Voronoi diagram (nonfiction): Difference between revisions

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[[File:Approximate Voronoi Diagram.svg.png|thumb|Approximate Voronoi diagram of a set of points. Notice the blended colors in the fuzzy boundary of the Voronoi cells.]]In [[mathematics (nonfiction)]], a '''Voronoi diagram''' is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.
[[File:Approximate Voronoi Diagram.svg.png|thumb|Approximate Voronoi diagram of a set of points. Notice the blended colors in the fuzzy boundary of the Voronoi cells.]]In [[mathematics (nonfiction)]], a '''Voronoi diagram''' is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.
That set of points (called seeds, sites, or generators) is specified beforehand, and for each seed there is a corresponding region consisting of all points closer to that seed than to any other.
These regions are called Voronoi cells.
== Description ==
The Voronoi diagram of a set of points is dual to its Delaunay triangulation.


It is named after Georgy Voronoi, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet).
It is named after Georgy Voronoi, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet).
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Voronoi diagrams have practical and theoretical applications to a large number of fields, mainly in science and technology but also including visual art.
Voronoi diagrams have practical and theoretical applications to a large number of fields, mainly in science and technology but also including visual art.


== Nonfiction cross-reference ==
== Fiction cross-reference ==


== Fiction cross-reference ==
<gallery mode="traditional">
File:Voronoi-diagram-color-commentators.jpg|thumb|[[Color commentators (nonfiction)|Color commentators]] discussing recent scores from hotly contested [[Voronoi diagrams (nonfiction)|Voronoi diagrams]].
</gallery>


* [[Fantasy Voronoi diagram]]
* [[Fantasy Voronoi diagram]]
== Nonfiction cross-reference ==


== External links ==
== External links ==

Revision as of 10:43, 12 June 2016

Approximate Voronoi diagram of a set of points. Notice the blended colors in the fuzzy boundary of the Voronoi cells.

In mathematics (nonfiction), a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.

It is named after Georgy Voronoi, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet).

Voronoi diagrams have practical and theoretical applications to a large number of fields, mainly in science and technology but also including visual art.

Fiction cross-reference

Nonfiction cross-reference

External links