von_mises#
- orix.quaternion.von_mises(x: ~orix.quaternion.rotation.Rotation, alpha: float, reference: ~orix.quaternion.rotation.Rotation = Rotation (1,) [[1. 0. 0. 0.]]) ndarray [source]#
A vastly simplified Von Mises-Fisher distribution calculation.
- Parameters:
- x
Rotations.
- alpha
Lower values of alpha lead to “looser” distributions.
- reference
Reference rotation. Default is the identity rotation.
- Returns:
R
Rotations.
Notes
This simplified version of the distribution is calculated using
\[\frac{\exp\left(2\alpha\cos\left(\omega\right)\right)}{\_0F\_1\left(\frac{N}{2}, \alpha^2\right)}\]where \(\omega\) is the angle between orientations and \(N\) is the number of relevant dimensions, in this case 3.