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### 29.3 Convex Hull

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.

— Function File: H = convhull (x, y)
— Function File: H = convhull (x, y, opt)

> Returns the index vector to the points of the enclosing convex hull. The data points are defined by the x and y vectors.

> A third optional argument, which must be a string, contains extra options passed to the underlying qhull command. See the documentation for the Qhull library for details.

> See also: delaunay, convhulln.

— Loadable Function: h = convhulln (p)
— Loadable Function: h = convhulln (p, opt)
— Loadable Function: [h, v] = convhulln (...)

> Return an index vector to the points of the enclosing convex hull. The input matrix of size [n, dim] contains n points of dimension dim.

> If a second optional argument is given, it must be a string or cell array of strings containing options for the underlying qhull command. (See the Qhull documentation for the available options.) The default options are "s Qci Tcv". If the second output v is requested the volume of the convex hull is calculated.

> See also: convhull, delaunayn.

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 fig:convhull.

Figure 29.5: The convex hull of a simple set of points