A symbolic method for calculating the integral properties of arbitrary nonconvex polyhedra

Volume, center of mass, moments of inertia, and similar properties of solids are defined by triple integrals over subsets of three-dimensional Euclidean space. Such quantities figure prominently in static and dynamic simulation equations, where the mass of an object or the effects during rotation must be calculated prior to manufacture, for instance; and therefore, the ability to compute the integral properties for geometrically complex solids is an important goal in CAD/CAM, robotics, and other fields.