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.