Weight Estimation of Rational Bézier Curves and Surfaces

Computer Aided Geometric Design has emerged from the needs of free form curves and surfaces in CAD/CAM technologies. Rational schemes are now replacing polynomial schemes in CAGD. This paper presents several methods to generate weights of rational Bezier curves and surfaces. The main idea is to find weights which minimize functional measuring a technical smoothness of the curves and surfaces. These functional are related to the energy of beams and plates in the sense of elasticity theory. A new result on the reparameterization of rational Bezier curves is also presented. This allows to find efficient algorithms minimizing the smoothing functional.