pytransform3d.rotations.euler_from_matrix

pytransform3d.rotations.euler_from_matrix(R, i, j, k, extrinsic, strict_check=True)

General method to extract any Euler angles from active rotation matrix.

Parameters:

Rarray-like, shape (3, 3)

Active rotation matrix

iint from [0, 1, 2]

The first rotation axis (0: x, 1: y, 2: z)

jint from [0, 1, 2]

The second rotation axis (0: x, 1: y, 2: z)

kint from [0, 1, 2]

The third rotation axis (0: x, 1: y, 2: z)

extrinsicbool

Do we use extrinsic transformations? Intrinsic otherwise.

strict_checkbool, optional (default: True)

Raise a ValueError if the rotation matrix is not numerically close enough to a real rotation matrix. Otherwise we print a warning.

Returns:

euler_anglesarray, shape (3,)

Extracted rotation angles in radians about the axes i, j, k in this order. The first and last angle are normalized to [-pi, pi]. The middle angle is normalized to either [0, pi] (proper Euler angles) or [-pi/2, pi/2] (Cardan / Tait-Bryan angles).

Raises:

ValueError

If basis is invalid

References

[1]

Shuster, M. D., Markley, F. L. (2006). General Formula for Extracting the Euler Angles. Journal of Guidance, Control, and Dynamics, 29(1), pp 2015-221, doi: 10.2514/1.16622. https://arc.aiaa.org/doi/abs/10.2514/1.16622