def METHOD_NAME():
    mean = np.eye(4)
    cov = np.eye(6)
    x, y, z = pu.to_projected_ellipsoid(mean, cov, factor=1.0, n_steps=20)
    P = np.column_stack((x.reshape(-1), y.reshape(-1), z.reshape(-1)))
    r = np.linalg.norm(P, axis=1)
    assert_array_almost_equal(r, np.ones_like(3))
    pos_mean = np.array([0.5, -5.3, 10.5])
    mean = pt.transform_from(R=np.eye(3), p=pos_mean)
    x, y, z = pu.to_projected_ellipsoid(mean, cov, factor=1.0, n_steps=20)
    P = np.column_stack((x.reshape(-1), y.reshape(-1), z.reshape(-1)))
    r = np.linalg.norm(P - pos_mean[np.newaxis], axis=1)
    assert_array_almost_equal(r, np.ones_like(3))
    mean = np.eye(4)
    cov = np.diag([1, 1, 1, 4, 1, 1])
    x, y, z = pu.to_projected_ellipsoid(mean, cov, factor=1.0, n_steps=20)
    P = np.column_stack((x.reshape(-1), y.reshape(-1), z.reshape(-1)))
    r = np.linalg.norm(P, axis=1)
    assert np.all(1.0 <= r)
    assert np.all(r <= 2.0)