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N-D Voronoi diagram

`[V,C] = voronoin(X)`

[V,C] = voronoin(X,options)

`[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-dimensional 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-dimensional 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.

`voronoin`

uses Qhull.

`[V,C] = voronoin(X,options)`

specifies a
cell array of Qhull options. The default options are:

`{'Qbb'}`

for 2- and 3-dimensional input`{'Qbb','Qx'}`

for 4 and higher-dimensional input

If `options`

is `[]`

, the default options are used. If
`code`

is `{''}`

, no options are used, not even
the default. For more information on Qhull and its options, see `http://www.qhull.org`

.

You can plot individual bounded cells of an n-dimensional 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.

`voronoin`

is based on Qhull [1]. For information about Qhull, see `http://www.qhull.org/`

.

[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.