WXRotation.as_euler(self, seq, degrees=False)#

Represent as Euler angles.

Any orientation can be expressed as a composition of 3 elementary rotations. Once the axis sequence has been chosen, Euler angles define the angle of rotation around each respective axis [1].

The algorithm from [2] has been used to calculate Euler angles for the rotation about a given sequence of axes.

Euler angles suffer from the problem of gimbal lock [3], where the representation loses a degree of freedom and it is not possible to determine the first and third angles uniquely. In this case, a warning is raised, and the third angle is set to zero. Note however that the returned angles still represent the correct rotation.

  • seq (string, length 3) – 3 characters belonging to the set {‘X’, ‘Y’, ‘Z’} for intrinsic rotations, or {‘x’, ‘y’, ‘z’} for extrinsic rotations [1]. Adjacent axes cannot be the same. Extrinsic and intrinsic rotations cannot be mixed in one function call.

  • degrees (boolean, optional) – Returned angles are in degrees if this flag is True, else they are in radians. Default is False.


angles – Shape depends on shape of inputs used to initialize object. The returned angles are in the range:

  • First angle belongs to [-180, 180] degrees (both inclusive)

  • Third angle belongs to [-180, 180] degrees (both inclusive)

  • Second angle belongs to:

    • [-90, 90] degrees if all axes are different (like xyz)

    • [0, 180] degrees if first and third axes are the same (like zxz)

Return type:

ndarray, shape (3,) or (N, 3)



Malcolm D. Shuster, F. Landis Markley, “General formula for extraction the Euler angles”, Journal of guidance, control, and dynamics, vol. 29.1, pp. 215-221. 2006


>>> from scipy.spatial.transform import Rotation as R
>>> import numpy as np

Represent a single rotation:

>>> r = R.from_rotvec([0, 0, np.pi/2])
>>> r.as_euler('zxy', degrees=True)
array([90.,  0.,  0.])
>>> r.as_euler('zxy', degrees=True).shape

Represent a stack of single rotation:

>>> r = R.from_rotvec([[0, 0, np.pi/2]])
>>> r.as_euler('zxy', degrees=True)
array([[90.,  0.,  0.]])
>>> r.as_euler('zxy', degrees=True).shape
(1, 3)

Represent multiple rotations in a single object:

>>> r = R.from_rotvec([
... [0, 0, np.pi/2],
... [0, -np.pi/3, 0],
... [np.pi/4, 0, 0]])
>>> r.as_euler('zxy', degrees=True)
array([[ 90.,   0.,   0.],
       [  0.,   0., -60.],
       [  0.,  45.,   0.]])
>>> r.as_euler('zxy', degrees=True).shape
(3, 3)