Rotation in two dimensions
This application calculates the two-dimensional rotation of a point $p$ around an arbitrary fixed point $f$ which is not neccessary the origin. Treating $p$ and $f$ as complex numbers, the 2D rotation is calculated from the formula \[ f+(p-f)\mathrm{e}^{i\theta} \] where $\theta$ is the angle of rotation, positive for counterclockwise.