Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves
type: Item
instance of: scholarly article
title: Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves
zbMATH Open document ID: 0571.65114
DOI: 10.1016/0167-8396(84)90020-7
published in: Computer Aided Geometric Design
publication date: 1984-01-01T00:00:00Z
review text: Let C be a planar rational polynomial curve defined parametrically. The solution of the problem: Find the polynomial equation of the curve \(F(x,y)=0\) which defines the same curve, C, as the parametric equations, is called the implicitization. The solution of the problem: Find the parametric(s), t, corresponding to the coordinates of a point \(p=(x,y)\) known to lie on the curve, is called the inversion. Using vector techniques and Bezout's resultant both problems are readily solved. In section 9 the authors obtain an intersection algorithm for planar rational polynomial curves. The presentation is elegant and the lecture of the text is attractive.
Mathematics Subject Classification ID: 65S05
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 65D99
zbMATH DE Number: 3911669
zbMATH Keywords: computer aided geometric design
zbMATH Keywords: computer graphics
zbMATH Keywords: computational geometry
zbMATH Keywords: object modeling
zbMATH Keywords: curve representations
zbMATH Keywords: algebraic geometry
zbMATH Keywords: elimination theory
zbMATH Keywords: resultant
author: Ron Goldman
author: T. W. Sederberg
author: David C. Anderson
MaRDI profile type: Publication
full work available at URL: 0167-8396(84)90020-7
OpenAlex ID: W2007778702
cites work: The method of resolvents: A technique for the implicitization, inversion, and intersection of non-planar, parametric, rational cubic curves
cites work: Implicitization, inversion, and intersection of planar rational cubic curves
cites work: Algorithm for algebraic curve intersection
cites work: Implicit representation of parametric curves and surfaces
cites work: Q5799167
description: scientific article; zbMATH DE number 3911669