# delaunayn

N-D Delaunay triangulation

## Syntax

``T = delaunayn(X)``
``T = delaunayn(X,opts)``

## Description

example

````T = delaunayn(X)` computes a set of simplices such that no data points of `X` are contained in any circumspheres of the simplices. The set of simplices forms the Delaunay triangulation. `X` is an `m`-by-`n` array representing `m` points in `n`-dimensional space. `T` is a `numt`-by-(`n+1`) array where each row contains the indices into `X` of the vertices of the corresponding simplex.```
````T = delaunayn(X,opts)` specifies a cell array of Qhull options to use in computing the delaunay triangulation.```

## Examples

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This example generates an n-dimensional Delaunay triangulation, where `n = 3`.

```d = [-1 1]; [x,y,z] = meshgrid(d,d,d); % A cube x = [x(:);0]; y = [y(:);0]; z = [z(:);0]; % [x,y,z] are corners of a cube plus the center. X = [x(:) y(:) z(:)]; Tes = delaunayn(X)```
```Tes = 12×4 4 3 9 1 4 9 2 1 7 9 3 1 7 5 9 1 7 9 4 3 7 8 4 9 6 2 9 1 6 9 5 1 6 4 9 2 6 4 8 9 ⋮ ```

You can use `tetramesh` to visualize the tetrahedrons that form the corresponding simplex. `camorbit` rotates the camera position to provide a meaningful view of the figure.

```tetramesh(Tes,X); camorbit(20,0)``` ## Input Arguments

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Points, specified as a matrix. `X` is an `m`-by-`n` matrix representing `m` points in `n`-dimensional space.

Data Types: `double`

Qhull options, specified as a cell array of character vectors indicating which Qhull algorithms to use. For a list of options, see Qhull control options.

The default options are:

• `{'Qt','Qbb','Qc'}` for 2- and 3-dimensional input

• `{'Qt','Qbb','Qc','Qx'}` for 4 and higher-dimensional input

If `opts` is `[]`, then the default options are used. If `opts` is an empty cell array, `{''}`, then no options are used, not even the defaults.

## Algorithms

`delaunayn` is based on Qhull. For more information, see http://www.qhull.org/. For copyright information, see http://www.qhull.org/COPYING.txt.

## Version History

Introduced before R2006a