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.
-
关键词:
- 计算机图形学 /
- 三角剖分 /
- 算法 /
- 约束Delaunay三角化 /
- Delaunay细化算法 /
- 带权
Abstract: As a conforming Delaunay triangulation (CDT) algorithm, Delaunay refinement method has widely application both in theory and practice. It always fails to terminate when there are some small angles intersected by input geometry constraints, so a sufficient condition for termination of Delaunay refinement method was introduced and a new conforming Delaunay triangulation algorithm was presented, which is based on Delaunay refinement method and optimized by weighted method. The algorithm imposes no angle restrictions on the input geometry domains by setting weight value to point where input constraints intersected with small angles and applying the rule of weighted Delaunay circumcircle/circumsphere claim to generate Delaunay triangular mesh, and it avoids appending any additional complex region and need not adding any Steiner points to mesh. Analysis of termination and some results applied by this algorithm were also presented. This method will be useful in the computation and analysis of complicated geometry objects.-
Key words:
- computer graphics /
- triangulation /
- algorithms /
- conforming Delaunay triangulation /
- Delaunay refinement /
- weighted
-
[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) -
点击查看大图
计量
- 文章访问数: 4067
- HTML全文浏览量: 180
- PDF下载量: 1135
- 被引次数: 0
下载:
