# VoronoiMesh

VoronoiMesh[{p1,,pn}]

gives a MeshRegion representing the Voronoi mesh from the points p1, p2, .

VoronoiMesh[{p1,,pn},{{xmin,xmax},}]

clips the mesh to the bounds .

# Details and Options • VoronoiMesh is also known as Voronoi diagram and Dirichlet tessellation.
• • The Voronoi mesh consists of n convex cells, each associated with a point pi and defined by , which is the region of points closer to pi than any other point pj for ji.
• The cells associated with the outer points will be unbounded, but only a bounded range will be returned. If no explicit range {{xmin,xmax},} is given, a range is computed automatically.
• The cells will be intervals in 1D and convex polygons in 2D.
• VoronoiMesh takes the same options as MeshRegion.

# Examples

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## Basic Examples(2)

Create a 1D Voronoi mesh from a set of points:

 In:= In:= Out= Each point corresponds to a Voronoi cell, which is an interval in the 1D case:

 In:= Out= Create a 2D Voronoi mesh from a set of points:

 In:= In:= Out= Each point corresponds to a Voronoi cell:

 In:= Out= ## Properties & Relations(5)

Introduced in 2014
(10.0)
|
Updated in 2015
(10.2)