凸多面体的体积问题，前人早有研究：
https://en.wikipedia.org/wiki/Convex_polytope
摘录一段：
Volume computation
The task of computing the volume of a convex polytope has been studied in the field of computational geometry. The volume can be computed approximately, for instance, using the convex volume approximation technique, when having access to a membership oracle. As for exact computation, one obstacle is that, when given a representation of the convex polytope as an equation system of linear inequalities, the volume of the polytope may have a bit-length which is not polynomial in this representation.[14]
https://en.wikipedia.org/wiki/Convex_polytope
摘录一段：
Volume computation
The task of computing the volume of a convex polytope has been studied in the field of computational geometry. The volume can be computed approximately, for instance, using the convex volume approximation technique, when having access to a membership oracle. As for exact computation, one obstacle is that, when given a representation of the convex polytope as an equation system of linear inequalities, the volume of the polytope may have a bit-length which is not polynomial in this representation.[14]
