Closure of Boolean operations on geometric entities

Boolean operations akin to set interaction, union, and difference play an imporatant role in CAD/CAM. Geometric entities of practical interest (e.g. polygons or polyhedra) are not algebraically closed under the conventional set operators, and therefore algorithms cannot implement conventional set operations if they are to produce results that can be used in subsequent calculations. This paper demonstrates that closure raises delicate issues, and presents a correct mathematical approach based on the topological notion of regularity.