Log-polar Coordinates

#Math
$$
\begin{align}
(\rho,\theta )&\rightarrow (\ln r,\theta ) \\&\rightarrow \left( \ln\left( \sqrt{ x^{2}+y^{2} },\tan ^{-1}\left( \frac{y}{x} \right) \right) \right) \\\end{align}
$$

• Definition of log-polar coordinates in terms of polar coordinates and cartesian coordinates