angle_with_outer

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

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 \(O_i\) and \(O_j\), the smallest angle is considered as the geodesic distance

\[d(O_i, O_j) = \arccos(2(O_i \cdot O_j)^2 - 1),\]

where \((O_i \cdot O_j)\) is the highest dot product between symmetrically equivalent orientations to \(O_{i,j}\).

Examples

>>> from orix.quaternion import Orientation, symmetry
>>> O1 = Orientation.random((5, 3))
>>> O2 = Orientation.random((6, 2))
>>> omega1 = O1.angle_with_outer(O2)
>>> omega1.shape
(5, 3, 6, 2)
>>> O1.symmetry = symmetry.Oh
>>> O2.symmetry = symmetry.Oh
>>> omega_sym = O1.angle_with_outer(O2)
>>> np.allclose(omega1.data, omega_sym.data)
False