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:

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

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

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Each point corresponds to a Voronoi cell:

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Scope  (2)

Options  (11)

Applications  (8)

Properties & Relations  (5)

See Also

DelaunayMesh  ConvexHullMesh  MeshRegion  RegionNearest

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