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## Copyright (C) 2024 David Legland
## 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.
function loops = polygonLoops(poly, varargin)
%POLYGONLOOPS Divide a possibly self-intersecting polygon into a set of simple loops.
%
% LOOPS = polygonLoops(POLYGON);
% POLYGON is a polygone defined by a series of vertices,
% 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:
% poly = [0 0;0 10;20 10;20 20;10 20;10 0];
% loops = polygonLoops(poly);
% figure(1); hold on;
% drawPolygon(loops);
% polygonArea(loops)
%
% See also
% polygons2d, polygonSelfIntersections
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2009-06-15, using Matlab 7.7.0.471 (R2008b)
% Copyright 2009-2023 INRA - Cepia Software Platform
% tolerance for detecting two vertices as equal
tol = 1e-14;
% parse optional arguments
while length(varargin) > 1
pname = varargin{1};
if ~ischar(pname)
error('Expect optional arguments as name-value pairs');
end
if strcmpi(pname, 'tolerance')
tol = varargin{2};
else
error(['Unknown parameter name: ' pname]);
end
varargin(1:2) = [];
end
%% Initialisations
% compute intersections
[inters, pos1, pos2] = polygonSelfIntersections(poly, 'tolerance', tol);
% case of a polygon without self-intersection
if isempty(inters)
loops = {poly};
return;
end
% array for storing loops
loops = cell(0, 1);
% sort intersection points with respect to their position on the polygon
[positions, order] = sortrows([pos1 pos2 ; pos2 pos1]);
inters = [inters ; inters];
inters = inters(order, :);
%% First loop
% initialize the beginning of the loop
pos0 = 0;
loop = polygonSubcurve(poly, pos0, positions(1, 1));
loop(end, :) = inters(1,:);
vertex = inters(1,:);
% prepare iteration on positions
pos = positions(1, 2);
positions(1, :) = [];
inters(1,:) = [];
while true
% index of next intersection point
ind = find(positions(:,1) > pos, 1, 'first');
% if not index is found, the current loop is complete
if isempty(ind)
break;
end
% compute the portion of curve between the two intersection points
portion = polygonSubcurve(poly, pos, positions(ind, 1));
% ensure extremities have been computed only once
portion(1, :) = vertex;
vertex = inters(ind, :);
portion(end, :) = vertex;
% add the current portion of curve
loop = [loop; portion]; %#ok<AGROW>
% update current position on the polygon
pos = positions(ind, 2);
% remove processed intersection
positions(ind, :) = [];
inters(ind,:) = [];
end
% append 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)
% initialize the next loop
loop = [];
pos0 = positions(1, 2);
pos = positions(1, 2);
vertex = inters(1,:);
while true
% index of next intersection point
ind = find(positions(:,1) > pos, 1, 'first');
% compute the portion of curve between the two intersection points
portion = polygonSubcurve(poly, pos, positions(ind, 1));
% ensure extremities have been computed only once
portion(1, :) = vertex;
vertex = inters(ind, :);
portion(end, :) = vertex;
% append the current portion of curve
loop = [loop ; portion]; %#ok<AGROW>
% update current position on the polygon
pos = positions(ind, 2);
% remove processed intersection
positions(ind, :) = [];
inters(ind,:) = [];
% if not found, current loop is processed
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, :) = [];
end
% add current loop to the list of loops
Nl = Nl + 1;
loops{Nl} = loop;
end
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