voronoin (MATLAB Function Reference)

n-D Voronoi diagram

Syntax

[V, C] = voronoin(X)

Description

[V, C] = voronoin(X) returns Voronoi vertices V and the Voronoi cells C of the Voronoi diagram of X. V is a numv-by-n array of the numv Voronoi vertices in n-D space, each row corresponds to a Voronoi vertex. C is a vector cell array where each element contains the indices into V of the vertices of the corresponding Voronoi cell. X is an m-by-n array, representing m n-D points.

Note voronoin is based on qhull [1]. For information about qhull, see http://www.geom.umn.edu/software/qhull/. For copyright information, see http://www.geom.umn.edu/software/download/COPYING.html.

Example

Let

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 ]

then [V,C] = voronoin(x) generates

V =       Inf       Inf
       0.3833    0.3833
       0.7000   -1.6500
       0.2875    0.0000
      -0.0000    0.2875
      -0.0000   -0.0000
      -0.0500   -0.5250
      -0.0500   -0.0500
      -1.7500    0.7500
      -1.4500    0.6500

and

C{:} = 4  2  1  3
       10 5  2  1  9
       9  1  3  7
       10 8  7  9
       10 5  6  8
       8  6  4  3  7
       6  4  2  5

In particular, the fifth Voronoi cell consists of 4 points: V(10,:), V(5,:), V(6,:), V(8,:).

See Also

convhulln, delaunayn, voronoi

Reference

[1] National Science and Technology Research Center for Computation and Visualization of Geometric Structures (The Geometry Center), University of Minnesota. 1993.

voronoi waitbar