Good degree reduction of Bézier curves using Jacobi polynomials
type: Item
instance of: scholarly article
title: Good degree reduction of Bézier curves using Jacobi polynomials
zbMATH Open document ID: 0962.65011
DOI: 10.1016/S0898-1221(00)00232-7
author: R. Smith
publication date: 2001-01-14T00:00:00Z
review text: The authors use the constrained Jacobi polynomial instead of the constrained Chebyshev polynomial as error function for degree reduction with \(C^1\)-continuity [cf. \textit{M. A. Lachance}, Rocky Mt. J. Math. 21, No. 1, 473-488 (1991; Zbl 0763.65008)]. Although the degree reduction is not the best approximation, it has the advantage that its coefficients are expressed explicitly. The authors also present the uniform error bounds of the constrained Jacobi polynomial and a subdivision scheme for degree reduction within given tolerance. An application of the method to a Bézier curve of degree six is also illustrated.
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 1550672
zbMATH Keywords: degree reduction
zbMATH Keywords: Jacobi polynomial
zbMATH Keywords: \(C^1\)-continuity
zbMATH Keywords: subdivision scheme
zbMATH Keywords: error bounds
zbMATH Keywords: Bézier curve
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1550672