Set models and Boolean operations for solids and assemblies

Applications of solid modeling in computer-aided design, computer-aided manufacturing, and robotics, which often involve aggregates or assemblies of disconnected pieces, are addressed. Models for such assemblies must be subjected to some of the same operations as models for single parts. The mathematical basis of constructive solid geometry (CSG), the usual formalism in solid modelers, leads to difficulties in dealing with assemblies. An alternative CSG-like formalism based on open sets, in which both assemblies and connected pieces are modeled as point sets is presented. Consequently the same Boolean operations apply uniformly to connected pieces and assemblies.>