runTetGen
Below is a demonstration of the features of the runTetGen function
Contents
- Syntax
- Description
- Examples
- Example 1: Meshing a model with a single region
- Example 2: Meshing imported geometry
- Example 3: Meshing a two-region model
- Example 4: Meshing a multi-region model
- Example 5: Meshing regions with holes
- Example 6: Meshing from a quadrilateral input surface
- Example 7: Specifying a sizing function to control local mesh density
- Example 8: Meshing of topology with holes and complex regions
- Example 9: Meshing 10-node (i.e. quadratic) tetrahedral elements
Syntax
[meshOutput]=runTetGen(inputStruct);
Description
This function creates a temporary .smesh file which it passes to TETGEN (http://wias-berlin.de/software/tetgen/) for tetrahedral meshing. The input structure should contain the following fields:
smeshStruct.stringOpt=stringOpt; Where stringOpt should contain a strin composed of valid TETGEN command line switches (e.g. '-pq1.2VAaY'). See info below and the TETGEN manual.
smeshStruct.Faces=F; Where F is an array for all the model (triangular) faces
smeshStruct.Nodes=V; Where V is the array containing the nodal coordinates
smeshStruct.holePoints=V_holes; Where V_holes describes a point (not part of V) that lies inside a prescribed hole inside the mesh. If V_holes=[] no holes are defined.
smeshStruct.faceBoundaryMarker=faceBoundaryMarker; Where faceBoundaryMarker defines a label for each face denoting its membership to a particular boundary (e.g. all outer faces could have the same boundary label while an internal set of faces defining a hole has a different label).
smeshStruct.regionPoints=V_regions; Where similarly to V_holes the array V_regions defines points (not part of V) that lie inside a specific region (e.g. a material can be contained within another material and this allows you to specify multiple materials with different mesh densities and output labels).
smeshStruct.regionA=regionA; Where regionA is a vector defining the A specification (volume) for the corrensponding regions (as defined in V_regions)
Optional parameters:
smeshStruct.minRegionMarker=2; %Minimum region marker Arbitrary region marker label. Regions are labeled minRegionMarker:1:... for all regions.
smeshStruct.smeshName=smeshName; Where smeshName is the file name for the input .smesh file. Only .smesh files are currently supported as input files. This function generates the .smesh file using the writeBasicSmesh function
Below is a list of command line switches from the user manual:
-p Tetrahedralizes a piecewise linear complex (PLC). -Y Preserves the input surface mesh (does not modify it). -r Reconstructs a previously generated mesh. -q Refines mesh (to improve mesh quality). -R Mesh coarsening (to reduce the mesh elements). -A Assigns attributes to tetrahedra in different regions. -a Applies a maximum tetrahedron volume constraint. -m Applies a mesh sizing function. -i Inserts a list of additional points. -O Specifies the level of mesh optimization. -S Specifies maximum number of added points. -T Sets a tolerance for coplanar test (default 10?8). -X Suppresses use of exact arithmetic. -M No merge of coplanar facets or very close vertices. -w Generates weighted Delaunay (regular) triangulation. -c Retains the convex hull of the PLC. -d Detects self-intersections of facets of the PLC. -z Numbers all output items starting from zero. -f Outputs all faces to .face file. -e Outputs all edges to .edge file. -n Outputs tetrahedra neighbors to .neigh file. -v Outputs Voronoi diagram to files. -g Outputs mesh to .mesh file for viewing by Medit. -k Outputs mesh to .vtk file for viewing by Paraview. -J No jettison of unused vertices from output .node file. -B Suppresses output of boundary information. -N Suppresses output of .node file. -E Suppresses output of .ele file. -F Suppresses output of .face and .edge file. -I Suppresses mesh iteration numbers. -C Checks the consistency of the final mesh. -Q Quiet: No terminal output except errors. -V Verbose: Detailed information, more terminal output. -h Help: A brief instruction for using TetGen.
See the TETGEN manual for more information.
