On de Casteljau-type algorithms for rational Bezier curves

Abstract

We consider the space of rational functions of degree n with a common denominator. It is shown that-in addition to the standard rational de Casteljau algorithm-the corresponding rational Bézier curves admit up to n! different de Casteljau-type algorithms, depending on the ordering of the elementary factors of the polynomial.

Our observations generalize recent results of Han et al. (2014).

Keywords

• Rational Bernstein functions
• De Casteljau-type algorithm
• Rational Bézier curves
• Lupaş q-analogue of Bernstein operator
• Degree elevation