class orix.quaternion.Rotation(data: Union[ndarray, Rotation, Quaternion, list, tuple])[source]#

Bases: Quaternion

Transformations of three-dimensional space, leaving the origin in place.

Rotations can be parametrized numerous ways, but in orix are handled as unit quaternions. Rotations can act on vectors, or other rotations, but not scalars. They are often most easily visualised as being a turn of a certain angle about a certain axis.

Rotation of an object illustrated with an axis and rotation angle.

Rotations can also be improper. An improper rotation in orix operates on vectors as a rotation by the unit quaternion, followed by inversion. Hence, a mirroring through the x-y plane can be considered an improper rotation of 180° about the z-axis, illustrated in the figure below.

180° rotation followed by inversion, leading to a mirror operation.
Rotations support the following mathematical operations:
  • Unary negation.

  • Inversion.

  • Multiplication with other rotations and vectors.

Rotations inherit all methods from Quaternion although behaviour is different in some cases.

Rotations can be converted to other parametrizations, notably the neo-Euler representations. See NeoEuler.



Return the angles of rotation.


Return this and the antipodally equivalent rotations.


Return the axes of rotation.


Return True for improper rotations and False otherwise.



Return the angles of rotation transforming the rotations to the other rotations.


Return the angles of rotation transforming the rotations to all the other rotations.


Return the outer dot products of the rotations and the other rotations.


A new object with the same data in a single column.

Rotation.from_axes_angles(axes, angles)

Create rotation(s) from axis-angle pair(s).

Rotation.from_euler(euler[, direction])

Create a rotation from an array of Euler angles in radians.


Return rotations from the orientation matrices [Rowenhorst et al., 2015].


Create rotations from a neo-euler (vector) representation.


Create identity rotations.

Rotation.outer(other[, lazy, chunk_size, ...])

Return the outer rotation products of the rotations and the other rotations or vectors.


Return uniformly distributed rotations.

Rotation.random_vonmises([shape, alpha, ...])

Return random rotations with a simplified Von Mises-Fisher distribution.


Return the rotations as Euler angles in the Bunge convention [Rowenhorst et al., 2015].


Return the rotations as orientation matrices [Rowenhorst et al., 2015].

Rotation.unique([return_index, ...])

Return the unique rotations from these rotations.