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.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
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)
