On de Casteljau-type algorithms for rational Bezier curves

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:288

Article

Sir, Zbynek¹  Juettler, Bert² 

[1] Charles Univ Prague, Prague, Czech Republic

[2] Johannes Kepler Univ Linz, A-4040 Linz, Austria

关键词: Rational Bernstein functions;    De Casteljau-type algorithm;    Rational Bezier curves;    Lupas q-analogue of Bernstein operator;    Degree elevation;   

DOI  :  10.1016/j.cam.2015.01.037

来源: Elsevier

【 摘 要 】

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 Bezier 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), which cover the case of denominators of the form Pi(n)(i=1)(1 - t + q(i-1)t) where q is a positive constant, to rational curves with general denominators. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free