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Topic: Intersection of Sphere and Polyhedron
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Posts: 23
Registered: 8/13/09
Intersection of Sphere and Polyhedron
Posted: May 9, 2013 11:15 AM
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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 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?

Thanks in advance.


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