With polar coordinates and Fourier transforms, you can draw the outlines of tons of figures. But you can’t go back. Imagine that you can go with your pen around the center in only one direction, but any distance from the center.

Yes. https://en.m.wikipedia.org/wiki/Polar_coordinate_system

Since this curve is cyclical, you can do it [-infinity ; +infinity] and it’s the same curve again and again.