as_euler#
- Rotation.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.
- Parameters:
- seqstring, 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.
- degreesboolean, optional
Returned angles are in degrees if this flag is True, else they are in radians. Default is False.
- Returns:
- anglesndarray, 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
[2]Bernardes E, Viollet S (2022) Quaternion to Euler angles conversion: A direct, general and computationally efficient method. PLoS ONE 17(11): e0276302. https://doi.org/10.1371/journal.pone.0276302
Examples
>>> 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 (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)