This paper is very useful in how it explains the mapping of any coordinates $(x,y)$ across an ellipse with the function $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$
to $$\left(\frac{a^2b^2x}{a^2y^2+b^2x^2},\frac{a^2b^2y}{a^2y^2+b^2x^2}\right)$$
But what if that ellipse is a rotated one, as described here?
I can't even figure it out if I compare it with a circle, but if anyone could help me convert $(x,y)$ to the inverted coordinates, I'd be very happy.