Stability of Delaunay-type structures for manifolds
Résumé
We introduce a parametrized notion of genericity for Delaunay
triangulations which, in particular, implies that the Delaunay
simplices of $\delta$-generic point sets are thick. Equipped with
this notion, we study the stability of Delaunay triangulations under
perturbations of the metric and of the vertex positions. We then
show that, for any sufficiently regular submanifold of Euclidean
space, and appropriate $\epsilon$ and $\delta$, any sample set which
meets a localized $\delta$-generic $\epsilon$-dense sampling
criteria yields a manifold intrinsic Delaunay complex which is equal
to the restricted Delaunay complex.
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Origine | Fichiers produits par l'(les) auteur(s) |
Format | Figure, Image |
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Origine | Fichiers produits par l'(les) auteur(s) |