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arXiv · 1804.07024

Delaunay simplices in diagonally distorted lattices

Aruni Choudhary·Arijit Ghosh
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Abstract

Delaunay protection is a measure of how far a Delaunay triangulation is from being degenerate. In this short paper we study the protection properties and other quality measures of the Delaunay triangulations of a family of lattices that is obtained by distorting the integer grid in $\mathbb{R}^d$. We show that the quality measures of this family are maximized for a certain distortion parameter, and that for this parameter, the lattice is isometric to the permutahedral lattice, which is a well-known object in discrete geometry.

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Aruni Choudhary, Arijit Ghosh. 2018-04-19. Delaunay simplices in diagonally distorted lattices. https://arxiv.org/abs/1804.07024

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