I have constructed a convex hull using Randomized Incremental Algorithm and I have the facets of the same. I need to compute the volume of this hull. Would some please share the algorithm for doing this?
One suggestion I found was to use the summation over facets but for that I would need to know the inradius of the polyhedron and I don't know how I can get that.
Thanks.
If the facets are oriented consistently (*), then the volume of the hull is the sum of the volumes of the tetrahedra defined by each facet and a fixed point, say the origin, which does not need to be inside the hull.
(*) Assuming that the facets are triangles, then the facets are oriented consistently if the volumes of the corresponding tetrahedra with respect to an interior point of the hull all have the same sign.