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Matt
Posts:
23
Registered:
8/13/09


Intersection of Sphere and Polyhedron
Posted:
May 9, 2013 11:15 AM


Hi, All 
Let's say I have a collection of spheres in some bounded 3D space. Let's also say I have some triangulation of that 3D space. I'd like to know which polyhedra contain each sphere and how much of each sphere is in each polyhedron.
I'm looking at the ND Voronoi and NS Delaunay functions for generating my mesh and inpolyhedron (http://www.mathworks.com/matlabcentral/fileexchange/37856) as possibly helpful, but the implementation seems particularly burdensome. Let's say that I can represent my space as a 5000 x 5000 x 5000 array and that roughly half of the entries in the array are flipped on (i.e., they belong to a sphere). This means that I have ~6e10 points to check using inpolyhedron.
Any thoughts on a slick way to manage this geometrically?
That said, if my entities were "blobs" rather than spheres, I might need a non geometric approach, so thoughts about that?
Thanks in advance.
Matt