Examples
clear; close all; clc;
Plot settings
fontSize=15; faceAlpha1=0.3; faceAlpha2=1; cMap=gjet(4); patchColor=cMap(1,:); markerSize=25;
Example 1: Meshing a model with a single region
Creating geometry
[F,V]=stanford_bunny('g'); %Bunny C=ones(size(F,1),1); %Face boundary markers (aka face colors) V_regions=getInnerPoint(F,V); %Define region points V_holes=[]; %Define hole points [regionTetVolumes]=tetVolMeanEst(F,V); %Volume estimate for regular tets stringOpt='-pq1.2AaY'; %Options for tetgen
Mesh using TetGen
%Create tetgen input structure inputStruct.stringOpt=stringOpt; %Tetgen options inputStruct.Faces=F; %Boundary faces inputStruct.Nodes=V; %Nodes of boundary inputStruct.faceBoundaryMarker=C; inputStruct.regionPoints=V_regions; %Interior points for regions inputStruct.holePoints=V_holes; %Interior points for holes inputStruct.regionA=regionTetVolumes; %Desired tetrahedral volume for each region % Mesh model using tetrahedral elements using tetGen [meshOutput]=runTetGen(inputStruct); %Run tetGen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 09-Jul-2021 15:16:54 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 09-Jul-2021 15:16:54 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 09-Jul-2021 15:16:54 --- Running TetGen to mesh input boundary--- 09-Jul-2021 15:16:54 Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh. Delaunizing vertices... Delaunay seconds: 0.012004 Creating surface mesh ... Surface mesh seconds: 0.00362 Recovering boundaries... Boundary recovery seconds: 0.003653 Removing exterior tetrahedra ... Spreading region attributes. Exterior tets removal seconds: 0.002263 Recovering Delaunayness... Delaunay recovery seconds: 0.002076 Refining mesh... 2026 insertions, added 1596 points, 52838 tetrahedra in queue. 674 insertions, added 520 points, 63961 tetrahedra in queue. 899 insertions, added 644 points, 76346 tetrahedra in queue. 1198 insertions, added 716 points, 85093 tetrahedra in queue. 1597 insertions, added 594 points, 66637 tetrahedra in queue. 2129 insertions, added 315 points, 1474 tetrahedra in queue. Refinement seconds: 0.110088 Smoothing vertices... Mesh smoothing seconds: 0.208863 Improving mesh... Mesh improvement seconds: 0.006997 Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.node. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.ele. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.face. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.edge. Output seconds: 0.084647 Total running seconds: 0.434448 Statistics: Input points: 1520 Input facets: 3036 Input segments: 4554 Input holes: 0 Input regions: 1 Mesh points: 6065 Mesh tetrahedra: 32735 Mesh faces: 66988 Mesh faces on exterior boundary: 3036 Mesh faces on input facets: 3036 Mesh edges on input segments: 4554 Steiner points inside domain: 4545 --- Done --- 09-Jul-2021 15:16:54 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 09-Jul-2021 15:16:54 --- Done --- 09-Jul-2021 15:16:54
Access mesh output structure
E=meshOutput.elements; %The elements V=meshOutput.nodes; %The vertices or nodes CE=meshOutput.elementMaterialID; %Element material or region id Fb=meshOutput.facesBoundary; %The boundary faces Cb=meshOutput.boundaryMarker; %The boundary markers
Visualization
hf=cFigure; subplot(1,2,1); hold on; title('Input boundaries','FontSize',fontSize); hp(1)=gpatch(Fb,V,Cb,'k',faceAlpha1); hp(2)=plotV(V_regions,'r.','MarkerSize',markerSize); legend(hp,{'Input mesh','Interior point(s)'},'Location','NorthWestOutside'); axisGeom(gca,fontSize); camlight headlight; colormap(cMap); icolorbar; hs=subplot(1,2,2); hold on; title('Tetrahedral mesh','FontSize',fontSize); % Visualizing using |meshView| optionStruct.hFig=[hf,hs]; meshView(meshOutput,optionStruct); axisGeom(gca,fontSize); gdrawnow;
Example 2: Meshing imported geometry
Import an STL model
defaultFolder = fileparts(fileparts(mfilename('fullpath'))); pathName=fullfile(defaultFolder,'data','STL'); fileName=fullfile(pathName,'femur.stl'); [stlStruct] = import_STL(fileName); F=stlStruct.solidFaces{1}; V=stlStruct.solidVertices{1}; % Merging nodes (nodes are not merged in stl) [F,V]=mergeVertices(F,V); C=ones(size(F,1),1); %Face boundary markers (aka face colors) V_regions=getInnerPoint(F,V); %Define region points V_holes=[]; %Define hole points [regionTetVolumes]=tetVolMeanEst(F,V); %Volume estimate for regular tets stringOpt='-pq1.2AaY'; %Options for tetgen
Mesh using TetGen
%Create tetgen input structure inputStruct.stringOpt=stringOpt; %Tetgen options inputStruct.Faces=F; %Boundary faces inputStruct.Nodes=V; %Nodes of boundary inputStruct.faceBoundaryMarker=C; inputStruct.regionPoints=V_regions; %Interior points for regions inputStruct.holePoints=V_holes; %Interior points for holes inputStruct.regionA=regionTetVolumes; %Desired tetrahedral volume for each region % Mesh model using tetrahedral elements using tetGen [meshOutput]=runTetGen(inputStruct); %Run tetGen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 09-Jul-2021 15:16:58 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 09-Jul-2021 15:16:58 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 09-Jul-2021 15:16:58 --- Running TetGen to mesh input boundary--- 09-Jul-2021 15:16:58 Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh. Delaunizing vertices... Delaunay seconds: 0.014145 Creating surface mesh ... Surface mesh seconds: 0.004451 Recovering boundaries... Boundary recovery seconds: 0.009701 Removing exterior tetrahedra ... Spreading region attributes. Exterior tets removal seconds: 0.004816 Recovering Delaunayness... Delaunay recovery seconds: 0.005499 Refining mesh... 3951 insertions, added 2867 points, 96839 tetrahedra in queue. 