New control massic polygon of a \(B\)-rational curve resulting from a homographic change of parameter
type: Item
instance of: scholarly article
title: New control massic polygon of a \(B\)-rational curve resulting from a homographic change of parameter
zbMATH Open document ID: 0799.65014
DOI: 10.1007/BF02142679
author: J. C. Fiorot
author: P. Jeannin
author: Salim Taleb
published in: Numerical Algorithms
publication date: 1994-05-09T00:00:00Z
review text: The authors call massic vector what \textit{H. Grassmann} [Die Ausdehnungslehre (1844)] used to call extensive quantity of step 1, i.e. the vector space generated by sums of points and vectors. They have developed an extensive theory of approximations using this vector space [cf. the first two authors, Courbes et surfaces rationnelles. Applications à la CAO (1989; Zbl 0713.68095)]. Rational Bézier curves are a subset of their BR-curves because they are based on point control only. These BR-curves allow infinitely far control on the same level as that through finite points. In this paper, they discuss four ways of computing projective changes of parameter for BR-approximations, using algorithms previously developed for operations on BR-curves. Each way is illustrated by explicit computation for the folium of Descartes and the trisectrix of MacLaurin.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 15A75
Mathematics Subject Classification ID: 14Q05
zbMATH DE Number: 553670
zbMATH Keywords: rational Bézier curves
zbMATH Keywords: massic vector
zbMATH Keywords: BR-curves
zbMATH Keywords: projective changes of parameter
zbMATH Keywords: BR-approximations
zbMATH Keywords: folium of Descartes
zbMATH Keywords: trisectrix of MacLaurin
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02142679
OpenAlex ID: W2039737112
description: scientific article; zbMATH DE number 553670