Weak witnesses for Delaunay triangulations of submanifolds

Weak witnesses for Delaunay triangulations of submanifolds
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DOI：
10.1145/1236246.1236267
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发表时间：
2007-06
期刊：
The Science of the total environment
影响因子：
--
通讯作者：
D. Attali;H. Edelsbrunner;Yuriy Mileyko
D. Attali;H. Edelsbrunner;Yuriy Mileyko
中科院分区：
其他
文献类型：
--
作者：
D. Attali;H. Edelsbrunner;Yuriy Mileyko

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本文的主要结果是将de Silva的弱Delaunay定理推广到欧氏空间中的光滑嵌入曲线曲面。假设一个足够细的采样，我们证明了样本中的i + 1点在限制Delaunay三角剖分中的i-单形的跨度当且仅当i + 1点的每个子集有一个弱见证。
The main result of this paper is an extension of de Silva's Weak Delaunay Theorem to smoothly embedded curves and surfaces in Euclidean space. Assuming a sufficiently fine sampling, we prove that i + 1 points in the sample span an i-simplex in the restricted Delaunay triangulation iff every subset of the i + 1 points has a weak witness.