1315 insertions, added 812 points, 113061 tetrahedra in queue. 1753 insertions, added 908 points, 127021 tetrahedra in queue. 2337 insertions, added 881 points, 127570 tetrahedra in queue. 3115 insertions, added 603 points, 79813 tetrahedra in queue. 4152 insertions, added 443 points, 4844 tetrahedra in queue. Refinement seconds: 0.242635 Smoothing vertices... Mesh smoothing seconds: 0.399694 Improving mesh... Mesh improvement seconds: 0.013018 Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.node. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.ele. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.face. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.edge. Output seconds: 0.119608 Total running seconds: 0.813822 Statistics: Input points: 2964 Input facets: 5924 Input segments: 8886 Input holes: 0 Input regions: 1 Mesh points: 9835 Mesh tetrahedra: 51987 Mesh faces: 106936 Mesh faces on exterior boundary: 5924 Mesh faces on input facets: 5924 Mesh edges on input segments: 8886 Steiner points inside domain: 6871 --- Done --- 09-Jul-2021 15:17:00 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 09-Jul-2021 15:17:00 --- Done --- 09-Jul-2021 15:17:00
Access mesh output structure
E=meshOutput.elements; %The elements V=meshOutput.nodes; %The vertices or nodes CE=meshOutput.elementMaterialID; %Element material or region id Fb=meshOutput.facesBoundary; %The boundary faces Cb=meshOutput.boundaryMarker; %The boundary markers
Visualization
hf=cFigure; subplot(1,2,1); hold on; title('Input boundaries','FontSize',fontSize); hp(1)=gpatch(Fb,V,Cb,'k',faceAlpha1); hp(2)=plotV(V_regions,'r.','MarkerSize',markerSize); legend(hp,{'Input mesh','Interior point(s)'},'Location','NorthWestOutside'); axisGeom(gca,fontSize); camlight headlight; colormap(cMap); icolorbar; hs=subplot(1,2,2); hold on; title('Tetrahedral mesh','FontSize',fontSize); % Visualizing using |meshView| optionStruct.hFig=[hf,hs]; meshView(meshOutput,optionStruct); axisGeom(gca,fontSize); gdrawnow;
Example 3: Meshing a two-region model
Create example geometry, here a torus containing a smaller torus
% An example surface r=2; %Sphere radius rc=3; %Central radius nr=20; nc=30; ptype='tri'; [F1,V1]=patchTorus(r,nr,rc,nc,ptype); r=1; %Sphere radius rc=3; %Central radius nr=15; nc=25; ptype='tri'; [F2,V2]=patchTorus(r,nr,rc,nc,ptype); [F,V,C]=joinElementSets({F1 F2},{V1 V2}); %Join sets [V_region1]=getInnerPoint(F(C==2,:),V); %First interior point [V_region2]=getInnerPoint({F1,F2},{V1,V2}); %Second interior point V_regions=[V_region1; V_region2]; %Collect region points V_holes=[]; %Define hole points [regionTetVolume1]=tetVolMeanEst(F1,V1); %Volume estimate for regular tets [regionTetVolume2]=tetVolMeanEst(F2,V2); %Volume estimate for regular tets regionTetVolumes=[regionTetVolume1 regionTetVolume2]; stringOpt='-pq1.2AaY'; %Tetgen options
mesh using tet
%Create tetgen input structure inputStruct.stringOpt=stringOpt; %Tetgen options inputStruct.Faces=F; %Boundary faces inputStruct.Nodes=V; %Nodes of boundary inputStruct.faceBoundaryMarker=C; inputStruct.regionPoints=V_regions; %Interior points for regions inputStruct.holePoints=V_holes; %Interior points for holes inputStruct.regionA=regionTetVolumes; %Desired tetrahedral volume for each region % Mesh model using tetrahedral elements using tetGen [meshOutput]=runTetGen(inputStruct); %Run tetGen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 09-Jul-2021 15:17:03 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 09-Jul-2021 15:17:03 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 09-Jul-2021 15:17:03 --- Running TetGen to mesh input boundary--- 09-Jul-2021 15:17:03 Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh. Delaunizing vertices... Delaunay seconds: 0.060803 Creating surface mesh ... Surface mesh seconds: 0.001265 Recovering boundaries... Boundary recovery seconds: 0.002395 Removing exterior tetrahedra ... Spreading region attributes. Exterior tets removal seconds: 0.000669 Recovering Delaunayness... Delaunay recovery seconds: 0.015408 Refining mesh... 1299 insertions, added 620 points, 18852 tetrahedra in queue. 432 insertions, added 85 points, 18840 tetrahedra in queue. 576 insertions, added 76 points, 17042 tetrahedra in queue. 768 insertions, added 93 points, 13066 tetrahedra in queue. 1023 insertions, added 82 points, 4833 tetrahedra in queue. 1364 insertions, added 66 points, 1024 tetrahedra in queue. Refinement seconds: 0.048568 Smoothing vertices... Mesh smoothing seconds: 0.041828 Improving mesh... Mesh improvement seconds: 0.002435 Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.node. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.ele. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.face. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.edge. Output seconds: 0.024134 Total running seconds: 0.197641 Statistics: Input points: 975 Input facets: 1950 Input segments: 2925 Input holes: 0 Input regions: 2 Mesh points: 2049 Mesh tetrahedra: 10808 Mesh faces: 22216 Mesh faces on exterior boundary: 1200 Mesh faces on input facets: 1950 Mesh edges on input segments: 2925 Steiner points inside domain: 1074 --- Done --- 09-Jul-2021 15:17:04 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 09-Jul-2021 15:17:04 --- Done --- 09-Jul-2021 15:17:04
