title: Generating quadrilateral mesh from Mathematica surface mesh
body: <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>