Fast and Accurate Computation of Polyhedral Mass Properties

Abstract

The location of a body’s center of mass, and its moments and products of inertia about various axes are important physical quantities needed for any type of dynamic simulation or physically based modeling. We present an algorithm for automatically computing these quantities for a general class of rigid bodies: those composed of uniform density polyhedra. The mass integrals may be converted into volume integrals under these assumptions, and the bulk of the paper is devoted to the computation of these volume integrals. Our algorithm is based on a three step reduction of the volume integrals to successively simpler integrals. The algorithm is designed to minimize the numerical errors that can result from poorly conditioned alignment of polyhedral faces. It is also designed for efficiency. All required volume integrals of a polyhedron are computed together during a single walk over the boundary of the polyhedron; exploiting common subexpressions reduces floating point operations. We present numerical results detailing the speed and accuracy of the algorithm, and also give a complete low level pseudocode description.