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Reports (Research Report) Year : 2018

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

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Olivier Devillers

#### 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)

### Identifiers

• HAL Id : hal-01962631 , version 1

### Cite

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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