Algebraic Representation of CSG Solids Built from Free-Form Primitives

Abstract

A mathematical model for free-form solid modelling was presented in previous published works. The key aspects of this model are the decomposition of the volume occupied by the solid into non-disjoint cells, and the representation of the solid as an algebraic sum of these cells. Here we apply this scheme to represent CSG solids built by combining free-form solids in boolean operations. As a proof of the validity of this scheme, we present an algorithm that allows us to visualize the nonevaluated result of the operations. We have worked with free-form solids whose surfaces are bounded by a set of low degree triangular parametric patches.