On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis (Q1955532)

The authors deal with the problem of evaluating rational triangular Bézier surfaces, a question of interest in application in fields as geometric modeling or finite elements. After motivating the problem and describing the state of the art, the paper focuses first on the evaluation algorithm to afterwards treat the stability and analysis the error. A comparison study with alternative algorithms is also considered. As main results one can mention the presentation of an efficient variant of the rational triangular de Casteljau algorithm, for the case of more than 3 barycentric coordinates, that uses Kahan's compensated summation. For the rational case, they also present a rational (Schumaker and Volk)-like algorithm.