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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 [centroid, area, Sx, Sy] = polygonCentroid(varargin)
%POLYGONCENTROID Computes the centroid (center of mass) of a polygon.
%
% CENTROID = polygonCentroid(POLY)
% CENTROID = polygonCentroid(PTX, PTY)
% Computes center of mass of a polygon defined by POLY. POLY is a N-by-2
% array of double containing coordinates of vertices.
%
% [CENTROID, AREA] = polygonCentroid(POLY)
% Also returns the (signed) area of the polygon.
%
% Example
% % Draws the centroid of a paper hen
% x = [0 10 20 0 -10 -20 -10 -10 0];
% y = [0 0 10 10 20 10 10 0 -10];
% poly = [x' y'];
% centro = polygonCentroid(poly);
% drawPolygon(poly);
% hold on; axis equal;
% drawPoint(centro, 'bo');
%
% References
% Algorithm adapted from P. Bourke's web page.
%
% See also
% polygons2d, polygonArea, polygonSecondAreaMoments, drawPolygon
% polylineCentroid, centroid
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2004-05-05
% Copyright 2004-2023
% parse input arguments
if nargin == 1
poly = varargin{1};
elseif nargin == 2
poly(:,1) = varargin{1};
poly(:,2) = varargin{2};
end
poly = parsePolygon(poly, 'repetition');
px = poly(:,1);
py = poly(:,2);
% vertex indices
N = length(px);
iNext = [2:N 1];
% compute cross products
common = px .* py(iNext) - px(iNext) .* py;
Sx = 1/6*sum((py + py(iNext)) .* common);
Sy = 1/6*sum((px + px(iNext)) .* common);
% area and centroid
area = sum(common) / 2;
centroid = [Sy Sx] / area;
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