Help creating a NURBS sphere

Could somebody give me info on/show me how to make a uniform perfect sphere using NURBS?

I’m working on a program that will slice up a sphere into multiple separate shards along great and small circles on its surface.
I’ve figured out all of the underlying math (slicing the circles and making compact regions out of the resulting arcs), and now I just need to display it. Unfortunately, I don’t know squat about NURBS.
All of my attempts to make a NURBS sphere have ended in strange ellipsoids, and I haven’t been able to find a single tutorial or code snippet that shows how to make one (I assume everybody just uses the built in sphere).
In my search I’ve read that it’s possible to make a perfect NURBS sphere, but I’m hoping that it can also be made uniformly so I can just convert from cartesian to spherical coordinates to get UV space. Otherwise I’ll also need help getting the uv coord of an xyz point. So could somebody out there give me some info or code?