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.
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Acknowledgments
This work was in part supported by a grant from the Natural Sciences and Engineering Research Council of Canada. This support is gratefully acknowledged. The authors would also like to thank Professor Vladimir Marianov for his assistance with the Thiessen reference and for providing some of the figures in this paper. Thanks also to our assistant #21 (Courtney Palmer) for providing some of the figures.
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Burkey, M.L., Bhadury, J., Eiselt, H.A. (2011). Voronoi Diagrams and Their Uses. In: Eiselt, H., Marianov, V. (eds) Foundations of Location Analysis. International Series in Operations Research & Management Science, vol 155. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7572-0_19
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