Access mesh output structure
E=meshOutput.elements; %The elements V=meshOutput.nodes; %The vertices or nodes CE=meshOutput.elementMaterialID; %Element material or region id Fb=meshOutput.facesBoundary; %The boundary faces Cb=meshOutput.boundaryMarker; %The boundary markers
Visualization
hf=cFigure; subplot(1,2,1); hold on; title('Input boundaries','FontSize',fontSize); hp(1)=gpatch(Fb,V,Cb,'k',faceAlpha1); hp(2)=plotV(V_regions,'r.','MarkerSize',markerSize); legend(hp,{'Input mesh','Interior point(s)'},'Location','NorthWestOutside'); axisGeom(gca,fontSize); camlight headlight; colormap(cMap); icolorbar; hs=subplot(1,2,2); hold on; title('Tetrahedral mesh','FontSize',fontSize); % Visualizing using |meshView| optionStruct.hFig=[hf,hs]; meshView(meshOutput,optionStruct); axisGeom(gca,fontSize); gdrawnow;
Example 4: Meshing a multi-region model
Creating boundary surfaces
%Outer bunny [F1,V1]=stanford_bunny('g'); %Bunny V1_mean=mean(V1,1); V1=V1-V1_mean(ones(size(V1,1),1),:); %Inner bunny V2=V1/4; V2(:,3)=V2(:,3)-35; V2(:,2)=V2(:,2)-15; V2(:,1)=V2(:,1)+10; V3=V1/4; V3(:,3)=V3(:,3)-10; V3(:,2)=V3(:,2)+10; V3(:,1)=V3(:,1)+40; %Joining surface sets [F,V,C]=joinElementSets({F1,F1,F1},{V1,V2,V3});
Find interior points
[V_region1]=getInnerPoint({F1,F1,F1},{V1,V2,V3});
[V_region2]=getInnerPoint(F1,V2);
[V_region3]=getInnerPoint(F1,V3);
V_regions=[V_region1; V_region2; V_region3];
% Volume parameters
[vol1]=tetVolMeanEst(F1,V1);
[vol2]=tetVolMeanEst(F1,V2);
[vol3]=tetVolMeanEst(F1,V3);
regionTetVolumes=[vol1 vol2 vol3]; %Element volume settings
stringOpt='-pq1.2AaY'; %Tetgen options
mesh using tet
%Create tetgen input structure inputStruct.stringOpt=stringOpt; %Tetgen options inputStruct.Faces=F; %Boundary faces inputStruct.Nodes=V; %Nodes of boundary inputStruct.faceBoundaryMarker=C; inputStruct.regionPoints=V_regions; %Interior points for regions inputStruct.holePoints=V_holes; %Interior points for holes inputStruct.regionA=regionTetVolumes; %Desired tetrahedral volume for each region % Mesh model using tetrahedral elements using tetGen [meshOutput]=runTetGen(inputStruct); %Run tetGen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 09-Jul-2021 15:17:09 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 09-Jul-2021 15:17:09 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 09-Jul-2021 15:17:09 --- Running TetGen to mesh input boundary--- 09-Jul-2021 15:17:09 Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh. Delaunizing vertices... Delaunay seconds: 0.025095 Creating surface mesh ... Surface mesh seconds: 0.008084 Recovering boundaries... Boundary recovery seconds: 0.016861 Removing exterior tetrahedra ... Spreading region attributes. Exterior tets removal seconds: 0.00463 Recovering Delaunayness... Delaunay recovery seconds: 0.014409 Refining mesh... 6078 insertions, added 4879 points, 201347 tetrahedra in queue. 2023 insertions, added 1455 points, 233749 tetrahedra in queue. 2697 insertions, added 1889 points, 273453 tetrahedra in queue. 3595 insertions, added 2282 points, 315106 tetrahedra in queue. 4792 insertions, added 2396 points, 336371 tetrahedra in queue. 6388 insertions, added 1906 points, 268161 tetrahedra in queue. 8515 insertions, added 1250 points, 1796 tetrahedra in queue. Refinement seconds: 0.589298 Smoothing vertices... Mesh smoothing seconds: 1.2179 Improving mesh... Mesh improvement seconds: 0.029469 Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.node. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.ele. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.face. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.edge. Output seconds: 0.300889 Total running seconds: 2.20712 Statistics: Input points: 4560 Input facets: 9108 Input segments: 13662 Input holes: 0 Input regions: 3 Mesh points: 21224 Mesh tetrahedra: 126673 Mesh faces: 254864 Mesh faces on exterior boundary: 3036 Mesh faces on input facets: 9108 Mesh edges on input segments: 13662 Steiner points inside domain: 16664 --- Done --- 09-Jul-2021 15:17:11 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 09-Jul-2021 15:17:11 --- Done --- 09-Jul-2021 15:17:11
Access mesh output structure
E=meshOutput.elements; %The elements V=meshOutput.nodes; %The vertices or nodes CE=meshOutput.elementMaterialID; %Element material or region id Fb=meshOutput.facesBoundary; %The boundary faces Cb=meshOutput.boundaryMarker; %The boundary markers
Visualization
