RATIONAL BÉZIER CURVES AND SURFACES WITH INDEPENDENT COORDINATE WEIGHTS

Abstract

A generalization of the rational Bézier curves and surfaces was made in [3]. In this paper we make another extending of the possibilities for the modelling curves and surfaces by attaching different weights to each coordinate of the control Bezier points. Derivatives of high orders in the initial and final points of the curves are also deduced. Some figures show the increased flexibility of these partial or toted rational Bézier curves and surfaces comparative with the polynomial and classical rational corresponding to the same control Bézier polygon. On observes that we do not always have the convex hull property (Fig. 2) and the affine invariance (Fig. 3).