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scripts/geometry/delaunay.m

changeset 10289: 4b124317dc38
parent:16f53d29049f
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (64 minutes ago)
permissions: -rw-r--r--
description: base_properties::set_children: account for hidden children 
     1## Copyright (C) 1999, 2000, 2007, 2008, 2009 Kai Habel

     2##

     3## This file is part of Octave.

     4##

     5## Octave is free software; you can redistribute it and/or modify it

     6## under the terms of the GNU General Public License as published by

     7## the Free Software Foundation; either version 3 of the License, or (at

     8## your option) any later version.

     9##

    10## Octave is distributed in the hope that it will be useful, but

    11## WITHOUT ANY WARRANTY; without even the implied warranty of

    12## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

    13## General Public License for more details.

    14##

    15## You should have received a copy of the GNU General Public License

    16## along with Octave; see the file COPYING.  If not, see

    17## <http://www.gnu.org/licenses/>.

    18

    19## -*- texinfo -*-

    20## @deftypefn {Function File} {@var{tri} =} delaunay (@var{x}, @var{y})

    21## @deftypefnx {Function File} {@var{tri} =} delaunay (@var{x}, @var{y}, @var{opt})

    22## The return matrix of size [n, 3] contains a set triangles which are

    23## described by the indices to the data point x and y vector.

    24## The triangulation satisfies the Delaunay circum-circle criterion.

    25## No other data point is in the circum-circle of the defining triangle.

    26##

    27## A third optional argument, which must be a string, contains extra options

    28## passed to the underlying qhull command.  See the documentation for the 

    29## Qhull library for details.

    30##

    31## @example

    32## @group

    33## x = rand (1, 10);

    34## y = rand (size (x));

    35## T = delaunay (x, y);

    36## X = [x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1))];

    37## Y = [y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1))];

    38## axis ([0,1,0,1]);

    39## plot (X, Y, "b", x, y, "r*");

    40## @end group

    41## @end example

    42## @seealso{voronoi, delaunay3, delaunayn}

    43## @end deftypefn

    44

    45## Author: Kai Habel <kai.habel@gmx.de>

    46

    47function ret = delaunay (x, y, opt)

    48

    49  if (nargin != 2 && nargin != 3)

    50    print_usage ();

    51  endif

    52  

    53  if (isvector (x) && isvector (y) && length (x) == length (y))

    54    if (nargin == 2)

    55      tri = delaunayn ([x(:), y(:)]);

    56    elseif (ischar (opt) || iscellstr (opt))

    57      tri = delaunayn ([x(:), y(:)], opt);

    58    else

    59      error ("delaunay: third argument must be a string");

    60    endif

    61  else

    62    error ("delaunay: first two input arguments must be vectors of same size");

    63  endif

    64

    65  if (nargout == 0)

    66    x = x(:).';

    67    y = y(:).';

    68    X = [x(tri(:,1)); x(tri(:,2)); x(tri(:,3)); x(tri(:,1))];

    69    Y = [y(tri(:,1)); y(tri(:,2)); y(tri(:,3)); y(tri(:,1))];

    70    plot(X, Y, 'b', x, y, 'r*');

    71  else

    72    ret = tri;

    73  endif

    74endfunction

    75

    76%!testif HAVE_QHULL

    77%! x = [-1, 0, 1, 0, 0];

    78%! y = [0, 1, 0, -1, 0];

    79%! assert (sortrows (sort (delaunay (x, y), 2)), [1,2,5;1,4,5;2,3,5;3,4,5])

    80

    81%!demo

    82%! rand ('state', 1);

    83%! x = rand(1,10);

    84%! y = rand(size(x));

    85%! T = delaunay(x,y);

    86%! X = [ x(T(:,1)); x(T(:,2)); x(T(:,3)); x(T(:,1)) ];

    87%! Y = [ y(T(:,1)); y(T(:,2)); y(T(:,3)); y(T(:,1)) ];

    88%! axis([0,1,0,1]);

    89%! plot(X,Y,'b',x,y,'r*');