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# delaunayn

N-D Delaunay triangulation

## Syntax

T = delaunayn(X)
T = delaunayn(X, options)

## Description

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, options) specifies a cell array of strings 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 options is [], the default options used. If options is {''}, no options are used, not even the default.

## Visualization

Plotting the output of delaunayn depends of the value of n:

• For n = 2, use triplot, trisurf, or trimesh as you would for delaunay.

• For n = 3, use tetramesh.

For more control over the color of the facets, use patch to plot the output.

• You cannot plot delaunayn output for n > 3.

## Examples

### Example 1

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 =

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
6     9     7     5
6     8     7     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)`

## See Also

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