An analysis of symmetry for plane curves and plane curve algorithms
type: Item
instance of: scholarly article
title: An analysis of symmetry for plane curves and plane curve algorithms
zbMATH Open document ID: 0757.65010
DOI: 10.1016/0167-8396(92)90012-E
published in: Computer Aided Geometric Design
publication date: 1992-10-13T00:00:00Z
review text: The work is complementary to that by the author [ibid. 6, 265-277 (1989; Zbl 0677.53016)]. General symmetry requirements for plane curve algorithms are defined. Planar paths and planar curves and connection with a functional equation are discussed. The definitions include symmetry and anti-symmetry properties of axis-invariant curve algorithms. Two classes, \(A\) and \(B\), of axis-invariant curve forms are characterized. Necessary and sufficient conditions are found for which algorithms, that take specific general forms, possess the symmetry properties. An extension to space curves and surfaces is suggested. An application in computer aided design is mentioned.
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 68934
zbMATH Keywords: plane curve algorithms
zbMATH Keywords: symmetry
zbMATH Keywords: anti-symmetry
zbMATH Keywords: axis-invariant curve algorithms
zbMATH Keywords: computer aided design
author: H. E. Bez
MaRDI profile type: Publication
cites work: A Unified Treatment of Invariance for Curve- and Surface-defining Algorithms
cites work: On invariant curve forms
cites work: An analysis of invariant curves
cites work: Q4144184
cites work: Q4776831
full work available at URL: 0167-8396(92)90012-e
OpenAlex ID: W2057440387
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description: scientific article; zbMATH DE number 68934