orientation_grid

anri.crystal.orientation_grid(step_deg, ops)

Orientations covering one fundamental zone of a Laue group, and their worst-case spacing.

Cubic groups (24 rotations) use a regular Rodrigues grid of the cubic fundamental zone: for cubic crystals it needs about half the orientations of a cubochoric grid for the same worst case. Other groups use the cubochoric grid of all rotations (cubochoric_quaternions(), with N = 131.97 / (step - 0.037) as in Singh & De Graef, so step_deg is about the mean spacing) reduced to the fundamental zone around the identity, plus a shell half a step wide outside it: without the shell, points just outside the zone leave gaps along its boundary (their symmetric images are not grid points).

Parameters:

• step_deg (float) – Grid step in degrees

• ops (Array | ndarray | bool | number | bool | int | float | complex) – [n, 3, 3] Laue-group rotations, from laue_rotations()

Returns:

• U (np.ndarray) – [N, 3, 3] orientations (float32)

• delta (float) – Largest misorientation (degrees) from any orientation to its nearest grid point: exact for the cubic grid, measured for the cubochoric one (at most 1.15 x step for every Laue group, 1.5 to 12 degrees; 1.2 x step)