ComputationalGeometry`
ComputationalGeometry`

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.

Details

  • 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.
Wolfram Research (2012), VoronoiDiagram, Wolfram Language function, https://reference.wolfram.com/language/ComputationalGeometry/ref/VoronoiDiagram.html.

Text

Wolfram Research (2012), VoronoiDiagram, Wolfram Language function, https://reference.wolfram.com/language/ComputationalGeometry/ref/VoronoiDiagram.html.

BibTeX

@misc{reference.wolfram_2020_voronoidiagram, author="Wolfram Research", title="{VoronoiDiagram}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ComputationalGeometry/ref/VoronoiDiagram.html}", note=[Accessed: 12-May-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_voronoidiagram, organization={Wolfram Research}, title={VoronoiDiagram}, year={2012}, url={https://reference.wolfram.com/language/ComputationalGeometry/ref/VoronoiDiagram.html}, note=[Accessed: 12-May-2021 ]}

CMS

Wolfram Language. 2012. "VoronoiDiagram." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ComputationalGeometry/ref/VoronoiDiagram.html.

APA

Wolfram Language. (2012). VoronoiDiagram. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ComputationalGeometry/ref/VoronoiDiagram.html