define rotations by homochoric coordinates
Description
The inverse of homochoric. A homochoric vector points along the rotational axis and has length
\[ \rho = \left(\frac{3}{4}\left(\omega - \sin\omega\right)\right)^{1/3} \]
for the rotational angle \(\omega\), so the rotation group is mapped onto a ball of radius \((3\pi/4)^{1/3}\). Recovering \(\omega\) from \(\rho\) has no closed form and is done by a Newton iteration started at the small angle limit \(\omega \approx 2\rho\), which is exact up to \(O(\rho^5)\).
Syntax
rot = rotation.byHomochoric(v)
rot = rotation.byHomochoric([x y z])Input
| v | homochoric vector3d |
Output
| rot | rotation |
See also
quaternion.homochoric quaternion.cubochoric rotation.byRodrigues