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.

ExamplesExamplesopen allclose all

Basic Examples  (2)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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Introduced in 2014
(10.0)