10.1007/BF02187681
Herbert Edelsbrunner
Herbert
Edelsbrunner0000-0002-9823-6833
Seidel, Raimund
Raimund
Seidel
Voronoi diagrams and arrangements
Springer
1986
2018-12-11T12:06:59Z
2019-04-26T07:22:40Z
journal_article
https://research-explorer.app.ist.ac.at/record/4108
https://research-explorer.app.ist.ac.at/record/4108.json
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.