VoronoiDiagram

As of Version 10, all the functionality of the ComputationalGeometry package is built into the Wolfram System. >>

VoronoiDiagram[{{x1,y1},{x2,y2},}]
yields the planar Voronoi diagram of the points {x1,y1},{x2,y2},.

VoronoiDiagram[{{x1,y1},{x2,y2},},val]
takes val to be the Delaunay triangulation vertex adjacency list.

VoronoiDiagram[{{x1,y1},{x2,y2},},val,hull]
takes hull to be the convex hull index list.

DetailsDetails

  • VoronoiDiagram functionality is now available in the built-in Wolfram Language function VoronoiMesh.
  • To use VoronoiDiagram, you first need to load the Computational Geometry Package using Needs["ComputationalGeometry`"].
  • The Voronoi diagram is represented by two lists, a vertex coordinate list and a vertex adjacency list.
  • An element {i,{v1,}} of the vertex adjacency list corresponds to the point {xi,yi}, and the indices v1, identify the vertices or rays in the vertex coordinate list that form the polygon associated with the point {xi,yi}.
  • The optional arguments val and hull may be used to speed up the Voronoi diagram computation if the Delaunay triangulation and convex hull are available.