Computing a (smooth) angular head velocity over time

[sfmig]

Is your feature request related to a problem? Please describe.
Right now to compute this one would: compute the polar angle of (user-defined) head vector, and then take the derivative.

But the output is probably noisy, we would need to think a bit more how this would be improved

• slerp maybe? - SM interested in trying
• Adam mentions scipy circular stats
• opendirection may be useful

[adamltyson]

I forgot, I also used to use: https://github.com/circstat/pycircstat

[niksirbi]

With #376 (this is my revival of #315, but still in draft), this can become a two step process:

from movement.kinematics import compute_heading_angle, compute_angle_time_derivative

head_angle = compute_heading_angle(ds.position, left_keypoint="left_ear", right_keypoint="right_ear")
angular_head_velocity = compute_angle_time_derivative(head_angle)

#376 just adds the first of these two functions. The envisioned 2nd function (not necessarily named as in the above example) should be added as a solution to this issue. That function should also provide some options for smoothing the derivative (see comments above).