Derivative of a NURBS

[EliaStocco]

Hello, I am writing my own library in Python for B-spline and NURBS.
Given a B-spline curve (degree P, N basis function, N+P+1 knots ) it is possible to express exactly its derivative with another B-spline (degree P-1, N-1 basis function, N+P-1 knots, i.e. eliminating the first the last knots).
Is it possible to make the analogous thing with NURBS?
How do you evaluate the derivative of a NURBS? Do you "generate" another NURBS or evaluate the derivative "numerically" i.e. with for example some finite difference algorithm.
Moreover, B-spline partial derivation is easily generalizable to B-spline surface, is it possible to do that for NURBS too?
Thanks

[rreusser]

Hi! It seems perfectly plausible that the derivative of a b-spline is just a spline of lower degree, though it's not the approach I took. This library pretty directly applies the chain rule and evaluates the derivative directly (in any number of dimensions), rather than explicitly constructing that spline or opting for numerical differentiation. I was not able to nail down a reasonable expression for NURBS though. If I recall, the weights resulted in an explosion of the chain rule so that some other approach or form is probably required.

I don't have a copy myself, but I'd highly recommend The NURBS Book, which I think felt like was everyone's go-to reference for the low-level details.

Peter Boyer's verb library is also a very nicely done library that's far more ergonomic than this library, which was really aimed primarily at evaluating the core expressions in n dimensions as fast as possible.

[EliaStocco]

Thank you very much