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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.

MORE INFORMATION

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 {x_i, y_i}, 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 {x_i, y_i}.

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.