Algorithm for algebraic curve intersection

A robust algorithm is presented for computing all real points at which two planar algebraic curves intersect within a specified area. The classical theory of polar curves is reviewed and applied to the problem of computing the double points on an algebraic curve. Using polar curves, the intersection...

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Bibliographic Details
Published inComputer aided design Vol. 21; no. 9; pp. 547 - 554
Main Author Sederberg, T.W.
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.11.1989
Elsevier Science
Subjects
Applied sciences
Computer aided design
Computer science; control theory; systems
curve intersections
Exact sciences and technology
geometry
Hessian curves
polar curves
Software
computer-aided design
polar curves
geometry
Hessian curves
curve intersections
Intersection
Curve
Computational geometry
Algorithm
Computer aided design
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Summary:A robust algorithm is presented for computing all real points at which two planar algebraic curves intersect within a specified area. The classical theory of polar curves is reviewed and applied to the problem of computing the double points on an algebraic curve. Using polar curves, the intersection algorithm can quickly and robustly compute all real double points on an algebraic curve, as well as silhouette points. Polar curves are shown to have a strikingly simple expression in Bernstein polynomial form. Hessian curves are also discussed. The inflection points of an algebraic curve can be found by intersecting the curve with its Hessian.
ISSN:0010-4485
1879-2685
DOI:10.1016/0010-4485(89)90015-8