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TitleComputing curve intersection by homotopy methods
Author(s) Erbao Feng, Wenyu Hu, Zhongxuan Luo
TypeArticle in Journal
AbstractIntersection 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.
KeywordsCurve intersection, Surface intersection, Characteristic point, Polyhedral homotopy, Linear homotopy
URL http://www.sciencedirect.com/science/article/pii/S0377042711002627
JournalJournal of Computational and Applied Mathematics
Pages892 - 905
NoteThe 7th International Conference on Scientific Computing and Applications, June 13–16, 2010, Dalian, China
Translation No
Refereed No