Degree reduction of Bézier curves and filter banks
type: Item
instance of: scholarly article
title: Degree reduction of Bézier curves and filter banks
zbMATH Open document ID: 0857.65020
DOI: 10.1016/0898-1221(96)00049-1
author: Yanyan Li
publication date: 1997-03-09T00:00:00Z
review text: The paper is on degree reduction of a given Bézier function (i.e., a polynomial) \(f^n\) of degree \(n\). That is, one has to find a polynomial \(f^{n-1}\) such that \(|e^n|:= |f^n-f^{n-1}|\) is minimal. The authors obtain a general solution for this problem, and apply it to the case of the \(L_1\)-, \(L_2\)- and the \(L_\infty\)-norm, where results in terms of the Legendre resp. Chebyshev polynomials are recovered.
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 915131
zbMATH Keywords: filter banks
zbMATH Keywords: Bézier curves
zbMATH Keywords: Legendre polynomials
zbMATH Keywords: degree reduction
zbMATH Keywords: Bézier function
zbMATH Keywords: Chebyshev polynomials
reviewed by: Guido Walz
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00049-1
OpenAlex ID: W2069751484
cites work: Degree reduction of Bézier curves
cites work: The error analysis for degree reduction of Bézier curves
cites work: Q3364412
cites work: Q3319163
cites work: Q4722198
cites work: A survey of curve and surface methods in CAGD
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 915131