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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] = polygonCentroid3d(varargin)
%POLYGONCENTROID3D Centroid (or center of mass) of a polygon.
%
% PTC = polygonCentroid3d(POLY)
% Computes center of mass of a polygon defined by POLY. POLY is a N-by-3
% array of double containing coordinates of polygon vertices. The result
% PTC is given as a 1-by-3 numeric array.
% The algorithm assumes (1) that the vertices of the polygon are within
% the same plane and (2) that the planar projection of the polygon (on
% the embedding plane) do not self-intersect.
%
% PTC = polygonCentroid3d(VX, VY, VZ)
% Specifies vertex coordinates as three separate arrays.
%
% Example
% % compute centroid of a basic polygon
% poly = [0 0 0; 10 0 10;10 10 20;0 10 10];
% centro = polygonCentroid3d(poly)
% centro =
% 5.0000 5.0000 10.0000
%
% See also
% polygons3d, polygonArea3d, polygonCentroid, planePosition, planePoint
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2007-09-18
% Copyright 2007-2023 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
if nargin == 1
% polygon is given as a single argument
pts = varargin{1};
elseif nargin == 3
% polygon is given as 3 coordinate arrays
px = varargin{1};
py = varargin{2};
pz = varargin{3};
pts = [px py pz];
end
pts = parsePolygon(pts, 'repetition');
% create supporting plane
plane = fitPlane(pts);
% project points onto the plane
pts = planePosition(pts, plane);
% compute centroid in 2D
[centro2d, area] = polygonCentroid(pts);
% project back in 3D
centroid = planePoint(plane, centro2d);
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