On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis
type: Item
instance of: scholarly article
title: On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis
zbMATH Open document ID: 1279.65021
author: J. Delgado
author: J. M. Peña
published in: Advances in Computational Mathematics
publication date: 2013-06-14T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65G50
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 6176104
zbMATH Keywords: rational triangular Bézier surfaces
zbMATH Keywords: rational triangular de Casteljau algorithm
zbMATH Keywords: Bernstein basis
zbMATH Keywords: optimal stability
zbMATH Keywords: geometric modeling
zbMATH Keywords: finite elements
reviewed by: R. G. Woods
describes a project that uses: mctoolbox
MaRDI profile type: Publication
full work available at URL: s10444-011-9256-6
OpenAlex ID: W2011422470
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DOI: 10.1007/S10444-011-9256-6
description: scientific article; zbMATH DE number 6176104