--- /dev/null
+%% Copyright (c) 2011, INRA
+%% 2003-2011, David Legland <david.legland@grignon.inra.fr>
+%% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%% All rights reserved.
+%% (simplified BSD License)
+%%
+%% 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 COPYRIGHT HOLDER 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 copyright holder.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {@var{c} = } centroid (@var{points})
+%% @deftypefnx {Function File} {@var{c} = } centroid (@var{px}, @var{py})
+%% @deftypefnx {Function File} {@var{c} = } centroid (@dots{}, @var{mass})
+%% Compute centroid (center of mass) of a set of points.
+%%
+%% Computes the ND-dimensional centroid of a set of points.
+%% @var{points} is an array with as many rows as the number of points, and as
+%% many columns as the number of dimensions.
+%% @var{px} and @var{py} are two column vectors containing coordinates of the
+%% 2-dimensional points.
+%% The result @var{c} is a row vector with ND columns.
+%%
+%% If @var{mass} is given, computes center of mass of @var{points}, weighted by coefficient @var{mass}.
+%% @var{points} is a Np-by-Nd array, @var{mass} is Np-by-1 array, and @var{px} and @var{py} are
+%% also both Np-by-1 arrays.
+%%
+%% Example:
+%%
+%% @example
+%% pts = [2 2;6 1;6 5;2 4];
+%% centroid(pts)
+%% ans =
+%% 4 3
+%%@end example
+%%
+%% @seealso{points2d, polygonCentroid}
+%% @end deftypefn
+
+function center = centroid(varargin)
+
+ %% 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
+
+endfunction
+
+%!test
+%! points = [0 0;10 0;10 10;0 10];
+%! centro = centroid(points);
+%! assert ([5 5], centro, 1e-6);
+
+%!test
+%! points = [0 0;10 0;10 10;0 10];
+%! centro = centroid(points(:,1), points(:,2));
+%! assert ([5 5], centro, 1e-6);
+
+%!test
+%! points = [0 0;30 0;30 30;0 30];
+%! centro = centroid(points, [1;1;1;3]);
+%! assert ([10 20], centro, 1e-6);
+
+%!test
+%! points = [0 0;30 0;30 30;0 30];
+%! centro = centroid(points(:,1), points(:,2), [1;1;1;3]);
+%! assert ([10 20], centro, 1e-6);
+