[sharnett]

Very interesting! I explored this method and compared it to Newton's method, you may like it: https://github.com/sharnett/point_to_ellipse/blob/master/poi...

[gylpm]

I found a paper using a similar idea (but using a different method to step the parameter) to find the orthogonal projection onto curves. It also converges quadraticaly, and seems a little faster through my experiments. http://www.geometrie.tugraz.at/wallner/sproj.pdf