I think I understand now the confusion. Non-uniform B-spline can but must not have equal-length base functions. As I explained in my previous post with the image, it is clear that just the weight alone makes it non-uniforum, independent of the knot vector.jnxd wrote: ↑Mon Mar 21, 2022 9:57 pm I do not have an authoritative book with me to give an exact definition, but there are multiple places that imply this:
In Wikipedia B-Spline Properties section
For NURBS however, there is a definition: https://en.wikipedia.org/wiki/B-spline#NURBS and it does not tell anything about the knot vector. You can use a base as you like (the base consists of B-Splines), you only have to introduce weights. So your are free in your implementation on what splines you use as base for NURBS. I cannot see a definition where the base of NURBS are defined. It seems that different programs create NURBS in different way, however I am no expert in this regards.