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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 = expandPolygon(poly, dist, varargin)
%EXPANDPOLYGON Expand a polygon by a given (signed) distance.
%
% POLY2 = expandPolygon(POLY, DIST);
% Associates to each edge of the polygon POLY the parallel line located
% at distance DIST from the current edge, and compute intersections with
% neighbor parallel lines. The input polygon POLY must be oriented
% counter-clockwise. Otherwise, distance is computed inside the polygon.
% The resulting polygon is simplified to remove inner "loops", and can
% eventually be disconnected.
% The result POLY2 is a cell array, each cell containing a simple linear
% ring.
%
% This is a kind of dilation, but behaviour on corners is different.
% This function keeps angles of polygons, but there is no direct relation
% between the lengths of each polygon.
%
% It is also possible to specify negative distance, and get all points
% inside the polygon. If the polygon is convex, the result equals
% morphological erosion of polygon by a ball with radius equal to the
% given distance.
%
% Example:
% % Computes the negative offset of a non-convex polygon
% poly = [10 10;30 10;30 30;20 20;10 30];
% poly2 = expandPolygon(poly, -3);
% figure;
% drawPolygon(poly, 'linewidth', 2);
% hold on; drawPolygon(poly2, 'm')
% axis equal; axis([0 40 0 40]);
%
% See also
% polygons2d, polygonLoops, polygonSelfIntersections
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-05-14
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% default options
cleanupLoops = false;
% process input argument
while length(varargin) > 1
paramName = varargin{1};
switch lower(paramName)
case 'cleanuploops'
cleanupLoops = varargin{2};
otherwise
error(['Unknown parameter name: ' paramName]);
end
varargin(1:2) = [];
end
% eventually copy first point at the end to ensure closed polygon
if sum(poly(end, :) == poly(1,:)) ~= 2
poly = [poly; poly(1,:)];
end
% number of vertices of the polygon
N = size(poly, 1)-1;
% find lines parallel to polygon edges located at distance DIST
lines = zeros(N, 4);
for i = 1:N
side = createLine(poly(i,:), poly(i+1,:));
lines(i, 1:4) = parallelLine(side, dist);
end
% compute intersection points of consecutive lines
lines = [lines;lines(1,:)];
poly2 = zeros(N, 2);
for i = 1:N
poly2(i,1:2) = intersectLines(lines(i,:), lines(i+1,:));
end
% split result polygon into set of loops (simple polygons)
loops = polygonLoops(poly2);
% keep only loops whose distance to original polygon is correct
if cleanupLoops
distLoop = zeros(length(loops), 1);
for i = 1:length(loops)
distLoop(i) = distancePolygons(loops{i}, poly);
end
loops = loops(abs(distLoop-abs(dist)) < abs(dist)/1000);
end
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