msh/src/Makefile.in000664 001750 001750 00000000435 12170446612 014102 0ustar00tedted000000 000000 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/inst/msh3m_nodes_on_faces.m000664 001750 001750 00000004460 11331502341 016445 0ustar00tedted000000 000000 ## 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/inst/msh2m_gmsh_write.m000664 001750 001750 00000006632 12175041666 015671 0ustar00tedted000000 000000 ## 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/src/mshm_dolfin_read.cc000664 001750 001750 00000014053 12301673665 015645 0ustar00tedted000000 000000 /* 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/src/000775 001750 001750 00000000000 12301673725 012036 5ustar00tedted000000 000000 msh/inst/msh2m_mesh_along_spline.m000664 001750 001750 00000005500 11331502341 017161 0ustar00tedted000000 000000 ## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 2 of the License, or ## (at your option) any later version. ## ## MSH is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mesh}]} = @ ## msh2m_mesh_along_spline(@var{xc},@var{yc},@var{Nnx},@var{Nny},@var{sigma}) ## ## Generate a structured mesh in a thin layer of size @var{sigma} ## sitting on a natural Catmull-Rom type cubic spline with control ## points @var{xc}, @var{yc}. ## ## If @var{Nnx} and @var{Nny} are scalars, the mesh has @var{Nnx} nodes ## in the direction along the spline and @var{Nny} in the normal ## direction. ## ## If @var{Nnx} and @var{Nny} are vectors they indicate the curvilinear ## coordinates of the mesh nodes. ## ## The returned value @var{mesh} is a PDE-tool like mesh structure. ## ## Be aware that if @var{sigma} is not much smaller than the curvature ## of the line the resulting mesh may be invalid. ## ## @seealso{msh2m_structured_mesh, msh2m_gmsh, msh3m_structured_mesh} ## @end deftypefn function msh2 = msh2m_mesh_along_spline(xc,yc,Nnx,Nny,sigma) ## Check input ## FIXME: input type not checked for the first 4 arguments if (nargin != 5) # Number of input parameters error("msh2m_mesh_along_spline: wrong number of input parameters."); elseif (!isscalar(sigma)) error("msh2m_mesh_along_spline: sigma must be a valid scalar value."); endif ## Construct mesh s = [0:length(xc)-1]; xsPP = catmullrom ( s, xc ); ysPP = catmullrom ( s, yc ); if (length(Nnx)>1) ss = Nnx(:).'; else ss = linspace(0,s(end),Nnx); endif xs = ppval(xsPP,ss); ys = ppval(ysPP,ss); dxsPP = fnder(xsPP,1); dysPP = fnder(ysPP,1); nx = -ppval(dysPP,ss)'; ny = ppval(dxsPP,ss)'; nx = nx ./ sqrt(nx.^2+ny.^2); ny = ny ./ sqrt(nx.^2+ny.^2); if (length(Nny)>1) ssy = Nny(:).'; else ssy = linspace(0,1,Nny); endif msh2 = msh2m_structured_mesh([1:length(ss)], ssy, 1, 1:4); jj = (msh2.p(1,:)); p(1,:) = xs(jj) + sigma*nx(jj)' .* msh2.p(2,:); p(2,:) = ys(jj) + sigma*ny(jj)' .* msh2.p(2,:); msh2.p = p; endfunctionmsh/INDEX000664 001750 001750 00000001364 12241124547 012041 0ustar00tedted000000 000000 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 mshm_refine Mesh extraction msh3e_surface_mesh msh2m_submesh msh3m_submesh Mesh plotting msh2p_mesh Mesh conversion from DOLFIN mshm_dolfin_read mshm_dolfin_write Mesh export to gmsh msh2m_gmsh_write msh3m_gmsh_writemsh/COPYING000664 001750 001750 00000043077 10751627243 012316 0ustar00tedted000000 000000 GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. 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GNU GENERAL PUBLIC LICENSE TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION 0. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The "Program", below, refers to any such program or work, and a "work based on the Program" means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term "modification".) Each licensee is addressed as "you". Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. 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If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. 