(octave.info)Convex Hull

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30.3 Convex Hull
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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.

     See also: Note: convhulln, *note delaunay:
     XREFdelaunay, Note: voronoi.

 -- : 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.

     See also: Note: convhull, *note delaunayn:
     XREFdelaunayn, Note: voronoin.

   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]);