size 3 times the number of mesh ## elements containing the center of mass coordinates. ## @item @code{"wjacdet"}: return the weigthed Jacobian determinant used ## for the numerical integration with trapezoidal rule over an element. ## @item @code{"shg"}: return a matrix of size 3 times the number of ## elements matrix containing the gradient of P1 shape functions. ## @item @code{"shp"}: return a matrix containing the the value of P1 shape ## functions. ## @item @code{"area"}: return a row vector containing the volume of each ## element. ## @end itemize ## ## The output will contain the geometrical properties requested in the ## input in the same order specified in the function call. ## ## If an unexpected string is given as input, an empty vector is ## returned in output. ## ## @seealso{msh2m_topological_properties, msh2m_geometrical_properties} ## @end deftypefn function [varargout] = msh3m_geometrical_properties (imesh,varargin) ## Check input if (nargin < 2) # Number of input parameters error ("msh3m_geometrical_properties: wrong number of input parameters."); elseif (! (isstruct (imesh) && isfield (imesh,"p") && isfield (imesh,"t") && isfield (imesh,"e"))) error ("msh3m_geometrical_properties: first input is not a valid mesh structure."); elseif (! iscellstr (varargin)) error ("msh3m_geometrical_properties: only string value admitted for properties."); endif ## Compute properties ## Extract tetrahedra node coordinates x1 = imesh.p(1,imesh.t(1,:)); y1 = imesh.p(2,imesh.t(1,:)); z1 = imesh.p(3,imesh.t(1,:)); x2 = imesh.p(1,imesh.t(2,:)); y2 = imesh.p(2,imesh.t(2,:)); z2 = imesh.p(3,imesh.t(2,:)); x3 = imesh.p(1,imesh.t(3,:)); y3 = imesh.p(2,imesh.t(3,:)); z3 = imesh.p(3,imesh.t(3,:)); x4 = imesh.p(1,imesh.t(4,:)); y4 = imesh.p(2,imesh.t(4,:)); z4 = imesh.p(3,imesh.t(4,:)); nelem = columns(imesh.t); # Number of elements in the mesh for nn = 1:length (varargin) request = varargin{nn}; switch request case "bar" # Center of mass coordinates if isfield (imesh,"bar") varargout{nn} = imesh.bar; else b = zeros (3, nelem); b(1,:) = ( x1 + x2 + x3 + x4 )/4; b(2,:) = ( y1 + y2 + y3 + y4 )/4; b(3,:) = ( z1 + z2 + z3 + z4 )/4; varargout{nn} = b; clear b; endif case "wjacdet" # Weighted Jacobian determinant if isfield (imesh,"wjacdet") varargout{nn} = imesh.wjacdet; else b = wjacdet (x1,y1,z1,... x2,y2,z2,... x3,y3,z3,... x4,y4,z4); varargout{nn} = b; clear b endif case "area" # Element area if isfield (imesh,"area") varargout{nn} = imesh.area; else tmp = wjacdet (x1,y1,z1,... x2,y2,z2,... x3,y3,z3,... x4,y4,z4); b = sum (tmp,1); varargout{nn} = b; clear b; endif case "shg" # Gradient of shape functions if isfield (imesh,"shg") varargout{nn} = imesh.shg; else b = shg (x1,y1,z1,... x2,y2,z2,... x3,y3,z3,... x4,y4,z4); varargout{nn} = b; clear b endif case "shp" # Value of shape functions if isfield (imesh,"shp") varargout{nn} = imesh.shp; else varargout{nn} = eye (4); endif otherwise warning ("msh3m_geometrical_properties: unexpected value in property string. Empty vector passed as output.") varargout{nn} = []; endswitch endfor endfunction function [b] = wjacdet(x1,y1,z1,x2,y2,z2,x3,y3,z3,x4,y4,z4) ## Compute weighted yacobian determinant weight = [1/4 1/4 1/4 1/4]'; Nb2 = y1.*(z3-z4) + y3.*(z4-z1) + y4.