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If this is what you want to do, use the GNU Library General Public License instead of this License. msh/inst/msh3m_structured_mesh.m000664 001750 001750 00000015736 12041560522 016734 0ustar00tedted000000 000000 ## 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 face edges. ## @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/inst/msh2m_jiggle_mesh.m000664 001750 001750 00000007556 11331502341 015765 0ustar00tedted000000 000000 ## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 2 of the License, or ## (at your option) any later version. ## ## MSH is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{newmsh}]} = @ ## msh2m_jiggle_mesh(@var{msh},@var{steps}) ## ## Equalize the size of triangle edges setting a spring of rest length ## @var{factor}*@var{area} along each edge of the mesh and solving for ## static equilibrium. ## ## The non-linear eqautions of the system obtained are solved via a ## non-linear Gauss-Seidel method. @var{step} is the number of steps of ## the method to be applied. ## ## May be useful when distorting a mesh, type @code{demo ## msh2m_jiggle_mesh} to see some examples. ## ## @seealso{msh2m_displacement_smoothing, msh2m_equalize_mesh} ## ## @end deftypefn function [msh] = msh2m_jiggle_mesh(msh,steps) ## Check input if nargin != 2 # Number of input parameters error("msh2m_jiggle_mesh: wrong number of input parameters."); elseif !(isstruct(msh) && isfield(msh,"p") && isfield(msh,"t") && isfield(msh,"e")) error("msh2m_jiggle_mesh: first input is not a valid mesh structure."); elseif !isscalar(steps) error("msh2m_jiggle_mesh: second argument is not a valid scalar"); endif ## Solve for static equilibrium nel= columns(msh.t); nnodes = columns(msh.p); x = msh.p(1,:)'; y = msh.p(2,:)'; dnodes = unique(msh.e(1:2,:)(:)); vnodes = setdiff(1:nnodes,dnodes); ## Find node neighbours ## FIXME: should this go into msh2m_topological_properties ? sides = msh2m_topological_properties(msh,"sides"); for inode = 1:nnodes neig{inode} = (sides(:, sides(1,:) == inode | sides(2,:) == inode))(:); neig{inode} (neig{inode} == inode) = []; endfor for istep = 1:steps for inode =vnodes xx = x(neig{inode}) * ones(size(neig{inode}))'; lx = abs ( xx - xx' )(:); mx = ( xx + xx' )(:)/2; x(inode) = sum(mx.*lx)/sum(lx); yy = y(neig{inode}) * ones(size(neig{inode}))'; ly = abs ( yy - yy' )(:); my = (yy + yy')(:)/2; y(inode) = sum(my.*ly)/sum(ly); endfor endfor msh.p = [x';y']; endfunction %!demo %! ### distort a mesh on a square equalizing at each step %! msh = msh2m_structured_mesh(linspace(0,1,10),linspace(0,1,10),1,1:4,"right"); %! dnodes = msh2m_nodes_on_sides(msh,1:4); %! varnodes = setdiff([1:columns(msh.p)],dnodes); %! x = msh.p(1,:)'; %! y = msh.p(2,:)'; %! dx = dy = zeros(columns(msh.p),1); %! dytot = dxtot = -.4*sin(x(dnodes).*y(dnodes)*pi/2); %! Nsteps = 30; %! for ii=1:Nsteps %! dx(dnodes) = dxtot; %! dy(dnodes) = dytot; %! [Ax,Ay] = msh2m_displacement_smoothing(msh,1); %! dx(varnodes) = Ax(varnodes,varnodes) \ ... %! (-Ax(varnodes,dnodes)*dx(dnodes)); %! dy(varnodes) = Ay(varnodes,varnodes) \ ... %! (-Ay(varnodes,dnodes)*dy(dnodes)); %! msh.p(1,:) += dx'/Nsteps; %! msh.p(2,:) += dy'/Nsteps; %! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)','r'); %! pause(.5) %! x = msh.p(1,:)'; %! y = msh.p(2,:)'; %! msh = msh2m_jiggle_mesh(msh,10); %! hold on; %! