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boundedCellVoronoi mPower Reference Home

boundedCellVoronoi calculates a modified Voronoi diagram of a set of points in the x-y plane. A temporary layer of artificial cells is added outside the convex hull of the points, and the Voronoi diagram is computed on the extended set. The cells corresponding to the artificial cell are then removed to generate the bounded cell Voronoi diagram.

boundedCellVoronoi[points, diameter, options]: If diameter is ≤ 0 then the mean delaunay triangulation edge length is used for the diameter.

boundedCellVoronoi[points,options] is equivalent to boundedCellVoronoi[points, -1, options].

visualization and visualize3D use boundedCellVoronoi.

boundedCellVoronoi is also an option for visualization, and can be used to provide a copy of the bound cell Voronoi Diagram as input to visualization to improve processing time.

Example

The following figures illustrate the concepts in two dimensions. Click on any of the figures to see a larger view; the example notebook illustrates how to generate these figures.

A set of 50 randomly placed points in a circular region.
Finite-length edges of the Voronoi Diagram.
Finite-length edges, colored regions, and points.
The Bounded Cell Voronoi of the same set of points.
Finite edges are shown in pink to illustrate where they were truncated.
Colored Bounded Cell Voronoi.
A 3-Dimensional set of points; the box is shown to give some perspective to the figure.
The bounded cell Voronoi Diagram in 3 Dimensions; each cell is shown randomly colored.
The bounded cell Voronoi Diagram showing only the cell edges and centers.

See Also:


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[20-Dec-2005]