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bundles / scipy latest / scipy / spatial / transform / _rotation / Rotation / as_euler

function

scipy.spatial.transform._rotation:Rotation.as_euler

source: build-install/usr/lib/python3.14/site-packages/scipy/spatial/transform/_rotation.py:1225

Signature

def as_euler(self, seq: str, degrees: bool = False, *, suppress_warnings: bool = False) → Array

Summary

Represent as Euler angles.

Extended Summary

Any orientation can be expressed as a composition of 3 elementary rotations. Once the axis sequence has been chosen, Euler angles define the angle of rotation around each respective axis [1].

The algorithm from [2] has been used to calculate Euler angles for the rotation about a given sequence of axes.

Euler angles suffer from the problem of gimbal lock [3], where the representation loses a degree of freedom and it is not possible to determine the first and third angles uniquely. In this case, a warning is raised (unless the suppress_warnings option is used), and the third angle is set to zero. Note however that the returned angles still represent the correct rotation.

Parameters

seq : str, length 3

3 characters belonging to the set {'X', 'Y', 'Z'} for intrinsic rotations, or {'x', 'y', 'z'} for extrinsic rotations [1]. Adjacent axes cannot be the same. Extrinsic and intrinsic rotations cannot be mixed in one function call.

degrees : bool, optional

Returned angles are in degrees if this flag is True, else they are in radians. Default is False.

suppress_warnings : bool, optional

Disable warnings about gimbal lock. Default is False.

Returns

angles : ndarray, shape (..., 3)

Shape depends on shape of inputs used to initialize object. The returned angles are in the range:

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

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

  • Second angle belongs to:

    • [-90, 90] degrees if all axes are different (like xyz)

    • [0, 180] degrees if first and third axes are the same (like zxz)

Examples

from scipy.spatial.transform import Rotation as R
import numpy as np
✓
Represent a single rotation: 
r = R.from_rotvec([0, 0, np.pi/2])
r.as_euler('zxy', degrees=True)
r.as_euler('zxy', degrees=True).shape
✓
(3,)
Represent a stack of single rotation: 
r = R.from_rotvec([[0, 0, np.pi/2]])
r.as_euler('zxy', degrees=True)
r.as_euler('zxy', degrees=True).shape
✓
(1, 3)
Represent multiple rotations in a single object: 
r = R.from_rotvec([
[0, 0, np.pi/2],
[0, -np.pi/3, 0],
[np.pi/4, 0, 0]])
r.as_euler('zxy', degrees=True)
r.as_euler('zxy', degrees=True).shape
✓
(3, 3)

Aliases

  • scipy.spatial.transform.Rotation.as_euler