This looks very complicated and needs more processing power the more complex the graphics is, same as my current formula. Once I wrote a spline Applet (probably doesn’t work in most browser nowadays because of disabled Java plugin). It needed only one polynomial of degree 3 for each curve segment, no matter how many segments I have. And the coefficients calculation is very fast and linear as well, see here for the full source code.
Drawback is that you can’t just feed any vector graphics to it, and needs some extensions to allow sharps edges as well. But this would even allow realtime modulation of the points. I was thinking of writing a waveform drawing module with it, something like the VCV Parametra module, but for drawing one audio cycle instead of a filter curve. I think this could be better than the standard bézier curve concept. Should be easy with my new Lua module.