%% 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>
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%% -*- 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);

