# Silhouette of a random polytope

1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
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 $\Theta(\sqrt{n})$.
Document type :
Reports

Cited literature [10 references]

https://hal.inria.fr/hal-00841374
Contributor : Marc Pouget <>
Submitted on : Wednesday, February 26, 2014 - 4:17:07 PM
Last modification on : Friday, September 20, 2019 - 4:56:38 PM
Long-term archiving on : Monday, May 26, 2014 - 12:50:25 PM

### File

RR_silh.pdf
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### Identifiers

• HAL Id : hal-00841374, version 2

### Citation

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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