PAR: A CSG-based unique representation scheme for rotational parts

A new representation scheme PAR (principal axis representation) for rotational parts (i.e., solids of revolution) is proposed as an internal representation scheme for constructive solid geometry (CSG). The key idea of PAR is to uniquely represent an object by its principal axis and a set of boundary curves. Since PAR is in an evaluated form, geometrical properties of parts can be computed more directly and efficiently from this evaluated representation than from the original CSG tree. In this paper, the PAR scheme is first described and operations (e.g., union) on PAR's are defined. The uniqueness of the PAR scheme is also proved. An algorithm that converts a CSG representation into PAR is presented along with examples. Finally, the equivalence of PAR to the CSG scheme for rotational parts is proved.