def add_splinepy_nurbs_to_mesh(
    mesh: _Mesh,
    element_type: type,
    splinepy_obj,
    *,
    material=None,
    data: dict
    | None = None,  # TODO: Check if this is really needed! Or unify this with how solid element data is processed
) -> _GeometryName:
    """Add a splinepy NURBS to the mesh.

    Args:
        mesh: Mesh that the created NURBS geometry will be added to.
        element_type: The type of element to be created.
        splinepy_obj (splinepy object): NURBS geometry created using splinepy.
        material (Material): Material for this geometry.
        data: General element data, e.g., material, formulation, ...

    Returns:
        GeometryName:
            Set with the control points that form the topology of the mesh.

            For a surface, the following information is stored:
                Vertices: 'vertex_u_min_v_min', 'vertex_u_max_v_min', 'vertex_u_min_v_max', 'vertex_u_max_v_max'
                Edges: 'line_v_min', 'line_u_max', 'line_v_max', 'line_u_min'
                Surface: 'surf'

            For a volume, the following information is stored:
                Vertices: 'vertex_u_min_v_min_w_min', 'vertex_u_max_v_min_w_min', 'vertex_u_min_v_max_w_min', 'vertex_u_max_v_max_w_min',
                        'vertex_u_min_v_min_w_max', 'vertex_u_max_v_min_w_max', 'vertex_u_min_v_max_w_max', 'vertex_u_max_v_max_w_max'
                Edges: 'line_v_min_w_min', 'line_u_max_w_min', 'line_v_max_w_min', 'line_u_min_w_min',
                    'line_u_min_v_min', 'line_u_max_v_min', 'line_u_min_v_max', 'line_u_max_v_max'
                    'line_v_min_w_max', 'line_u_max_w_max', 'line_v_max_w_max', 'line_u_min_w_max'
                Surfaces: 'surf_w_min', 'surf_w_max', 'surf_v_min', 'surf_v_max', 'surf_v_max', 'surf_u_min'
                Volume: 'vol'
    """

    # Make sure that the control points are 3D
    nurbs_cp_dim = splinepy_obj.control_points.shape[1]
    if not nurbs_cp_dim == 3:
        raise ValueError(f"Invalid control point dimension: {nurbs_cp_dim}")

    # Make sure the material is in the mesh
    mesh.add_material(material)

    # Fill control points
    control_points = [
        _ControlPoint(coord, weight[0])
        for coord, weight in zip(
            _np.asarray(splinepy_obj.control_points), _np.asarray(splinepy_obj.weights)
        )
    ]

    # Fill element
    element = element_type(
        [_np.asarray(knot_vector) for knot_vector in splinepy_obj.knot_vectors],
        _np.asarray(splinepy_obj.degrees),
        nodes=control_points,
        material=material,
        data=data,
    )