> it’s a bit of a tragedy that NURBS and other curve families that are more intuitive to work with haven’t caught on.
I feel like it’s even more tragic that Uniform B-splines aren’t more common, especially quadratic and cubic versions. Git rid of knots, and talk specifically about degree 2 or 3, and you don’t need a PhD in math to follow the explanation. You can explain it without the sums of sums of recursive basis functions while juggling several different indices, no need to discuss knot insertion and removal. Uniform B-splines segments have a 1:1 mapping to Bézier curves, and understanding them before diving into non-uniform curves would be so helpful and actually cover two thirds of what people need and what happens in practice.
The big problem with NURBS is that the only information you can find on them dives into unwieldy math notation and discussion about knots, there’s almost nothing out there that’s simple and quick to follow, or tailored specifically to constrained cases, people writing drawing apps and games. The material all seems to be abstract and arbitrary degree and arbitrary complex uses. I feel like NURBS is a case where it becomes clear that the notation gets in the way of understanding, it truly feels like there should be a simpler notation because the concepts are easier to grok than the math.