angle_with_outer#

Orientation.angle_with_outer(other: Orientation, lazy: bool = False, chunk_size: int = 20, progressbar: bool = True, degrees: bool = False) → ndarray[source]#

Return the symmetry reduced smallest angle of rotation transforming every orientation in this instance to every orientation in another instance.

Parameters:

other: Another orientation.
lazy: Whether to perform the computation lazily with Dask. Default is False.
chunk_size: Number of orientations per axis to include in each iteration of the computation. Default is 20. Only applies when lazy is True. Increasing this might reduce the computation time at the cost of increased memory use.
progressbar: Whether to show a progressbar during computation if lazy is True. Default is True.
degrees: If True, the angles are returned in degrees. Default is False.

Returns:

angles: Smallest symmetry reduced angles in radians (degrees is False) or degrees (degrees is True).

See also

angle_with

Notes

Given two orientations \(g_i\) and \(g_j\), the smallest angle is considered as the geodesic distance

\[d(g_i, g_j) = \arccos(2(g_i \cdot g_j)^2 - 1),\]

where \((g_i \cdot g_j)\) is the highest dot product between symmetrically equivalent orientations to \(g_{i,j}\).

Examples

>>> import numpy as np
>>> from orix.quaternion import Orientation, symmetry
>>> ori1 = Orientation.random((5, 3))
>>> ori2 = Orientation.random((6, 2))
>>> omega1 = ori1.angle_with_outer(ori2)
>>> omega1.shape
(5, 3, 6, 2)
>>> ori1.symmetry = symmetry.Oh
>>> ori2.symmetry = symmetry.Oh
>>> omega_sym = ori1.angle_with_outer(ori2)
>>> np.allclose(omega1.data, omega_sym.data)
False