def compute_lifting_parameter(lamb, lambda_plane_idxs, lambda_offset_idxs, cutoff):
    """One way to compute a per-particle "4D" offset in terms of an adjustable lamb and
    constant per-particle parameters.

    Notes
    -----
    (ytz): this initializes the 4th dimension to a fixed plane adjust by an offset
    followed by a scaling by cutoff.

    lambda_plane_idxs are typically 0 or 1 and allows us to turn off an interaction
    independent of the lambda value.

    lambda_offset_idxs are typically 0 and 1, and allows us to adjust the w coordinate
    in a lambda-dependent way.
    """

    w = cutoff * (lambda_plane_idxs + lambda_offset_idxs * lamb)
    return w