# The Stability of Delaunay Triangulations

* Corresponding author
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : 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 quantify the magnitude of the perturbations under which the Delaunay triangulation remains unchanged.
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Reports

Cited literature [19 references]

https://hal.inria.fr/hal-00807050
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Submitted on : Tuesday, April 2, 2013 - 7:32:14 PM
Last modification on : Saturday, January 27, 2018 - 1:30:57 AM
Long-term archiving on: : Sunday, April 2, 2017 - 11:30:17 PM

### Files

RR-8276.pdf
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### Identifiers

• HAL Id : hal-00807050, version 1
• ARXIV : 1304.2947

### Citation

Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh. The Stability of Delaunay Triangulations. [Research Report] RR-8276, INRIA. 2013, pp.29. ⟨hal-00807050⟩

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