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 N-D Voronoi and N-S 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?