hf=cFigure; subplot(1,2,1); hold on; title('Input boundaries','FontSize',fontSize); hp(1)=gpatch(Fb,V,Cb,'k',faceAlpha1); hp(2)=plotV(V_regions,'r.','MarkerSize',markerSize); legend(hp,{'Input mesh','Interior point(s)'},'Location','NorthWestOutside'); axisGeom(gca,fontSize); camlight headlight; colormap(cMap); icolorbar; hs=subplot(1,2,2); hold on; title('Tetrahedral mesh','FontSize',fontSize); % Visualizing using |meshView| optionStruct.hFig=[hf,hs]; meshView(meshOutput,optionStruct); axisGeom(gca,fontSize); gdrawnow;
Example 5: Meshing regions with holes
Simulating a multiregion mesh containing a void
[F1,V1]=parasaurolophus; %A dino %An internal region [F2,V2,~]=geoSphere(3,0.4); V2(:,1)=2*V2(:,1)+0.6; V2(:,3)=V2(:,3)+0.25; %An internal hole [F3,V3,~]=geoSphere(2,0.3); V3(:,1)=V3(:,1)+0.6; V3(:,3)=V3(:,3)+0.25; %Joining surface sets [F,V,C]=joinElementSets({F1,F2,F3},{V1,V2,V3});
Find interior points
[V_region1]=getInnerPoint({F1,F2,F3},{V1,V2,V3});
[V_region2]=getInnerPoint(F2,V2);
[V_holes]=getInnerPoint(F3,V3);
V_regions=[V_region1; V_region2];
% Volume parameters
[vol1]=tetVolMeanEst(F1,V1);
[vol2]=tetVolMeanEst(F2,V2);
regionTetVolumes=[vol1 vol2]; %Element volume settings
stringOpt='-pq1.2AaY'; %Tetgen options
mesh using tet
%Create tetgen input structure inputStruct.stringOpt=stringOpt; %Tetgen options inputStruct.Faces=F; %Boundary faces inputStruct.Nodes=V; %Nodes of boundary inputStruct.faceBoundaryMarker=C; inputStruct.regionPoints=V_regions; %Interior points for regions inputStruct.holePoints=V_holes; %Interior points for holes inputStruct.regionA=regionTetVolumes; %Desired tetrahedral volume for each region % Mesh model using tetrahedral elements using tetGen [meshOutput]=runTetGen(inputStruct); %Run tetGen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 09-Jul-2021 15:17:16 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 09-Jul-2021 15:17:16 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 09-Jul-2021 15:17:16 --- Running TetGen to mesh input boundary--- 09-Jul-2021 15:17:16 Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh. Delaunizing vertices... Delaunay seconds: 0.036408 Creating surface mesh ... Surface mesh seconds: 0.003949 Recovering boundaries... Boundary recovery seconds: 0.008611 Removing exterior tetrahedra ... Spreading region attributes. Exterior tets removal seconds: 0.003755 Recovering Delaunayness... Delaunay recovery seconds: 0.00779 Refining mesh... 3452 insertions, added 2075 points, 68090 tetrahedra in queue. 1149 insertions, added 447 points, 75231 tetrahedra in queue. 1532 insertions, added 441 points, 78109 tetrahedra in queue. 2042 insertions, added 384 points, 71670 tetrahedra in queue. 2722 insertions, added 263 points, 45257 tetrahedra in queue. 3628 insertions, added 247 points, 2820 tetrahedra in queue. 4836 insertions, added 313 points, 598 tetrahedra in queue. Refinement seconds: 0.184304 Smoothing vertices... Mesh smoothing seconds: 0.196975 Improving mesh... Mesh improvement seconds: 0.008126 Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.node. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.ele. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.face. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.edge. Output seconds: 0.077197 Total running seconds: 0.527413 Statistics: Input points: 2590 Input facets: 5168 Input segments: 7752 Input holes: 1 Input regions: 2 Mesh points: 6887 Mesh tetrahedra: 36644 Mesh faces: 75232 Mesh faces on exterior boundary: 3888 Mesh faces on input facets: 5168 Mesh edges on input segments: 7752 Steiner points inside domain: 4297 --- Done --- 09-Jul-2021 15:17:17 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 09-Jul-2021 15:17:17 --- Done --- 09-Jul-2021 15:17:17
Access mesh output structure
E=meshOutput.elements; %The elements V=meshOutput.nodes; %The vertices or nodes CE=meshOutput.elementMaterialID; %Element material or region id Fb=meshOutput.facesBoundary; %The boundary faces Cb=meshOutput.boundaryMarker; %The boundary markers
Visualization
hf=cFigure; subplot(1,2,1); hold on; title('Input boundaries','FontSize',fontSize); hp(1)=gpatch(Fb,V,Cb,'k',faceAlpha1); hp(2)=plotV(V_regions,'r.','MarkerSize',markerSize); legend(hp,{'Input mesh','Interior point(s)'},'Location','NorthWestOutside'); axisGeom(gca,fontSize); camlight headlight; colormap(cMap); icolorbar; hs=subplot(1,2,2); hold on; title('Tetrahedral mesh','FontSize',fontSize); % Visualizing using |meshView| optionStruct.hFig=[hf,hs]; meshView(meshOutput,optionStruct); axisGeom(gca,fontSize); gdrawnow;
Example 6: Meshing from a quadrilateral input surface
Build a quadrilateral surface
boxDim =[12 2 3]; boxEl =[12 2 3]; [F,V,C]=quadBox(boxDim,boxEl); regionTetVolumes=tetVolMeanEst(F,V); V_regions=mean(V,1); stringOpt='-pq1.2AaY'; %Tetgen options V_holes=[];
Mesh using TetGen
