Algorithms for computing the volume and other integral properties of solids. II. A family of algorithms based on representation conversion and cellular approximation

Abstract

This paper discusses a family of algorithms for computing the volume, moments of inertia, and other integral properties of geometrically complex solids, e.g. typical mechanical parts. The algorithms produce approximate decompositions of solids into cuboid cells whose integral properties are easy to compute. The paper focuses on versions of the algorithms which operate on solids represented by Constructive Solid Geometry (CSG), i.e., as set-theoretical combinations of primitive solid “building blocks.” Two known algorithms are summarized and a new algorithm is presented. The efficiencies and accuracies of the three algorithms are analyzed theoretically and compared experimentally. The new algorithm uses recursive subdivision to convert CSG representations of complex solids into approximate cellular decompositions based on variably sized blocks. Experimental data show that the new algorithm is efficient and has predictable accuracy. It also has other potential applications, e.g., in producing approximate octree representations of complex solids and in robot navigation.