from_davenport#
- classmethod Rotation.from_davenport(cls, axes, order, angles, degrees=False)#
Initialize from Davenport angles.
Rotations in 3-D can be represented by a sequence of 3 rotations around a sequence of axes.
The three rotations can either be in a global frame of reference (extrinsic) or in a body centred frame of reference (intrinsic), which is attached to, and moves with, the object under rotation [1].
For both Euler angles and Davenport angles, consecutive axes must be are orthogonal (
axis2
is orthogonal to bothaxis1
andaxis3
). For Euler angles, there is an additional relationship betweenaxis1
oraxis3
, with two possibilities:axis1
andaxis3
are also orthogonal (asymmetric sequence)axis1 == axis3
(symmetric sequence)
For Davenport angles, this last relationship is relaxed [2], and only the consecutive orthogonal axes requirement is maintained.
- Parameters:
- axesarray_like, shape (3,) or ([1 or 2 or 3], 3)
Axis of rotation, if one dimensional. If two dimensional, describes the sequence of axes for rotations, where each axes[i, :] is the ith axis. If more than one axis is given, then the second axis must be orthogonal to both the first and third axes.
- orderstring
If it is equal to ‘e’ or ‘extrinsic’, the sequence will be extrinsic. If it is equal to ‘i’ or ‘intrinsic’, sequence will be treated as intrinsic.
- anglesfloat or array_like, shape (N,) or (N, [1 or 2 or 3])
Euler angles specified in radians (degrees is False) or degrees (degrees is True). For a single axis, angles can be:
a single value
array_like with shape (N,), where each angle[i] corresponds to a single rotation
array_like with shape (N, 1), where each angle[i, 0] corresponds to a single rotation
For 2 and 3 axes, angles can be:
array_like with shape (W,) where W is the number of rows of axes, which corresponds to a single rotation with W axes
array_like with shape (N, W) where each angle[i] corresponds to a sequence of Davenport angles describing a single rotation
- degreesbool, optional
If True, then the given angles are assumed to be in degrees. Default is False.
- Returns:
- rotation
Rotation
instance Object containing the rotation represented by the sequence of rotations around given axes with given angles.
- rotation
References
[2]Shuster, Malcolm & Markley, Landis. (2003). Generalization of the Euler Angles. Journal of the Astronautical Sciences. 51. 123-132. 10.1007/BF03546304.
Examples
>>> from scipy.spatial.transform import Rotation as R
Davenport angles are a generalization of Euler angles, when we use the canonical basis axes:
>>> ex = [1, 0, 0] >>> ey = [0, 1, 0] >>> ez = [0, 0, 1]
Initialize a single rotation with a given axis sequence:
>>> axes = [ez, ey, ex] >>> r = R.from_davenport(axes, 'extrinsic', [90, 0, 0], degrees=True) >>> r.as_quat().shape (4,)
It is equivalent to Euler angles in this case:
>>> r.as_euler('zyx', degrees=True) array([90., 0., -0.])
Initialize multiple rotations in one object:
>>> r = R.from_davenport(axes, 'extrinsic', [[90, 45, 30], [35, 45, 90]], degrees=True) >>> r.as_quat().shape (2, 4)
Using only one or two axes is also possible:
>>> r = R.from_davenport([ez, ex], 'extrinsic', [[90, 45], [35, 45]], degrees=True) >>> r.as_quat().shape (2, 4)
Non-canonical axes are possible, and they do not need to be normalized, as long as consecutive axes are orthogonal:
>>> e1 = [2, 0, 0] >>> e2 = [0, 1, 0] >>> e3 = [1, 0, 1] >>> axes = [e1, e2, e3] >>> r = R.from_davenport(axes, 'extrinsic', [90, 45, 30], degrees=True) >>> r.as_quat() [ 0.701057, 0.430459, -0.092296, 0.560986]