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A Poisson sample of a smooth surface is a good sample

Un échantillon de Poisson d’une surface est un bon échantillon

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Abstract

The complexity of the Delaunay triangulation of $n$ points distributed on a surface ranges from linear to quadratic. When the points are a deterministic good sample of a smooth compact generic surface, the size of the Delaunay triangulation is $O(n\log n)$ [Attali et al.]. Using this result, we prove that when points are Poisson distributed on a surface under the same hypothesis, with intensity $\lambda$, the expected size is $O(\lambda \log^2 \lambda)$.
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Dates and versions

hal-01962631 , version 1 (20-12-2018)

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  • HAL Id : hal-01962631 , version 1

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Olivier Devillers, Charles Duménil. A Poisson sample of a smooth surface is a good sample. [Research Report] RR-9239, INRIA Nancy. 2018, pp.8. ⟨hal-01962631⟩
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