平面代数曲线间最近距离的计算  

Computing the Minimum Distance between Two Planar Algebraic Curves

作　　者：陈小雕[1] 雍俊海[2] 汪国昭[3] 

机构地区：[1]杭州电子科技大学计算机学院,杭州310018 [2]清华大学软件学院,北京100084 [3]浙江大学数学系计算机图象图形研究所,杭州310027

出　　处：《计算机辅助设计与图形学学报》2008年第4期459-463,共5页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家“九七三”重点基础研究发展规划项目(2004CB318000,2004CB719403);国家自然科学基金(60625202,60533070,60473130);宁波市自然科学基金(1140157B703)

摘　　要：通过几何观察,指出一条曲线上的最近点是另一条曲线的等距曲线与该曲线的切点这一事实,同时提出基于等距思想的方法来求解2条平面代数曲线间的最近距离.该方法几何意义明显,可同时用来计算代数曲线/参数曲线间的最近距离.对于平面二次曲线,采用文中方法得到的单变量多项式方程次数比已有类似方法中结果方程的次数更低,从而可以降低方程求解的计算复杂度或提高求解的稳定性.Through geometric observation, it is found that the nearest point on a curve is a tangent point between the curve and an offset curve of the other curve. Based on this observation, an offset method is presented for computing the minimum distance between two planar algebraic curves. The new method is geometrically instructive, 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.

关 键 词：最近距离 平面代数曲线 等距方法 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]