%Create tetgen input structure inputStruct.stringOpt=stringOpt; %Tetgen options inputStruct.Faces=F; %Boundary faces inputStruct.Nodes=V; %Nodes of boundary inputStruct.faceBoundaryMarker=C; inputStruct.regionPoints=V_regions; %Interior points for regions inputStruct.holePoints=V_holes; %Interior points for holes inputStruct.regionA=regionTetVolumes; %Desired tetrahedral volume for each region % Mesh model using tetrahedral elements using tetGen [meshOutput]=runTetGen(inputStruct); %Run tetGen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 09-Jul-2021 15:17:20 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 09-Jul-2021 15:17:20 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 09-Jul-2021 15:17:20 --- Running TetGen to mesh input boundary--- 09-Jul-2021 15:17:20 Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh. Delaunizing vertices... Delaunay seconds: 0.002721 Creating surface mesh ... Surface mesh seconds: 0.000593 Recovering boundaries... Boundary recovery seconds: 0.002528 Removing exterior tetrahedra ... Spreading region attributes. Exterior tets removal seconds: 9.6e-05 Recovering Delaunayness... Delaunay recovery seconds: 0.002407 Refining mesh... 178 insertions, added 49 points, 1216 tetrahedra in queue. 59 insertions, added 7 points, 999 tetrahedra in queue. 78 insertions, added 2 points, 424 tetrahedra in queue. 104 insertions, added 8 points, 168 tetrahedra in queue. 139 insertions, added 9 points, 84 tetrahedra in queue. Refinement seconds: 0.005852 Smoothing vertices... Mesh smoothing seconds: 0.007428 Improving mesh... Mesh improvement seconds: 0.0002 Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.node. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.ele. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.face. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.edge. Output seconds: 0.001947 Total running seconds: 0.023854 Statistics: Input points: 134 Input facets: 132 Input segments: 264 Input holes: 0 Input regions: 1 Mesh points: 217 Mesh tetrahedra: 836 Mesh faces: 1804 Mesh faces on exterior boundary: 264 Mesh faces on input facets: 264 Mesh edges on input segments: 264 Steiner points inside domain: 83 --- Done --- 09-Jul-2021 15:17:20 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 09-Jul-2021 15:17:20 --- Done --- 09-Jul-2021 15:17:20
Access mesh output structure
E=meshOutput.elements; %The elements V=meshOutput.nodes; %The vertices or nodes CE=meshOutput.elementMaterialID; %Element material or region id Fb=meshOutput.facesBoundary; %The boundary faces Cb=meshOutput.boundaryMarker; %The boundary markers
Visualization
hf=cFigure; subplot(1,2,1); hold on; title('Input boundaries','FontSize',fontSize); hp(1)=gpatch(F,V,C,'k',faceAlpha1); hp(2)=plotV(V_regions,'r.','MarkerSize',markerSize); legend(hp,{'Input mesh','Interior point(s)'},'Location','NorthWestOutside'); axisGeom(gca,fontSize); camlight headlight; colormap(cMap); icolorbar; hs=subplot(1,2,2); hold on; title('Tetrahedral mesh','FontSize',fontSize); % Visualizing using |meshView| optionStruct.hFig=[hf,hs]; meshView(meshOutput,optionStruct); axisGeom(gca,fontSize); gdrawnow;
Example 7: Specifying a sizing function to control local mesh density
Build example geometry
boxDim =[12 2 3]; boxEl =[12 2 3]; [F,V,C]=quadBox(boxDim,boxEl); V_input=V;
Defining a size function on the boundary nodes
%Get edge lengths and base minimum size on input edge lengths [edgeLengths]=patchEdgeLengths(F,V); minEdgeSize=mean(edgeLengths)/5; %The smallest element size n=5; %The largest element edge length is n times minEdgeSize edgeSizeField=V(:,1); edgeSizeField=edgeSizeField-min(edgeSizeField(:)); edgeSizeField=edgeSizeField./max(edgeSizeField(:)); edgeSizeField=(edgeSizeField*(n-1))+1; %Range from 0-n depending on V(:,1) i.e. X-dir edgeSizeField=(edgeSizeField*minEdgeSize); regionTetVolumes=tetVolMeanEst(F,V); V_regions=mean(V,1); stringOpt='-pq1.2Aa'; %Tetgen options V_holes=[];
Mesh using TetGen
%Create tetgen input structure inputStruct.stringOpt=stringOpt; %Tetgen options inputStruct.Faces=F; %Boundary faces inputStruct.Nodes=V; %Nodes of boundary inputStruct.faceBoundaryMarker=C; inputStruct.regionPoints=V_regions; %Interior points for regions inputStruct.holePoints=V_holes; %Interior points for holes inputStruct.regionA=regionTetVolumes; %Desired tetrahedral volume for each region inputStruct.sizeData=edgeSizeField; %The size data % Mesh model using tetrahedral elements using tetGen [meshOutput]=runTetGen(inputStruct); %Run tetGen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 09-Jul-2021 15:17:23 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 09-Jul-2021 15:17:23 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 09-Jul-2021 15:17:23 --- Writing MTR file --- 09-Jul-2021 15:17:23 --- Running TetGen to mesh initial Delaunay tesselation using sizing function--- 09-Jul-2021 15:17:23 Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh. Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.mtr. Cannot access file /mnt/data/MATLAB/GIBBON/data/temp/temp.b.node. Delaunizing vertices... Delaunay seconds: 0.003064 Creating surface mesh ... Surface mesh seconds: 0.000522 Recovering boundaries... Boundary recovery seconds: 0.002096 Removing exterior tetrahedra ... Spreading region attributes. Exterior tets removal seconds: 6.5e-05 Mesh coarsening ... Mesh coarsening seconds: 3e-06 Recovering Delaunayness... Delaunay recovery seconds: 0.002292 Refining mesh... 178 insertions, added 111 points, 2184 tetrahedra in queue. 59 insertions, added 38 points, 2770 tetrahedra in queue. 78 insertions, added 49 points, 3452 tetrahedra in queue. 104 insertions, added 73 points, 4701 tetrahedra in queue. 139 insertions, added 92 points, 6154 tetrahedra in queue. 185 insertions, added 124 points, 8181 tetrahedra in queue. 