Algorithm for algebraic curve intersection
type: Item
instance of: scholarly article
title: Algorithm for algebraic curve intersection
zbMATH Open document ID: 0688.65012
DOI: 10.1016/0010-4485(89)90015-8
published in: CAD. Computer-Aided Design
publication date: 1989-01-01T00:00:00Z
review text: The paper addresses the area of intersection problems in computer aided geometric design. An algorithm for computing all real points at which two planar algebraic curves (that is, curves defined by a polynomial implicit equation \(f(x,y)=0)\) intersect within a specified area is presented. The algorithm makes use of the expression of the curves in Bernstein form. The algorithm is suitable for curves of higher degree; by the author's claim up to degree 25. The use of polar curves in computing double points and silhouette ones is reviewed, too, as well as how to compute all points on an algebraic curve with specified tangent direction. The intersection algorithm can also be used to compute the inflection points of an algebraic curve by the use of its Hessian.
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 51N05
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 4128284
zbMATH Keywords: computer aided geometric design
zbMATH Keywords: polar curves
zbMATH Keywords: intersection algorithm
zbMATH Keywords: inflection points
zbMATH Keywords: algebraic curve
author: T. W. Sederberg
MaRDI profile type: Publication
full work available at URL: 0010-4485(89)90015-8
OpenAlex ID: W2054185827
description: scientific article; zbMATH DE number 4128284