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# Coxeter triangulations have good quality

2 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : Coxeter triangulations are triangulations of Euclidean space based on a simple simplex. By this we mean that given an individual simplex we can recover the entire triangulation of Euclidean space by inductively reflecting in the faces of the simplex. In this paper we establish that the quality of the simplices in all Coxeter triangulations is $O(1/ √ d)$ of the quality of regular simplex. We further investigate the Delaunay property (and an extension thereof) for these triangulations. In particular, one family of Coxeter triangulations achieves the protection $O(1/d 2)$. We conjecture that both bounds are optimal for triangulations in Euclidean space.
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Cited literature [35 references]

https://hal.inria.fr/hal-01667404
Contributor : Siargey Kachanovich Connect in order to contact the contributor
Submitted on : Tuesday, December 19, 2017 - 12:31:47 PM
Last modification on : Friday, February 4, 2022 - 3:12:39 AM

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• HAL Id : hal-01667404, version 1

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Aruni Choudhary, Siargey Kachanovich, Mathijs Wintraecken. Coxeter triangulations have good quality. {date}. ⟨hal-01667404⟩

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