convhulln (MATLAB Functions)

n-D convex hull

Syntax

```
K = convhulln(X)
[K,v] = convhulln(X)
```

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-D space. If the convex hull has p facets then K is p-by-n.

[K,v] = convhulln(X) 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))

For more control over the color of the facets, use patch to plot the output. For an example, see Tessellation and Interpolation of Scattered Data in Higher Dimensions in the MATLAB documentation.

You cannot plot convhulln output for n > 3.

Algorithm

convhulln 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.

See Also

convhull, delaunayn, dsearchn, tsearchn, voronoin

Reference

[1] 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 HTML format at http://www.acm.org/ pubs/citations/journals/toms/1996-22-4/p469-barber/ and in PostScript format at ftp://geom.umn.edu/pub/software/qhull-96.ps.

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

convhull convn