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voronoiDiagram

Class: DelaunayTri

(Not recommended) Voronoi diagram

Note

voronoiDiagram(DelaunayTri) is not recommended. Use voronoiDiagram(delaunayTriangulation) instead.

DelaunayTri is not recommended. Use delaunayTriangulation instead.

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.

Input Arguments

DTDelaunay triangulation.

Output Arguments

Vnumv-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.
RVector cell array of length(DR.X), representing the Voronoi cell associated with each point.

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)	

Definitions

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