| 三维限定Voronoi网格剖分细化算法 |
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| 引用本文： | 李吉刚,杨钦,孟宪海,蔡强. 三维限定Voronoi网格剖分细化算法[J]. 计算机辅助设计与图形学学报, 2009, 21(1) |
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| 作者姓名： | 李吉刚 杨钦 孟宪海 蔡强 |
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| 作者单位： | 软件开发环境国家重点实验室,北京,100083;北京航空航天大学计算机学院,北京,100083;北京工商大学计算机学院,北京,100037 |
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| 摘 要： | 针对分段线性复合形约束条件下的三维限定Voronoi剖分问题,提出一种细化算法.首先证明了分段线性复合形中的元素在最终生成的三维限定Voronoi网格中可表示为Power图结构;受此启发,提出了对限定线段平面片分别进行一维二维Power图细化以实现三维限定Voronoi 网格生成的细化算法,并且证明了该算法对于任意分段线性复合形收敛.最后通过实例验证了文中算法的有效性.
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| 关 键 词： | 限定Voronoi网格 Delaunay三角化 细化算法 Power图 Regular三角化 |
3D Conforming Voronoi Mesh Generation by Refinement Algorithm |
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| Li Jigang,Yang Qin,Meng Xianhai,Cai Qiang. 3D Conforming Voronoi Mesh Generation by Refinement Algorithm[J]. Journal of Computer-Aided Design & Computer Graphics, 2009, 21(1) |
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| Authors: | Li Jigang Yang Qin Meng Xianhai Cai Qiang |
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| Affiliation: | State Key Laboratory of Software Development Environment;Beijing 100083;School of Computer Science and Engineering;Beihang University;Beijing 100083;College of Computer Science and Engineering;Beijing Technology & Business University;Beijing 100037 |
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| Abstract: | We describe an algorithm which,for any piecewise linear complex(PLC) in 3D,builds a Voronoi tessellation conforming to this PLC.Based on the proven insight that once a face f in PLC is a union of faces of Voronoi diagram in 3D,the subdivision structure on the face f can be seen as a power diagram,we devised a conforming Voronoi tessellation algorithm by maintaining a power diagram refinement for each 1D 2D faces of PLC and a Voronoi tessellation in 3D.The power diagram refinement for each 1D 2D faces of PLC... |
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| Keywords: | conforming Voronoi mesh Delaunay triangulation refinement algorithm power diagram regular triangulation |
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