Summary: A tight bound for the Delaunay triangulation of points on a
polyhedron
Nina Amenta
UC Davis
Dominique Attali
Gipsa-lab, CNRS Grenoble
Olivier Devillers
INRIA Sophia-Antipolis
May 5, 2008
Abstract
We show that the Delaunay triangulation of a set of n points distributed nearly uni-
formly on a p-dimensional polyhedron (not necessarily convex) in d-dimensional Eu-
clidean space is O(n
d-k+1
p ), where k = d+1
p+1 . This bound is tight, and improves on
amenta@ucdavis.edu. Computer Science Department, University of California, One Sheilds Ave,
Davis, CA 95616. Fax 1-530-752-5767. Supported by NSF CCF­0093378.
Dominique.Attali@lis.inpg.fr. Gipsa-lab, ENSIEG, Domaine Universitaire, BP 46, 38402
Saint Martin d'H`eres, France. Supported by the EU under contract IST-2002-506766 (Aim@Shape) and

Source: Amenta, Nina - Department of Computer Science, University of California, Davis

Collections: Biology and Medicine; Computer Technologies and Information Sciences