A Poisson sample of a smooth surface is a good sample
Un échantillon de Poisson d’une surface est un bon échantillon
Résumé
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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