comparison toolboxes/FullBNT-1.0.7/KPMtools/polygon_centroid.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function [x0,y0] = centroid(x,y)
+% CENTROID Center of mass of a polygon.
+%	[X0,Y0] = CENTROID(X,Y) Calculates centroid 
+%	(center of mass) of planar polygon with vertices 
+%	coordinates X, Y.
+%	Z0 = CENTROID(X+i*Y) returns Z0=X0+i*Y0 the same
+%	as CENTROID(X,Y).
+
+%  Copyright (c) 1995 by Kirill K. Pankratov,
+%       [e-mail].
+%       06/01/95, 06/07/95
+
+% Algorithm:
+%  X0 = Int{x*ds}/Int{ds}, where ds - area element
+%  so that Int{ds} is total area of a polygon.
+%    Using Green's theorem the area integral can be 
+%  reduced to a contour integral:
+%  Int{x*ds} = -Int{x^2*dy}, Int{ds} = Int{x*dy} along
+%  the perimeter of a polygon.
+%    For a polygon as a sequence of line segments
+%  this can be reduced exactly to a sum:
+%  Int{x^2*dy} = Sum{ (x_{i}^2+x_{i+1}^2+x_{i}*x_{i+1})*
+%  (y_{i+1}-y_{i})}/3;
+%  Int{x*dy} = Sum{(x_{i}+x_{i+1})(y_{i+1}-y_{i})}/2.
+%    Similarly
+%  Y0 = Int{y*ds}/Int{ds}, where
+%  Int{y*ds} = Int{y^2*dx} = 
+%  = Sum{ (y_{i}^2+y_{i+1}^2+y_{i}*y_{i+1})*
+%  (x_{i+1}-x_{i})}/3.
+
+ % Handle input ......................
+if nargin==0, help centroid, return, end
+if nargin==1
+  sz = size(x);
+  if sz(1)==2      % Matrix 2 by n
+    y = x(2,:); x = x(1,:);
+  elseif sz(2)==2  % Matrix n by 2
+    y = x(:,2); x = x(:,1);
+  else
+    y = imag(x);
+    x = real(x);
+  end
+end 
+
+ % Make a polygon closed ..............
+x = [x(:); x(1)];
+y = [y(:); y(1)];
+
+ % Check length .......................
+l = length(x);
+if length(y)~=l
+  error(' Vectors x and y must have the same length')
+end
+
+ % X-mean: Int{x^2*dy} ................
+del = y(2:l)-y(1:l-1);
+v = x(1:l-1).^2+x(2:l).^2+x(1:l-1).*x(2:l);
+x0 = v'*del;
+
+ % Y-mean: Int{y^2*dx} ................
+del = x(2:l)-x(1:l-1);
+v = y(1:l-1).^2+y(2:l).^2+y(1:l-1).*y(2:l);
+y0 = v'*del;
+
+ % Calculate area: Int{y*dx} ..........
+a = (y(1:l-1)+y(2:l))'*del;
+tol= 2*eps;
+if abs(a)<tol
+  disp(' Warning: area of polygon is close to 0')
+  a = a+sign(a)*tol+(~a)*tol;
+end
+ % Multiplier
+a = 1/3/a;
+
+ % Divide by area .....................
+x0 = -x0*a;
+y0 =  y0*a;
+
+if nargout < 2, x0 = x0+i*y0; end