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POGenerating quadrilateral mesh from Mathematica surface mesh
 

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  1. POGenerating quadrilateral mesh from Mathematica surface mesh
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    <p>I am trying to make a quadrilateral mesh from a surface mesh (which is mostly triangular) generated by Mathematica. I am not looking for high quality mesher but a simple work around algorithm. I use <a href="http://geuz.org/gmsh/" rel="noreferrer">GMSH</a> for doing it externally. We can make use of Mathematic's CAD import capabilities to generate 3D geometries that are understood by the Mathematica kernel.</p> <p>We can see the imported <code>Geometry3D</code> objects and the plots of number of sides in each polygons they consist of. It become visible that the polygons that form the mesh are not always triangles.</p> <pre><code>Name3D=RandomChoice[ExampleData["Geometry3D"][[All,2]],6]; AllPic= Table[ Vertex=ExampleData[{"Geometry3D",Name3D[[i]]},"VertexData"]; Polygons=ExampleData[{"Geometry3D",Name3D[[i]]},"PolygonData"]; GraphicsGrid[ {{ListPlot[#,Frame-&gt; True,PlotLabel-&gt;Name3D[[i]] ]&amp;@(Length[#]&amp;/@Polygons), Graphics3D[GraphicsComplex[Vertex,Polygon[Polygons]],Boxed-&gt; False]}} ,ImageSize-&gt; 300,Spacings-&gt; {0,0}], {i,1,Length@Name3D}]; GraphicsGrid[Partition[AllPic,2],Spacings-&gt; {0,0}] </code></pre> <p><img src="https://i.stack.imgur.com/EFMYR.png" alt="enter image description here"></p> <p>Now what I am looking for is an algorithm to form a quadrilateral mesh from that polygon information available to MMA. Any easy solution is very much welcome. By easy solution I mean which is not going to work in a very general setting (where mesh constitutes of polygons with sides more than 5 or 6) and which might be quite inefficient compared to commercial software. But one can see that there are not many quadrilateral surface mesh generator available other than few expensive commercial one.</p> <p>BR</p>
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      1. POGenerating quadrilateral mesh from Mathematica surface mesh
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    1. COAre you looking for a full mesh (hexahedra/bricks) or a surface mesh (quads)? How do you want to deal with triangles that look like this: Graphics3D[ GraphicsComplex[{{0, 0, 0.5}, {1, 0, 0}, {1, 1, 0}, {0, 1, 0}}, Polygon[{{1, 2, 3}, {3, 4, 1}}]]] - propably you'd need a normal test. And what to do with intersecting triangles like shown at the bottom of http://reference.wolfram.com/mathematica/TetGenLink/tutorial/UsingTetGenLink.html. The "SpaceShuttle" is watertight.. Could you upload a picture of a result done with GMSH of, say, the cow?
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    2. COIf you want the quad surface the qmorph algorithm could be a basis: pages.cs.wisc.edu/~csverma/CS899_09/qmorph.pdf
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    3. COAre you considering solutions like removing the shared side from a two-triangle set?
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      1. USDr. belisarius
 

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