三维几何约束的球面几何求解  

3D Geometric Constraint Solution Based on Spherical Geometry

作　　者：王小刚[1] 陈立平[1] 赵建军[1] 王波兴[1] 

机构地区：[1]华中科技大学国家CAD支撑软件工程技术研究中心,武汉430074

出　　处：《计算机辅助设计与图形学学报》2005年第11期2433-2440,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家重点基础研究发展计划(2003CB716207);国家"八六三"高技术研究发展计划(2003AA001031)

摘　　要：研究了球面几何学在三维几何约束求解中的应用,提出了球面求解法.该方法建立在姿态约束与位置约束解耦的基础上,并以求解关键的姿态约束为主,一旦姿态约束被解出,则位置约束很容易求解;同时将表征刚体姿态的矢量映射到球平面上的点,将姿态约束映射为球平面上两点的距离,借助球面几何的知识,能够高效、直观地推理出多数情况下姿态约束的解析解,而特殊的情况则结合数值法求解,并很好地解决了数值法的初值问题.The paper studies the application of spherical geometry to the field of 3D geometric constraint solution and presents a geometric constraint solution method, called spherical solution method. The method is based on decoupling the constraints into postural constraints and positional constraints, and the postural constraint solution is emphasized as once the postural constraints are solved, the positional ones can be solved easily. The method maps the vectors representing the postures of rigid bodies to the points on spherical plane, and maps postural constraints to the distances between the points. Via spherical geometry, the method can infer efficiently and intuitively the analytical solution of postural constraints in most cases. For the other cases, the postural constraints can be solved by a mixed algorithm of numerical solution method and spherical solution method.

关 键 词：几何约束求解 球面求解法 球面几何学 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]