# scipy.spatial.transform.Rotation.as_quat

Rotation.as_quat(self, canonical=False)

  Represent as quaternions.

  Active rotations in 3 dimensions can be represented using unit norm quaternions [1]. The mapping from quaternions to rotations is two-to-one, i.e. quaternions `q` and `-q`, where `-q` simply reverses the sign of each component, represent the same spatial rotation. The returned value is in scalar-last (x, y, z, w) format.

  Parameters:
    canonical bool, default False

      Whether to map the redundant double cover of rotation space to a unique “canonical” single cover. If True, then the quaternion is chosen from {q, -q} such that the w term is positive. If the w term is 0, then the quaternion is chosen such that the first nonzero term of the x, y, and z terms is positive.

  Returns:
    quat `numpy.ndarray`, shape (4,) or (N, 4)

      Shape depends on shape of inputs used for initialization.

  References

  [1]

  https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation

  Examples

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

  Represent a single rotation:

      >>> r = R.from_matrix([[0, -1, 0],
      ...                    [1, 0, 0],
      ...                    [0, 0, 1]])
      >>> r.as_quat()
      array([0.        , 0.        , 0.70710678, 0.70710678])
      >>> r.as_quat().shape
      (4,)

  Represent a stack with a single rotation:

      >>> r = R.from_quat([[0, 0, 0, 1]])
      >>> r.as_quat().shape
      (1, 4)

  Represent multiple rotations in a single object:

      >>> r = R.from_rotvec([[np.pi, 0, 0], [0, 0, np.pi/2]])
      >>> r.as_quat().shape
      (2, 4)

  Quaternions can be mapped from a redundant double cover of the rotation space to a canonical representation with a positive w term.

      >>> r = R.from_quat([0, 0, 0, -1])
      >>> r.as_quat()
      array([0. , 0. , 0. , -1.])
      >>> r.as_quat(canonical=True)
      array([0. , 0. , 0. , 1.])