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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.
  • 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 which 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.