247 insertions, added 178 points, 11206 tetrahedra in queue. 329 insertions, added 228 points, 14867 tetrahedra in queue. 439 insertions, added 294 points, 16828 tetrahedra in queue. Refinement seconds: 0.026821 Smoothing vertices... Mesh smoothing seconds: 0.040161 Improving mesh... Mesh improvement seconds: 0.001258 Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.node. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.ele. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.face. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.edge. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.mtr. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.p2t. Output seconds: 0.015564 Total running seconds: 0.091924 Statistics: Input points: 134 Input facets: 132 Input segments: 68 Input holes: 0 Input regions: 1 Mesh points: 1406 Mesh tetrahedra: 6194 Mesh faces: 13133 Mesh faces on exterior boundary: 1490 Mesh faces on input facets: 1490 Mesh edges on input segments: 131 Steiner points on input facets: 550 Steiner points on input segments: 63 Steiner points inside domain: 659 --- Done --- 09-Jul-2021 15:17:23 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 09-Jul-2021 15:17:23 --- Done --- 09-Jul-2021 15:17:23
Access mesh output structure
E=meshOutput.elements; %The elements V=meshOutput.nodes; %The vertices or nodes CE=meshOutput.elementMaterialID; %Element material or region id Fb=meshOutput.facesBoundary; %The boundary faces Cb=meshOutput.boundaryMarker; %The boundary markers
Visualization
hf=cFigure; subplot(1,2,1); hold on; title('Input boundaries','FontSize',fontSize); hp(1)=gpatch(F,V,'kw','none',faceAlpha1); hp(2)=plotV(V_regions,'r.','MarkerSize',markerSize); hp(3)=scatterV(V_input,75,edgeSizeField,'fill'); legend(hp,{'Input mesh','Interior point(s)','Sizing function points'},'Location','NorthWestOutside'); axisGeom(gca,fontSize); camlight headlight; colormap(cMap); colorbar; hs=subplot(1,2,2); hold on; title('Tetrahedral mesh','FontSize',fontSize); % Visualizing using |meshView| optionStruct.hFig=[hf,hs]; meshView(meshOutput,optionStruct); axisGeom(gca,fontSize); gdrawnow; clear hp;
Example 8: Meshing of topology with holes and complex regions
Simulating nested spheres with a hollow core and "tunnel" to outside
w=0.25; r=0.1; [Fs1,Vs1]=geoSphere(4,1); [Fs2,Vs2]=geoSphere(4,1-w); [Fs3,Vs3]=geoSphere(4,1-2*w); R=sqrt(sum(Vs1(:,[1 2]).^2,2)); logicCropVertices=R<=(r+mean(patchEdgeLengths(Fs1,Vs1))) & Vs1(:,3)>0; logicCropFaces=any(logicCropVertices(Fs1),2); logicCropFaces=triSurfLogicSharpFix(Fs1,logicCropFaces); Fs1=Fs1(~logicCropFaces,:); Fs2=Fs2(~logicCropFaces,:); Fs3=Fs3(~logicCropFaces,:); Eb=patchBoundary(Fs1,Vs1); indB=edgeListToCurve(Eb); indB=indB(1:end-1); cPar.closeLoopOpt=1; cPar.patchType='tri_slash'; [Fs4,Vs4]=polyLoftLinear(Vs3(indB,:),Vs2(indB,:),cPar); [Fs5,Vs5]=polyLoftLinear(Vs2(indB,:),Vs1(indB,:),cPar); [F,V,C]=joinElementSets({Fs1,Fs2,Fs3,Fs4,Fs5},{Vs1,Vs2,Vs3,Vs4,Vs5}); [F,V]=mergeVertices(F,V); [F,V]=patchCleanUnused(F,V); logicRegion1=ismember(C,[1 2 max(C(:))]); logicRegion2=ismember(C,[2 3 4]); V_inner1=getInnerPoint(F(logicRegion1,:),V); V_inner2=getInnerPoint(F(logicRegion2,:),V); V_regions=[V_inner1; V_inner2]; regionTetVolumes=tetVolMeanEst(F,V); stringOpt='-pq1.2AaY'; %Tetgen options V_holes=[];
Mesh using TetGen
%Create tetgen input structure inputStruct.stringOpt=stringOpt; %Tetgen options inputStruct.Faces=F; %Boundary faces inputStruct.Nodes=V; %Nodes of boundary inputStruct.faceBoundaryMarker=C; inputStruct.regionPoints=V_regions; %Interior points for regions inputStruct.holePoints=V_holes; %Interior points for holes inputStruct.regionA=regionTetVolumes*ones(size(V_regions,1),1); %Desired tetrahedral volume for each region % Mesh model using tetrahedral elements using tetGen [meshOutput]=runTetGen(inputStruct); %Run tetGen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 09-Jul-2021 15:17:27 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 09-Jul-2021 15:17:27 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 09-Jul-2021 15:17:27 --- Writing MTR file --- 09-Jul-2021 15:17:27 --- Running TetGen to mesh initial Delaunay tesselation using sizing function--- 09-Jul-2021 15:17:27 Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh. Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.mtr. !! Point numbers are not equal. Ignored. Cannot access file /mnt/data/MATLAB/GIBBON/data/temp/temp.b.node. Delaunizing vertices... Delaunay seconds: 0.636653 Creating surface mesh ... Surface mesh seconds: 0.016217 Recovering boundaries... Boundary recovery seconds: 0.042972 Removing exterior tetrahedra ... Spreading region attributes. Exterior tets removal seconds: 0.009288 Mesh coarsening ... Mesh coarsening seconds: 0.00011 Recovering Delaunayness... Delaunay recovery seconds: 0.215868 Refining mesh... 10361 insertions, added 9301 points, 334201 tetrahedra in queue. 3450 insertions, added 2890 points, 399552 tetrahedra in queue. 4599 insertions, added 3698 points, 479251 tetrahedra in queue. 6130 insertions, added 4662 points, 574559 tetrahedra in queue. 8171 insertions, added 5746 points, 677577 tetrahedra in queue. 10892 insertions, added 5892 points, 715672 tetrahedra in queue. 