Next: Interpolation on Scattered Data, Previous: Voronoi Diagrams, Up: Geometry [Contents][Index]

The convex hull of a set of points is the minimum convex envelope
containing all of the points. Octave has the functions `convhull`

and `convhulln`

to calculate the convex hull of 2-dimensional and
N-dimensional sets of points.

`H`=**convhull***(*`x`,`y`)`H`=**convhull***(*`x`,`y`,`options`)Compute the convex hull of the set of points defined by the arrays

`x`and`y`. The hull`H`is an index vector into the set of points and specifies which points form the enclosing hull.An optional third argument, which must be a string or cell array of strings, contains options passed to the underlying qhull command. See the documentation for the Qhull library for details http://www.qhull.org/html/qh-quick.htm#options. The default option is

`{"Qt"}`

.If

`options`is not present or`[]`

then the default arguments are used. Otherwise,`options`replaces the default argument list. To append user options to the defaults it is necessary to repeat the default arguments in`options`. Use a null string to pass no arguments.

`h`=**convhulln***(*`pts`)`h`=**convhulln***(*`pts`,`options`)*[*`h`,`v`] =**convhulln***(…)*Compute the convex hull of the set of points

`pts`.`pts`is a matrix of size [n, dim] containing n points in a space of dimension dim.The hull

`h`is an index vector into the set of points and specifies which points form the enclosing hull.An optional second argument, which must be a string or cell array of strings, contains options passed to the underlying qhull command. See the documentation for the Qhull library for details http://www.qhull.org/html/qh-quick.htm#options. The default options depend on the dimension of the input:

- 2D, 3D, 4D:
`options`=`{"Qt"}`

- 5D and higher:
`options`=`{"Qt", "Qx"}`

If

`options`is not present or`[]`

then the default arguments are used. Otherwise,`options`replaces the default argument list. To append user options to the defaults it is necessary to repeat the default arguments in`options`. Use a null string to pass no arguments.If the second output

`v`is requested the volume of the enclosing convex hull is calculated.- 2D, 3D, 4D:

An example of the use of `convhull`

is

x = -3:0.05:3; y = abs (sin (x)); k = convhull (x, y); plot (x(k), y(k), "r-", x, y, "b+"); axis ([-3.05, 3.05, -0.05, 1.05]);

The output of the above can be seen in Figure 30.5.

Next: Interpolation on Scattered Data, Previous: Voronoi Diagrams, Up: Geometry [Contents][Index]