“Average” of multiple quaternions?

Question

I\'m trying to make the switch from matrices to quaternions for skeletal animation in my OpenGL program, but I\'ve encountered a problem:

Given a number of unit quat

Answer 1

The easiest implementation (with Numpy in Python>=3.6) of Markley's solution would be:

import numpy as np
def q_average(Q, W=None):
    if W is not None:
        Q *= W[:, None]
    eigvals, eigvecs = np.linalg.eig(Q.T@Q)
    return eigvecs[:, eigvals.argmax()]

where Q is of size N-by-4. The resulting quaternion is already normalized.

In this case the weights are equal to 1 by default. Otherwise you can give a list of weights of size N (one per quaternion.)

That's it.