%%%%%%%%%%%%%%%%%%%%%%%%%%%% Geodesic Ray Matrix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% RAYMAT
% Usage: RAYMAT(seg)
% Inputs:  seg - a segment [x y]  
%   
% Output:  a matrix L used to construct the ray from P to Q

function L = raymat(seg)             

   x = seg(1);
   y = seg(2);
   u = sqrt(1-abs(x)^2);          % a normalizing factor
   v = (y-x)/(1-conj(x)*y);       % an image of y
   w = conj(sqrt(v/abs(v)));      % rotation factor
   a = w/u;
   b = -x*a;
   L = [conj(a) -b; -conj(b) a];  % inverse of the matrix [a b; conj(b) conj(a)]