Let \(\mathbb{S}^{d}_R\) be the \(d\)-sphere with radius \(R>0\). The spherical distance is defined by
\begin{equation*} d_R(x,y)=R \arccos \Bigl(\frac{x\cdot y}{R^2}\Bigr)\qquad x,y \in \mathbb{S}^d_R. \end{equation*}
Remarks
- \(d_1(x,y)\) corresponds to the angle between \(x\) and \(y\) in radians.