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Voronoi Diagrams and Their Uses

In: Foundations of Location Analysis

Author

Listed:
  • Mark L. Burkey

    (North Carolina A & T State University)

  • Joy Bhadury

    (University of North Carolina – Greensboro)

  • H. A. Eiselt

    (University of New Brunswick)

Abstract

Voronoi diagrams are a very simple geometrical construct with a large variety of applications. Simply put, the problem can be described as follows. Consider some d-dimensional space in which a number of given points (sometimes referred to as seeds, attractors, or generators) are located. To each seed we assign a set that includes all points that are closer to the seed it is assigned to than to any other seed. Such a set is called a Voronoi set. The collection of all Voronoi sets is then a Voronoi diagram. Voronoi diagrams can be constructed for a number of different metrics. Clearly, different metrics will lead to different measures of proximity that result in rather different Voronoi diagrams.

Suggested Citation

  • Mark L. Burkey & Joy Bhadury & H. A. Eiselt, 2011. "Voronoi Diagrams and Their Uses," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Foundations of Location Analysis, chapter 0, pages 445-470, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-7572-0_19
    DOI: 10.1007/978-1-4419-7572-0_19
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    Cited by:

    1. Yaolin Liu & Ying Jing & Enxiang Cai & Jiaxing Cui & Yang Zhang & Yiyun Chen, 2017. "How Leisure Venues Are and Why? A Geospatial Perspective in Wuhan, Central China," Sustainability, MDPI, vol. 9(10), pages 1-21, October.

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