Representation of piecewise continuous algebraic surfaces in terms of B-splines

Abstract

A method for representing shape using portions of algebraic surfaces bounded by rectangular boxes defined in terms of triple product Bernstein polynomials is described and some of its properties are outlined. The method is extended to handle piecewise continuous algebraic surfaces within rectangular boxes defined in terms of triple products of B-spline basis functions. Next, two techniques for sculptured shape creation are studied. The first is based on geometric manipulation of existing primitives and the second on approximation/interpolation of lower dimensional entities using least-squares techniques based on singular value decomposition. In addition, several interrogation techniques, such as contouring, ray tracing and curvature evaluation, used in the design and analysis of piecewise continuous algebraic surfaces are discussed.