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.
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Communicated by Tomas Sauer.
Partially supported by MTM2009-07315 Spanish Research Grant and by Gobierno de Aragón.
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Delgado, J., Peña, J.M. On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis. Adv Comput Math 38, 701–721 (2013). https://doi.org/10.1007/s10444-011-9256-6
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DOI: https://doi.org/10.1007/s10444-011-9256-6
Keywords
- Rational triangular Bézier surfaces
- Rational triangular de Casteljau algorithm
- Bernstein basis
- Optimal stability