Quote Originally Posted by halfeye View Post
Yeah, and that is sort of good and not obvious either, but it still leaves you with an infinitly long line to find the point along, and the far end doesn't reduce to a line before you reach infinite accuracy in rotation.
Radius value you can search for in the same manner:

1. Is x^2+y^2<r^2?
If yes, then you have an upper bound and can bisect to get the exact result.
If not, increase r and repeat until yes. Then the last and second to last r gives upper and lower bounds, so you can continue with bisection.

Mix those questions with those concerning asimuth and it will be a fully fuctional algorithm, which for any finite (x,y) will give the sought point with arbitrary precision with finite number of questions. For integer pairs it will find the exact number in finite time, while for real number pairs it will require countable infinity of questions to be exact.

I am not sure, which radius incrementation method would be optimal, but I would guess exponential. Anything faster would leave a much larger area to search through once you have the upper bound while anything slower will take way more questions to reach upper bound.