Delaunay simplices in diagonally distorted lattices

摘要

Delaunay protection is a measure of how far is a Delaunay triangulation 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. (C) 2019 Elsevier B.V. All rights reserved.