Hi, I'm currently working on a raytracing rendering engine for a research project. Since raytracing doesn't need triangle meshes I thought about using curves like NURBS or rational bezier patches. My question is: What do you think is better suiting for this purpose?

I have only worked with bezier curves before and just read a few papers and wiki articles about NURBS. Therefore I have some other questions about them:

1. Is there anything only a NURBS can form and a set of rational bezier patches can not?

I read some thing like: It is possible to convert a NURBS into a set of rational bezier patches and vice versa too, but I'm not sure about it.

2. What exactly is the knot vector of a NURBS and what is it needed for?

A set of rational bezier patches just needs the control points and their weights and a NURBS needs control points, weights and the knot vector. Isn't that redundant data?

3. Are calculations (finding a point, derivative or normal) of a NURBS more time expensive or complex than the ones of bezier patches?

4. NURBS seem to end before actually reaching the first / last control point, bezier curves reach the first and last control point in every case. That is a bit confusing but seems to be natural. Any explanation here?