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## Copyright (C) 2003-2011 David Legland <david.legland@grignon.inra.fr>
## 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
## documentation and/or other materials provided with the distribution.
##
## 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
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{loops} = } polygonLoops (@var{poly})
## Divide a possibly self-intersecting polygon into a set of simple loops
##
## @var{poly} is a polygone defined by a series of vertices,
## @var{loops} is a cell array of polygons, containing the same vertices of the
## original polygon, but no loop self-intersect, and no couple of loops
## intersect each other.
##
## Example:
## @example
## poly = [0 0;0 10;20 10;20 20;10 20;10 0];
## loops = polygonLoops(poly);
## figure(1); hold on;
## drawPolygon(loops);
## polygonArea(loops)
## @end example
##
## @seealso{polygons2d, polygonSelfIntersections}
## @end deftypefn
function loops = polygonLoops(poly)
## Initialisations
# compute intersections
[inters pos1 pos2] = polygonSelfIntersections(poly);
# case of a polygon without self-intersection
if isempty(inters)
loops = {poly};
return;
end
# array for storing loops
loops = cell(0, 1);
positions = sortrows([pos1 pos2;pos2 pos1]);
## First loop
pos0 = 0;
loop = polygonSubcurve(poly, pos0, positions(1, 1));
pos = positions(1, 2);
positions(1, :) = [];
while true
# index of next intersection point
ind = find(positions(:,1)>pos, 1, 'first');
# if not found, break
if isempty(ind)
break;
end
# add portion of curve
loop = [loop;polygonSubcurve(poly, pos, positions(ind, 1))]; ##ok<AGROW>
# look for next intersection point
pos = positions(ind, 2);
positions(ind, :) = [];
end
# add the last portion of curve
loop = [loop;polygonSubcurve(poly, pos, pos0)];
# remove redundant vertices
loop(sum(loop(1:end-1,:) == loop(2:end,:) ,2)==2, :) = [];
if sum(diff(loop([1 end], :))==0)==2
loop(end, :) = [];
end
# add current loop to the list of loops
loops{1} = loop;
## Other loops
Nl = 1;
while ~isempty(positions)
loop = [];
pos0 = positions(1, 2);
pos = positions(1, 2);
while true
# index of next intersection point
ind = find(positions(:,1)>pos, 1, 'first');
# add portion of curve
loop = [loop;polygonSubcurve(poly, pos, positions(ind, 1))]; ##ok<AGROW>
# look for next intersection point
pos = positions(ind, 2);
positions(ind, :) = [];
# if not found, break
if pos==pos0
break;
end
end
# remove redundant vertices
loop(sum(loop(1:end-1,:) == loop(2:end,:) ,2)==2, :) = []; ##ok<AGROW>
if sum(diff(loop([1 end], :))==0)==2
loop(end, :) = []; ##ok<AGROW>
end
# add current loop to the list of loops
Nl = Nl + 1;
loops{Nl} = loop;
end
endfunction
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