1. Computing the minimum distance between two planar algebraic curves
- Author
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Chen, Xiao-Diao, Yong, Jun-Hai, Wang, Guozhao, Hangzhou Dianzi University (HDU), School of Software (THSS), Tsinghua University [Beijing] (THU), Department of Mathematics [Hangzhou], Zhejiang University, and Tsinghua, Thss
- Subjects
[INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR] ,[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR] - Abstract
National audience; Through geomet ric observation , it is found that the nearest point on a curve is a tangent point between the curve and an off set curve of the other curve. Based on this observation , an off set method is presented for computing the minimum distance between two planar algebraic curves. The new method is geomet rically inst ructive , and can be used for computing the minimum distance between an algebraic curve and a parametric one on the same plane. For planar quadratic curves , the degree of the resulting univariate polynomial equation by our method is much lower than that of the equations in previous comparable methods , which may lead to lower computation complexity or higher robustness of the solutions.
- Published
- 2008