scipy.spatial.transform.Rotation.as_euler¶

Rotation.
as_euler
(seq, degrees=False)[source]¶ 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.
Parameters:  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.
Returns:  angles :
numpy.ndarray
, shape (3,) or (N, 3) 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)
References
[1] (1, 2, 3) Euler angle definitions [2] (1, 2) Malcolm D. Shuster, F. Landis Markley General Formula for Euler Angles [3] (1, 2) Gimbal lock Examples
>>> from scipy.spatial.transform import Rotation as R
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 (3,)
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)