/usr/share/octave/packages/geometry-1.7.0/geom2d/intersectEdges.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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## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{point} = } intersectEdges (@var{edge1}, @var{edge2})
## Return all intersections between two set of edges
##
## P = intersectEdges(E1, E2);
## returns the intersection point of lines L1 and L2. E1 and E2 are 1-by-4
## arrays, containing parametric representation of each edge (in the form
## [x1 y1 x2 y2], see 'createEdge' for details).
##
## In case of colinear edges, returns [Inf Inf].
## In case of parallel but not colinear edges, returns [NaN NaN].
##
## If each input is [N*4] array, the result is a [N*2] array containing
## intersections of each couple of edges.
## If one of the input has N rows and the other 1 row, the result is a
## [N*2] array.
##
## @seealso{edges2d, intersectLines}
## @end deftypefn
function point = intersectEdges(edge1, edge2)
## Initialisations
# ensure input arrays are same size
N1 = size(edge1, 1);
N2 = size(edge2, 1);
# ensure input have same size
if N1~=N2
if N1==1
edge1 = repmat(edge1, [N2 1]);
N1 = N2;
elseif N2==1
edge2 = repmat(edge2, [N1 1]);
end
end
# tolerance for precision
tol = 1e-14;
# initialize result array
x0 = zeros(N1, 1);
y0 = zeros(N1, 1);
## Detect parallel and colinear cases
# indices of parallel edges
#par = abs(dx1.*dy2 - dx1.*dy2)<tol;
par = isParallel(edge1(:,3:4)-edge1(:,1:2), edge2(:,3:4)-edge2(:,1:2));
# indices of colinear edges
# equivalent to: |(x2-x1)*dy1 - (y2-y1)*dx1| < eps
col = abs( (edge2(:,1)-edge1(:,1)).*(edge1(:,4)-edge1(:,2)) - ...
(edge2(:,2)-edge1(:,2)).*(edge1(:,3)-edge1(:,1)) )<tol & par;
# Parallel edges have no intersection -> return [NaN NaN]
x0(par & ~col) = NaN;
y0(par & ~col) = NaN;
## Process colinear edges
# colinear edges may have 0, 1 or infinite intersection
# Discrimnation based on position of edge2 vertices on edge1
if sum(col)>0
# array for storing results of colinear edges
resCol = Inf*ones(size(col));
# compute position of edge2 vertices wrt edge1
t1 = edgePosition(edge2(col, 1:2), edge1(col, :));
t2 = edgePosition(edge2(col, 3:4), edge1(col, :));
# control location of vertices: we want t1<t2
if t1>t2
tmp = t1;
t1 = t2;
t2 = tmp;
end
# edge totally before first vertex or totally after last vertex
resCol(col(t2<-eps)) = NaN;
resCol(col(t1>1+eps)) = NaN;
# set up result into point coordinate
x0(col) = resCol;
y0(col) = resCol;
# touches on first point of first edge
touch = col(abs(t2)<1e-14);
x0(touch) = edge1(touch, 1);
y0(touch) = edge1(touch, 2);
# touches on second point of first edge
touch = col(abs(t1-1)<1e-14);
x0(touch) = edge1(touch, 3);
y0(touch) = edge1(touch, 4);
end
## Process non parallel cases
# process intersecting edges whose interecting lines intersect
i = find(~par);
# use a test to avoid process empty arrays
if sum(i)>0
# extract base parameters of supporting lines for non-parallel edges
x1 = edge1(i,1);
y1 = edge1(i,2);
dx1 = edge1(i,3)-x1;
dy1 = edge1(i,4)-y1;
x2 = edge2(i,1);
y2 = edge2(i,2);
dx2 = edge2(i,3)-x2;
dy2 = edge2(i,4)-y2;
# compute intersection points of supporting lines
delta = (dx2.*dy1-dx1.*dy2);
x0(i) = ((y2-y1).*dx1.*dx2 + x1.*dy1.*dx2 - x2.*dy2.*dx1) ./ delta;
y0(i) = ((x2-x1).*dy1.*dy2 + y1.*dx1.*dy2 - y2.*dx2.*dy1) ./ -delta;
# compute position of intersection points on each edge
# t1 is position on edge1, t2 is position on edge2
t1 = ((y0(i)-y1).*dy1 + (x0(i)-x1).*dx1) ./ (dx1.*dx1+dy1.*dy1);
t2 = ((y0(i)-y2).*dy2 + (x0(i)-x2).*dx2) ./ (dx2.*dx2+dy2.*dy2);
# check position of points on edges.
# it should be comprised between 0 and 1 for both t1 and t2.
# if not, the edges do not intersect
out = t1<-tol | t1>1+tol | t2<-tol | t2>1+tol;
x0(i(out)) = NaN;
y0(i(out)) = NaN;
end
## format output arguments
point = [x0 y0];
endfunction
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