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<p class="MsoNormal"><span lang="NL" style="font-size:11.0pt">Dear all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="NL" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">With the help of Christophe Geuzaine and the gmsh FAQ, I was able to create a tetrahedral mesh from a mask file (3D boolean matrix with 0=outside, 1=inside) by combining matlab and gmesh.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">For future reference, I summarize my workflow. Perhaps it can be useful to others. Most likely, it can be further optimized.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Best regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Hans<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Step-by-step guide to convert a mask in matlab to a tetrahedral mesh in matlab, using gmesh:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">1) Create a surface mesh in matlab and save it as a stl file<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">-- <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">mask = smooth3(mask, 'gaussian');<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">[f,v] = isosurface(mask, 0.2);<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">stlwrite2('heart_sm2.stl', f,v);<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">--<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">stlwrite2 can be found on matlab central.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Smoothing and putting a lower threshold helps to avoid some mesh errors in highly curved regions later on.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">2) Remesh the surface mesh using gmsh:
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">(After support from gmsh developer Christophe Geuzaine, thank you!)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">On the command line / in terminal do:
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">$ gmsh heart_sm2.stl -reparam 180<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">This means reparameterising the mesh, dividing it in regions when the angle between adjacent faces is smaller/larger than 180 degrees(?). This seems to be mostly useful for cubes etc. since the
faces are then stored separately. <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">It makes filename.msh.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">If you want to see it, open the GUI and in the top bar: file > open > ... select this .msh file<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Then in command window:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">$ gmsh heart_sm2.msh -clcurv 2 -2 -o heart_sm2_2.msh<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">This remeshes the surface according to curvature (-clcurv). The higher the number that follows, the more elements are created. I put it as low as possible without getting errors. (-clcurv 1 did
not work). <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">-2 argument means meshing in 2D, so it creates edges and faces. We cannot do a 3D mesh here, another step is needed.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">-o heart_sm2_2.msh : output, otherwise the previous msh file is overwritten.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">3) Make gmsh recognize the interior region as the part to be meshed with tetrahedra<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">(see gmsh FAQs)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">open the lastly created heart_sm2_2.msh in the GUI and do file > export as .stl file.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">then, create a gmsh script to add the volume. E.g. make a file "heart_sm2_2.geo" containing:
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Merge "heart_sm2_2.stl";<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Surface Loop(1) = {1};<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Volume(1) = {1};<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Then open this script in gmesh GUI: file > open > heart_sm2.2.geo.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Now gmsh recognizes that there is an interior.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">4) Create and export the tetrahedral mesh<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">In the GUI, with the geo-file opened (and the 2D mesh visible): in the left navigation bar, click Modules > Mesh > 3D and the 3D mesh generation starts.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Thereafter you may want to click 'optimize 3D' just beneath.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">Finally, in order to work with it in matlab: file > export > as matlab file (or use extension .m), e.g. heart_sm2_2.m<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">In matlab, run the file as a script<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">heart_sm2_2;<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt">which creates a structure called 'msh' listing the vertices, edges, faces and tetrahedra.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span style="color:black">From: </span></b><span style="color:black">Hans Dierckx <h.dierckx@kuleuven.be><br>
<b>Date: </b>Wednesday, 18 March 2020 at 08:56<br>
<b>To: </b>"gmsh@onelab.info" <gmsh@onelab.info><br>
<b>Subject: </b>surface mesh coarsening</span><span style="color:black;mso-fareast-language:EN-GB"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;color:black;mso-fareast-language:EN-GB">Dear all, </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;color:black;mso-fareast-language:EN-GB"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;color:black;mso-fareast-language:EN-GB">Can someone explain me how to use gmesh to coarsen a closed surface mesh? I attach a simple geometry as test data.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;color:black;mso-fareast-language:EN-GB">I tried in vain in the GUI to put ‘options > mesh > element size’ to a value bigger than one.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;color:black;mso-fareast-language:EN-GB">The data I want to apply it to is a heart geometry which has originally 10^6 vertices and 5 10^5 faces, which should be reduced to approx. 500 faces.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;color:black;mso-fareast-language:EN-GB"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;color:black;mso-fareast-language:EN-GB">Thank you very much for your assistance.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;color:black;mso-fareast-language:EN-GB"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;color:black;mso-fareast-language:EN-GB">Hans Dierckx</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;color:black;mso-fareast-language:EN-GB">Leuven University</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt;mso-fareast-language:EN-GB"> </span><o:p></o:p></p>
<p class="MsoNormal"> <o:p></o:p></p>
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