I've recently fallen down the spline rabbit hole and appreciate how many other people are making notebooks about splines! Your notebook has sparked two ideas. The easy one is, it would be nice to optionally toggle the actual cubic curve so we can visually compare the geometric accuracy of the quartic approximation. You could also animate a point along each curve to show the parametric accuracy too. The harder one is, I wonder if quartic or quintic curves could be approximated with two cubic curves! This would give a way to render higher order splines as SVG using cubic splines If you could, I bet you could upgrade some of the spline interpolations to higher geometric and parametric continuity. For example, the Catmull-Rom spline is G1 continuous, and the Cardinal spline is C1 continuous. If they could be upgraded to quartic or quintic splines, the extra degrees of freedom could be used to constrain higher continuity. Then the cubic approximation would make usable and fast (assuming it worked).

Yes, interesting ideas! I don't have time to work on this right now (alas) but I'd a fork with some additions could be a way to explore some of this and I bet others might be interested too -- maybe you could send it to the authors of the paper since I bet they'd appreciate it! Btw, the spline discussed here is the one (with quadratic lowering) I'm using on https://silk.art, which is another project I currently don't have time to work on... (It's a continuation of http://weavesilk.com which is a decade-ago generative art experiment that I've been wanting to get back to for a long time). (Note of caution: it uses webgpu, which might fail in your browser).