期刊文献+

三维几何约束的球面几何求解 被引量:4

3D Geometric Constraint Solution Based on Spherical Geometry
下载PDF
导出
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.
出处 《计算机辅助设计与图形学学报》 EI CSCD 北大核心 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)
关键词 几何约束求解 球面求解法 球面几何学 geometric constraint solution spherical solution method spherical geometry
  • 相关文献

参考文献15

  • 1Light R A, Gosssard D C. Modification of geometric models through variational geometry[J]. Computer-Aided Design, 1982, 14(4): 209~214.
  • 2Aldefeld B. Variational of geometries based on a geometric reasoning method[J]. Computer-Aided Design, 1988, 20(3): 117~126.
  • 3Buchberger B, Collins G, Kutzler B. Algebraic methods for geometric reasoning[A]. In: Annual Review Computer Science[C]. Palo Alto: Annual Reviews Inc, 1998. 85~120.
  • 4Kondo K. Algebraic method for manipulation of dimensional relationships in geometric models[J]. Computer-Aided Design, 1992, 24(3): 141~147.
  • 5Owen J C. Algebraic solution for geometry from dimensional constraints[A]. In: ACM Symposium Foundations of Solid Modeling[C]. New York: ACM, 1991. 397~407.
  • 6Bouma W, Fudos I, Hoffmann C M, et al. A geometric constraint solver[J]. Computer Aided Design, 1995, 27(6): 487~501.
  • 7陈立平,王波兴,彭小波,周济.一种面向欠约束几何系统求解的二部图匹配优化处理方法[J].计算机学报,2000,23(5):523-530. 被引量:27
  • 8吴永明.三维几何约束闭环的动态识别与满足[J].计算机辅助设计与图形学学报,2000,12(8):624-629. 被引量:11
  • 9Gao X S, Chou S C. Solving geometric constraint systems I: A global propagation approach[J]. Computer Aided Design, 1998, 30(1): 47~54.
  • 10Essert-Villard C, Schreck P, Dufourd J F. Sketch-based pruning of a solution space within a formal geometric constraint solver[J]. Artificial Intelligence, 2000, 124(1): 139~159.

二级参考文献104

共引文献93

同被引文献48

  • 1高小山,蒋鲲.几何约束求解研究综述[J].计算机辅助设计与图形学学报,2004,16(4):385-396. 被引量:43
  • 2王彦伟,陈立平,黄正东,钟毅芳.面向与历史无关造型的三维约束求解方法研究[J].计算机辅助设计与图形学学报,2004,16(5):648-654. 被引量:7
  • 3夏鸿建,王波兴,陈立平.三维几何约束求解的变分算法[J].计算机辅助设计与图形学学报,2006,18(12):1878-1883. 被引量:6
  • 4陈立平,向文,张新访,周济.基于实例图形的几何约束满足策略[J].计算机辅助设计与图形学学报,1996,8(5):381-388. 被引量:12
  • 5Chung J C, Hwang T S, Wu C T. Extended variationaldesign technology-foundation for integrated design automation [C]//Proceedings of 5th ACM SM'99. Ann Arbor MI, 1999: 13-22.
  • 6Chung J C, Huang T S, Wu C T, et al. Framework for integrated mechanical design automation [J]. Computer-Aided Design, 2000, 32 (5/6): 355-365.
  • 7Chen L P, Peng X B. An approach to a 2D/3D geometric constraint solver [C]//Proceedings of ASME DETC'2000/DAC-14515. Baltimore, Maryland, 2000: 10-13.
  • 8Hoffmann C M, Lomonosov A, Sitharam M. Decomposition plans for geometric constraint problems, part II: new algorithms [J]. Journal of Symbolic Computation, 2001, 31(4): 409-427.
  • 9Chung J C,Huang T S,Wu C T,et al.Framework for integrated mechanical design automation[J].Computer-Aided Design,2000,32(5/6):355-365
  • 10Shapiro V,Raghothama S.Boundary representation deformation in parametric solid modeling[J].ACM Transactions on Graphics,1998,17(4):259-286

引证文献4

二级引证文献12

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部