Modeling Polyhedral Solids Bounded by Multi-Curved Parametric Surfaces

Abstract

Since the beginning of geometric modeling as a field of CAD a decade ago, the methods for interactive design of solid objects and interactive design of free-formed surfaces (of degree 3 and higher) were developed along parallel but disjoint strands. One led to the development of techniques for representing and manipulating the shape of polyhedral solids bounded mostly by planes, while the other led to the development of techniques for the mathematical representation of curved surfaces, without paying attention to their combination into volumetric solids. Though the need for integrating solid object modeling with surface modeling for the design of such artifacts as machine parts, aircraft, cars and ships has been widely recognized, there is so-far no modeling system which provides such capabilities in a general way. An integrated solids modeling system for representing and manipulating polyhedral objects bounded by bicubic parametric surfaces, is presented. Its basic capabilities include the representation of solids through a surface-based model, such that the surface underlying any face can be replaced by another surface that has been modeled independently. Other functionalities include scaling, rotation and translation of shapes, and their pairwise combination into more complex shapes by means of spatial set operators.