*(z1-z3); Nb3 = y1.*(z4-z2) + y2.*(z1-z4) + y4.*(z2-z1); Nb4 = y1.*(z2-z3) + y2.*(z3-z1) + y3.*(z1-z2); ## Determinant of the Jacobian of the ## transformation from the base tetrahedron ## to the tetrahedron K detJ = (x2-x1).*Nb2 +(x3-x1).*Nb3 +(x4-x1).*Nb4; ## Volume of the reference tetrahedron Kkvolume = 1/6; b(:,:) = Kkvolume * weight * detJ; endfunction function [b] = shg(x1,y1,z1,x2,y2,z2,x3,y3,z3,x4,y4,z4) ## Compute gradient of shape functions Nb2 = y1.*(z3-z4) + y3.*(z4-z1) + y4.*(z1-z3); Nb3 = y1.*(z4-z2) + y2.*(z1-z4) + y4.*(z2-z1); Nb4 = y1.*(z2-z3) + y2.*(z3-z1) + y3.*(z1-z2); ## Determinant of the Jacobian of the ## transformation from the base tetrahedron ## to the tetrahedron K detJ = (x2-x1).*Nb2 +(x3-x1).*Nb3 +(x4-x1).*Nb4; ## Shape function gradients follow ## First index represents space direction ## Second index represents the shape function ## Third index represents the tetrahedron number b(1,1,:) = (y2.*(z4-z3) + y3.*(z2-z4) + y4.*(z3-z2))./ detJ; b(2,1,:) = (x2.*(z3-z4) + x3.*(z4-z2) + x4.*(z2-z3))./ detJ; b(3,1,:) = (x2.*(y4-y3) + x3.*(y2-y4) + x4.*(y3-y2))./ detJ; b(1,2,:) = ( Nb2 ) ./ detJ; b(2,2,:) = (x1.*(z4-z3) + x3.*(z1-z4) + x4.*(z3-z1)) ./ detJ; b(3,2,:) = (x1.*(y3-y4) + x3.*(y4-y1) + x4.*(y1-y3)) ./ detJ; b(1,3,:) = ( Nb3 ) ./ detJ; b(2,3,:) = (x1.*(z2-z4) + x2.*(z4-z1) + x4.*(z1-z2)) ./ detJ; b(3,3,:) = (x1.*(y4-y2) + x2.*(y1-y4) + x4.*(y2-y1)) ./ detJ; b(1,4,:) = ( Nb4) ./ detJ; b(2,4,:) = (x1.*(z3-z2) + x2.*(z1-z3) + x3.*(z2-z1)) ./ detJ; b(3,4,:) = (x1.*(y2-y3) + x2.*(y3-y1) + x3.*(y1-y2)) ./ detJ; endfunction %!shared mesh,wjacdet,shg,shp % x = y = z = linspace(0,1,2); % [mesh] = msh3m_structured_mesh(x,y,z,1,1:6) % [wjacdet] = msh3m_geometrical_properties(mesh,"wjacdet") % [shg] = msh3m_geometrical_properties(mesh,"shg") % [shp] = msh3m_geometrical_properties(mesh,"shp") %!test % assert(columns(mesh.t),columns(wjacdet)) %!test % assert(size(shg),[3 4 6]) %!test % assert(shp,eye(4)) %!test % fail(msh3m_geometrical_properties(mesh,"samanafattababbudoiu"),"warning","Unexpected value in passed string. Empty vector passed as output.") msh-1.0.12/inst/msh3m_gmsh.m000066400000000000000000000121311426661027500155710ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010,2012 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mesh}]} = @ ## msh3m_gmsh(@var{geometry},@var{option},@var{value},...) ## @deftypefnx {Function File}{[@var{mesh}, @var{gmsh_out}]} = msh3m_gmsh(...) ## ## Construct an unstructured tetrahedral 3D mesh making use of the free ## software gmsh. ## ## The required argument @var{geometry} is the basename of the ## @code{*.geo} file to be meshed. ## ## The optional arguments @var{option} and @var{value} identify ## respectively a gmsh option and its value. For more information ## regarding the possible option to pass, refer to gmsh manual or gmsh ## site @url{http://www.geuz.org/gmsh/}. ## ## The returned value @var{mesh} is a PDE-tool like mesh structure. ## If the function is called with two outputs @var{gmsh_out} is the verbose output ## of the gmsh subprocess. ## ## @seealso{msh3m_structured_mesh, msh2m_gmsh, msh2m_mesh_along_spline} ## @end deftypefn function [mesh, gmsh_output] = msh3m_gmsh (geometry, varargin) ## Check input ## Number of input if !mod(nargin,2) warning("WRONG NUMBER OF INPUT."); print_usage; endif ## FIXME: add input type check? ## Build mesh noptions = (nargin - 1) / 2; # Number of passed options ## Construct system command string verbose = 1; optstring = ""; for ii = 1:noptions option = varargin{2*(ii)-1}; value = varargin{2*ii}; ## Check for verbose option if strcmp(option,"v") verbose = value; endif if !ischar(value) value = num2str(value); endif optstring = [optstring," -",option," ",value]; endfor ## Generate mesh using Gmsh if (verbose) printf("\n"); printf("Generating mesh...\n"); endif msh_name = strcat (tempname (), ".msh"); fclose (fopen (msh_name, "w")); [status, gmsh_output] = system (["gmsh -format msh2 -3 -o " msh_name optstring " " geometry ".geo 2>&1"]); if (status) error ("msh3m_gmsh: the gmesh subprocess exited abnormally"); endif if (verbose) printf("Processing gmsh data...\n"); endif fname = tempname (); fclose (fopen (strcat (fname, "_e.txt"), "w")); e_filename = canonicalize_file_name (strcat (fname, "_e.txt")); fclose (fopen (strcat (fname, "_p.txt"), "w")); p_filename = canonicalize_file_name (strcat (fname, "_p.txt")); fclose (fopen (strcat (fname, "_t.txt"), "w")); t_filename = canonicalize_file_name (strcat (fname, "_t.txt")); fclose (fopen (strcat (fname, "_s.txt"), "w")); s_filename = canonicalize_file_name (strcat (fname, "_s.txt")); ## Points com_p = sprintf ("awk '/\\$Nodes/,/\\$EndNodes/ {print $2, $3, $4 > ""%s""}' ", p_filename); ## Surface edges com_e = sprintf ("awk '/\\$Elements/,/\\$EndElements/ {n=3+$3; if ($2 == ""2"") print $(n+1), $(n+2), $(n+3), $5 > ""%s""}' ", e_filename); ## Tetrahedra com_t = sprintf ("awk '/\\$Elements/,/\\$EndElements/ {n=3+$3; if ($2 == ""4"") print $(n+1), $(n+2), $(n+3), $(n+4), $5 > ""%s""}' ", t_filename); ## Side edges com_s = sprintf ("awk '/\\$Elements/,/\\$EndElements/ {n=3+$3; if ($2 == ""1"") print $(n+2), $(n+2), $5 > ""%s""}' ", s_filename); command = [com_p, msh_name, ";"]; command = [command, com_e, msh_name, ";"]; command = [command, com_t, msh_name, ";"]; command = [command, com_s, msh_name]; system (command); ## Create PDE-tool like structure if (verbose) printf("Creating PDE-tool like mesh...\n"); endif ## Mesh-points p = load(p_filename)'; ## Mesh side-edges s = load(s_filename)'; ## Mesh surface-edges tmp = load(e_filename)'; be = zeros(10,columns(tmp)); be([1,2,3,10],:) = tmp; ## Mesh tetrahedra t = load(t_filename)'; ## Remove hanging nodes if (verbose) printf("Check for hanging nodes...\n"); endif nnodes = columns(p); in_msh = intersect( 1:nnodes , t(1:4,:) ); if length(in_msh) != nnodes new_num(in_msh) = [1:length(in_msh)]; t(1:4,:) = new_num(t(1:4,:)); be(1:3,:) = new_num(be(1:3,:)); p = p(:,in_msh); endif mesh = struct("p",p,"s",s,"e",be,"t",t); if (verbose) printf("Deleting temporary files...