Total positivity and convexity preservation
type: Item
instance of: scholarly article
title: Total positivity and convexity preservation
zbMATH Open document ID: 0929.41007
author: Michael S. Floater
published in: Journal of Approximation Theory
publication date: 2000-01-25T00:00:00Z
review text: In this paper the author introduces a concept of \(d\)-convexity of curves in the \(d\)-dimensional space and characterizes totally positive blending systems in terms of \(d\)-convexity. He shows that for certain systems total positivity and rational convexity preservation are equivalent. He also characterizes certain convexity preserving systems in terms of weak Chebychev systems. Among other things he derives some results on Wronskians and uses them to obtain formulas for alternating functions of sequences of derivatives of Bézier curves in terms of points in the de Casteljau algorithm. These formulas generlize some earlier results of the author.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 41A29
zbMATH DE Number: 1251371
zbMATH Keywords: shape preservation
zbMATH Keywords: total positivity
zbMATH Keywords: convexity
zbMATH Keywords: Bézier curves
zbMATH Keywords: Casteljau algorithm
reviewed by: Ganesh Datta Dikshit
MaRDI profile type: Publication
OpenAlex ID: W2049178311
cites work: Totally positive matrices
cites work: Q4525496
cites work: Q4856403
cites work: Convexity of rational curves and total positivity
cites work: Generalized convexity preserving transformations
cites work: Q4324638
cites work: Derivatives of rational Bézier curves
cites work: Q3468070
cites work: Q5624248
cites work: Q4064107
DOI: 10.1006/JATH.1998.3219
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description: scientific article; zbMATH DE number 1251371