/usr/share/octave/packages/geometry-1.7.0/polygons2d/polylineSelfIntersections.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
## notice, this list of conditions and the following disclaimer in the
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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
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
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## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{pts} = } polylineSelfIntersections (@var{poly})
## Find self-intersections points of a polyline
##
## Return the position of self intersection points
##
## Also return the 2 positions of each intersection point (the position
## when meeting point for first time, then position when meeting point
## for the second time).
##
## Example
## @example
## # use a gamma-shaped polyline
## poly = [0 0;0 10;20 10;20 20;10 20;10 0];
## polylineSelfIntersections(poly)
## ans =
## 10 10
##
## # use a 'S'-shaped polyline
## poly = [10 0;0 0;0 10;20 10;20 20;10 20];
## polylineSelfIntersections(poly)
## ans =
## 10 10
## @end example
##
## @seealso{polygons2d, intersectPolylines, polygonSelfIntersections}
## @end deftypefn
function varargout = polylineSelfIntersections(poly, varargin)
## Initialisations
# determine whether the polyline is closed
closed = false;
if ~isempty(varargin)
closed = varargin{1};
if ischar(closed)
if strcmp(closed, 'closed')
closed = true;
elseif strcmp(closed, 'open')
closed = false;
end
end
end
# if polyline is closed, ensure the last point equals the first one
if closed
if sum(abs(poly(end, :)-poly(1,:))<1e-14)~=2
poly = [poly; poly(1,:)];
end
end
# arrays for storing results
points = zeros(0, 2);
pos1 = zeros(0, 1);
pos2 = zeros(0, 1);
# number of vertices
Nv = size(poly, 1);
## Main processing
# index of current intersection
ip = 0;
# iterate over each couple of edge ( (N-1)*(N-2)/2 iterations)
for i=1:Nv-2
# create first edge
edge1 = [poly(i, :) poly(i+1, :)];
for j=i+2:Nv-1
# create second edge
edge2 = [poly(j, :) poly(j+1, :)];
# check conditions on bounding boxes
if min(edge1([1 3]))>max(edge2([1 3]))
continue;
end
if max(edge1([1 3]))<min(edge2([1 3]))
continue;
end
if min(edge1([2 4]))>max(edge2([2 4]))
continue;
end
if max(edge1([2 4]))<min(edge2([2 4]))
continue;
end
# compute intersection point
inter = intersectEdges(edge1, edge2);
if sum(isfinite(inter))==2
# add point to the list
ip = ip + 1;
points(ip, :) = inter;
# also compute positions on the polyline
pos1(ip, 1) = i+edgePosition(inter, edge1)-1;
pos2(ip, 1) = j+edgePosition(inter, edge2)-1;
end
end
end
# if polyline is closed, the first vertex was found as an intersection, so
# we need to remove it
if closed
dist = distancePoints(points, poly(1,:));
[minDist ind] = min(dist); ##ok<ASGLU>
points(ind,:) = [];
pos1(ind) = [];
pos2(ind) = [];
end
## Post-processing
# process output arguments
if nargout<=1
varargout{1} = points;
elseif nargout==3
varargout{1} = points;
varargout{2} = pos1;
varargout{3} = pos2;
end
endfunction
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