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########################################################################
##
## Copyright (C) 1999-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{tri} =} delaunay (@var{x}, @var{y})
## @deftypefnx {} {@var{tetr} =} delaunay (@var{x}, @var{y}, @var{z})
## @deftypefnx {} {@var{tri} =} delaunay (@var{x})
## @deftypefnx {} {@var{tri} =} delaunay (@dots{}, @var{options})
## Compute the Delaunay triangulation for a 2-D or 3-D set of points.
##
## For 2-D sets, the return value @var{tri} is a set of triangles which
## satisfies the Delaunay circum-circle criterion, i.e., no 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.
##
## For 3-D sets, the return value @var{tetr} is a set of tetrahedrons which
## satisfies the Delaunay circum-circle criterion, i.e., no data point from
## [@var{x}, @var{y}, @var{z}] is within the circum-circle of the defining
## tetrahedron. The set of tetrahedrons is a matrix of size [n, 4]. Each row
## defines a tetrahedron and the four columns are the four vertices of the
## tetrahedron. The value of @code{@var{tetr}(i,j)} is an index into @var{x},
## @var{y}, @var{z} for the location of the j-th vertex of the i-th
## tetrahedron.
##
## The input @var{x} may also be a matrix with two or three columns where the
## first column contains x-data, the second y-data, and the optional third
## column contains z-data.
##
## An optional final 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"@}}.
## If Qhull fails for 2-D input the triangulation is attempted again with
## the options @code{@{"Qt", "Qbb", "Qc", "Qz"@}} which may result in
## reduced accuracy.
##
## 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.
##
## @example
## @group
## x = rand (1, 10);
## y = rand (1, 10);
## tri = delaunay (x, y);
## triplot (tri, x, y);
## hold on;
## plot (x, y, "r*");
## axis ([0,1,0,1]);
## @end group
## @end example
## @seealso{delaunayn, convhull, voronoi, triplot, trimesh, tetramesh, trisurf}
## @end deftypefn
function tri = delaunay (varargin)
if (nargin < 1 || nargin > 4)
print_usage ();
endif
z = [];
options = [];
switch (nargin)
case 1
if (! ismatrix (varargin{1})
|| (columns (varargin{1}) != 2 && columns (varargin{1}) != 3))
error ("delaunay: X must be a matrix with 2 or 3 columns");
else
x = varargin{1}(:,1);
y = varargin{1}(:,2);
if (columns (varargin{1}) == 3)
z = varargin{1}(:,3);
endif
endif
case 2
if (isnumeric (varargin{2}))
x = varargin{1};
y = varargin{2};
elseif (! (ischar (varargin{2}) || iscellstr (varargin{2})))
error ("delaunay: OPTIONS must be a string or cell array of strings");
else
options = varargin{2};
ncols = columns (varargin{1});
if (! ismatrix (varargin{1}) || (ncols != 2 && ncols != 3))
error ("delaunay: X must be a matrix with 2 or 3 columns");
else
x = varargin{1}(:,1);
y = varargin{1}(:,2);
if (ncols == 3)
z = varargin{1}(:,3);
endif
endif
endif
case 3
if (isnumeric (varargin{3}))
x = varargin{1};
y = varargin{2};
z = varargin{3};
elseif (! (ischar (varargin{3}) || iscellstr (varargin{3})))
error ("delaunay: OPTIONS must be a string or cell array of strings");
else
x = varargin{1};
y = varargin{2};
options = varargin{3};
endif
case 4
x = varargin{1};
y = varargin{2};
z = varargin{3};
options = varargin{4};
if (! (ischar (options) || iscellstr (options)))
error ("delaunay: OPTIONS must be a string or cell array of strings");
endif
endswitch
if (isempty (z))
x = x(:); y = y(:);
if (! size_equal (x, y))
error ("delaunay: X and Y must be the same size");
endif
tri = delaunayn ([x, y], options);
else
x = x(:); y = y(:); z = z(:);
if (! size_equal (x, y, z))
error ("delaunay: X, Y, and Z must be the same size");
endif
tri = delaunayn ([x, y, z], options);
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);
%! tri = delaunay (x,y);
%! clf;
%! triplot (tri, x, y);
%! hold on;
%! plot (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];
%! mat = [x(:), y(:)];
%! assert (sortrows (sort (delaunay (mat), 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]);
## Test 3-D input
%!testif HAVE_QHULL
%! x = [-1, -1, 1, 0, -1]; y = [-1, 1, 1, 0, -1]; z = [0, 0, 0, 1, 1];
%! assert (sortrows (sort (delaunay (x, y, z), 2)), [1,2,3,4;1,2,4,5]);
## Input validation tests
%!error <Invalid call> delaunay ()
%!error <Invalid call> delaunay (1,2,3,4,5)
%!error <X must be a matrix with 2 or 3 columns> delaunay (ones (2,4))
%!error <OPTIONS must be a string or cell array> delaunay (ones (2,2), struct ())
%!error <X must be a matrix with 2 or 3 columns> delaunay (ones (2,4), "")
%!error <OPTIONS must be a string or cell array> delaunay (ones (2,2), ones (2,2), struct ())
%!error <OPTIONS must be a string or cell array> delaunay (ones (2,2), ones (2,2), ones (2,2), struct ())
%!error <X and Y must be the same size> delaunay (1, [1 2])
%!error <X, Y, and Z must be the same size> delaunay (1, [1 2], [1 2])
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