MATLAB Function Reference
delaunayn

n-D Delaunay tessellation

Syntax

• ```T = delaunayn(X)
```

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 tessellation. `X` is an `m`-by-`n` array representing m points in `n`-D space. `T` is a `numt`-by-(`n+1`) array where each row contains the indices into `X` of the vertices of the corresponding simplex.

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` as you would for `delaunay3`.
• You cannot plot `delaunayn` output for `n > 3`.

Example

This example generates an n-D Delaunay tessellation, 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 =
```   9  1  5  6
``````   3  9  1  5
``````   2  9  1  6
``````   2  3  9  4
``````   2  3  9  1
``````   7  9  5  6
``````   7  3  9  5
``````   8  7  9  6
``````   8  2  9  6
``````   8  2  9  4
``````   8  3  9  4
``````   8  7  3  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)

```

Algorithm

`delaunayn` 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.

`convhulln`, `delaunayn`, `delaunay3`, `tetramesh`, `voronoin`