A Tight Bound for the Delaunay Triangulation of Points on a Polyhedron

We show that the Delaunay triangulation of a set of n points distributed nearly uniformly on a p-dimensional polyhedron (not necessarily convex) in d-dimensional Euclidean space is O(n d−k+1 p ), where k = ⌈ p+1⌉. This bound is tight in the worst case, and improves on the prior upper bound for most values of p. [email protected]. Computer Science Department, University of California, One Sheilds Ave, Davis, CA 95616. Fax 1-530-752-5767. Supported by NSF CCF–0093378. [email protected]. Gipsa-lab – CNRS UMR 5216, 961 rue de la Houille Blanche, BP 46, 38402 Grenoble Cedex, France. Supported by ANR ProjectGIGAANR-09-BLAN0331-01. [email protected]. INRIA Sophia Antipolis Méditerranée, BP 93, 06902 SophiaAntipolis, France. Supported by the EU under STREP contract FET-255827 (CGLearning)