I need to compute a $n-$dimensional integral with $n<10$ on a convex polytope. Since most numerical integration libraries (e.g. Cuba) expect the function to be integrated defined inside an axis aligned bounding box (AABB), I need to compute a (minimum volume) AABB enclosing the polytope. Since the polytope is defined by a set of linear inequalities (H-polytope), the easiest way to compute the AABB would be converting the polytope to the V-form using the Fourier–Motzkin elimination (FME) algorithm. The problem is that the number of vertices generated by FME grows so quickly to make the method not practical. So my question is: is there a way to compute the AABB directly from the H-polytope while avoiding the conversion to V-polytope?


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