def dirCosToGnomonic(alpha, beta, gamma):
    """Convert direction cosines to gnomonic tangent plane projection.

    Parameters
    ----------
    alpha, beta, gamma : float
        Direction cosines (unit vector projected onto x, y, z in order)

    Returns
    -------
    u, v : float
        Gnomonic tangent plane coordinates in radians.

    Notes
    -----
    The tangent plane reference is at (u,v) = (0,0), which corresponds to
    (alpha, beta, gamma) = (0, 0, -1) (a ray coming directly from above).  The
    orientation is such that vx (vy) is positive when u (v) is positive.
    """
    u = -alpha / gamma
    v = -beta / gamma
    return u, v
