convhull (MATLAB Functions)

Convex hull

Syntax

K = convhull(x,y)
K = convhull(x,y,options)
[K,a] = convhull(...)

Description

K = convhull(x,y) returns indices into the x and y vectors of the points on the convex hull.

convhull uses Qhull.

K = convhull(x,y,options) specifies a cell array of strings options to be used in Qhull via convhulln. The default option is {'Qt'}.

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

[K,a] = convhull(...) also returns the area of the convex hull.

Visualization

Use plot to plot the output of convhull.

Examples

Example 1.

xx = -1:.05:1; yy = abs(sqrt(xx));
[x,y] = pol2cart(xx,yy);
k = convhull(x,y);
plot(x(k),y(k),'r-',x,y,'b+')

Example 2. The following example illustrates the options input for convhull. The following commands

X = [0 0 0 1];
Y = [0 1e-10 0 1];
K = convhull(X,Y)

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 this warning, use the option 'Pp'. The following command passes the option 'Pp', along with the default 'Qt', to convhull.

K = convhull(X,Y,{'Qt','Pp'}) 

K =

     2
     1
     4
     2

Algorithm

convhull is based on Qhull [2]. For information about Qhull, see http://www.qhull.org/. For copyright information, see http://www.qhull.org/COPYING.txt.

See Also

convhulln, delaunay, plot, polyarea, voronoi

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

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

conv2 convhulln