BoundedDiagram

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

BoundedDiagram[{{a1,b1},},{{x1,y1},}]
yields the bounded Voronoi diagram of the points {x1,y1},{x2,y2}, where the bound is the convex polygon formed from the points {{a1,b1},}.

BoundedDiagram[{{a1,b1},},{{x1,y1},},val]
takes val to be the Delaunay triangulation vertex adjacency list.

BoundedDiagram[{{a1,b1},},{{x1,y1},},val,hull]
takes hull to be the convex hull index list.

DetailsDetails

  • BoundedDiagram functionality is now available in the built-in Wolfram Language function VoronoiMesh.
  • To use BoundedDiagram, you first need to load the Computational Geometry Package using Needs["ComputationalGeometry`"].
  • The bounded 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 in the vertex coordinate list that form its bounding polygon.
  • BoundedDiagram begins by finding the unbounded Voronoi diagram and then incorporating the bounding polygon vertices into the diagram.
  • The bounding polygon should be large enough to contain all the points {xi,yi}.
  • The optional arguments val and hull may be used to speed up the initial Voronoi diagram computation if the Delaunay triangulation and convex hull are available.