Rational Bezier form of hodographs of rational Bezier curves and surfaces

Abstract

Applications of rational Bezier curves or surfaces often require the computation of derivatives. Even though there are several algorithms or representations for the derivatives of rational Bezier curves or surfaces, their advantages and disadvantages have not been explicitly discussed from the viewpoint of computational requirements. This paper presents the representation of the hodographs of rational Bezier curves and surfaces in rational Bezier curves and surfaces with appropriate degrees. In addition, this paper presents the evaluation of the performances of different representations. (C) 2001 Elsevier Science Ltd. All rights reserved.