\n"); endif unlink (p_filename); unlink (e_filename); unlink (t_filename); unlink (s_filename); unlink (msh_name); endfunction msh-1.0.12/inst/msh3m_gmsh_write.m000066400000000000000000000067041426661027500170140ustar00rootroot00000000000000## Copyright (C) 2013 Carlo de Falco ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## -*- texinfo -*- ## @deftypefn {Function File} {} = msh3m_gmsh_write (@var{filename}, @var{msh}) ## @seealso{msh2m_gmsh_write} ## @end deftypefn function msh3m_gmsh_write (filename, msh, node_data, cell_data) if (! ((fid = fopen (filename, "w")) >= 0)); error ("msh3m_gmsh_write: unable to open file %s for writing", filename); else ## file format string fprintf (fid, "$MeshFormat\n2.0 0 8\n$EndMeshFormat\n"); ## node coordinates nnodes = columns (msh.p); fprintf (fid, "$Nodes\n%d\n", nnodes); p = [1:nnodes; msh.p]; fprintf (fid, "%d %17.17g %17.17g %17.17g\n", p); fprintf (fid, "$EndNodes\n"); ## elements number_of_tets = columns (msh.t); number_of_tri = columns (msh.e); fprintf (fid, "$Elements\n%d\n", number_of_tets + number_of_tri); ## 3-node triangles e = [1:number_of_tri; ## element number 2*ones(1, number_of_tri); ## element type, 2 = triangle 3*ones(1, number_of_tri); ## number of tags zeros(1, number_of_tri); ## first tag, physical entity: 0 = unspecified msh.e(10, :); ## second tag, geometrical entity zeros(1, number_of_tri); ## third tag, partition: 0 = unspecified msh.e(1:3, :)]; ## node number list fprintf (fid, "%d %d %d %d %d %d %d %d %d\n", e); ## 4-node tetrahedra t = [[(number_of_tri+1):(number_of_tets+number_of_tri)]; ## element number 3*ones(1, number_of_tets); ## element type, 3 = tetrahedron 3*ones(1, number_of_tets); ## number of tags zeros(1, number_of_tets); ## first tag, physical entity: 0 = unspecified msh.t(5, :); ## first tag, geometrical entity zeros(1, number_of_tets); ## third tag, partition: 0 = unspecified msh.t(1:4, :)]; ## node number list fprintf (fid, "%d %d %d %d %d %d %d %d %d %d\n", t); fprintf(fid, "$EndElements\n"); ## node data if (! isempty (node_data)) for ii = 1:rows (node_data) fprintf (fid, "$NodeData\n") fprintf (fid, "%d\n", 1) ## number of string tags fprintf (fid, """%s""\n", node_data{ii, 1}) ## name of view fprintf (fid, "%d\n", 1) ## number of real tags fprintf (fid, "%g\n", 0.0) ## time fprintf (fid, "%d\n", 4) ## number of int tags fprintf (fid, "%d\n", [1, 1, nnodes, 0]) v = [1:nnodes; node_data{ii, 2}(:)']; fprintf (fid, "%d %g\n", v); fprintf (fid, "$EndNodeData\n"); endfor endif fclose (fid); endif endfunction msh-1.0.12/inst/msh3m_join_structured_mesh.m000066400000000000000000000126351426661027500211030ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mesh}]} = @ ## msh3m_join_structured_mesh(@var{mesh1},@var{mesh2},@var{s1},@var{s2}) ## ## Join the two structured meshes @var{mesh1} and @var{mesh2} into one ## single mesh. ## ## The two meshes must share a common face identified by @var{s1} and ## @var{s2}. ## ## @strong{WARNING}: the two meshes must share the same vertexes on the ## common face. ## ## @seealso{msh3m_structured_mesh, msh3m_gmsh, msh3m_submesh, ## msh2m_join_structured_mesh} ## @end deftypefn function mesh = msh3m_join_structured_mesh(mesh1,mesh2,s1,s2) ## Check input if nargin != 4 # Number of input parameters error("msh3m_join_structured_mesh: wrong number of input parameters."); elseif !(isstruct(mesh1) && isfield(mesh1,"p") && isfield (mesh1,"e") && isfield(mesh1,"t") && isstruct(mesh2) && isfield(mesh2,"p") && isfield (mesh2,"e") && isfield(mesh2,"t") ) error("msh3m_join_structured_mesh: invalid mesh structure passed as input."); elseif !