计算两圆环面之间的最近距离  

Computing the Minimum Distance between Two Tori

作　　者：刘晓明[1,2,3,4,5] 刘长远[1,4,5] 胡强[3] 雍俊海[1,4,5] 

机构地区：[1]清华大学软件学院,北京100084 [2]清华大学计算机科学与技术系,北京100084 [3]防化指挥工程学院一系,北京102205 [4]信息系统安全教育部重点实验室,北京100084 [5]清华信息科学与技术国家实验室,北京100084

出　　处：《计算机辅助设计与图形学学报》2011年第2期240-246,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60625202);国家自然科学基金国际合作项目(60911130368);国家"九七三"重点基础研究发展计划项目(2010CB328001);清华大学自主科研计划(2009THZ0);霍英东教育基金会(111070)

摘　　要：圆环面之间的距离计算是求解其碰撞检测和相交问题的基础.文中提出了一种判断两圆环之间包含、分离和相交3种位置关系,以及计算最近距离的方法.首先证明了空间两圆的Hausdorff距离可以通过计算共线法向点获得,并通过解一个一元八次方程求出三维空间中两圆的共线法向点;然后对共线法向点进行分类比较,得到两圆之间的最近距离和Hausdorff距离.证明了两圆环面间的位置关系不仅与其中心圆的最近距离相关,还与两中心圆的单向Hausdorff距离相关,进而解决了两圆环面之间的最近距离计算问题.最后通过实验说明了该方法的稳定性和高效性.The minimal distance computing between two tori is the basis of their collision detection and intersection. A method is proposed for discriminating three types of position relationship （i. e., inclusion, disjunction and intersection） between two tori, and for computing their minimal distance. This paper proves {hat the Hausdorff distance between two circles in three-dlmensional space can be obtained by computing their collinear normal points, which can be calculated by solving an equation of degree 8. With classification and comparison of the collinear normal points, the minimum distance and the Hausdorff distance between these two circles are obtained. In addition, this paper proves that the position relationship between two tori relates to not only the minimum distance but also the directed Hausdorff distance between their central circles. And then the minimum distance between two tori is calculated. Numerical results are presented to illustrate the stability and efficiency of the method.

关 键 词：HAUSDORFF距离 圆环面 共线法向点 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]