function [xx,yy] = coordinate_transformation(x,y,A,B)
%
%  The function [xx,yy] = coordinate_transformation(x,y,A,B)
%  transforms the coordinates (x,y) into (xx,yy),
%  translating the origin to the midpoint of AB,
%  and rotating along the direction of AB.
%
%  ON ENTRY:
%    x      x-coordinates;
%    y      y-coordinates;
%    A      x and y coordinates of start position;
%    B      x and y coordinates of end position.
%
%  ON RETURN:
%    xx     x-coordinates after the transformation;
%    yy     y-coordinates after the transformation;
%
midpoint = [ (A(1)+B(1))/2; (A(2)+B(2))/2 ];  % defines translation
new_e1 = [ B(1) - midpoint(1); B(2) - midpoint(2) ];
new_e2 = [ -new_e1(2); new_e1(1) ];
rotation = [ new_e1  new_e2 ];  % new basis vectors define rotation
xy = [x; y];
new_xy = rotation*xy;
xx = new_xy(1,:) + midpoint(1);
yy = new_xy(2,:) + midpoint(2);