%%%%%%%%%%%%%%%%%%%%%     Reflection Matrix   %%%%%%%%%%%%%%%%%%%%%
%
% REFLMAT
% Usage: REFLMAT(seg)
% Inputs:  seg = [x y] -  x,y are points inside or on the unit circle  
%
%     The matrix effecting the reflection in the hyperbolic 
%     geodesic connecting x and y is constructed. 
%     to effect the reflection act on a complect number via L and then 
%     conjugate the result

function L = reflmat(seg)             
   I = sqrt(-1); 
   x = seg(1); y = seg(2);
   m = (x+y)/2;
   d = I*(x-y)/2;  
   w = 2*real(m*conj(d));
   if (w < 0) d = -d; w = -w; end;
   u = abs(m); 
   v = abs(d);
   ti  = w/(v^2+1-u^2);
   tr  = 1/sqrt(v^2*(1+ti^2));
   ri  = ti*tr;
   cr = ri*m +tr*d;
   a = -I*conj(cr);
   b = I*ri;
   L = [a b; conj(b) conj(a)];