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带权优化约束Delaunay三角化算法

孟宪海 李吉刚 杨钦

孟宪海, 李吉刚, 杨钦等 . 带权优化约束Delaunay三角化算法[J]. 北京航空航天大学学报, 2005, 31(12): 1284-1288.
引用本文: 孟宪海, 李吉刚, 杨钦等 . 带权优化约束Delaunay三角化算法[J]. 北京航空航天大学学报, 2005, 31(12): 1284-1288.
Meng Xianhai, Li Jigang, Yang Qinet al. Conforming Delaunay triangulation optimized by weighted method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2005, 31(12): 1284-1288. (in Chinese)
Citation: Meng Xianhai, Li Jigang, Yang Qinet al. Conforming Delaunay triangulation optimized by weighted method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2005, 31(12): 1284-1288. (in Chinese)

带权优化约束Delaunay三角化算法

详细信息
    作者简介:

    孟宪海(1977-),男,黑龙江安达人,博士生,x h meng@sina.com.

  • 中图分类号: TP 391.4

Conforming Delaunay triangulation optimized by weighted method

  • 摘要: Delaunay细化算法是目前大多数约束Delaunay三角化算法的主要思想,针对其要求输入的约束条件中不能包含夹角较小的尖角的问题,给出了Delaunay细化算法收敛的充分条件,并通过在尖角点和尖角边处引入带权点和带权Delaunay空圆/球准则的方法提出了一种带权优化约束Delaunay三角化算法,解决了经典的细化算法在尖角处算法不收敛时需引入辅助控制区域以及过多辅助点的问题,对算法的收敛性进行了分析,给出了相应的算法应用实例,可以应用于复杂几何对象的科学计算和工程分析.

     

  • [1] Ruppert J. A Delaunay refinement algorithm for quality 2-dimensional mesh generation[J]. Journal of Algorithms, 1995, 18(3):548~585 [2] Shewchuk J R. Tetrahedral mesh generation by Delaunay refinement. Proceedings of the 14th ACM Symposium on Computational Geometry. New York:ACM, 1998.86~95 [3] Shewchuk J R. Delaunay refinement algorithms for triangular mesh generation[J]. Computational Geometry, 2002, 22(1-3):21~74 [4] Cheng S W, Dey T K. Quality meshing with weighted Delaunay refinement. Proceeding of the 13th ACM-SIAM Symposium on Discrete Algorithms. New York:ACM-SIAM Press, 2002.137~146 [5] Li X Y. Generating well-shaped d-dimensional Delaunay meshes[J]. Theoretical Computer Science, 2003, 296(1):145~165 [6] Cheng S W, Dey T K, Edelsbrunner H, et al. Silver exudation[J]. Journal of the ACM, 2000, 47(5):883~904 [7] 杨 钦. 限定Delaunay三角剖分. 北京:北京航空航天大学计算机学院,2001 Yang Qin. Constrained Delaunay triangulation. Beijing:School of Computer Science and Technology, Beijing University of Aeronautics and Astronautics,2001(in Chinese) [8] Murphy M, Mount D M, Gable C W. A point-placement strategy for conforming Delaunay tetrahedralization. Proceeding of the 11th ACM-SIAM Symposium on Discrete Algorithms. New York:ACM, 2000.67~74 [9] Cohen-Steiner D, De Verdiere E C, Yvinec M. Conforming Delaunay triangulations in 3D. Proceeding of the 18th Annual Symposium on Computational Geometry. New York:ACM, 2002.199~208 [10] Cheng S W, Poon S H. Graded conforming Delaunay tetrahedralization with bounded radius-edge ratio. Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms. New York:ACM, 2003.295~304 [11] Edelsbrunner H. Geometry and topology for mesh generation[M]. New York:Cambridge University Press, 2001 [12] 吴壮志,怀进鹏,杨 钦. Ed带权点集的Regular三角化的构造算法[J]. 计算机学报,2002, 25(11):1243~1249 Wu Zhuangzhi, Huai Jinpeng, Yang Qin. Algorithm for constructing the regular triangulation of a set of weighted points in Ed[J]. Chinese Journal of Computers, 2002, 25(11):1243~1249(in Chinese)
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出版历程
  • 收稿日期:  2004-09-09
  • 网络出版日期:  2005-12-31

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