In general polar representation of a closed curve is done by coordinate $(\theta,r(\theta))$, $\theta\in (0,360)$.
When working with real data, I got a closed curves whose graph looks like the below
I want to approximate this type of closed curve by some polar equation. But I doubt if it possible or not.
Note that, here we will get points like $(\theta,r^1(\theta)),(\theta,r^2(\theta)),(\theta,r^3(\theta)),\ldots$, that is for same $\theta$ we may get different $r(\theta)$.
Could anyone please suggest how to approximate this type curves using polar coordinate system.
Thanks in advance.