If anyone is really interested in this stuff and wants to make a major contribution to open source software... First study these and then move on to NURBS, surfaces, and then trimmed NURBS surfaces. These are the core of all CAD software and a clean library for trimmed NURBS is sorely lacking. There are two that I'm aware of, the one in OpenCascade which is a huge ball of mud (but works) and the one in SolveSpace which doesn't scale well and has some other limitations - that is the one I feel is most worthy of someones time.
Intersections are computed approximatively within some prescribed geometrical tolerance, and intersection curves are "marched out".
BTW they don't explicitly say "trimmed NURBS" but doing boolean operations implies that is the case ;-)
NLib has a lot of sophisticated NURBS math tools. It was literally written by one of the men who wrote The NURBS Book.
As far as I know, it doesn't do anything much for trimmed NURBS surfaces, in the sense of a surface trimmed by an arbitrary series of curves. (Might be a tessellation routine for that case?) Basically it is mostly geometry, with only very limited topology support.
There are lots of products which provide geometry & topology support: SMLib, SOLIDS++, Acis, and Parasolid come to mind. The first two are built on NLib. I don't think any of them have as sophisticated NURBS geometry tools as NLib does. (Except to the extent that you can call NLib routines directly with the first two.)
I'm not aware of any commercial product which directly competes with NLib at all. Which doesn't mean one doesn't exist! I'd be interested if anyone has experience with other libraries.
Look at the list of applications that use it.