--- _id: '4108' abstract: - lang: eng text: 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. acknowledgement: 'We would like to thank John Gilbert for his careful reading of the manuscript and his many suggestions for improvement. We also want to thank Bennett Battaile, Gianfranco Bilardi, Joseph O''Rourke, and Chee Yap for their comments. ' article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Raimund full_name: Seidel, Raimund last_name: Seidel citation: ama: Edelsbrunner H, Seidel R. Voronoi diagrams and arrangements. Discrete & Computational Geometry. 1986;1(1):25-44. doi:10.1007/BF02187681 apa: Edelsbrunner, H., & Seidel, R. (1986). Voronoi diagrams and arrangements. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02187681 chicago: Edelsbrunner, Herbert, and Raimund Seidel. “Voronoi Diagrams and Arrangements.” Discrete & Computational Geometry. Springer, 1986. https://doi.org/10.1007/BF02187681. ieee: H. Edelsbrunner and R. Seidel, “Voronoi diagrams and arrangements,” Discrete & Computational Geometry, vol. 1, no. 1. Springer, pp. 25–44, 1986. ista: Edelsbrunner H, Seidel R. 1986. Voronoi diagrams and arrangements. Discrete & Computational Geometry. 1(1), 25–44. mla: 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. short: H. Edelsbrunner, R. Seidel, Discrete & Computational Geometry 1 (1986) 25–44. date_created: 2018-12-11T12:06:59Z date_published: 1986-01-01T00:00:00Z date_updated: 2022-02-01T08:53:39Z day: '01' doi: 10.1007/BF02187681 extern: '1' intvolume: ' 1' issue: '1' language: - iso: eng month: '01' oa_version: None page: 25 - 44 publication: Discrete & Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer publist_id: '2012' quality_controlled: '1' status: public title: Voronoi diagrams and arrangements type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 1 year: '1986' ...