pax_global_header 0000666 0000000 0000000 00000000064 14266610275 0014523 g ustar 00root root 0000000 0000000 52 comment=0a9bab0975a223651fee77a011844da4afd918fe
msh-1.0.12/ 0000775 0000000 0000000 00000000000 14266610275 0012373 5 ustar 00root root 0000000 0000000 msh-1.0.12/.hgignore 0000664 0000000 0000000 00000001423 14266610275 0014176 0 ustar 00root root 0000000 0000000 syntax: 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/COPYING 0000664 0000000 0000000 00000043077 14266610275 0013441 0 ustar 00root root 0000000 0000000 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
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Preamble
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0. This License applies to any program or other work which contains
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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
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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
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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
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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
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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
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You should also get your employer (if you work as a programmer) or your
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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/DESCRIPTION 0000664 0000000 0000000 00000000744 14266610275 0014106 0 ustar 00root root 0000000 0000000 Name: 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/INDEX 0000664 0000000 0000000 00000001243 14266610275 0013165 0 ustar 00root root 0000000 0000000 MSH >> 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_write msh-1.0.12/NEWS 0000664 0000000 0000000 00000003020 14266610275 0013065 0 ustar 00root root 0000000 0000000 Summary 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/ 0000775 0000000 0000000 00000000000 14266610275 0013516 5 ustar 00root root 0000000 0000000 msh-1.0.12/cruft/src/ 0000775 0000000 0000000 00000000000 14266610275 0014305 5 ustar 00root root 0000000 0000000 msh-1.0.12/cruft/src/Makefile.in 0000664 0000000 0000000 00000000435 14266610275 0016354 0 ustar 00root root 0000000 0000000 MKOCTFILE ?= 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/bootstrap 0000775 0000000 0000000 00000000113 14266610275 0016243 0 ustar 00root root 0000000 0000000 #!/bin/bash
## Octave-Forge: msh package bootstrap script
set -e
autoconf
msh-1.0.12/cruft/src/configure.ac 0000664 0000000 0000000 00000001042 14266610275 0016570 0 ustar 00root root 0000000 0000000 AC_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.cc 0000664 0000000 0000000 00000014053 14266610275 0020111 0 ustar 00root root 0000000 0000000 /* 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.cc 0000664 0000000 0000000 00000042654 14266610275 0020340 0 ustar 00root root 0000000 0000000 /* 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.cc 0000664 0000000 0000000 00000055420 14266610275 0017116 0 ustar 00root root 0000000 0000000 /* 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/ 0000775 0000000 0000000 00000000000 14266610275 0013350 5 ustar 00root root 0000000 0000000 msh-1.0.12/inst/msh2m_displacement_smoothing.m 0000664 0000000 0000000 00000011110 14266610275 0021365 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000010120 14266610275 0017461 0 ustar 00root root 0000000 0000000 ## 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)
%! endfor msh-1.0.12/inst/msh2m_geometrical_properties.m 0000664 0000000 0000000 00000041503 14266610275 0021406 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000015300 14266610275 0015571 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000006632 14266610275 0017013 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000007556 14266610275 0017126 0 ustar 00root root 0000000 0000000 ## 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)
%! endfor msh-1.0.12/inst/msh2m_join_structured_mesh.m 0000664 0000000 0000000 00000014072 14266610275 0021077 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000005500 14266610275 0020322 0 ustar 00root root 0000000 0000000 ## 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;
endfunction msh-1.0.12/inst/msh2m_nodes_on_sides.m 0000664 0000000 0000000 00000004411 14266610275 0017627 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000020157 14266610275 0020061 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000012365 14266610275 0016311 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000023137 14266610275 0021432 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000003124 14266610275 0015573 0 ustar 00root root 0000000 0000000 ## 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);
endfunction msh-1.0.12/inst/msh3e_surface_mesh.m 0000664 0000000 0000000 00000006771 14266610275 0017304 0 ustar 00root root 0000000 0000000 ## 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);
endfunction msh-1.0.12/inst/msh3m_geometrical_properties.m 0000664 0000000 0000000 00000016434 14266610275 0021414 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000012131 14266610275 0015571 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000006704 14266610275 0017014 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000012635 14266610275 0021103 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000004460 14266610275 0017606 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000015747 14266610275 0020073 0 ustar 00root root 0000000 0000000 ## 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.m 0000664 0000000 0000000 00000006131 14266610275 0016304 0 ustar 00root root 0000000 0000000 ## 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))