\theta = \begin{cases} \sin^{-1} \frac{1}{\beta}, & \text{if }\beta \ge 1 \\ \pi - \sin^{-1}{\beta}, & \text{if }\beta\le 1\end{cases} .
For any two points p and q in the plane, let Rpq be the set of points for which angle prq is greater than θ.