I' m looking for an efficient (in terms of lowest number of additions/multiplications) way to compare two (directed) angles $\measuredangle p_1 p_0 q$, $\measuredangle p_1 p_0 r$ in a plane.
For example, the orientation of $r$ in respect of the line $g(p_0,p_1)$ can be efficiently obtained by calculating the third coordinate of the cross product $(p_1-p_0) \times (q-p_0)$ - if it's positive, $r$ lies left of $g(p_0,p_1)$, if it's 0, $r$ is on the line and right, if negative.
Is there a comparable way for determining which angle is bigger?