Hi, your first link talks about NURBS curves, not NURBS surfaces. Cutting a surface in half is significantly more complicated than cutting a curve in half.
And your second link is to a commercial result, an entire book. Presumably because the topic is complicated enough that people are willing to pay $69 to $78 to understand the challenge well enough.
If your DDG search for "splitting a NURBS surface in half" are successful, I'd love to see the results.