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带权优化约束Delaunay三角化算法 被引量：7

Conforming Delaunay triangulation optimized by weighted method
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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Delau-nay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Delau-nay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. 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/cireumsphere 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.
作者 孟宪海 李吉刚 杨钦
机构地区 北京航空航天大学计算机学院 北京航空航天大学机械工程及自动化学院
出处 《北京航空航天大学学报》 EI CAS CSCD 北大核心 2005年第12期1284-1288,共5页 Journal of Beijing University of Aeronautics and Astronautics
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 computer graphics triangulation algorithms conforming Delaunay triangulation Delaunay refinement weighted
分类号 TP391.4 [自动化与计算机技术—计算机应用技术]
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参考文献11

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共引文献2

同被引文献69

引证文献7

二级引证文献39

北京航空航天大学学报
2005年 第12期

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