function [fx,fy,fz]=hopfmap(a,b,c)

phi=0:pi/100:2*pi;
theta=atan2(b,-a)-phi;
alpha=sqrt((1+c)/2);
beta=sqrt((1-c)/2);

x=beta*cos(phi);
y=beta*sin(phi);
w=alpha*cos(theta);
z=alpha*sin(theta);

r=acos(w)/pi;
%r=1;
fx=r./sqrt(1-w.^2).*x;
fy=r./sqrt(1-w.^2).*y;
fz=r./sqrt(1-w.^2).*z;