(isvector(s1) && isvector(s2)) error("msh3m_join_structured_mesh: shared geometrical sides are not vectors."); elseif (length(s1) != length(s2)) error("msh3m_join_structured_mesh: vectors containing shared geometrical sides are not of the same length."); endif ## Join meshes ## Make sure that the outside world is always on the same side of the ## boundary of mesh1 [mesh1.e(8:9,:),I] = sort(mesh1.e(8:9,:)); ## IF THE REGIONS ARE INVERTED THE VERTEX ORDER SHOULD ALSO BE ## INVERTED!! ## FIXME: here a check could be added to see whether ## the coordinate points of the two meshes coincide on the ## side edges ## Get interface nodes intfcnodes1 = msh3m_nodes_on_faces(mesh1,s1)'; intfcnodes2 = msh3m_nodes_on_faces(mesh2,s2)'; ## Sort interface nodes by position [tmp,I] = sort(mesh1.p(1,intfcnodes1)); intfcnodes1 = intfcnodes1(I); [tmp,I] = sort(mesh1.p(2,intfcnodes1)); intfcnodes1 = intfcnodes1(I); [tmp,I] = sort(mesh1.p(3,intfcnodes1)); intfcnodes1 = intfcnodes1(I); [tmp,I] = sort(mesh2.p(1,intfcnodes2)); intfcnodes2 = intfcnodes2(I); [tmp,I] = sort(mesh2.p(2,intfcnodes2)); intfcnodes2 = intfcnodes2(I); [tmp,I] = sort(mesh2.p(3,intfcnodes2)); intfcnodes2 = intfcnodes2(I); ## Delete redundant boundary faces but first remeber what region they ## were connected to for is = 1:length(s2) ii = find( mesh2.e(10,:)==s2(is) ); adreg(is,:) = unique(mesh2.e(9,ii)); endfor for is = 1:length(s2) mesh2.e(:,find( mesh2.e(10,:)==s2(is) )) = []; endfor ## Change face numbers idx = []; consecutives = []; idx = unique(mesh2.e(10,:)); consecutives (idx) = [1:length(idx)] + max(mesh1.e(10,:)); mesh2.e(10,:) = consecutives(mesh2.e(10,:)); ## Change node indices in connectivity matrix and edge list idx = []; consecutives = []; idx = 1:size(mesh2.p,2); offint = setdiff(idx,intfcnodes2); consecutives (offint) = [1:length(offint)]+size(mesh1.p,2); consecutives (intfcnodes2) = intfcnodes1; mesh2.e(1:3,:) = consecutives(mesh2.e(1:3,:)); mesh2.t(1:4,:) = consecutives(mesh2.t(1:4,:)); ## Delete redundant points mesh2.p(:,intfcnodes2) = []; ## Set region numbers regions = unique(mesh1.t(5,:));# Mesh 1 newregions(regions) = 1:length(regions); mesh1.t(5,:) = newregions(mesh1.t(5,:)); regions = unique(mesh2.t(5,:));# Mesh 2 newregions(regions) = [1:length(regions)]+max(mesh1.t(5,:)); mesh2.t(5,:) = newregions(mesh2.t(5,:)); ## Set adjacent region numbers in face structure 2 [i,j] = find(mesh2.e(8:9,:)); i += 7; mesh2.e(i,j) = newregions(mesh2.e(i,j)); ## Set adjacent region numbers in edge structure 1 for is = 1:length(s1) ii = find( mesh1.e(10,:)==s1(is) ); mesh1.e(8,ii) = newregions(adreg(is,:)); endfor ## Build new mesh structure mesh.p = [mesh1.p mesh2.p]; mesh.e = [mesh1.e mesh2.e]; mesh.t = [mesh1.t mesh2.t]; endfunction %!shared mesh1,mesh2,jmesh % x = y = z = linspace(0,1,2); % x2 = linspace(1,2,2); % [mesh1] = msh3m_structured_mesh(x,y,z,1,1:6); % [mesh2] = msh3m_structured_mesh(x2,y,z,3,1:6); % [jmesh] = msh3m_join_structured_mesh(mesh1,mesh2,2,1); %!test % assert(columns(jmesh.p),12) %!test % tmp = sort(unique(jmesh.e(10,:))); % assert(tmp,1:11) %!test % assert(columns(jmesh.t),columns(mesh1.t)+columns(mesh2.t)) %!test % assert(unique(jmesh.e(8:9,:)),0:2) msh-1.0.12/inst/msh3m_nodes_on_faces.m000066400000000000000000000044601426661027500176060ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{nodelist}]} = @ ## msh3m_nodes_on_faces(@var{mesh},@var{facelist}) ## ## Return a list of @var{mesh} nodes lying on the faces specified in ## @var{facelist}. ## ## @seealso{msh3m_geometrical_properties, msh2m_nodes_on_faces} ## @end deftypefn function [nodelist] = msh3m_nodes_on_faces(mesh,facelist); ## Check input if nargin != 2 # Number of input parameters error("msh3m_nodes_on_faces: wrong number of input parameters."); elseif !