Coxeter triangulations have good quality

A. Choudhary, S. Kachanovich, M. Wintraecken, Mathematics in Computer Science (2020).

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Journal Article | Epub ahead of print | English
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Abstract
Coxeter 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/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/d2). We conjecture that both bounds are optimal for triangulations in Euclidean space.
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2020-03-04
Journal Title
Mathematics in Computer Science
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Choudhary A, Kachanovich S, Wintraecken M. Coxeter triangulations have good quality. Mathematics in Computer Science. 2020. doi:10.1007/s11786-020-00461-5
Choudhary, A., Kachanovich, S., & Wintraecken, M. (2020). Coxeter triangulations have good quality. Mathematics in Computer Science. https://doi.org/10.1007/s11786-020-00461-5
Choudhary, Aruni, Siargey Kachanovich, and Mathijs Wintraecken. “Coxeter Triangulations Have Good Quality.” Mathematics in Computer Science, 2020. https://doi.org/10.1007/s11786-020-00461-5.
A. Choudhary, S. Kachanovich, and M. Wintraecken, “Coxeter triangulations have good quality,” Mathematics in Computer Science, 2020.
Choudhary A, Kachanovich S, Wintraecken M. 2020. Coxeter triangulations have good quality. Mathematics in Computer Science.
Choudhary, Aruni, et al. “Coxeter Triangulations Have Good Quality.” Mathematics in Computer Science, Springer Nature, 2020, doi:10.1007/s11786-020-00461-5.
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