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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 center = centroid(varargin)
%CENTROID Compute centroid (center of mass) of a set of points.
%
% PTS = centroid(POINTS)
% PTS = centroid(PTX, PTY)
% Computes the ND-dimensional centroid of a set of points.
% POINTS is an array with as many rows as the number of points, and as
% many columns as the number of dimensions.
% PTX and PTY are two column vectors containing coordinates of the
% 2-dimensional points.
% The result PTS is a row vector with Nd columns.
%
% PTS = centroid(POINTS, MASS)
% PTS = centroid(PTX, PTY, MASS)
% Computes center of mass of POINTS, weighted by coefficient MASS.
% POINTS is a Np-by-Nd array, MASS is Np-by-1 array, and PTX and PTY are
% also both Np-by-1 arrays.
%
% Example:
% pts = [2 2;6 1;6 5;2 4];
% centroid(pts)
% ans =
% 4 3
%
% See also
% points2d, polygonCentroid
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2003-04-07
% Copyright 2003-2023 INRA - Cepia Software Platform
%% extract input arguments
% use empty mass by default
mass = [];
if nargin==1
% give only array of points
pts = varargin{1};
elseif nargin==2
% either POINTS+MASS or PX+PY
var = varargin{1};
if size(var, 2)>1
% arguments are POINTS, and MASS
pts = var;
mass = varargin{2};
else
% arguments are PX and PY
pts = [var varargin{2}];
end
elseif nargin==3
% arguments are PX, PY, and MASS
pts = [varargin{1} varargin{2}];
mass = varargin{3};
end
%% compute centroid
if isempty(mass)
% no weight
center = mean(pts);
else
% format mass to have sum equal to 1, and column format
mass = mass(:)/sum(mass(:));
% compute weighted centroid
center = sum(bsxfun(@times, pts, mass), 1);
% equivalent to:
% center = sum(pts .* mass(:, ones(1, size(pts, 2))));
end
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