Hello,

I´m trying to draw a Hopf Fibration in a graphics program that I´m writing but I have trouble understanding the math behind it. I´m not a math student, I´m a graphics programmer and simply want to animate a Hopf torus bundle with all it´s interconnected circles. The only thing I know about complex numbers is the basic theory that I read in the past few days.

My problem is that although there are lots of websites that explain how a Hopf fibration is made, I cannot seem to find any that explains how to get the real x, y, z, w coordinates in 4D space of each of the circles. The explanations on the websites always start with complex numbers and end with complex numbers, but never explain how to get the coordinates.

One thing I don´t need further explanation for is how to do stereographic projection. I´ve done hypercubes and other 4D shapes in the past so I already know how to do projection.

Here is a scan of the math that I attempted so far:

http://www.home.zonnet.nl/petervenis/Hopf.gif

Now, I don´t know for sure if what I did above is correct. And if it´s correct, I don´t know what to do next. How do I solve the equation and get the coordinates so I can plot the circles?

Peter