Delaunay simplices in diagonally distorted lattices

04/19/2018

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by   Aruni Choudhary, et al.

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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 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.