I was curious about the "natural spline" part, since I haven't heard of those before. As usual when it comes to maths topics, Wikipedia was disappointing, but this article seems like a decent real-world example of how they work in practice: https://www.clayford.net/statistics/using-natural-splines-in-linear-modeling/ (just figured I'd share for anyone else who is curious)

You can also read about the relationship between Basis Splines and Natural Splines in sections 4 and 5 of this PDF: https://www.math.ucla.edu/~baker/149.1.02w/handouts/dd_splines.pdf In a nutshell, for the Basis Spline you use *values* as the *control points* for the curve, and the curve doesn't interpolate the values. For the Natural Spline, you ask: what are the *control points* for a basis spline that does interpolate my *values*? The answer is succinct, but it involves [inverting a matrix](https://en.wikipedia.org/wiki/Tridiagonal_matrix#Inversion) so [the code](https://github.com/evercoder/culori/blob/main/src/interpolate/splineNatural.js) for natural spline is mostly doing the inversion, then rendering a basis spline on the resulting control points.

Thanks, that's a very clear PDF!