MATLAB Function Reference
delaunay3

3-D Delaunay tessellation

Syntax

• ```TES = delaunay3(x,y,z)
```

Description

```TES = delaunay3(x,y,z) ``` returns an array `TES`, each row of which contains the indices of the points in `(x,y,z)` that make up a tetrahedron in the tessellation of `(x,y,z)`. `TES` is a `numtes`-by-`4` array where `numtes` is the number of facets in the tessellation. `x`, `y`, and `z` are vectors of equal length. If the original data points are collinear or `x`, `y`, and `z` define an insufficient number of points, the triangles cannot be computed and `delaunay3` returns an empty matrix.

Visualization

Use `tetramesh` to plot `delaunay3` output. `tetramesh` displays the tetrahedrons defined in `TES` as mesh. `tetramesh` uses the default tranparency parameter value `'FaceAlpha' = 0.9`.

Example

This example generates a 3-D Delaunay tessellation, then uses `tetramesh` to plot the tetrahedrons that form the corresponding simplex. `camorbit` rotates the camera position to provide a meaningful view of the figure.

• ```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.
Tes = delaunay3(x,y,z)

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

X = [x(:) y(:) z(:)];
tetramesh(Tes,X);camorbit(20,0)

```

Algorithm

`delaunay3` 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.

`delaunay`, `delaunayn`