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)'); %! hold off; %! pause(.5) %! endformsh/inst/msh3m_gmsh_write.m000664 001750 001750 00000006704 12175041666 015672 0ustar00tedted000000 000000 ## 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/inst/msh3m_geometrical_properties.m000664 001750 001750 00000016434 12242360672 020266 0ustar00tedted000000 000000 ## 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/inst/000775 001750 001750 00000000000 12301673673 012226 5ustar00tedted000000 000000 msh/src/mshm_refine.cc000664 001750 001750 00000055420 12301673665 014652 0ustar00tedted000000 000000 /* 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/inst/msh3m_join_structured_mesh.m000664 001750 001750 00000012635 11707224262 017754 0ustar00tedted000000 000000 ## 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/inst/msh3m_submesh.m000664 001750 001750 00000006131 11331502341 015143 0ustar00tedted000000 000000 ## 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))msh/000775 001750 001750 00000000000 12301673673 011251 5ustar00tedted000000 000000 msh/src/configure000775 001750 001750 00000353525 12301673706 013761 0ustar00tedted000000 000000 #! /bin/sh # Guess values for system-dependent variables and create Makefiles. # Generated by GNU Autoconf 2.69 for Msh Package 1.0. # # # Copyright (C) 1992-1996, 1998-2012 Free Software Foundation, Inc. # # # This configure script is free software; the Free Software Foundation # gives unlimited permission to copy, distribute and modify it. ## -------------------- ## ## M4sh Initialization. ## ## -------------------- ## # Be more Bourne compatible DUALCASE=1; export DUALCASE # for MKS sh if test -n "${ZSH_VERSION+set}" && (emulate sh) >/dev/null 2>&1; then : emulate sh NULLCMD=: # Pre-4.2 versions of Zsh do word splitting on ${1+"$@"}, which # is contrary to our usage. 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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/inst/msh3e_surface_mesh.m000664 001750 001750 00000006771 11331502341 016143 0ustar00tedted000000 000000 ## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 2 of the License, or ## (at your option) any later version. ## ## MSH is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{emesh},@var{snodes},@var{ssides},@var{striangles}]} = @ ## msh3e_surface_mesh(@var{mesh},@var{nsrf},@var{nsides}) ## ## Extract the plane surface @var{nsrf} delimited by @var{nsides} from ## @var{mesh}. ## ## Return the vector @var{snodes} containing the references to input ## mesh nodes (field @code{mesh.p}), the vector @var{ssides} containing ## the references to input mesh side (field @code{mesh.s}) and the ## vector @var{striangles} containing the references to input mesh side ## edges (field @code{mesh.e}). ## ## @strong{WARNING}: the suface MUST be ortogonal to either X, Y or Z ## axis. This should be changed to account for generic 2D surface. ## ## @end deftypefn function [emesh,snodes,ssides,striangles] = msh3e_surface_mesh(mesh,nsrf,nsides) ## Check input if nargin != 3 error("msh3e_surface_mesh: wrong number of input parameters."); elseif !(isstruct(mesh) && isfield(mesh,"p") && isfield (mesh,"t") && isfield(mesh,"e")) error("msh3e_surface_mesh: first input is not a valid mesh structure."); elseif !isscalar(nsrf) error("msh3e_surface_mesh: second input is not a valid scalar."); elseif !(isvector(nsides) && isnumeric(nsides)) error("msh3e_surface_mesh: third input is not a valid numeric vector."); endif ## Surface extraction ## Extraction of 2D surface elements striangles = find( mesh.e(10,:) == nsrf ); t = mesh.e(1:3,striangles); tmp = reshape(t,[],1); ## Renumbering [snodes,ii,jj] = unique(tmp); nds = 1:length(snodes); emesh.t = reshape(nds(jj),3,[]); ## Extraction of 2D mesh points points = mesh.p(:,snodes); ## Test for normals ## FIXME: this should disappear as soon as 2D mesh are not supposed to ## lie on a plane. if length(unique(points(1,:))) == 1 xyz = [2,3]; # normal to X coordinate elseif length(unique(points(2,:))) == 1 xyz = [1,3]; # normal to Y coordinate else xyz = [1,2]; # normal to Z coordinate endif emesh.p = points(xyz,:); ## Extraction of 1D side edges ssides = []; for ll = nsides tmp = find ( mesh.s(3,:) == ll ); ssides = [ssides,tmp]; endfor nedges = length(ssides); emesh.e = zeros(7,nedges); emesh.e(5,:) = mesh.s(3,ssides); tmp = reshape(mesh.s(1:2,ssides),[],1); [enodes,nn,mm] = unique(tmp); [tmp1, nds, tmp2] = intersect(snodes,enodes); emesh.e(1:2,:) = reshape(nds(mm),2,[]); ## Compute mesh properties ## FIXME: this has to be removed. MSH should not depend on BIM. emesh = bim2c_mesh_properties(emesh); endfunctionmsh/src/mshm_dolfin_write.cc000664 001750 001750 00000042654 12301673665 016074 0ustar00tedted000000 000000 /* 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/inst/msh2p_mesh.m000664 001750 001750 00000003124 11331502341 014432 0ustar00tedted000000 000000 ## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 2 of the License, or ## (at your option) any later version. ## ## MSH is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} msh2p_mesh(@var{mesh}, @var{linespec}) ## ## Plot @var{mesh} with the line specification in @var{linespec} using ## @code{triplot}. ## ## @seealso{triplot} ## ## @end deftypefn function msh2p_mesh(mesh,linespec) ## Check input if nargin > 2 error("msh2p_mesh: wrong number of input parameters."); elseif !(isstruct(mesh) && isfield(mesh,"p") && isfield (mesh,"t") && isfield(mesh,"e")) error("msh2p_mesh: first input is not a valid mesh structure."); endif tri = mesh.t(1:3,:)'; x = mesh.p(1,:)'; y = mesh.p(2,:)'; if ~exist("linespec") linespec = "r"; endif triplot(tri,x,y,linespec); endfunctionmsh/DESCRIPTION000664 001750 001750 00000001127 12301673665 012761 0ustar00tedted000000 000000 Name: msh Version: 1.0.10 Date: 2014-02-21 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 (>= 1.6.5 (optional)), awk (optional), dolfin (>= 1.3 optional) Autoload: no License: GPLv2+ Url: http://octave.sf.net, http://www.geuz.org/gmsh, http://fenicsproject.org/ msh/inst/msh2m_submesh.m000664 001750 001750 00000012365 11356050031 015151 0ustar00tedted000000 000000 ## 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/inst/msh3m_gmsh.m000664 001750 001750 00000012123 12041007311 014425 0ustar00tedted000000 000000 ## 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 (tmpnam (), ".msh"); fclose (fopen (msh_name, "w")); [status, gmsh_output] = system (["gmsh -format msh -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 = tmpnam (); 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); endfunctionmsh/inst/msh2m_nodes_on_sides.m000664 001750 001750 00000004411 11331502341 016466 0ustar00tedted000000 000000 ## 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/inst/msh2m_geometrical_properties.m000664 001750 001750 00000041505 12241124547 020260 0ustar00tedted000000 000000 ## 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/inst/msh2m_gmsh.m000664 001750 001750 00000015266 12041007311 014437 0ustar00tedted000000 000000 ## 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 (tmpnam (), ".msh"); fclose (fopen (msh_name, "w")); [status, gmsh_output] = system (["gmsh -format msh -2 -o " msh_name optstring " " geometry ".geo 2>&1 "]); if (status) error ("msh2m_gmsh: the gmesh subprocess exited abnormally"); endif fname = tmpnam (); 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 = [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"); %! trimesh (mesh.t(1:3,:)', mesh.p(1,:)', mesh.p(2,:)'); %! unlink (canonicalize_file_name (name));msh/inst/msh2m_join_structured_mesh.m000664 001750 001750 00000014072 11331502341 017736 0ustar00tedted000000 000000 ## 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/inst/msh2m_topological_properties.m000664 001750 001750 00000023137 11331502341 020271 0ustar00tedted000000 000000 ## 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/inst/msh2m_equalize_mesh.m000664 001750 001750 00000010120 11331502341 016320 0ustar00tedted000000 000000 ## Copyright (C) 2006,2007,2008,2009,2010 