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## Copyright (C) 1999-2013 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} {} delaunay (@var{x})
## @deftypefnx {Function File} {} delaunay (@dots{}, @var{options})
## @deftypefnx {Function File} {@var{tri} =} delaunay (@dots{})
## 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 input @var{x} may also be a matrix with two columns where the first
## column contains x-data and the second y-data.
##
## 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.
##
## The optional last 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, triplot, trimesh, trisurf}
## @end deftypefn
## Author: Kai Habel <kai.habel@gmx.de>
function tri = delaunay (varargin)
if (nargin < 1 || nargin > 3)
print_usage ();
endif
options = [];
switch (nargin)
case 1
if (! ismatrix (varargin{1}) || columns (varargin{1}) != 2)
error ("delaunay: X must be a matrix with 2 columns");
else
x = varargin{1}(:,1);
y = varargin{1}(:,2);
endif
case 2
if (isnumeric (varargin{2}))
x = varargin{1};
y = varargin{2};
elseif (ischar (varargin{2}) || iscellstr (varargin{2}))
options = varargin{2};
if (! ismatrix (varargin{1}) && columns (varargin{1}) != 2)
error ("delaunay: X must be a matrix with 2 columns");
else
x = varargin{1}(:,1);
y = varargin{1}(:,2);
endif
else
error ("delaunay: OPTIONS must be a string or cell array of strings");
endif
case 3
x = varargin{1};
y = varargin{2};
options = varargin{3};
if (! (ischar (options) || iscellstr (options)))
error ("delaunay: OPTIONS must be a string or cell array of strings");
endif
endswitch
if (! (isequal(size(x),size(y))))
error ("delaunay: X and Y must be the same size");
endif
T = delaunayn ([x(:), y(:)], options);
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)) ];
%! clf;
%! plot (VX,VY,"b", x,y,"r*");
%! axis ([0,1,0,1]);
%!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];
%! 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]);
%!testif HAVE_QHULL
%! x = [-1, 0; 0, 1; 1, 0; 0, -1; 0, 0];
%! assert (sortrows (sort (delaunay (x), 2)), [1,2,5;1,4,5;2,3,5;3,4,5]);
%!testif HAVE_QHULL
%! x = [1 5 2; 5 6 7];
%! y = [5 7 8; 1 2 3];
%! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,4;1,3,4;1,3,5;3,4,6]);
%% FIXME: Need input validation tests
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