Question on accuracy of NURBS

 From:  mhein

I'm a computer science student from Germany. For my diploma thesis I'm working on several algorithms dealing with nurbs surfaces, i.e. distance calculation and ray-surface intersection. My software implementation is using the openNURBS Toolkit to be able to read *.3dm files.
Since Rhino is very expensive (and kind of complicated to use, in my point of view) I'm using MoI to create some test models, it's a very cool programm and easy to understand.

To see how accurate my distance algorithm is, I want to do some distance queries on a sphere described by a NURBS surface and compare it to a sphere described by its center and radius. I've already learned to create a NURBS sphere in MoI, entering its coordinates and radius with my keyboard.
Now I've already done some testing, and the average error on the distance calculation is at about 2.5e-13, which I think is already a very good result.

But know I'm a little bit curios about where this small error occurs: Is it in my distance computation (thats what I guess), or is it in the difference between the NURBS sphere and the sphere described by radius and center? Or in another way: How accurate is the NURBS representation of simple objects like a sphere?

Thanks for your help!

PS: If the answer to this question is rather complicated (or large), then it would also be very nice to point me to some literature or web sources for further reading, if possible.