14519 insertions, added 4593 points, 345657 tetrahedra in queue. 19354 insertions, added 2235 points, 21330 tetrahedra in queue. Refinement seconds: 1.421 Smoothing vertices... Mesh smoothing seconds: 3.3753 Improving mesh... Mesh improvement seconds: 0.081561 Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.node. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.ele. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.face. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.edge. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.mtr. Writing /mnt/data/MATLAB/GIBBON/data/temp/temp.1.p2t. Output seconds: 0.643161 Total running seconds: 6.4429 Statistics: Input points: 7773 Input facets: 15558 Input segments: 23328 Input holes: 0 Input regions: 2 Mesh points: 47268 Mesh tetrahedra: 275809 Mesh faces: 556864 Mesh faces on exterior boundary: 10492 Mesh faces on input facets: 15558 Mesh edges on input segments: 23328 Steiner points inside domain: 39495 --- Done --- 09-Jul-2021 15:17:34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 09-Jul-2021 15:17:34 --- Done --- 09-Jul-2021 15:17:34
Access mesh output structure
E=meshOutput.elements; %The elements V=meshOutput.nodes; %The vertices or nodes CE=meshOutput.elementMaterialID; %Element material or region id Fb=meshOutput.facesBoundary; %The boundary faces Cb=meshOutput.boundaryMarker; %The boundary markers
Visualization
hf=cFigure; subplot(1,2,1); hold on; title('Input boundaries','FontSize',fontSize); hp(1)=gpatch(F,V,'kw','none',faceAlpha1); hp(2)=plotV(V_regions,'r.','MarkerSize',markerSize); legend(hp,{'Input mesh','Interior point(s)'},'Location','NorthWestOutside'); axisGeom(gca,fontSize); camlight headlight; colormap(cMap); colorbar; hs=subplot(1,2,2); hold on; title('Tetrahedral mesh','FontSize',fontSize); % Visualizing using |meshView| optionStruct.hFig=[hf,hs]; meshView(meshOutput,optionStruct); axisGeom(gca,fontSize); gdrawnow; clear hp;
Example 9: Meshing 10-node (i.e. quadratic) tetrahedral elements
% Building spherical surface models [F,V,~]=geoSphere(2,1); C=ones(size(F,1),1); V_regions=[0 0 0]; V_holes=[]; regionTetVolumes=tetVolMeanEst(F,V); stringOpt='-pq1.2AaYQ';
Mesh using TetGen
%Create tetgen input structure inputStruct.stringOpt=stringOpt; %Tetgen options inputStruct.Faces=F; %Boundary faces inputStruct.Nodes=V; %Nodes of boundary inputStruct.faceBoundaryMarker=C; inputStruct.regionPoints=V_regions; %Interior points for regions inputStruct.holePoints=V_holes; %Interior points for holes inputStruct.regionA=regionTetVolumes; %Desired tetrahedral volume for each region inputStruct.tetType='tet10'; %Set desired element type % Mesh model using tetrahedral elements using tetGen [meshOutput]=runTetGen(inputStruct); %Run tetGen
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- TETGEN Tetrahedral meshing --- 09-Jul-2021 15:17:41 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Writing SMESH file --- 09-Jul-2021 15:17:41 ----> Adding node field ----> Adding facet field ----> Adding holes specification ----> Adding region specification --- Done --- 09-Jul-2021 15:17:41 --- Writing MTR file --- 09-Jul-2021 15:17:41 --- Running TetGen to mesh initial Delaunay tesselation using sizing function--- 09-Jul-2021 15:17:41 Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.smesh. Opening /mnt/data/MATLAB/GIBBON/data/temp/temp.mtr. !! Point numbers are not equal. Ignored. Cannot access file /mnt/data/MATLAB/GIBBON/data/temp/temp.b.node. --- Done --- 09-Jul-2021 15:17:41 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Importing TetGen files --- 09-Jul-2021 15:17:41 --- Done --- 09-Jul-2021 15:17:41
Access mesh output structure
E=meshOutput.elements; %The elements V=meshOutput.nodes; %The vertices or nodes CE=meshOutput.elementMaterialID; %Element material or region id Fb=meshOutput.facesBoundary; %The boundary faces Cb=meshOutput.boundaryMarker; %The boundary markers
Visualization
%Selecting half of the model to see interior Y=V(:,2); YE=mean(Y(E),2); logicCutView=YE>mean(Y); [Fs,Cs]=element2patch(E(logicCutView,:),CE(logicCutView),'tet10'); hf=cFigure; subplot(1,2,1); hold on; title('Input boundaries','FontSize',fontSize); hp(1)=gpatch(F,V,C,'k',faceAlpha1); hp(2)=plotV(V_regions,'r.','MarkerSize',markerSize); legend(hp,{'Input mesh','Interior point(s)'},'Location','NorthWestOutside'); axisGeom(gca,fontSize); camlight headlight; colormap(cMap); icolorbar; hs=subplot(1,2,2); hold on; title('Tetrahedral mesh','FontSize',fontSize); title('Cut view of tetrahedral mesh model','FontSize',fontSize); gpatch(Fb,V,0.5*ones(1,3),'none',faceAlpha1); gpatch(Fs,V,Cs,'k',faceAlpha2); % patchNormPlot(Fs,V); plotV(V(unique(Fs(:)),:),'k.','MarkerSize',markerSize); camlight headlight; axisGeom(gca,fontSize); colormap(cMap); gdrawnow;
GIBBON www.gibboncode.org
Kevin Mattheus Moerman, [email protected]
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License: https://github.com/gibbonCode/GIBBON/blob/master/LICENSE
GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.
Copyright (C) 2006-2021 Kevin Mattheus Moerman and the GIBBON contributors
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
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