By Topic

On the Triangle-Perimeter Two-Site Voronoi Diagram

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Iddo Hanniel ; Res. Group, SolidWorks Corp., Concord, MA, USA ; Gill Barequet

The triangle-perimeter 2-site distance function defines the "distance" P(x, (p, q)) from a point x to two other points p, q as the perimeter of the triangle whose vertices are x, p, q. Accordingly, given a set S of n points in the plane, the Voronoi diagram of S with respect to P, denoted as VP(S), is the subdivision of the plane into regions, where the region of p, q ¿ S is the locus of all points closer to p, q (according to P) than to any other pair of sites in S. In this paper we prove a theorem about the perimeters of triangles, two of whose vertices are on a given circle. We use this theorem to show that the combinatorial complexity of VP(S) is O(n2+¿) (for any ¿ > 0). Consequently, we show that one can compute VP(S) on O(n2+¿) time and space.

Published in:

Voronoi Diagrams, 2009. ISVD '09. Sixth International Symposium on

Date of Conference:

23-26 June 2009