%%%%%%%%%%%%%%%%%%%%% Hyperbolic Midpoint of Hyperbolic Line Segment %%%%%%%%%%%%%%%%%%%%%
%
% HMIDPOINT
% Usage: z = HMIDPOINT(x,y)
% Inputs:  x,y are points in the euclidean disc
%
% Output: z the euclidean center of the line connecting the points
%         if x and y are not distinct or lie on a diameter inf is returned     


function z = hmidpoint(x,y)
if abs(x-y) == 0 z = x, return, end
if real(conj(x)*y) == 0 
    if abs(x) == 0
        E(1) = y/abs(y);
    else 
        E(1) = x/abs(x);
    end
    E(2)= - E(1);
else
    E = endpoints(euccentre(x,y));
end

L  = lft([E(1),x,E(2)],[-1,0,1]);
y1 = lftact(L,y);
z1 = hyptoeuc(0.5*euctohyp(y1));
z= lftact(inv(L),z1);