Discrete & Computational Geometry

, Volume 1, Issue 1, pp 25–44

Voronoi diagrams and arrangements

  • Herbert Edelsbrunner
  • Raimund Seidel

DOI: 10.1007/BF02187681

Cite this article as:
Edelsbrunner, H. & Seidel, R. Discrete Comput Geom (1986) 1: 25. doi:10.1007/BF02187681


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 domainD induced by a finite number of real valued functions onD. Valuable insight can be gained when one considers how these real valued functions partitionD ×R. With this view it turns out that the standard Euclidean Voronoi diagram of point sets inRd along with its order-k 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.

Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Herbert Edelsbrunner
    • 1
  • Raimund Seidel
    • 2
  1. 1.Institute f. InformationsverarbeitungTechnical University of GrazGrazAustria
  2. 2.Computer Science DepartmentCornell UniversityIthaca
  3. 3.Department of Computer ScienceUniversity of IllinoisUrbana