[sfpotter]

This is quite a complicated approach that misses out on most of the basic numerical and geometric methods that will make the problem simpler. I would recommend looking outside of recent SIGGRAPH papers. Brushing up on the basics of Bernstein polynomials, B-splines, and rootfinding methods will lead you to develop simpler algorithms which are likely faster.

[raphlinus]

I'm extremely curious what those basic methods are. We're in the process of replacing the higher order rootfinding in kurbo with a new solver based on Yuksel's method[1]. If you know of simpler, faster techniques that would be quite interesting.

[1]: https://crates.io/crates/polycool

[mmorse1217]

This is a pretty good foundational reference for Bézier curves and b-splines https://www.sciencedirect.com/book/9780122490521/curves-and-...