From euler angles to rotation matrix and vice versa

Question

I want to check if I am using the correct functions to transform from euler angles to rotation matrix and viceversa. I am using XY’Z” convention of euler intrinsic angles. As example, I have the following euler angles:

roll = 0, pitch = -90, yaw = 90,

I am using the following python function to transform it to rotation matrix:

  def fromeulertorotationmatrix(theta1, theta2, theta3, order='xyz'):
    """
    input
        theta1, theta2, theta3 = rotation angles in rotation order (degrees)
        oreder = rotation order of x,y,z　e.g. XZY rotation -- 'xzy'
    output
        3x3 rotation matrix (numpy array)
    """
    c1 = np.cos(theta1 * np.pi / 180)
    s1 = np.sin(theta1 * np.pi / 180)
    c2 = np.cos(theta2 * np.pi / 180)
    s2 = np.sin(theta2 * np.pi / 180)
    c3 = np.cos(theta3 * np.pi / 180)
    s3 = np.sin(theta3 * np.pi / 180)

    
    if order=='xyz':
        matrix=np.array([[c2*c3, -c2*s3, s2],
                         [c1*s3+c3*s1*s2, c1*c3-s1*s2*s3, -c2*s1],
                         [s1*s3-c1*c3*s2, c3*s1+c1*s2*s3, c1*c2]])
  
    return matrix

The result rotationm atrix is: [![enter image description here][1]][1] that is correct.

Now, I want to go the opposite way. I want to transform that rotation matrix to euler angles, where I am using the following function:

def fromrotationmatrixtoeuler(R):
    

    r =  Rotation.from_matrix(R)
    angles = r.as_euler("xyz",degrees=True)
    return angles

The result that gives is: (-90,0,90) where does not match with the angles I am using.

Any idea of whats is wrong? What function should I use to transform from rotation matrix to XYZ intrinsic euler angles?

Answer 1

Assuming that Rotation is scipy.spatial.transform.Rotation, the seq string specifying the rotation convention is case-sensitive and uses capital letters for intrinsic rotations:

https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.transform.Rotation.as_euler.html

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.