This library has a very interesting algorithm for computing the curve point closest to a given point, seemingly based on a root-finder that doesn't need any complex numbers. Does anyone know of any resources about such an algorithm?
For general polynomials, it matters a great deal in what basis it is represented. The typical monomial basis is usually not the best from a numerical standpoint. I am aware of some modern methods such as this: https://arxiv.org/pdf/1611.02435
For polynomials expressed in e.g. a Bernstein basis, there are often much faster and stable tailored methods working solving for the eigenvalues of a companion matrix of a different form.
[0] https://github.com/GraphiteEditor/Graphite/blob/master/libra...
Curiously, the poly-cool crate appears to use the monomial basis instead of the Bernstein basis that the old version was using.
[0] https://github.com/GraphiteEditor/Graphite/pull/3031
[1] https://crates.io/crates/poly-cool
[2] https://github.com/GraphiteEditor/Graphite/blob/beb1c6ae6489...