Release Time:2019-03-11  Hits:

Indexed by: Journal Article

Date of Publication: 2011-10-01

Journal: 7th International Conference on Scientific Computing and Applications

Included Journals: Scopus、CPCI-S、EI、SCIE

Volume: 236

Issue: 5,SI

Page Number: 892-905

ISSN: 0377-0427

Key Words: Curve intersection; Surface intersection; Characteristic point; Polyhedral homotopy; Linear homotopy

Abstract: Intersection problems are fundamental in computational geometry, geometric modeling and design and manufacturing applications, and can be reduced to solving polynomial systems. This paper introduces two homotopy methods, i.e. polyhedral homotopy method and linear homotopy method, to compute the intersections of two plane rational parametric curves. Extensive numerical examples show that computing curve intersection by homotopy methods has better accuracy, efficiency and robustness than by the Ehrlich-Aberth iteration method. Finally, some other applications of homotopy methods are also presented. (C) 2011 Elsevier B.V. All rights reserved.