Hi Michael, I'm glad that MoI was useful for your diploma thesis project!

> How accurate is the NURBS representation of simple objects like a sphere?

Purely mathematically it is completely accurate - one of the properties of a NURBS curve or surface is that it can have the 100% exact same geometric shape as a conic, that's a big reason why they have become the standard for CAD applications.

One reference for this is "The NURBS Book 2nd Edition", Les Piegl and Wayne Tiller, Chapter 7 Conics and circles.

Basically, the R (rational) part of NURBS was introduced specifically to make this possible.

But like any kind of math done on the computer, each calculation only has a limited precision, and you will do more calculations and just generally have more data in the definition of a NURBS sphere rather than a pure analytic point and radius definition. So there is more opportunity for tiny rounding errors to accumulate for the NURBS version, but I'd think that these would be less than 1e-13.

2.5e-13 for your distance accuracy sounds like a really good result to me. You're probably doing just a lot more calculations in general for your NURBS distance computation so again with more calculations your rounding error increases, that's just a normal side effect.

- Michael