`scipy.spatial.transform._rotation:Rotation.as_euler`

source: /scipy/spatial/transform/_rotation.py :1191

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 : string, 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 : boolean, optional: Returned angles are in degrees if this flag is True, else they are in radians. Default is False.
suppress_warnings : boolean, 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)

Notes

Array API Standard Support

as_euler has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ✅                   
JAX                   ✅                     ✅                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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

✓

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

✓

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

✓

Aliases

scipy.spatial.transform.Rotation.as_euler