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BoundedDiagram

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.
  • 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 which 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.