MATLAB Function Reference  convhulln

N-dimensional convex hull

Syntax

• ```K = convhulln(X)
```K = convulln(X, options)
```[K,v] = convhulln(...)
```

Description

```K = convhulln(X) ``` returns the indices `K` of the points in `X` that comprise the facets of the convex hull of `X`. `X` is an `m`-by-`n` array representing `m` points in N-dimensional space. If the convex hull has `p` facets then `K` is `p`-by-`n`.

`convhulln` uses Qhull.

`K = convulln(X, options)` specifies a cell array of strings `options` to be used as options in Qhull. The default options are:

• `{'Qt'}` for 2-, 3-. and 4-dimensional input
• `{'Qt','Qx'}` for 5-dimensional input and higher.

If `options` is `[]`, the default options are used. If `options` is `{''}`, no options are used, not even the default. For more information on Qhull and its options, see http://www.qhull.org/.

`[K, v] = convhulln(...)` also returns the volume `v` of the convex hull.

Visualization

Plotting the output of `convhulln` depends on the value of `n`:

• For `n = 2`, use `plot` as you would for `convhull`.
• For `n = 3`, you can use `trisurf` to plot the output. The calling sequence is
• ```K = convhulln(X);
trisurf(K,X(:,1),X(:,2),X(:,3))
```
• You cannot plot `convhulln` output for `n > 3`.

Example

The following example illustrates the `options` input for `convhulln`. The following commands

• ```X = [0 0; 0 1e-10; 0 0; 1 1];
K = convhulln(X)
```

return a warning.

• ```Warning: qhull precision warning:
The initial hull is narrow (cosine of min. angle is
0.9999999999999998).
A coplanar point may lead to a wide facet. Options 'QbB' (scale
to unit box)
or 'Qbb' (scale last coordinate) may remove this warning. Use 'Pp'
to skip
this warning.
```

To suppress the warning, use the option `'Pp'`.The following command passes the option `'Pp'`, along with the default `'Qt'`, to `convhulln`.

• ```K = convhulln(X,{'Qt','Pp'})

K =

1     4
1     2
4     2
```

Algorithm

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

See Also

`convhull`, `delaunayn`, `dsearchn`, `tsearchn`, `voronoin`

Reference

  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. Available in PDF format at http://www.acm.org/pubs/ citations/journals/toms/1996-22-4/p469-barber/.

  National Science and Technology Research Center for Computation and Visualization of Geometric Structures (The Geometry Center), University of Minnesota. 1993.

© 1994-2005 The MathWorks, Inc.