On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis

Authors:
Jorge Delgado;Juan Manuel Peña
Affiliations:
Universidad de Zaragoza, Zaragoza, Spain;Universidad de Zaragoza, Zaragoza, Spain
Venue:
Advances in Computational Mathematics
Year:
2013

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Abstract

An efficient evaluation algorithm for rational triangular Bernstein---Bézier surfaces with any number of barycentric coordinates is presented and analyzed. In the case of three barycentric coordinates, it coincides with the usual rational triangular de Casteljau algorithm. We perform its error analysis and prove the optimal stability of the basis. Comparisons with other evaluation algorithms are included, showing the better stability properties of the analyzed algorithm.