def _project_on_ellipsoid(c, r, locations):
    """displace locations to the nearest point on ellipsoid surface"""
    p0 = locations - c  # original locations

    l2 = 1 / np.sum(p0**2 / r**2, axis=1, keepdims=True)
    p = p0 * np.sqrt(l2)  # initial approximation (projection of points towards center of ellipsoid)

    fun = lambda x: np.sum((x.reshape(p0.shape) - p0)**2)              # minimize distance between new and old points
    con = lambda x: np.sum(x.reshape(p0.shape)**2 / r**2, axis=1) - 1  # new points constrained to surface of ellipsoid
    res = sp.optimize.minimize(fun, p, constraints={'type': 'eq', 'fun': con}, method='SLSQP')

    return res['x'].reshape(p0.shape) + c
displace locations to the nearest point on ellipsoid surface