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| 计算两圆环面之间的最近距离 | |
| 引用本文： | 刘晓明,刘长远,胡强,雍俊海. 计算两圆环面之间的最近距离[J]. 计算机辅助设计与图形学学报, 2011, 23(2) |
| 作者姓名： | 刘晓明 刘长远 胡强 雍俊海 |
| 作者单位： | 1. 清华大学软件学院,北京,100084;清华大学计算机科学与技术系,北京,100084;防化指挥工程学院一系,北京,102205;信息系统安全教育部重点实验室,北京,100084;清华信息科学与技术国家实验室,北京,100084 2. 清华大学软件学院,北京,100084;信息系统安全教育部重点实验室,北京,100084;清华信息科学与技术国家实验室,北京,100084 3. 防化指挥工程学院一系,北京,102205 |
| 基金项目： | 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. |
| 关 键 词： | Hausdorff距离 圆环面 共线法向点 |
Computing the Minimum Distance between Two Tori |
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| Liu Xiaoming,Liu Changyuan,Hu Qiang,Yong Junhai. Computing the Minimum Distance between Two Tori[J]. Journal of Computer-Aided Design & Computer Graphics, 2011, 23(2) | |
| Authors: | Liu Xiaoming Liu Changyuan Hu Qiang Yong Junhai |
| Affiliation: | Liu Xiaoming1,2,3,4,5),Liu Changyuan1,Hu Qiang3),and Yong Junhai1,5)1)(School of Software,Tsinghua University,Beijing 100084) 2)(Department of Computer Science and Technology,Beijing 100084) 3)(Department One,Command and Engineering College of Chemical Defense,Beijing 102205) 4)(Key Laboratory for Information System Security,Ministry of Education,Beijing 100084) 5)(Tsinghua National Laboratory for Information Science and Technology,Beijing 100084) |
| Abstract: | 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 that the Hausdorff distance between two circles in three-dimensional space can be obtained by computing their collinear normal points,which can be calculated by solving an equation of degree 8.With classific... |
| Keywords: | Hausdorff distance torus collinear normal points |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |