Alpha and beta calculation in pyTg43

[AdnanJafar]

Hi,
Hope you are doing well. Thanks for sharing this pyTG43 code and it is really helpful. I have a question regarding the calculation of alpha and beta for dwell points. I am just confused whether alpha and beta belong to azimuthal and polar angles for each of those dwell position? If so, why they are calculated like this

    nv = v / r
    cosines = [np.arccos(x) for x in nv]
    alpha = np.arccos(
        (np.cos(cosines[1])) / (np.cos(np.arcsin(-np.cos(cosines[0]))))
    )
    beta = np.arcsin(-np.cos(cosines[0]))

    if abs(np.cos(cosines[2]) - np.sin(alpha) * np.cos(beta)) > 1e-15:
        v = closest[1] - closest[0]
        r = euclidzip(closest[1], closest[0])
        nv = v / r
        cosines = [np.arccos(x) for x in nv]
        alpha = (
            np.arccos(
                (np.cos(cosines[1])) / (np.cos(np.arcsin(-np.cos(cosines[0]))))
            )
            + np.pi
        )
        beta = -np.arcsin(-np.cos(cosines[0]))

I though they are supposed to be calculated using cos-1(z/r) and arctan2(y,x). Could you please comment on it?

Secondly, with my calculation, beta is coming out as both positive and negative angles (if I convert it into degree) that should not between 0 and 180 degrees?

Regards,
Adnan