--- /dev/null
+## Copyright (C) 2008-2012 Bill Denney
+##
+## 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{area} =} rectint (@var{a}, @var{b})
+##
+## Compute the area of intersection of rectangles in @var{a} and
+## rectangles in @var{b}. Rectangles are defined as [x y width height]
+## where x and y are the minimum values of the two orthogonal
+## dimensions.
+##
+## If @var{a} or @var{b} are matrices, then the output, @var{area}, is a
+## matrix where the i-th row corresponds to the i-th row of a and the j-th
+## column corresponds to the j-th row of b.
+##
+## @seealso{polyarea}
+## @end deftypefn
+
+## Author: Bill Denney <bill@denney.ws>
+
+function area = rectint (a, b)
+
+ if (nargin != 2)
+ print_usage ();
+ elseif (ndims (a) != 2 || ndims (b) != 2)
+ error ("rectint: expecting arguments to be 2-d arrays");
+ elseif (columns (a) != 4)
+ error ("rectint: A must have 4 columns");
+ elseif (columns (b) != 4)
+ error ("rectint: B must have 4 columns");
+ elseif any ([a(:,3:4);b(:,3:4)](:) < 0)
+ error ("rectint: all widths and heights must be > 0");
+ endif
+
+ ## This runs faster if the number of rows of a is greater than the
+ ## number of rows of b. Swap them and transpose to make it run
+ ## faster.
+ swapinputs = false ();
+ if (rows (a) > rows (b))
+ tmp = a;
+ a = b;
+ b = tmp;
+ swapinputs = true ();
+ endif
+
+ area = zeros (rows (a), rows (b));
+ r1 = [a(:,1:2) a(:,1:2)+a(:,3:4)];
+ r2 = [b(:,1:2) b(:,1:2)+b(:,3:4)];
+ for i = 1:columns (area)
+ ## Find the location of each point relative to the other points.
+ r1x1small = r1(:,1) < r2(i,1);
+ r1x1large = r1(:,1) > r2(i,3);
+ r1x1mid = (r1(:,1) >= r2(i,1)) & (r1(:,1) <= r2(i,3));
+ r1x2small = r1(:,3) < r2(i,1);
+ r1x2large = r1(:,3) > r2(i,3);
+ r1x2mid = (r1(:,3) >= r2(i,1)) & (r1(:,3) <= r2(i,3));
+
+ r1y1small = r1(:,2) < r2(i,2);
+ r1y1large = r1(:,2) > r2(i,4);
+ r1y1mid = (r1(:,2) >= r2(i,2)) & (r1(:,2) <= r2(i,4));
+ r1y2small = r1(:,4) < r2(i,2);
+ r1y2large = r1(:,4) > r2(i,4);
+ r1y2mid = (r1(:,4) >= r2(i,2)) & (r1(:,4) <= r2(i,4));
+
+ ## determine the width of the rectangle
+ ## r1 completely encloses r2
+ area(r1x1small & r1x2large,i) = r2(i,3) - r2(i,1);
+ ## the range goes from r2x min to r1x max
+ mask = r1x1small & r1x2mid;
+ area(mask,i) = r1(mask,3) - r2(i,1);
+ ## the range goes from r1x min to r2x max
+ mask = r1x1mid & r1x2large;
+ area(mask,i) = r2(i,3) - r1(mask,1);
+ ## the range goes from r1x min to r1x max
+ mask = r1x1mid & r1x2mid;
+ area(mask,i) = r1(mask,3) - r1(mask,1);
+
+ ## determine the height of the rectangle
+ ## r1 completely encloses r2
+ area(r1y1small & r1y2large,i) .*= r2(i,4) - r2(i,2);
+ ## the range goes from r2y min to r1y max
+ mask = r1y1small & r1y2mid;
+ area(mask,i) .*= r1(mask,4) - r2(i,2);
+ ## the range goes from r1y min to r2y max
+ mask = r1y1mid & r1y2large;
+ area(mask,i) .*= r2(i,4) - r1(mask,2);
+ ## the range goes from r1x min to r1x max
+ mask = r1y1mid & r1y2mid;
+ area(mask,i) .*= r1(mask,4) - r1(mask,2);
+
+ endfor
+
+ if swapinputs
+ area = area';
+ endif
+
+endfunction
+
+## Tests
+## Exactly overlapping
+%!assert(rectint([0 0 1 1], [0 0 1 1]), 1)
+## rect2 completely enclosed by rect1
+%!assert(rectint([-1 -1 3 3], [0 0 1 1]), 1)
+## rect1 completely enclosed by rect2
+%!assert(rectint([0 0 1 1], [-1 -1 3 3]), 1)
+## rect1 right and top in rect2
+%!assert(rectint([-1 -1 1.5 1.5], [0 0 1 1]), 0.25)
+## rect2 right and top in rect1
+%!assert(rectint([0 0 1 1], [-1 -1 1.5 1.5]), 0.25)
+## no overlap - shared corner
+%!assert(rectint([0 0 1 1], [1 1 2 2]), 0)
+## no overlap - shared edge
+%!assert(rectint([0 0 1 1], [0 1 2 2]), 0)
+## Correct orientation of output
+%!assert(rectint([0 0 1 1;0.5 0.5 1 1;-1 -1 2 2], [1 1 2 2]), [0;0.25;0])
+%!assert(rectint([1 1 2 2], [0 0 1 1;0.5 0.5 1 1;-1 -1 2 2]), [0 0.25 0])
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff