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Silhouette of a random polytope

Marc Glisse 1 Sylvain Lazard 2 Julien Michel 3 Marc Pouget 2
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry, Inria Nancy - Grand Est
Abstract : 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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Submitted on : Wednesday, February 26, 2014 - 4:17:07 PM
Last modification on : Friday, January 21, 2022 - 3:20:49 AM
Long-term archiving on: : Monday, May 26, 2014 - 12:50:25 PM


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  • HAL Id : hal-00841374, version 2


Marc Glisse, Sylvain Lazard, Julien Michel, Marc Pouget. Silhouette of a random polytope. [Research Report] RR-8327, INRIA. 2013, pp.13. ⟨hal-00841374v2⟩



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