1 %% Copyright (c) 2011, INRA
2 %% 2003-2011, David Legland <david.legland@grignon.inra.fr>
3 %% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
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35 %% @deftypefn {Function File} {@var{c} = } centroid (@var{points})
36 %% @deftypefnx {Function File} {@var{c} = } centroid (@var{px}, @var{py})
37 %% @deftypefnx {Function File} {@var{c} = } centroid (@dots{}, @var{mass})
38 %% Compute centroid (center of mass) of a set of points.
40 %% Computes the ND-dimensional centroid of a set of points.
41 %% @var{points} is an array with as many rows as the number of points, and as
42 %% many columns as the number of dimensions.
43 %% @var{px} and @var{py} are two column vectors containing coordinates of the
44 %% 2-dimensional points.
45 %% The result @var{c} is a row vector with ND columns.
47 %% If @var{mass} is given, computes center of mass of @var{points}, weighted by coefficient @var{mass}.
48 %% @var{points} is a Np-by-Nd array, @var{mass} is Np-by-1 array, and @var{px} and @var{py} are
49 %% also both Np-by-1 arrays.
54 %% pts = [2 2;6 1;6 5;2 4];
60 %% @seealso{points2d, polygonCentroid}
63 function center = centroid(varargin)
65 %% extract input arguments
67 % use empty mass by default
71 % give only array of points
75 % either POINTS+MASS or PX+PY
78 % arguments are POINTS, and MASS
82 % arguments are PX and PY
83 pts = [var varargin{2}];
87 % arguments are PX, PY, and MASS
88 pts = [varargin{1} varargin{2}];
99 % format mass to have sum equal to 1, and column format
100 mass = mass(:)/sum(mass(:));
102 % compute weighted centroid
103 center = sum(bsxfun(@times, pts, mass), 1);
105 % center = sum(pts .* mass(:, ones(1, size(pts, 2))));
111 %! points = [0 0;10 0;10 10;0 10];
112 %! centro = centroid(points);
113 %! assert ([5 5], centro, 1e-6);
116 %! points = [0 0;10 0;10 10;0 10];
117 %! centro = centroid(points(:,1), points(:,2));
118 %! assert ([5 5], centro, 1e-6);
121 %! points = [0 0;30 0;30 30;0 30];
122 %! centro = centroid(points, [1;1;1;3]);
123 %! assert ([10 20], centro, 1e-6);
126 %! points = [0 0;30 0;30 30;0 30];
127 %! centro = centroid(points(:,1), points(:,2), [1;1;1;3]);
128 %! assert ([10 20], centro, 1e-6);