# scipy.spatial.transform.Rotation.from_euler¶

Rotation.from_euler()

Initialize from Euler angles.

Rotations in 3-D can be represented by a sequence of 3 rotations around a sequence of axes. In theory, any three axes spanning the 3-D Euclidean space are enough. In practice, the axes of rotation are chosen to be the basis vectors.

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].

Parameters
seqstring

Specifies sequence of axes for rotations. Up to 3 characters belonging to the set {‘X’, ‘Y’, ‘Z’} for intrinsic rotations, or {‘x’, ‘y’, ‘z’} for extrinsic rotations. Extrinsic and intrinsic rotations cannot be mixed in one function call.

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 character seq, 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-character wide seq, angles can be:

• array_like with shape (W,) where W is the width of seq, which corresponds to a single rotation with W axes

• array_like with shape (N, W) where each angle[i] corresponds to a sequence of Euler angles describing a single rotation

degreesbool, optional

If True, then the given angles are assumed to be in degrees. Default is False.

Returns
rotationRotation instance

Object containing the rotation represented by the sequence of rotations around given axes with given angles.

References

1

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

Examples

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


Initialize a single rotation along a single axis:

>>> r = R.from_euler('x', 90, degrees=True)
>>> r.as_quat().shape
(4,)


Initialize a single rotation with a given axis sequence:

>>> r = R.from_euler('zyx', [90, 45, 30], degrees=True)
>>> r.as_quat().shape
(4,)


Initialize a stack with a single rotation around a single axis:

>>> r = R.from_euler('x', [90], degrees=True)
>>> r.as_quat().shape
(1, 4)


Initialize a stack with a single rotation with an axis sequence:

>>> r = R.from_euler('zyx', [[90, 45, 30]], degrees=True)
>>> r.as_quat().shape
(1, 4)


Initialize multiple elementary rotations in one object:

>>> r = R.from_euler('x', [90, 45, 30], degrees=True)
>>> r.as_quat().shape
(3, 4)


Initialize multiple rotations in one object:

>>> r = R.from_euler('zyx', [[90, 45, 30], [35, 45, 90]], degrees=True)
>>> r.as_quat().shape
(2, 4)