RSC: A CALCULUS OF SHAPES

Constructive Solid Geometry (CSG) is a mathematical modeling scheme for representation of physical objects [12]. In recent years, CSG has become popular as an underlying logical model in Computer Aided Design/Computer Aided Manufacturing (CAD/CAM) systems for definition of mechanical parts [3, 4, 6, 7, 8, 10, 11]. Fundamental simplicity of CSG together with its sound mathematical basis are reasons for this popularity. This paper discusses a number of problems in CSG's modeling of solid objects. In particular, treatment of assemblies in CSG is shown to be inconsistent. As an alternative, a new coherent mathematical scheme, called Realizable Shape Calculus (RSC), is presented. RSC is a modeling formalism in the same spirit as CSG, for consistent representation of physical objects — assemblies as well as connected pieces.