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=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=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=False) or degrees (degrees=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

>>> from orix.quaternion import Orientation, symmetry
>>> ori1 = Orientation.random((5, 3))
>>> ori2 = Orientation.random((6, 2))
>>> dist1 = ori1.angle_with_outer(ori2)
>>> dist1.shape
(5, 3, 6, 2)
>>> ori1.symmetry = symmetry.Oh
>>> ori2.symmetry = symmetry.Oh
>>> dist_sym = ori1.angle_with_outer(ori2)
>>> np.allclose(dist1.data, dist_sym.data)
False