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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:
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## 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
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function axis = polygonSymmetryAxis(poly)
%POLYGONSYMMETRYAXIS Try to identify symmetry axis of polygon.
%
% LINE = polygonSymmetryAxis(POLY)
% Returns a line that minimize difference between the polygon POLY and
% its reflection with the line.
% The difference metric between the two polygons is the sum of distances
% between each vertex of original polygon to the reflected polygon.
%
% Example
% % identify symmetry axis of an ellipse
% elli = [50 50 40 20 30];
% poly = ellipseToPolygon(elli, 100);
% line = polygonSymmetryAxis(poly);
% figure; hold on;
% drawEllipse(elli);
% axis equal; axis ([0 100 0 100]);
% drawLine(line);
%
% See also
% transforms2d, transformPoint, distancePointPolygon
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2015-04-28, using Matlab 8.4.0.150421 (R2014b)
% Copyright 2015-2023 INRA - Cepia Software Platform
% start by centering the polygon
center = polygonCentroid(poly);
poly = bsxfun(@minus, poly, center);
% first performs a rough search with 8 angles
initAngles = linspace(0, pi, 9);
initAngles(end) = [];
initRes = zeros(8, 1);
for i = 1:8
line = createLine([0 0 cos(initAngles(i)) sin(initAngles(i))]);
rotMat = createLineReflection(line);
polyRot = transformPoint(poly, rotMat);
initRes(i) = sum(distancePointPolygon(poly, polyRot).^2);
end
% keep the angle that gives best result
[dummy, indMin] = min(initRes); %#ok<ASGLU>
initAngle = initAngles(indMin);
% Compute angle that best fit between polygon and its symmetric along line
thetaMin = fminbnd(...
@(theta) sum(distancePointPolygon(transformPoint(poly, createLineReflection([0 0 cos(theta) sin(theta)])), poly).^2), ...
initAngle-pi/4, initAngle+pi/4);
% format as a line
axis = [center cos(thetaMin) sin(thetaMin)];
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