Carlo de Falco, Massimiliano Culpo ## ## This file is part of: ## MSH - Meshing Software Package for Octave ## ## MSH is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 2 of the License, or ## (at your option) any later version. ## ## MSH is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with MSH; If not, see . ## ## author: Carlo de Falco ## author: Massimiliano Culpo ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{mesh}]} = @ ## msh2m_equalize_mesh(@var{mesh}) ## ## Apply a baricentric regularization to equalize the size of triangle ## edges, i.e. move each node to the center of mass of the patch of ## triangles to which it belongs. ## ## May be useful when distorting a mesh. ## Type @code{demo msh2m_equalize_mesh} to see some examples. ## ## @seealso{msh2m_displacement_smoothing} ## ## @end deftypefn function [msh] = msh2m_equalize_mesh(msh) ## Check input if nargin != 1 # Number of input parameters error("msh2m_equalize_mesh: wrong number of input parameters."); elseif !(isstruct(msh) && isfield(msh,"p") && isfield(msh,"t") && isfield(msh,"e")) error("msh2m_equalize_mesh: first input is not a valid mesh structure."); endif ## Apply regularization nel= columns(msh.t); x = msh.p(1,:)'; y = msh.p(2,:)'; dnodes = unique(msh.e(1:2,:)(:)); varnodes = setdiff([1:columns(msh.p)],dnodes); Ax = spalloc(length(x),length(x),1); Ay = spalloc(length(x),length(x),1); ax = zeros(3,3,nel); ay = zeros(3,3,nel); for inode=1:3 giinode(inode,:)=msh.t(inode,:); for jnode=1:3 ginode(inode,jnode,:)=msh.t(inode,:); gjnode(inode,jnode,:)=msh.t(jnode,:); endfor endfor for ii=1:3 for jj=ii+1:3 ax(ii,jj,:) = ax(jj,ii,:) = -ones(1,1,nel); ay(ii,jj,:) = ay(jj,ii,:) = -ones(1,1,nel); ax(ii,ii,:) -= ax(ii,jj,:); ax(jj,jj,:) -= ax(ii,jj,:); ay(ii,ii,:) -= ay(ii,jj,:); ay(jj,jj,:) -= ay(ii,jj,:); endfor endfor Ax = sparse(ginode(:),gjnode(:),ax(:)); Ay = sparse(ginode(:),gjnode(:),ay(:)); x(varnodes) = Ax(varnodes,varnodes) \ (-Ax(varnodes,dnodes)*x(dnodes)); y(varnodes) = Ay(varnodes,varnodes) \ (-Ay(varnodes,dnodes)*y(dnodes)); msh.p(1,:) = x'; msh.p(2,:) = y'; endfunction %!demo %! ### equalize a structured mesh without moving boundary nodes %! msh = msh2m_structured_mesh(linspace(0,1,10),linspace(0,1,10),1,1:4,"random"); %! dnodes = msh2m_nodes_on_sides(msh,1:4); %! varnodes = setdiff([1:columns(msh.p)],dnodes); %! x = msh.p(1,:)'; %! y = msh.p(2,:)'; %! msh = msh2m_equalize_mesh(msh); %! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)'); %! pause(.01) %!demo %! ### distort a mesh on a square equalizing at each step %! msh = msh2m_structured_mesh(linspace(0,1,10),linspace(0,1,10),1,1:4,"random"); %! dnodes = msh2m_nodes_on_sides(msh,1:4); %! varnodes = setdiff([1:columns(msh.p)],dnodes); %! x = msh.p(1,:)'; %! y = msh.p(2,:)'; %! dx = dy = zeros(columns(msh.p),1); %! dytot = dxtot = -.7*sin(x(dnodes).*y(dnodes)*pi/2); %! Nsteps = 10; %! for ii=1:Nsteps %! dx(dnodes) = dxtot; %! dy(dnodes) = dytot; %! [Ax,Ay] = msh2m_displacement_smoothing(msh,1); %! dx(varnodes) = Ax(varnodes,varnodes) \ ... %! (-Ax(varnodes,dnodes)*dx(dnodes)); %! dy(varnodes) = Ay(varnodes,varnodes) \ ... %! (-Ay(varnodes,dnodes)*dy(dnodes)); %! msh.p(1,:) += dx'/Nsteps; %! msh.p(2,:) += dy'/Nsteps; %! triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)','r'); %! pause(.5) %! x = msh.p(1,:)'; %! y = msh.p(2,:)'; %! msh = msh2m_equalize_mesh(msh); %! hold on;triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)');hold off %! pause(.5) %! endformsh/inst/msh2m_displacement_smoothing.m000664 001750 001750 00000011110 11331502341 020224 0ustar00tedted000000 000000 ## 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/inst/msh2m_structured_mesh.m000664 001750 001750 00000020157 11331502341 016720 0ustar00tedted000000 000000 ## 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)