International Meshing Roundtable ( IMR 25 ) Recursive Spoke Darts : Local Hyperplane Sampling for Delaunay and Voronoi Meshing in Arbitrary Dimensions
International Meshing Roundtable ( IMR 25 ) Recursive Spoke Darts : Local Hyperplane Sampling for Delaunay and Voronoi Meshing in Arbitrary Dimensions
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国际网格划分圆桌会议 (IMR 25) 递归辐条飞镖：任意尺寸的 Delaunay 和 Voronoi 网格划分的局部超平面采样
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发表时间：
2016
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通讯作者：
A. Rushdi
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作者：
Mohamed S. Ebeida;A. Rushdi
我们介绍递归辐条飞镖（RSD）：一个递归超平面采样算法，利用各种尺寸的Voronoi和Delaunay实体之间的充分的二元性。该算法摒弃了Delaunay单纯形生成中对空球原理的依赖，为可扩展一致网格划分提供了基础。该算法依赖于两个简单的操作：线超平面修剪和球形范围搜索。因此，这种方法提高了可扩展性，因为多个处理器可以同时对不同的种子进行操作。此外，跨处理器生成一致的网格消除了它们之间所需的通信，从而进一步提高了可扩展性。我们引入了一个简单的调整算法，使它有可能不访问所有顶点的Voronoi细胞，生成几乎精确的Delaunay图，同时避免了自然灾难的维数在高维度。© 2016作者。由Elsevier Ltd.出版，由第25届国际网格圆桌会议（IMR25）组委会负责同行评审。
We introduce Recursive Spoke Darts (RSD): a recursive hyperplane sampling algorithm that exploits the full duality between Voronoi and Delaunay entities of various dimensions. Our algorithm abandons the dependence on the empty sphere principle in the generation of Delaunay simplices providing the foundation needed for scalable consistent meshing. The algorithm relies on two simple operations: line-hyperplane trimming and spherical range search. Consequently, this approach improves scalability as multiple processors can operate on different seeds at the same time. Moreover, generating consistent meshes across processors eliminates the communication needed between them, improving scalability even more. We introduce a simple tweak to the algorithm which makes it possible not to visit all vertices of a Voronoi cell, generating almost-exact Delaunay graphs while avoiding the natural curse of dimensionality in high dimensions. c © 2016 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of organizing committee of the 25th International Meshing Roundtable (IMR25).