linguistic:voice_change, information:highlighting, stylistic:style_transfer, structural:summarization
Geodesic norm

The geodesic distance d (p, q) between unit quaternions p and q is defined as:

d g (p, q) = ‖ ln (p − 1 q) ‖. {\displaystyle d_{\text{g}}(p,q)=\lVert \ln(p^{-1}q)\rVert.}

and amounts to the absolute value of half the angle subtended by p and q along a great arc of the S sphere.This angle can also be computed from the quaternion dot product without the logarithm as:

arccos (2 (p ⋅ q) 2 − 1). {\displaystyle \arccos(2(p\cdot q)^{2}-1).}