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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 = polylineCentroid(varargin)
%POLYLINECENTROID Computes the centroid of a curve defined by a series of points.
%
% PT = polylineCentroid(POINTS);
% Computes center of mass of a polyline defined by POINTS. POINTS is a
% N-by-D array of double, representing a set of N points in a
% D-dimensional space.
%
% PT = polylineCentroid(PTX, PTY);
% PT = polylineCentroid(PTX, PTY, PTZ);
% Specifies points as separate column vectors
%
% PT = polylineCentroid(..., TYPE);
% Specifies if the last point is connected to the first one. TYPE can be
% either 'closed' or 'open'.
%
% Example
% poly = [0 0;10 0;10 10;20 10];
% polylineCentroid(poly)
% ans =
% [10 5]
%
% See also
% polygons2d, centroid, polygonCentroid, polylineLength
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2006-05-22
% Copyright 2006-2023 INRA - TPV URPOI - BIA IMASTE
%% process input arguments
% check whether the curve is closed
closed = false;
var = varargin{end};
if ischar(var)
if strcmpi(var, 'closed')
closed = true;
end
% remove last argument
varargin(end) = [];
end
% extract point coordinates
if length(varargin)==1
points = varargin{1};
elseif length(varargin)==2
points = [varargin{1} varargin{2}];
end
%% Main computation
% compute centers and lengths composing the curve
if closed
centers = (points + points([2:end 1],:))/2;
lengths = sqrt(sum(diff(points([1:end 1],:)).^2, 2));
else
centers = (points(1:end-1,:) + points(2:end,:))/2;
lengths = sqrt(sum(diff(points).^2, 2));
end
% centroid of edge centers weighted by edge length
%weigths = repmat(lengths/sum(lengths), [1 size(points, 2)]);
center = sum(centers .* repmat(lengths, [1 size(points, 2)]), 1) / sum(lengths);
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