%%%%%%%%%%%%%%%%%%%%% Euclidean Centre of Hyperbolic Lines %%%%%%%%%%%%%%%%%%%%%
%
% EUCCENTRE
% Usage: z = EUCCENTRE(x,y)
% Inputs:  x,y are points in or on the hyperbolic 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 = euccentre(x,y)
b = [x*conj(x)+1; y*conj(y)+1];
A = 2*[real(x), imag(x); real(y), imag(y)];
if det(A) == 0 z = inf; 
else c = A\b; z = c(1) +i*c(2);
end