Voronoi Diagrams

Compute and plot Voronoi diagrams

A Voronoi diagram of a discrete set of points decomposes the space around the points into regions of influence. This decomposition has the property that an arbitrary point within a region of influence is closer to the point than to any other point. These regions of influence are called Voronoi regions, and together they form the Voronoi diagram. The Voronoi diagram is an N-D geometric construct, but most practical applications are in 2-D and 3-D space.

Compute the topology of a Voronoi diagram by using one of these approaches:

For discrete points in 2-D or 3-D, you can use the voronoiDiagram function of the delaunayTriangulation object. This approach is more robust and demonstrates better performance for large data sets.
For discrete points in N-D, where N ≥ 2, you also can use the voronoin function.

Both approaches represent the topology of a Voronoi diagram using a matrix format. For details on this data structure, see Triangulations.

Functions

`voronoiDiagram`	Compute Voronoi diagram of Delaunay triangulation
`voronoin`	Compute Voronoi diagram in N-D space
`voronoi`	Plot Voronoi diagram in 2-D space

Topics

2-D Voronoi Diagram
Compute and plot the Voronoi diagram for a set of 2-D points.
3-D Voronoi Diagram
Compute the Voronoi diagram for a set of 3-D points, and plot a single region associated with one point.