# Voronoi diagram

In mathematics, a **Voronoi diagram** is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a **Voronoi cell**, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation.

The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a **Voronoi tessellation**, a **Voronoi decomposition**, a **Voronoi partition**, or a **Dirichlet tessellation** (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as **Thiessen polygons**.^{[1]}^{[2]}^{[3]} Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology, but also in visual art.^{[4]}^{[5]}

## References[edit | edit source]

- ↑ Burrough, Peter A.; McDonnell, Rachael; McDonnell, Rachael A.; Lloyd, Christopher D. (2015). "8.11 Nearest neighbours: Thiessen (Dirichlet/Voroni) polygons".
*Principles of Geographical Information Systems*. Oxford University Press. pp. 160–. ISBN 978-0-19-874284-5. - ↑ Longley, Paul A.; Goodchild, Michael F.; Maguire, David J.; Rhind, David W. (2005). "14.4.4.1 Thiessen polygons".
*Geographic Information Systems and Science*. Wiley. pp. 333–. ISBN 978-0-470-87001-3. - ↑ Sen, Zekai (2016). "2.8.1 Delaney, Varoni, and Thiessen Polygons".
*Spatial Modeling Principles in Earth Sciences*. Springer. pp. 57–. ISBN 978-3-319-41758-5. - ↑ Aurenhammer, Franz (1991). "Voronoi Diagrams – A Survey of a Fundamental Geometric Data Structure".
*ACM Computing Surveys*.**23**(3): 345–405. doi:10.1145/116873.116880. Unknown parameter`|s2cid=`

ignored (help) - ↑ Okabe, Atsuyuki; Boots, Barry; Sugihara, Kokichi; Chiu, Sung Nok (2000).
*Spatial Tessellations – Concepts and Applications of Voronoi Diagrams*(2nd ed.). John Wiley. ISBN 978-0-471-98635-5.