Voronoi diagrams and arrangements

Authors:
Herbert Edelsbrunner;Raimund Seidel
Affiliations:
Institute fir Informationsverarbeitung, Technical University of Gras, Schiesstattgasse 4A, A-8010 aan AUSTRIA;Computer Science Department, Cornell University, Ithaca NY
Venue:
SCG '85 Proceedings of the first annual symposium on Computational geometry
Year:
1985

Citing 5
Cited 3

Two-Dimensional Voronoi Diagrams in the Lp-Metric

Journal of the ACM (JACM)
Convex hulls of finite sets of points in two and three dimensions

Communications of the ACM
A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions

A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions
Generalized voronoi diagrams and geometric searching.

Generalized voronoi diagrams and geometric searching.
Geometric transforms for fast geometric algorithms

Geometric transforms for fast geometric algorithms

Toughness and Delaunay triangulations

SCG '87 Proceedings of the third annual symposium on Computational geometry
An empirical comparison of techniques for updating Delaunay triangulations

SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
A generic topology library

Science of Computer Programming

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose a uniform and general framework for defining and dealing with Voronoi Diagrams. In this framework a Voronoi Diagram is a partition of a domain D induced by a finite number of real valued functions on D. Valuable insight can be gained when one considers how these real valued functions partition DXR. With this view it turns out that the standard Euclidean Voronoi Diagram of point sets in R along with its order-&kgr; generalizations are intimately related to certain arrangements of hyperplanes. This fact can be used to obtain new Voronoi Diagram algorithms. We also discuss how the formalism of arrangements can be used to solve certain intersection and union problems.