/usr/share/octave/packages/geometry-1.7.0/geom2d/intersectLineEdge.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.
##
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## modification, are permitted provided that the following conditions are met:
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## 2 Redistributions in binary form must reproduce the above copyright
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{point} = } intersecLineEdge (@var{line}, @var{edge})
## Return intersection between a line and an edge.
##
## Returns the intersection point of lines @var{line} and edge @var{edge}.
## @var{line} is a 1x4 array containing parametric representation of the line
## (in the form [x0 y0 dx dy], see @code{createLine} for details).
## @var{edge} is a 1x4 array containing coordinates of first and second point
## (in the form [x1 y1 x2 y2], see @code{createEdge} for details).
##
## In case of colinear line and edge, returns [Inf Inf].
## If line does not intersect edge, returns [NaN NaN].
##
## If each input is [N*4] array, the result is a [N*2] array containing
## intersections for each couple of edge and line.
## If one of the input has N rows and the other 1 row, the result is a
## [N*2] array.
##
## @seealso{lines2d, edges2d, intersectEdges, intersectLine}
## @end deftypefn
function point = intersectLineEdge(lin, edge)
x0 = lin(:,1);
y0 = lin(:,2);
dx1 = lin(:,3);
dy1 = lin(:,4);
x1 = edge(:,1);
y1 = edge(:,2);
x2 = edge(:,3);
y2 = edge(:,4);
dx2 = x2-x1;
dy2 = y2-y1;
N1 = length(x0);
N2 = length(x1);
# indices of parallel lines
par = abs(dx1.*dy2-dx2.*dy1)<1e-14;
# indices of colinear lines
col = abs((x1-x0).*dy1-(y1-y0).*dx1)<1e-14 & par ;
xi(col) = Inf;
yi(col) = Inf;
xi(par & ~col) = NaN;
yi(par & ~col) = NaN;
i = ~par;
# compute intersection points
if N1==N2
xi(i) = ((y1(i)-y0(i)).*dx1(i).*dx2(i) + x0(i).*dy1(i).*dx2(i) - x1(i).*dy2(i).*dx1(i)) ./ ...
(dx2(i).*dy1(i)-dx1(i).*dy2(i)) ;
yi(i) = ((x1(i)-x0(i)).*dy1(i).*dy2(i) + y0(i).*dx1(i).*dy2(i) - y1(i).*dx2(i).*dy1(i)) ./ ...
(dx1(i).*dy2(i)-dx2(i).*dy1(i)) ;
elseif N1==1
xi(i) = ((y1(i)-y0).*dx1.*dx2(i) + x0.*dy1.*dx2(i) - x1(i).*dy2(i).*dx1) ./ ...
(dx2(i).*dy1-dx1.*dy2(i)) ;
yi(i) = ((x1(i)-x0).*dy1.*dy2(i) + y0.*dx1.*dy2(i) - y1(i).*dx2(i).*dy1) ./ ...
(dx1.*dy2(i)-dx2(i).*dy1) ;
elseif N2==1
xi(i) = ((y1-y0(i)).*dx1(i).*dx2 + x0(i).*dy1(i).*dx2 - x1(i).*dy2.*dx1(i)) ./ ...
(dx2.*dy1(i)-dx1(i).*dy2) ;
yi(i) = ((x1-x0(i)).*dy1(i).*dy2 + y0(i).*dx1(i).*dy2 - y1(i).*dx2.*dy1(i)) ./ ...
(dx1(i).*dy2-dx2.*dy1(i)) ;
end
point = [xi' yi'];
out = find(~isPointOnEdge(point, edge));
point(out, :) = repmat([NaN NaN], [length(out) 1]);
endfunction
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