steinerPoint

STEINERPOINT Compute steiner point (weighted centroid) of a polygon.

   PT = steinerPoint(POINTS);
   PT = steinerPoint(PTX, PTY);
   Computes steiner point of a polygon defined by POINTS. POINTS is a
   [N*2] array of double.

   The steiner point is computed the same way as the polygon centroid,
   except that a weight depending on the angle is given to each vertex.

   See also:
   polygons2d, polygonArea, polygonCentroid, drawPolygon

   ---------
   author : David Legland
   INRA - TPV URPOI - BIA IMASTE
   created the 11/11/2004.

0001 function pt = steinerPoint(varargin)
0002 %STEINERPOINT Compute steiner point (weighted centroid) of a polygon.
0003 %
0004 %   PT = steinerPoint(POINTS);
0005 %   PT = steinerPoint(PTX, PTY);
0006 %   Computes steiner point of a polygon defined by POINTS. POINTS is a
0007 %   [N*2] array of double.
0008 %
0009 %   The steiner point is computed the same way as the polygon centroid,
0010 %   except that a weight depending on the angle is given to each vertex.
0011 %
0012 %   See also:
0013 %   polygons2d, polygonArea, polygonCentroid, drawPolygon
0014 %
0015 %   ---------
0016 %   author : David Legland
0017 %   INRA - TPV URPOI - BIA IMASTE
0018 %   created the 11/11/2004.
0019 %
0020 
0021 
0022 if nargin==1
0023     var = varargin{1};
0024     px = var(:,1);
0025     py = var(:,2);
0026 elseif nargin==2
0027     px = varargin{1};
0028     py = varargin{2};
0029 end
0030 
0031 % Algorithme P. Bourke
0032 sx = 0;
0033 sy = 0;
0034 N = length(px);
0035 for i=1:N-1
0036     sx = sx + (px(i)+px(i+1))*(px(i)*py(i+1) - px(i+1)*py(i));
0037     sy = sy + (py(i)+py(i+1))*(px(i)*py(i+1) - px(i+1)*py(i));
0038 end
0039 sx = sx + (px(N)+px(1))*(px(N)*py(1) - px(1)*py(N));
0040 sy = sy + (py(N)+py(1))*(px(N)*py(1) - px(1)*py(N));
0041 
0042 pt = [sx sy]/6/polygonArea(px, py);