find the characteristic deltas between two sets of quaternions, then sample based on that and check the results are similar

quat_sample.py

import kornia as kn
import kornia.geometry
import kornia.geometry.quaternion
def try_random():
    """
    - for two sets of poses A and B
    - find the rotations between them, A->B = d1
    - find the standard deviation of the components of d rotation
    - sample some random quaternions, C
    - scale the the components according the standard deviation and re-normalize
    - rotate A by C to get new sampled B2
    - find differences between A->B2 = d2
    - compare the resulting deltas d1, d2
    """
    with torch.no_grad():
        # two sets of random rotations as per: https://lavalle.pl/planning/node198.html
        # gt and inferred pose, say:
        A_q = kornia.geometry.quaternion.Quaternion.random(10, device='cuda')
        B_q = kornia.geometry.quaternion.Quaternion.random(10, device='cuda')
        
        # what's the (rotational) difference between the two sets of quats? Now find the std for each component
        d1_q = B_q * A_q.inv()
        delta_std = d1_q.data.std(dim=-2)
            
        # let's sample some (small?) random rotations, scale the std according to above
        C_q = kornia.geometry.quaternion.Quaternion.random(10, device='cuda')
        C_q = kornia.geometry.quaternion.Quaternion(C_q.data * delta_std)
        C_q.normalize()
        
        # now perturb the gt data, multiply quats = rotate
        B2_q = C_q * A_q
        
        # calc the difference with gt
        d2_q = B2_q * A_q.inv()
        
        # why are they different?
        print(d1_q.polar_angle.mean(), d2_q.polar_angle.mean())