Author:
Choudhary Aruni,Kachanovich Siargey,Wintraecken Mathijs
Abstract
AbstractCoxeter triangulations are triangulations of Euclidean space based on a single 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 $$O(1/\sqrt{d})$$O(1/d) of the quality of regular simplex. We further investigate the Delaunay property for these triangulations. Moreover, we consider an extension of the Delaunay property, namely protection, which is a measure of non-degeneracy of a Delaunay triangulation. In particular, one family of Coxeter triangulations achieves the protection $$O(1/d^2)$$O(1/d2). We conjecture that both bounds are optimal for triangulations in Euclidean space.
Funder
Institute of Science and Technology
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics
Cited by
5 articles.
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