This class implements quaternion used for 3D rotations. Attributes: w (``float``): same as ``quaternion[0]``. x (``float``): same as ``quaternion[1]``. y (``float``): same as ``quaternion[2]``. z (``float``): same as ``quaternion[3]``.
| 3 | from math import pi,sin,cos,atan2,sqrt |
| 4 | |
| 5 | class Quaternion: |
| 6 | """ This class implements quaternion used for 3D rotations. |
| 7 | |
| 8 | Attributes: |
| 9 | w (``float``): same as ``quaternion[0]``. |
| 10 | x (``float``): same as ``quaternion[1]``. |
| 11 | y (``float``): same as ``quaternion[2]``. |
| 12 | z (``float``): same as ``quaternion[3]``. |
| 13 | """ |
| 14 | |
| 15 | def __init__(self, quat=[1, 0, 0, 0]): |
| 16 | self.__quat = np.array(quat, dtype=np.float) |
| 17 | self.normalize() |
| 18 | |
| 19 | @classmethod |
| 20 | def fromAxisAngle(cls, axis, angle): |
| 21 | """ Crate quaternion from axis angle representation |
| 22 | |
| 23 | Args: |
| 24 | angle (``float``): Angle in radian. |
| 25 | axis (``numpy.ndarray``): Rotational axis. Not necessarily |
| 26 | normalized. |
| 27 | |
| 28 | Returns: |
| 29 | The following values are returned. |
| 30 | |
| 31 | * ``quat`` (:class:`Quaternion`): The corresponding quaternion object. |
| 32 | """ |
| 33 | axis = axis / norm(axis) |
| 34 | quat = np.array([ |
| 35 | cos(angle/2), |
| 36 | sin(angle/2)*axis[0], |
| 37 | sin(angle/2)*axis[1], |
| 38 | sin(angle/2)*axis[2] |
| 39 | ]) |
| 40 | return cls(quat) |
| 41 | |
| 42 | @classmethod |
| 43 | def fromData(cls, v1, v2): |
| 44 | """ Create the rotation to rotate v1 to v2 |
| 45 | |
| 46 | Args: |
| 47 | v1 (``numpy.ndarray``): From vector. Normalization not necessary. |
| 48 | v2 (``numpy.ndarray``): To vector. Normalization not necessary. |
| 49 | |
| 50 | Returns: |
| 51 | The following values are returned. |
| 52 | |
| 53 | * ``quat`` (:class:`Quaternion`): Corresponding quaternion that |
| 54 | rotates ``v1`` to ``v2``. |
| 55 | """ |
| 56 | eps = 1e-12 |
| 57 | v1 /= norm(v1) |
| 58 | v2 /= norm(v2) |
| 59 | c = np.dot(v1, v2) |
| 60 | if c < -1.0 + eps: |
| 61 | # v1 is parallel and opposite of v2 |
| 62 | u,s,v = svd(np.array([v1, v2])) |