Voronoi diagrams and arrangements

H. Edelsbrunner, R. Seidel, Discrete & Computational Geometry 1 (1986) 25–44.

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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 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 inR d 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.
Publishing Year
Date Published
1986-01-01
Journal Title
Discrete & Computational Geometry
Volume
1
Issue
1
Page
25 - 44
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Edelsbrunner H, Seidel R. Voronoi diagrams and arrangements. Discrete & Computational Geometry. 1986;1(1):25-44. doi:10.1007/BF02187681
Edelsbrunner, H., & Seidel, R. (1986). Voronoi diagrams and arrangements. Discrete & Computational Geometry, 1(1), 25–44. https://doi.org/10.1007/BF02187681
Edelsbrunner, Herbert, and Raimund Seidel. “Voronoi Diagrams and Arrangements.” Discrete & Computational Geometry 1, no. 1 (1986): 25–44. https://doi.org/10.1007/BF02187681.
H. Edelsbrunner and R. Seidel, “Voronoi diagrams and arrangements,” Discrete & Computational Geometry, vol. 1, no. 1, pp. 25–44, 1986.
Edelsbrunner H, Seidel R. 1986. Voronoi diagrams and arrangements. Discrete & Computational Geometry. 1(1), 25–44.
Edelsbrunner, Herbert, and Raimund Seidel. “Voronoi Diagrams and Arrangements.” Discrete & Computational Geometry, vol. 1, no. 1, Springer, 1986, pp. 25–44, doi:10.1007/BF02187681.

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