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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

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Algorithm for finding the volume of a convex polytope

You could use a finite element method. If you stuff the surface with tetrahedra http://www.cs.berkeley.edu/~jrs/papers/stuffing.pdf‎ (pdf link not allowed), you could then sum the volumes of those te …
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