function [centroid area] = polygonCentroid(varargin)

%POLYGONCENTROID Compute the centroid (center of mass) of a polygon

%

%   CENTROID = polygonCentroid(POLY)

%   CENTROID = polygonCentroid(PTX, PTY)

%   Computes center of mass of a polygon defined by POLY. POLY is a N-by-2

%   array of double containing coordinates of vertices.

%

%   [CENTROID AREA] = polygonCentroid(POLY)

%   Also returns the (signed) area of the polygon. 

%

%   Example

%     % Draws the centroid of a paper hen

%     x = [0 10 20  0 -10 -20 -10 -10  0];

%     y = [0  0 10 10  20  10  10  0 -10];

%     poly = [x' y'];

%     centro = polygonCentroid(poly);

%     drawPolygon(poly);

%     hold on; axis equal;

%     drawPoint(centro, 'bo');

% 

%   References

%   algo adapted from P. Bourke web page

%

%   See also:

%   polygons2d, polygonArea, drawPolygon

%

%   ---------

%   author : David Legland 

%   INRA - TPV URPOI - BIA IMASTE

%   created the 05/05/2004.

%

% Algorithme P. Bourke, vectorized version

% HISTORY

% 2012.02.24 vectorize code

% parse input arguments

if nargin == 1

    var = varargin{1};

    px = var(:,1);

    py = var(:,2);

elseif nargin == 2

    px = varargin{1};

    py = varargin{2};

end

% vertex indices

N = length(px);

iNext = [2:N 1];

% compute cross products

common = px .* py(iNext) - px(iNext) .* py;

sx = sum((px + px(iNext)) .* common);

sy = sum((py + py(iNext)) .* common);

% area and centroid

area = sum(common) / 2;

centroid = [sx sy] / 6 / area;

end