Sculptured Surfaces in Solid Models: Issues and Alternative Approaches

The fields of surface modeling and solid modeling have been developing quite independently. Today users of each system find they must employ functionality traditionally present only in the other system. This article focuses on issues related to the incorporation of sculptured surface functionality into solid modeling systems. Mathematical concepts related to sculptured surface modeling are reviewed and approaches to the representation of intersection curves and trimmed surfaces are discussed. Difficulties arise from the high polynomial degree resulting from many free-form surface operations. Some methods are described that keep the surface degree low, while retaining many of the advantages of sculptured surfaces. Compromises may be required when integrating this technology into boundary representation (B-rep) and constructive solid geometry (CSG) solid modelers.