def METHOD_NAME(c1):
    # Random vector for other endpoint:
    x = rng.uniform(size=3)
    x /= np.linalg.norm(x)
    c2 = coord.SkyCoord(coord.CartesianRepresentation(x))
    midpt = coord.SkyCoord(sph_midpoint(c1.squeeze(), c2))
    origin_off = midpt.spherical_offsets_by(1.423 * u.deg, -2.182 * u.deg)
    f1 = GreatCircleICRSFrame.from_endpoints(c1, c2)
    f2 = GreatCircleICRSFrame.from_endpoints(c1, c2, origin=midpt)
    with pytest.warns():
        f3 = GreatCircleICRSFrame.from_endpoints(c1, c2, origin=origin_off)
    assert u.isclose(f3.origin.ra, origin_off.ra)
    assert u.isclose(f3.origin.dec, origin_off.dec)
    if np.abs(c1.dec) != 90 * u.deg:
        f4 = GreatCircleICRSFrame.from_endpoints(c1, c2, ra0=origin_off.ra)
    with pytest.warns():
        f5 = GreatCircleICRSFrame.from_endpoints(
            c1, c2, origin=origin_off, priority="pole"
        )
    assert u.isclose(f5.pole.ra, f1.pole.ra)
    assert u.isclose(f5.pole.dec, f1.pole.dec)