ktk.geometry.get_angles

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ktk.geometry.get_angles#

get_angles(T, seq, degrees=False, flip=False)[source]#

Extract Euler angles from a transform series.

In case of gimbal lock, a warning is raised, and the third angle is set to zero. Note however that the returned angles still represent the correct rotation.

Parameters:

  • T (ArrayLike) – An Nx4x4 transform series.

  • seq (str) – Specifies the sequence of axes for successive rotations. Up to 3 characters belonging to the set {“X”, “Y”, “Z”} for intrinsic rotations (moving axes), or {“x”, “y”, “z”} for extrinsic rotations (fixed axes). Adjacent axes cannot be the same. Extrinsic and intrinsic rotations cannot be mixed in one function call.

  • degrees (bool) – If True, the returned angles are in degrees. If False, they are in radians. Default is False.

  • flip (bool) – Return an alternate sequence with the second angle inverted, but that leads to the same rotation matrices. See below for more information.

Returns:

An Nx3 series of Euler angles, with the second dimension containing the first, second and third angles, respectively.

Return type:

np.ndarray

Notes

The range of the returned angles is dependent on the flip parameter. If flip is False:

  • First angle belongs to [-180, 180] degrees (both inclusive)

  • Second angle belongs to:

    • [-90, 90] degrees if all axes are different. e.g., xyz

    • [0, 180] degrees if first and third axes are the same e.g., zxz

  • Third angle belongs to [-180, 180] degrees (both inclusive)

If flip is True:

  • First angle belongs to [-180, 180] degrees (both inclusive)

  • Second angle belongs to:

    • [-180, -90], [90, 180] degrees if all axes are different. e.g., xyz

    • [-180, 0] degrees if first and third axes are the same e.g., zxz

  • Third angle belongs to [-180, 180] degrees (both inclusive)

This function is a wrapper for scipy.transform.Rotation.as_euler. Please consult scipy help for more help on intrinsic/extrinsic angles and the seq parameter.

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