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scipy.spatial.transform.Rotation.

# 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:
    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 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)

  https://en.wikipedia.org/wiki/Euler_angles#Definition_by_intrinsic_rotations

  [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

  [3]

  https://en.wikipedia.org/wiki/Gimbal_lock#In_applied_mathematics

  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)