TY  - GEN 
T1  - On de Casteljau-type algorithms for rational B´ezier curves
A1  - Jüttler, Bert
A1  - Šír, Zbyněk
Y1  - 2014
KW  - De Casteljau algorithm
KW  - degree elevation
KW  - Lupa¸s numbers
KW  - rational Bernstein functions
KW  - rational B´ezier curves
N2  - We consider the space of rational functions of degree n with a common denominator. It is shown that the corresponding rational B´ezier curves admit up to 1   n! different de Casteljau-type algorithms, depending on the ordering of the elementary factors of the polynomial. Our observations generalize recent results of Han, Chu and Qiu [2], which cover the case of denominators of the formQn i=1(1− t qi−1t) where q is a positive constant, to rational curves with general denominators.
M1  - Preprint project = NCMM
M1  - Preprint year = 2014
M1  - Preprint number = 13
M1  - Preprint ID = NCMM/2014/13
ER  -