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voronoiDiagram - Class: DelaunayTri

Voronoi diagram

Syntax

[V, R] = voronoiDiagram(DT)

Description

[V, R] = voronoiDiagram(DT) returns the vertices V and regions R of the Voronoi diagram of the points DT.X. The region R{i} is a cell array of indices into V that represents the Voronoi vertices bounding the region. The Voronoi region associated with the i'th point, DT.X(i) is R{i}. For 2-D, vertices in R{i} are listed in adjacent order, i.e. connecting them will generate a closed polygon (Voronoi diagram). For 3-D the vertices in R{i} are listed in ascending order.

The Voronoi regions associated with points that lie on the convex hull of DT.X are unbounded. Bounding edges of these regions radiate to infinity. The vertex at infinity is represented by the first vertex in V.

Inputs

`DT`	Delaunay triangulation.

Outputs

`V`	`numv`-by-`ndim` matrix representing the coordinates of the Voronoi vertices, where `numv` is the number of vertices and `ndim` is the dimension of the space where the points reside.
`R`	Vector cell array of `length(DR.X)`, representing the Voronoi cell associated with each point.

Definitions

The Voronoi diagram of a discrete set of points X decomposes the space around each point X(i) into a region of influence R{i}. Locations within the region are closer to point i than any other point. The region of influence is called the Voronoi region. The collection of all the Voronoi regions is the Voronoi diagram.

The convex hull of a set of points X is the smallest convex polygon (or polyhedron in higher dimensions) containing all of the points of X.

Examples

Compute the Voronoi Diagram of a set of points:

X = [ 0.5    0
      0      0.5
     -0.5   -0.5
     -0.2   -0.1
     -0.1    0.1
      0.1   -0.1
      0.1    0.1 ]
dt = DelaunayTri(X)
[V,R] = voronoiDiagram(dt)