%%%%%%%%%%%%%%%%%%%%% Parametrization of Geodesic Line  %%%%%%%%%%%%%%%%%%%%%
%
% GEOLINE
% Usage: GEOLINE(seg)
% Inputs:  seg = [x y] -  x,y are points inside or on the unit circle  
%
% Outputs:  the hyperbolic geodesic connecting x and y is constructed
%           and is returned as a vector of complex points in the plane  

function w = geoline(seg)             

I = sqrt(-1);
T  = 0:(1/(narcpnts-1)):1; 
oT = ones(T)-T;
x = seg(1); y = seg(2); 

   z = x*T+y*oT;                   % construct chord from x to y
   m = (x+y)/2;                    % midpoint of segment from x to y
   v = abs((x-y)/2);               % distance from midpoint to endpoints
   mc = m/(1+v);                   % point on geodesic closest to zero
   L = lft([x m y], [x mc y]);     % LFT mapping chord to arc
   w = lftact(L,z);                % map chord to arc 

   clear T;
   clear oT;
   clear z;