English: The Log-Polar Mapping. Point (x,y) is mapped to ${\displaystyle (\rho ,\theta )}$ where ${\displaystyle \rho =\log {\sqrt {x^{2}+y^{2}}}}$ and ${\displaystyle \theta =\arctan({\frac {y}{x}})}$. In general circles around orogin and radii are mapped to horizontal and vertical lines.