(isstruct(mesh) && isfield(mesh,"p") && isfield(mesh,"t") && isfield(mesh,"e")) error("msh3m_nodes_on_faces: first input is not a valid mesh structure."); elseif !isnumeric(facelist) error("msh3m_nodes_on_faces: only numeric value admitted as facelist."); endif ## Search nodes facefaces = []; for ii=1:length(facelist) facefaces = [facefaces,find(mesh.e(10,:)==facelist(ii))]; endfor facenodes = mesh.e(1:3,facefaces); nodelist = unique(facenodes(:)); endfunction %!shared x,y,z,mesh % x = y = z = linspace(0,1,2); % [mesh] = msh3m_structured_mesh(x,y,z,1,1:6); %!test % nodelist = msh3m_nodes_on_faces(mesh,1); % assert(nodelist,[1 2 5 6]') %!test % nodelist = msh3m_nodes_on_faces(mesh,2); % assert(nodelist,[3 4 7 8]') %!test % nodelist = msh3m_nodes_on_faces(mesh,3); % assert(nodelist,[1 3 5 7]') %!test % nodelist = msh3m_nodes_on_faces(mesh,[1 2 3]); % assert(nodelist,[1:8]')msh-1.0.12/inst/msh3m_structured_mesh.m000066400000000000000000000157471426661027500200730ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mesh}]} = @ ## msh3m_structured_mesh(@var{x},@var{y},@var{z},@var{region},@var{sides}) ## ## Construct a structured tetrahedral 3D mesh on a parallelepipedal ## domain. ## ## @itemize @bullet ## @item @var{x}, @var{y} and @var{z} are the one dimensional mesh ## vector of the corresponding Cartesian axis. ## @item @var{region} is a number identifying the geometrical volume, ## while @var{sides} is a 6 components vector containing the numbers ## used to identify the geometrical face edges. ## @end itemize ## ## The returned value @var{mesh} is a PDE-tool like mesh structure ## composed of the following fields: ## @itemize @minus ## @item @var{p}: matrix with size 3 times number of mesh points. ## @itemize @bullet ## @item 1st row: x-coordinates of the points. ## @item 2nd row: y-coordinates of the points. ## @item 3rd row: z-coordinates of the points. ## @end itemize ## @item @var{e}: matrix with size 10 times number of mesh boundary triangles. ## @itemize @bullet ## @item 1st row: number of the first vertex of the face edge. ## @item 2nd row: number of the second vertex of the face edge. ## @item 3rd row: number of the third vertex of the face edge. ## @item 4th row: set to 0, present for compatibility with MatLab PDE-tool. ## @item 5th row: set to 0, present for compatibility with MatLab PDE-tool. ## @item 6th row: set to 0, present for compatibility with MatLab PDE-tool. ## @item 7th row: set to 0, present for compatibility with MatLab PDE-tool. ## @item 8th row: number of the geometrical volume to the right of the ## face edge. ## @item 9th row: number of the geometrical volume to the left of the ## face edge. ## @item 10th row: number of the geometrical border containing the face ## edge. ## @end itemize ## @item @var{t}: matrix with size 5 times number of mesh elements. ## @itemize @bullet ## @item 1st row: number of the first vertex of the element. ## @item 2nd row: number of the second vertex of the element. ## @item 3rd row: number of the third vertex of the element. ## @item 4th row: number of the fourth vertex of the element. ## @item 5th row: number of the geometrical volume containing the element. ## @end itemize ## @end itemize ## ## @seealso{msh2m_structured_mesh, msh3m_gmsh, msh2m_mesh_along_spline, ## msh3m_join_structured_mesh, msh3m_submesh} ## @end deftypefn function mesh = msh3m_structured_mesh (x, y, z, region, sides) ## Check input if (nargin != 5) # Number of input parameters print_usage (); elseif !(isvector (x) && isnumeric (x) && ! isscalar (x) && isvector (y) && isnumeric (y) && ! isscalar (y) && isvector (z) && isnumeric (z) && ! isscalar (z)) error("msh3m_structured_mesh: X, Y, Z must be valid numeric vectors."); elseif !isscalar(region) error("msh3m_structured_mesh: REGION must be a valid scalar."); elseif !(isvector(sides) && (length(sides) == 6)) error("msh3m_structured_mesh: SIDES must be a 6 components vector."); endif ## Build mesh ## Sort point coordinates x = sort (x); y = sort (y); z = sort (z); ## Compute # of points in each direction nx = length (x); ny = length (y); nz = length (z); ## Generate vertices [XX, YY, ZZ] = meshgrid (x, y, z); p = [XX(:), YY(:), ZZ(:)]'; iiv (ny,nx,nz)=0; iiv(:)=1:nx*ny*nz; iiv(end,:,:)=[]; iiv(:,end,:)=[]; iiv(:,:,end)=[]; iiv=iiv(:)'; ## Generate connections: n1 = iiv; # bottom faces n2 = iiv + 1; n3 = iiv + ny; n4 = iiv + ny + 1; N1 = iiv + nx * ny; # top faces N2 = N1 + 1; N3 = N1 + ny; N4 = N3 + 1; t = [[n1; n3; n2; N2],... [N1; N2; N3; n3],... [N1; N2; n3; n1],... [N2; n3; n2; n4],... [N3; n3; N2; N4],... [N4; n3; N2; n4]]; ## Generate boundary face list ## left T = t; T(:) = p(1, t)' == x(1); [~, order] = sort (T, 1); ii = (find(sum(T,1)==3)); order(1,:) = []; for jj=1:length (ii) e1(:,jj) = t(order(:,ii(jj)),ii(jj)); endfor e1(10,:) = sides(1); ## right T(:) = p(1,t)' == x(end); [~, order] = sort (T, 1); ii = (find (sum (T, 1) == 3)); order(1,:) = []; for jj=1:length (ii) e2(:,jj) = t(order(:,ii(jj)),ii(jj)); end e2(10,:) = sides(2); ## front T(:) = p(2,t)' == y(1); [~, order] = sort (T, 1); ii = (find (sum (T, 1) == 3)); order(1,:) = []; for jj=1:length (ii) e3(:,jj) = t(order(:,ii(jj)),ii(jj)); endfor e3(10,:) = sides(3); ## back T(:) = p(2,t)' == y(end); [~,order] = sort (T,1); ii = (find (sum (T,1) == 3)); order(1,:) = []; for jj=1:length (ii) e4(:,jj) = t(order(:,ii(jj)),ii(jj)); endfor e4(10,:) = sides(4); ## bottom T = t; T(:) = p(3,t)'==z(1); [ignore,order] = sort(T,1); ii = (find (sum (T,1)==3)); order(1,:) = []; for jj=1:length(ii) e5(:,jj) = t(order(:,ii(jj)),ii(jj)); endfor e5(10,:) = sides(5); ## top T = t; T(:) = p(3,t)'==z(end); [ignore,order] = sort(T,1); ii = (find (sum (T,1) == 3)); order(1,:) = []; for jj=1:length(ii) e6(:,jj) = t(order(:,ii(jj)),ii(jj)); endfor e6(10,:) = sides(6); ## Assemble structure mesh.e = [e1,e2,e3,e4,e5,e6]; mesh.t = t; mesh.e (9,:) = region; mesh.t (5,:) = region; mesh.p = p; endfunction %!test % x = y = z = linspace (0,1,2) % [mesh] = msh3m_structured_mesh (x, y, z, 1, 