update packages

[CreaPhase.git] / octave_packages / m / geometry / delaunay.m

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+## Copyright (C) 1999-2012 Kai Habel
+##
+## This file is part of Octave.
+##
+## Octave is free software; you can redistribute it and/or modify it
+## under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or (at
+## your option) any later version.
+##
+## Octave is distributed in the hope that it will be useful, but
+## WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+## General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn  {Function File} {} delaunay (@var{x}, @var{y})
+## @deftypefnx {Function File} {@var{tri} =} delaunay (@var{x}, @var{y})
+## @deftypefnx {Function File} {@var{tri} =} delaunay (@var{x}, @var{y}, @var{options})
+## Compute the Delaunay triangulation for a 2-D set of points.
+## The return value @var{tri} is a set of triangles which satisfies the
+## Delaunay circum-circle criterion, i.e., only a single data point from
+## [@var{x}, @var{y}] is within the circum-circle of the defining triangle.
+##
+## The set of triangles @var{tri} is a matrix of size [n, 3].  Each
+## row defines a triangle and the three columns are the three vertices
+## of the triangle.  The value of @code{@var{tri}(i,j)} is an index into
+## @var{x} and @var{y} for the location of the j-th vertex of the i-th
+## triangle.
+##
+## 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
+## @url{http://www.qhull.org/html/qh-quick.htm#options}.
+## The default options are @code{@{"Qt", "Qbb", "Qc", "Qz"@}}.
+##
+## If @var{options} is not present or @code{[]} then the default arguments are
+## used.  Otherwise, @var{options} replaces the default argument list. 
+## To append user options to the defaults it is necessary to repeat the 
+## default arguments in @var{options}.  Use a null string to pass no arguments.
+##
+## If no output argument is specified the resulting Delaunay triangulation 
+## is plotted along with the original set of points.
+##
+## @example
+## @group
+## x = rand (1, 10);
+## y = rand (1, 10);
+## T = delaunay (x, y);
+## VX = [ x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1)) ];
+## VY = [ y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1)) ];
+## axis ([0,1,0,1]);
+## plot (VX, VY, "b", x, y, "r*");
+## @end group
+## @end example
+## @seealso{delaunay3, delaunayn, convhull, voronoi}
+## @end deftypefn
+
+## Author: Kai Habel <kai.habel@gmx.de>
+
+function tri = delaunay (x, y, options)
+
+  if (nargin != 2 && nargin != 3)
+    print_usage ();
+  endif
+
+  if (! (isvector (x) && isvector (y) && length (x) == length (y))
+      && ! size_equal (x, y))
+    error ("delaunay: X and Y must be the same size");
+  elseif (nargin == 3 && ! (ischar (options) || iscellstr (options)))
+    error ("delaunay: OPTIONS must be a string or cell array of strings");
+  endif
+
+  if (nargin == 2)
+    T = delaunayn ([x(:), y(:)]);
+  else
+    T = delaunayn ([x(:), y(:)], options);
+  endif
+
+  if (nargout == 0)
+    x = x(:).';
+    y = y(:).';
+    VX = [ x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1)) ];
+    VY = [ y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1)) ];
+    plot (VX, VY, "b", x, y, "r*");
+  else
+    tri = T;
+  endif
+
+endfunction
+
+
+%!demo
+%! old_state = rand ("state");
+%! restore_state = onCleanup (@() rand ("state", old_state));
+%! rand ("state", 1);
+%! x = rand (1,10);
+%! y = rand (1,10);
+%! T = delaunay (x,y);
+%! VX = [ x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1)) ];
+%! VY = [ y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1)) ];
+%! axis ([0,1,0,1]);
+%! plot (VX,VY,"b", x,y,"r*");
+
+%!testif HAVE_QHULL
+%! x = [-1, 0, 1, 0];
+%! y = [0, 1, 0, -1];
+%! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,4;2,3,4]);
+
+%!testif HAVE_QHULL
+%! x = [-1, 0, 1, 0, 0];
+%! y = [0, 1, 0, -1, 0];
+%! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]);
+
+%% FIXME: Need input validation tests
+