# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# VoronoiMesh

VoronoiMesh[{p1,,pn}]
gives a MeshRegion representing the Voronoi mesh from the points , , .

VoronoiMesh[{p1,,pn},{{xmin,xmax},}]
clips the mesh to the bounds .

## Details and OptionsDetails 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 and defined by , which is the region of points closer to than any other point for .
• The cells associated with the outer points will be unbounded, but only a bounded range will be returned. If no explicit range is given, a range is computed automatically.
• The cells will be intervals in 1D, convex polygons in 2D, and convex polyhedra in 3D.
• VoronoiMesh takes the same options as MeshRegion.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

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

 Out[2]=

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

 Out[3]=

Create a 2D Voronoi mesh from a set of points:

 Out[2]=

Each point corresponds to a Voronoi cell:

 Out[3]=