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## Copyright (C) 2006-2013 Frederick (Rick) A Niles
## and Søren Hauberg
##
## 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} {[@var{in}, @var{on}] =} inpolygon (@var{x}, @var{y}, @var{xv}, @var{yv})
##
## For a polygon defined by vertex points @code{(@var{xv}, @var{yv})}, determine
## if the points @code{(@var{x}, @var{y})} are inside or outside the polygon.
## The variables @var{x}, @var{y}, must have the same dimension. The optional
## output @var{on} gives the points that are on the polygon.
##
## @end deftypefn
## Author: Frederick (Rick) A Niles <niles@rickniles.com>
## Created: 14 November 2006
## Vectorized by Søren Hauberg <soren@hauberg.org>
## The method for determining if a point is in in a polygon is based on
## the algorithm shown on
## http://local.wasp.uwa.edu.au/~pbourke/geometry/insidepoly/ and is
## credited to Randolph Franklin.
function [in, on] = inpolygon (x, y, xv, yv)
if (nargin != 4)
print_usage ();
endif
if (! (isreal (x) && isreal (y) && ismatrix (y) && ismatrix (y)
&& size_equal (x, y)))
error ("inpolygon: first two arguments must be real matrices of same size");
elseif (! (isreal (xv) && isreal (yv) && isvector (xv) && isvector (yv)
&& size_equal (xv, yv)))
error ("inpolygon: last two arguments must be real vectors of same size");
endif
npol = length (xv);
do_boundary = (nargout >= 2);
in = zeros (size (x), "logical");
if (do_boundary)
on = zeros (size (x), "logical");
endif
j = npol;
for i = 1 : npol
delta_xv = xv(j) - xv(i);
delta_yv = yv(j) - yv(i);
## distance = [distance from (x,y) to edge] * length(edge)
distance = delta_xv .* (y - yv(i)) - (x - xv(i)) .* delta_yv;
##
## is y between the y-values of edge i,j
## AND (x,y) on the left of the edge ?
idx1 = (((yv(i) <= y & y < yv(j)) | (yv(j) <= y & y < yv(i)))
& 0 < distance.*delta_yv);
in (idx1) = !in (idx1);
## Check if (x,y) are actually on the boundary of the polygon.
if (do_boundary)
idx2 = (((yv(i) <= y & y <= yv(j)) | (yv(j) <= y & y <= yv(i)))
& ((xv(i) <= x & x <= xv(j)) | (xv(j) <= x & x <= xv(i)))
& (0 == distance | !delta_xv));
on (idx2) = true;
endif
j = i;
endfor
endfunction
%!demo
%! xv = [ 0.05840, 0.48375, 0.69356, 1.47478, 1.32158, ...
%! 1.94545, 2.16477, 1.87639, 1.18218, 0.27615, ...
%! 0.05840 ];
%! yv = [ 0.60628, 0.04728, 0.50000, 0.50000, 0.02015, ...
%! 0.18161, 0.78850, 1.13589, 1.33781, 1.04650, ...
%! 0.60628 ];
%! xa = [0:0.1:2.3];
%! ya = [0:0.1:1.4];
%! [x,y] = meshgrid (xa, ya);
%! [in,on] = inpolygon (x, y, xv, yv);
%! inside = in & !on;
%!
%! clf;
%! plot (xv, yv);
%! hold on;
%! plot (x(inside), y(inside), "@g")
%! plot (x(!in), y(!in), "@m");
%! plot (x(on), y(on), "@b");
%! hold off;
%! disp ("Green points are inside polygon, magenta are outside,");
%! disp ("and blue are on boundary.");
%!demo
%! xv = [ 0.05840, 0.48375, 0.69356, 1.47478, 1.32158, ...
%! 1.94545, 2.16477, 1.87639, 1.18218, 0.27615, ...
%! 0.05840, 0.73295, 1.28913, 1.74221, 1.16023, ...
%! 0.73295, 0.05840 ];
%! yv = [ 0.60628, 0.04728, 0.50000, 0.50000, 0.02015, ...
%! 0.18161, 0.78850, 1.13589, 1.33781, 1.04650, ...
%! 0.60628, 0.82096, 0.67155, 0.96114, 1.14833, ...
%! 0.82096, 0.60628];
%! xa = [0:0.1:2.3];
%! ya = [0:0.1:1.4];
%! [x,y] = meshgrid (xa, ya);
%! [in,on] = inpolygon (x, y, xv, yv);
%! inside = in & !on;
%!
%! clf;
%! plot (xv, yv);
%! hold on;
%! plot (x(inside), y(inside), "@g");
%! plot (x(!in), y(!in), "@m");
%! plot (x(on), y(on), "@b");
%! hold off;
%! disp ("Green points are inside polygon, magenta are outside,");
%! disp ("and blue are on boundary.");
%!test
%! [in, on] = inpolygon ([1, 0], [1, 0], [-1, -1, 1, 1], [-1, 1, 1, -1]);
%! assert (in, [false, true]);
%! assert (on, [true, false]);
%% Test input validation
%!error inpolygon ()
%!error inpolygon (1, 2)
%!error inpolygon (1, 2, 3)
%!error inpolygon (1, [1,2], [3, 4], [5, 6])
%!error inpolygon ([1,2], [3, 4], [5, 6], 1)
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