Detecting cusps and inflection points in curves
type: Item
instance of: scholarly article
title: Detecting cusps and inflection points in curves
zbMATH Open document ID: 0757.65012
DOI: 10.1016/0167-8396(92)90050-Y
published in: Computer Aided Geometric Design
publication date: 1992-10-13T00:00:00Z
review text: The authors call `cusp of order \(k\)' a point on a curve where the \(k\)-th osculating space is not of maximal dimension. \{The underlying theory, not noticed by the authors, of higher order contact and singularities was developed by \textit{W. F. Pohl} [Topology 1, 169-211 (1962; Zbl 0112.366)] and \textit{E. A. Feldman} [Trans. Am. Math. Soc. 20, 185-225 (1966; Zbl 0137.178), ibid. 125, 181-215 (1966; Zbl 0156.424)]\}. The authors note that if a curve is given in parametric form by rational functions the existence of singularities of any order in a given interval can be detected by using Sturm chains.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 14Q10
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 68925
zbMATH Keywords: cusps
zbMATH Keywords: inflection points
zbMATH Keywords: regular curves
zbMATH Keywords: rational curves
zbMATH Keywords: proper parametrizations
zbMATH Keywords: geometric continuity
zbMATH Keywords: Sturm chains
author: Dinesh Manocha
author: John Canny
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
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full work available at URL: 0167-8396(92)90050-y
OpenAlex ID: W1970663370
Wikidata QID: Q126340523
description: scientific article; zbMATH DE number 68925