def METHOD_NAME(
    port1: Port,
    port2: Port,
    width1: float | None = None,
    width2: float | None = None,
    layer: gf.typings.LayerSpec = "M1",
    manhattan_target_step: float | None = None,
) -> gf.Component:
    """Routes a basic quadrilateral polygon directly between two ports.
    Args:
        port1: Port to start route.
        port2 : Port objects to end route.
        width1: Width of quadrilateral at ports. If None, uses port widths.
        width2: Width of quadrilateral at ports. If None, uses port widths.
        layer: Layer to put the route on.
        manhattan: if not none, min step to manhattanize the polygon
    .. plot::
        :include-source:
        import gdsfactory as gf
        c = gf.Component()
        pad1 = c << gf.components.pad(size=(50, 50))
        pad2 = c << gf.components.pad(size=(10, 10))
        pad2.movex(100)
        pad2.movey(50)
        route_gnd = c << gf.routing.route_quad(
            pad1.ports["e2"],
            pad2.ports["e4"],
            width1=None,
            width2=None,
        )
        c.show()
        c.plot()
    """
    def get_port_edges(port, width):
        _, e1 = _get_rotated_basis(port.orientation)
        pt1 = port.center + e1 * width / 2
        pt2 = port.center - e1 * width / 2
        return pt1, pt2
    if width1 is None:
        width1 = port1.width
    if width2 is None:
        width2 = port2.width
    vertices = np.array(get_port_edges(port1, width1) + get_port_edges(port2, width2))
    center = np.mean(vertices, axis=0)
    displacements = vertices - center
    # sort vertices by angle from center of quadrilateral to make convex polygon
    angles = np.array([np.arctan2(disp[0], disp[1]) for disp in displacements])
    vertices = [vert for _, vert in sorted(zip(angles, vertices), key=lambda x: x[0])]
    component = gf.Component()
    if manhattan_target_step:
        poly = gdstk.Polygon(vertices)
        component.add_polygon(
            points=manhattanize_polygon(poly, target_step=manhattan_target_step),
            layer=layer,
        )
    else:
        component.add_polygon(points=vertices, layer=layer)
    component.add_port(
        name="e1",
        center=port1.center,
        orientation=port1.orientation + 180,
        width=width1,
        layer=layer,
    )
    component.add_port(
        name="e2",
        center=port2.center,
        orientation=port2.orientation + 180,
        width=width2,
        layer=layer,
    )
    return component