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[Thiago Milanetto Schlittler <>]

Hello!

   If you only want the intersection volume, and if both your meshes are convex, maybe converting each mesh to a convex hull, then to a polyhedron, and then to a Nef polyhedron might be faster, or at least simpler to code. I never tried to do so, though, and I have no idea how the Nef polyhedron cost scales with its complexity.

   In my case, I want to mesh each intersection between two cells, and so I have no other option than finding and constructing all intersections. In my code, the conversion to Nef polyhedra, intersection construction and meshing of ~650,000 intersections takes around ~4 minutes of CPU time, while the search takes ~30 seconds. The meshes, in this case, have each 600 elements / 200 nodes and 100,000 elements / 24,000 nodes.

   I'm not using CGAL's data structures, but it has a package to find the intersections between two sets of bounding boxes (see here). It could be useful in this situation.

Regards,

Thiago

2016-11-27 1:02 GMT+01:00 pbarletta <>:

Hi, thanks for the reply. Yes, its 3D, I forgot to mention that.

      I don't have the list of intersecting cells, I'd have to iterate over
every vertex of every cell of the *B* triangulation to find out if its
outside the  *A* triangulation, inside of it, or intersecting it; in which
case I would then convert to Nef Polyhedron.
      I'm dealing with triangulations of (2,000 - 20,000) points. How much
time did it take you to perform these volume calculations from the
intersections?
     Do you think it would be (easier/faster/possible) to just convert both
triangulations to Nef Polyhedrons and then calculate their intersection
spaces, to then calculate its volume?

Regards.




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