1:6) % assert = (columns (mesh.p), 8) % assert = (columns (mesh.t), 6) % assert = (columns (mesh.e), 12) %!test %! x = y = z = linspace (0, 1, 3); %! mesh = msh3m_structured_mesh (x, y, z, 1, 1:6); %! assert (columns (mesh.p), 27) %! assert (columns (mesh.t), 48) %! assert (columns (mesh.e), 48) %!test %! x = y = z = linspace (0,1,4); %! [mesh] = msh3m_structured_mesh (x, y, z, 1, 1:6); %! assert (columns (mesh.p), 64) %! assert (columns (mesh.t), 162) %! assert (columns (mesh.e), 108) %!test %! x = y = z = linspace (0, 1, 1); %! fail("mesh = msh3m_structured_mesh (x, y, z, 1, 1:6)", "msh3m_structured_mesh: X, Y, Z must be valid numeric vectors."); %!test %! x = y = z = eye (2); %! fail("mesh = msh3m_structured_mesh (x, y, z, 1, 1:6)", "msh3m_structured_mesh: X, Y, Z must be valid numeric vectors."); msh-1.0.12/inst/msh3m_submesh.m000066400000000000000000000061311426661027500163040ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH 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 of the License, or ## (at your option) any later version. ## ## MSH 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 MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{omesh},@var{nodelist},@var{elementlist}]} = @ ## msh3m_submesh(@var{imesh},@var{intrfc},@var{sdl}) ## ## Extract the subdomain(s) in @var{sdl} from @var{imesh}. ## ## The row vector @var{intrfc} contains the internal interface sides to ## be maintained (field @code{mesh.e(5,:)}). It can be empty. ## ## Return the vectors @var{nodelist} and @var{elementlist} containing ## respectively the list of nodes and elements of the original mesh that ## are part of the selected subdomain(s). ## ## @seealso{msh3m_join_structured_mesh, msh2m_join_structured_mesh, ## msh3m_submesh} ## @end deftypefn function [omesh,nodelist,elementlist] = msh3m_submesh(imesh,intrfc,sdl) ## Check input if nargin != 3 error("msh3m_submesh: wrong number of input parameters."); elseif !(isstruct(imesh) && isfield(imesh,"p") && isfield (imesh,"t") && isfield(imesh,"e")) error("msh3m_submesh: first input is not a valid mesh structure."); elseif !isvector(sdl) error("msh3m_submesh: third input is not a valid vector."); endif ## Extract sub-mesh ## Build element list elementlist=[]; for ir = 1:length(sdl) elementlist = [ elementlist find(imesh.t(5,:)==sdl(ir)) ]; endfor ## Build nodelist nodelist = reshape(imesh.t(1:4,elementlist),1,[]); nodelist = unique(nodelist); ## Extract submesh omesh.p = imesh.p (:,nodelist); indx(nodelist) = 1:length (nodelist); omesh.t = imesh.t (:,elementlist); omesh.t(1:4,:) = indx(omesh.t(1:4,:)); omesh.e = []; for ifac = 1:size(imesh.e,2) if (length(intersect(imesh.e(1:3,ifac),nodelist) )== 3) omesh.e = [omesh.e imesh.e(:,ifac)]; endif endfor omesh.e(1:3,:) = indx(omesh.e(1:3,:)); endfunction %!shared mesh1,mesh2,jmesh,exmesh,nodelist,elemlist % x = y = z = linspace(0,1,2); % x2 = linspace(1,2,2); % [mesh1] = msh3m_structured_mesh(x,y,z,1,1:6); % [mesh2] = msh3m_structured_mesh(x2,y,z,1,1:6); % [jmesh] = msh3m_join_structured_mesh(mesh1,mesh2,2,1); % [exmesh,nodelist,elemlist] = msh3m_submesh(jmesh,2,1); %!test % assert(size(exmesh.p),size(mesh1.p)) %!test % assert(size(exmesh.t),size(mesh1.t)) %!test % assert(size(exmesh.e),size(mesh1.e))