随机多面体的剪影

Q4 Mathematics

International Journal of Computational Geometry & Applications Pub Date : 2016-03-18 DOI:10.20382/jocg.v7i1a5

M. Glisse, S. Lazard, J. Michel, M. Pouget

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引用次数: 4

摘要

我们考虑随机多面体，其定义为$\R^3$中球面上泊松点过程的凸包，其平均点数为$n$。我们证明了从无穷远处观察所有这些最大轮廓尺寸的随机多面体的期望是$\Theta(\sqrt{n})$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Silhouette of a random polytope

We consider random polytopes defined as the convex hull of a Poisson point process on a sphere in $\R^3$ such that its average number of points is $n$. We show that the expectation over all such random polytopes of the maximum size of their silhouettes viewed from infinity is $\Theta(\sqrt{n})$.

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来源期刊

International Journal of Computational Geometry & Applications 数学-计算机：理论方法

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The International Journal of Computational Geometry & Applications (IJCGA) is a quarterly journal devoted to the field of computational geometry within the framework of design and analysis of algorithms. Emphasis is placed on the computational aspects of geometric problems that arise in various fields of science and engineering including computer-aided geometry design (CAGD), computer graphics, constructive solid geometry (CSG), operations research, pattern recognition, robotics, solid modelling, VLSI routing/layout, and others. Research contributions ranging from theoretical results in algorithm design — sequential or parallel, probabilistic or randomized algorithms — to applications in the above-mentioned areas are welcome. Research findings or experiences in the implementations of geometric algorithms, such as numerical stability, and papers with a geometric flavour related to algorithms or the application areas of computational geometry are also welcome.