The Construction of Delaunay Diagrams by Lob Reduction

Authors:
Pierre Kauffmann;Jean-Claude Spehner
Affiliations:
-;-
Venue:
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Year:
2000

Citing 3
Cited 0

Algorithms in combinatorial geometry

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Discrete & Computational Geometry
Closest-point problems

SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science

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Abstract

In this paper we present an algorithm that generalizes Lawson's algorithm for transforming any triangulation of a point set into the Delaunay triangulation. Lawson's algorithm flips illegal edges into legal edges. Our algorithm uses lob reductions instead of flips, in a lob reduction an arbitrary number (possibly zero) of illegal edges are replaced by a single edge. Our algorithm reaches the Delaunay triangulation of a set S of n sites in O(n2) time. If the elements of S are the vertices of a convex polygon our algorithm is very efficient.