The use of orix should feel familiar to the use of numpy, but rather than cells of numbers, the cells contain single 3d objects, such as vectors or quaternions. They can all be created using tuples, lists, numpy arrays, or other numpy-compatible iterables, and will raise an error if constructed with the incorrect number of dimensions. Basic examples are given below.
Vectors are 3d objects representing positions or directions with "magnitude". They can be added and subtracted with integers, floats, or other vectors (provided the data are of compatible shapes) and have several further unique operations.
>>> import numpy as np
>>> from orix.vector import Vector3d
>>> v = Vector3d((1, 1, -1))
>>> w_array = np.array([[[1, 0, 0], [0, 0, -1]], [[1, 1, 0], [-1, 0, -1]]])
>>> w = Vector3d(w_array)
>>> v + w
# Vector3d (2, 2)
# [[[ 2 1 -1]
# [ 1 1 -2]]
#
# [[ 2 2 -1]
# [ 0 1 -2]]]
>>> v.dot(w)
# array([[1, 1],
# [2, 0]])
>>> v.cross(w)
# Vector3d (2, 2)
# [[[ 0 -1 -1]
# [-1 1 0]]
#
# [[ 1 -1 0]
# [-1 2 1]]]
>>> v.unit
# Vector3d (1,)
# [[ 0.5774 0.5774 -0.5774]]
>>> w[0]
# Vector3d (2,)
# [[ 1 0 0]
# [ 0 0 -1]]
>>> w[:, 0]
# Vector3d (2,)
# [[1 0 0]
# [1 1 0]]Quaternions are four-dimensional data structures. Unit quaternions are often used for representing rotations in 3d. Quaternion multiplication is defined and can be applied to either other quaternions or vectors.
>>> from orix.quaternion.rotation import Rotation
>>> p = Rotation([0.5, 0.5, 0.5, 0.5])
>>> q = Rotation([0, 1, 0, 0])
>>> p.axis
# Vector3d (1,)
# [[0.5774 0.5774 0.5774]]
>>> p.angle
# array([2.0943951])
>>> p * q
# Rotation (1,)
# [[-0.5 0.5 0.5 -0.5]]
>>> p * ~p # (unit rotation)
# Rotation (1,)
# [[1. 0. 0. 0.]]
>>> p.to_euler() # (Euler angles in the Bunge convention)
# array([[1.57079633, 1.57079633, 0. ]])