二维复杂限定Delaunay三角化算法  

The Algorithm of 2D Complex Conforming Delaunay Triangulation

作　　者：杨钦[1] 刘瑞刚[1] 孟宪海[1] 张俊安[1] 

机构地区：[1]北京航空航天大学计算机学院,北京100083

出　　处：《计算机辅助设计与图形学学报》2007年第2期145-150,共6页Journal of Computer-Aided Design & Computer Graphics

摘　　要：针对包括曲线边界和内部带有曲线限定条件的二维Delaunay三角化问题,提出了一种细化算法.首先给出了曲线段的逼近边定义,以保证限定曲线在网格中的存在;然后证明了该算法的收敛性和最终曲线的逼近边集合与原曲线的拓扑一致性,并且生成的网格符合Delaunay优化准则;最后给出了算法的应用实例,验证了其有效性.A new conforming Delaunay triangulation is presented in two-dimensional domains with curved boundaries and inner curve restrictions. Approximated segments of curved boundaries and inner curve restrictions are defined. A new conforming Delaunay refinement method is presented and the convergence of this algorithm is proved. The presentation of curved boundaries and inner curve restrictions in the generated mesh is implemented. The uniform topology of approximated segments and primitive curves is proved. Some examples that generating guaranteed-quality triangulation meshes with curved boundaries and inner curve restrictions are presented.

关 键 词：三角化 Delaunay准则 限定Delaunay三角化 Delaunay细化算法 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]