MATLAB Function Reference |

**Syntax**

**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, where `n > 1`

and `m >= n+1`

.

The first row of `V`

is a point at infinity. If any index in a cell of the cell array is `1`

, then the corresponding Voronoi cell contains the first point in `V`

, a point at infinity. This means the Voronoi cell is unbounded.

**Visualization**

You can plot individual bounded cells of an n-D Voronoi diagram. To do this, use `convhulln`

to compute the vertices of the facets that make up the Voronoi cell. Then use `patch`

and other plot functions to generate the figure. For an example, see Tessellation and Interpolation of Scattered Data in Higher Dimensions in the MATLAB documentation.

**Examples**

[V,C] = voronoin(x) 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 C = [1x4 double] [1x5 double] [1x4 double] [1x4 double] [1x4 double] [1x5 double] [1x4 double]

Use a `for`

loop to see the contents of the cell array `C`

.

In particular, the fifth Voronoi cell consists of 4 points: `V(10,:)`

, `V(5,:)`

, `V(6,:)`

, `V(8,:)`

.

**Algorithm**

`voronoin`

is based on Qhull [2]. It uses the Qhull joggle option (`'QJ'`

). 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.

**See Also**

`convhull`

, `convhulln`

, `delaunay`

, `delaunayn`

, `voronoi`

**Reference**

[1] Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for
Convex Hulls," *ACM Transactions on Mathematical Software*, Vol. 22, No. 4,
Dec. 1996, p. 469-483. Available in HTML format at http://www.acm.org/
pubs/citations/journals/toms/1996-22-4/p469-barber/ and in PostScript
format at ftp://geom.umn.edu/pub/software/qhull-96.ps.

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

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