/usr/share/octave/packages/geometry-1.7.0/geom2d/intersectLines.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
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## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{point} =} intersectLines (@var{line1}, @var{line2})
## @deftypefnx {Function File} {@var{point} =} intersectLines (@var{line1}, @var{line2},@var{eps})
## Return all intersection points of N lines in 2D.
##
## Returns the intersection point of lines @var{line1} and @var{line2}.
## @var{line1} and @var{line2} are [1*4]
## arrays, containing parametric representation of each line (in the form
## [x0 y0 dx dy], see @code{createLine} for details).
##
## In case of colinear lines, returns [Inf Inf].
## In case of parallel but not colinear lines, returns [NaN NaN].
##
## If each input is [N*4] array, the result is a [N*2] array containing
## intersections of each couple of lines.
## If one of the input has N rows and the other 1 row, the result is a
## [N*2] array.
##
## A third input argument specifies the tolerance for detecting parallel lines.
## Default is 1e-14.
##
## Example
##
## @example
## line1 = createLine([0 0], [10 10]);
## line2 = createLine([0 10], [10 0]);
## point = intersectLines(line1, line2)
## point =
## 5 5
## @end example
##
## @seealso{lines2d, edges2d, intersectEdges, intersectLineEdge, intersectLineCircle}
## @end deftypefn
function point = intersectLines(line1, line2, varargin)
# extreact tolerance
tol = 1e-14;
if !isempty(varargin)
tol = varargin{1};
end
x1 = line1(:,1);
y1 = line1(:,2);
dx1 = line1(:,3);
dy1 = line1(:,4);
x2 = line2(:,1);
y2 = line2(:,2);
dx2 = line2(:,3);
dy2 = line2(:,4);
N1 = length(x1);
N2 = length(x2);
# indices of parallel lines
par = abs(dx1.*dy2 - dx2.*dy1) < tol;
# indices of colinear lines
col = abs((x2-x1) .* dy1 - (y2-y1) .* dx1) < tol & par ;
x0(col) = Inf;
y0(col) = Inf;
x0(par & !col) = NaN;
y0(par & !col) = NaN;
i = !par;
# compute intersection points
if N1==N2
x0(i) = ((y2(i)-y1(i)).*dx1(i).*dx2(i) + x1(i).*dy1(i).*dx2(i) - x2(i).*dy2(i).*dx1(i)) ./ ...
(dx2(i).*dy1(i)-dx1(i).*dy2(i)) ;
y0(i) = ((x2(i)-x1(i)).*dy1(i).*dy2(i) + y1(i).*dx1(i).*dy2(i) - y2(i).*dx2(i).*dy1(i)) ./ ...
(dx1(i).*dy2(i)-dx2(i).*dy1(i)) ;
elseif N1==1
x0(i) = ((y2(i)-y1).*dx1.*dx2(i) + x1.*dy1.*dx2(i) - x2(i).*dy2(i).*dx1) ./ ...
(dx2(i).*dy1-dx1.*dy2(i)) ;
y0(i) = ((x2(i)-x1).*dy1.*dy2(i) + y1.*dx1.*dy2(i) - y2(i).*dx2(i).*dy1) ./ ...
(dx1.*dy2(i)-dx2(i).*dy1) ;
elseif N2==1
x0(i) = ((y2-y1(i)).*dx1(i).*dx2 + x1(i).*dy1(i).*dx2 - x2.*dy2.*dx1(i)) ./ ...
(dx2.*dy1(i)-dx1(i).*dy2) ;
y0(i) = ((x2-x1(i)).*dy1(i).*dy2 + y1(i).*dx1(i).*dy2 - y2.*dx2.*dy1(i)) ./ ...
(dx1(i).*dy2-dx2.*dy1(i)) ;
else
# formattage a rajouter
x0(i) = ((y2(i)-y1(i)).*dx1(i).*dx2(i) + x1(i).*dy1(i).*dx2(i) - x2(i).*dy2(i).*dx1(i)) ./ ...
(dx2(i).*dy1(i)-dx1(i).*dy2(i)) ;
y0(i) = ((x2(i)-x1(i)).*dy1(i).*dy2(i) + y1(i).*dx1(i).*dy2(i) - y2(i).*dx2(i).*dy1(i)) ./ ...
(dx1(i).*dy2(i)-dx2(i).*dy1(i)) ;
end
# concatenate result
point = [x0' y0'];
endfunction
%!test # basic test with two orthogonal lines
%! line1 = [3 1 0 1];
%! line2 = [1 4 1 0];
%! assert (intersectLines(line1, line2), [3 4], 1e-6);
%!test # orthognal diagonal lines
%! line1 = [0 0 3 2];
%! line2 = [5 -1 4 -6];
%! assert (intersectLines(line1, line2), [3 2], 1e-6);
%!test # one diagonal and one horizontal line
%! line1 = [10 2 25 0];
%! line2 = [5 -1 4 -6];
%! assert (intersectLines(line1, line2), [3 2], 1e-6);
%!test # check for dx and dy very big compared to other line
%! line1 = [3 1 0 1000];
%! line2 = [1 4 -14 0];
%! assert (intersectLines(line1, line2), [3 4], 1e-6);
%!test
%! line1 = [2 0 20000 30000];
%! line2 = [1 6 1 -1];
%! assert (intersectLines(line1, line2), [4 3], 1e-6);
%!test
%! line1 = [3 1 0 1];
%! line2 = repmat([1 4 1 0], 5, 1);
%! res = repmat([3 4], 5, 1);
%! inters = intersectLines(line1, line2);
%! assert (res, inters, 1e-6);
%!test
%! line1 = repmat([3 1 0 1], 5, 1);
%! line2 = [1 4 1 0];
%! res = repmat([3 4], 5, 1);
%! inters = intersectLines(line1, line2);
%! assert (res, inters, 1e-6);
%!test
%! line1 = repmat([3 1 0 1], 5, 1);
%! line2 = repmat([1 4 1 0], 5, 1);
%! res = repmat([3 4], 5, 1);
%! inters = intersectLines(line1, line2);
%! assert (res, inters, 1e-6);
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