Routing#

Optical and high speed RF ports have an orientation that routes need to follow to avoid sharp turns that produce reflections.

we have routing functions that route:

  • single route between 2 ports

    • route_single

    • route_single_from_steps

  • group of routes between 2 groups of ports using a bundle/river/bus router. At the moment it works only when all ports on each group have the same orientation.

    • route_bundle

    • route_bundle_from_steps

The most useful function is route_bundle which supports both single and groups of routes, and can also route with length matching, which ensures that all routes have the same length.

The biggest limitation is that it requires to have all the ports with the same orientation, for that you can use gf.routing.route_ports_to_side

import gdsfactory as gf
from gdsfactory.component import Component
from gdsfactory.port import Port
c = gf.Component()
mmi1 = c << gf.components.mmi1x2()
mmi2 = c << gf.components.mmi1x2()
mmi2.dmove((100, 50))
c
../_images/dffdd81add882a7c33432343dd577159e2992ce21af7a08667c11363d4ebffd8.png

route_single#

route_single returns a Manhattan route between 2 ports

help(gf.routing.route_single)
Help on function route_single in module gdsfactory.routing.route_single:

route_single(component: 'Component', port1: 'Port', port2: 'Port', bend: 'ComponentSpec' = 'bend_euler', straight: 'ComponentSpec' = 'straight', taper: 'ComponentSpec | None' = None, start_straight_length: 'float' = 0.0, end_straight_length: 'float' = 0.0, cross_section: 'CrossSectionSpec | MultiCrossSectionAngleSpec' = 'strip', waypoints: 'Coordinates | None' = None, port_type: 'str' = 'optical', allow_width_mismatch: 'bool' = False, radius: 'float | None' = None, route_width: 'float | None' = None) -> 'OpticalManhattanRoute'
    Returns a Manhattan Route between 2 ports.
    
    The references are straights, bends and tapers.
    `route_single` is an automatic version of `route_single_from_steps`.
    
    Args:
        component: to place the route into.
        port1: start port.
        port2: end port.
        bend: bend spec.
        straight: straight spec.
        taper: taper spec.
        start_straight_length: length of starting straight.
        end_straight_length: length of end straight.
        cross_section: spec.
        waypoints: list of points to pass through.
        port_type: port type to route.
        allow_width_mismatch: allow different port widths.
        radius: bend radius. If None, defaults to cross_section.radius.
        route_width: width of the route. If None, defaults to cross_section.width.
    
    
    .. plot::
        :include-source:
    
        import gdsfactory as gf
    
        c = gf.Component('sample_connect')
        mmi1 = c << gf.components.mmi1x2()
        mmi2 = c << gf.components.mmi1x2()
        mmi2.dmove((40, 20))
        gf.routing.route_single(c, mmi1.ports["o2"], mmi2.ports["o1"], radius=5)
        c.plot()
c = gf.Component()
mmi1 = c << gf.components.mmi1x2()
mmi2 = c << gf.components.mmi1x2()
mmi2.dmove((100, 50))
route = gf.routing.route_single(c, port1=mmi1.ports["o2"], port2=mmi2.ports["o1"])
c
../_images/1db19829d08edbd4891fbe0f378f41d82146f0c3bda4c79fc265b76d15be791d.png
route
OpticalManhattanRoute(backbone=[15500,625, 25500,625, 25500,50000, 90000,50000], start_port=Port(, dwidth: 0.5, trans: r180 *1 15.5,0.625, layer: WG, port_type: optical), end_port=Port(, dwidth: 0.5, trans: r0 *1 90,50, layer: WG, port_type: optical), instances=[Unnamed_4: ports ['o1', 'o2'], bend_euler_R10_A90_P0p5_2f1f5c6d: ports ['o1', 'o2'], 0 instances, Unnamed_4: ports ['o1', 'o2'], straight_L29p375_N2_CSstrip_W0p5: ports ['o1', 'o2'], 0 instances, Unnamed_4: ports ['o1', 'o2'], bend_euler_R10_A90_P0p5_2f1f5c6d: ports ['o1', 'o2'], 0 instances, Unnamed_4: ports ['o1', 'o2'], straight_L54p5_N2_CSstrip_W0p5: ports ['o1', 'o2'], 0 instances], n_bend90=2, length=83875, length_straights=83875)

Problem: route_single with obstacles

sometimes there are obstacles that connect strip does not see!

c = gf.Component()
mmi1 = c << gf.components.mmi1x2()
mmi2 = c << gf.components.mmi1x2()
mmi2.dmove((110, 50))
x = c << gf.components.cross(length=20)
x.dmove((135, 20))
route = gf.routing.route_single(c, mmi1.ports["o2"], mmi2.ports["o2"])
c
../_images/479a6e83dc3fade3b0939819697f50be08307362f9d5d12bf517edc8c9a5c8eb.png

Solutions:

  • specify the route steps

route_single_from_steps#

route_single_from_steps is a manual version of route_single where you can define only the new steps x or y together with increments dx or dy

c = gf.Component()
w = gf.components.straight()
left = c << w
right = c << w
right.dmove((100, 80))

obstacle = gf.components.rectangle(size=(100, 10))
obstacle1 = c << obstacle
obstacle2 = c << obstacle
obstacle1.dymin = 40
obstacle2.dxmin = 25

port1 = left.ports["o2"]
port2 = right.ports["o2"]

routes = gf.routing.route_single_from_steps(
    c,
    port1=port1,
    port2=port2,
    steps=[
        {"x": 20, "y": 0},
        {"x": 20, "y": 20},
        {"x": 120, "y": 20},
        {"x": 120, "y": 80},
    ],
)
c
/home/runner/work/gdsfactory/gdsfactory/gdsfactory/pdk.py:388: UserWarning: {'width': 0.5} are ignored for cross_section 'xs_34e31a19'
  warnings.warn(
../_images/dcfe0b336e9f77666aaf6a1cdcecb0c8001b82ab69a86b6b2b6eddab2828f222.png
c = gf.Component()
w = gf.components.straight()
left = c << w
right = c << w
right.dmove((100, 80))

obstacle = gf.components.rectangle(size=(100, 10))
obstacle1 = c << obstacle
obstacle2 = c << obstacle
obstacle1.dymin = 40
obstacle2.dxmin = 25

port1 = left.ports["o2"]
port2 = right.ports["o2"]

routes = gf.routing.route_single_from_steps(
    c,
    port1=port1,
    port2=port2,
    steps=[
        {"x": 20},
        {"y": 20},
        {"x": 120},
        {"y": 80},
    ],
)
c
../_images/dcfe0b336e9f77666aaf6a1cdcecb0c8001b82ab69a86b6b2b6eddab2828f222.png

route_bundle#

To route groups of ports avoiding waveguide collisions, you should use route_bundle instead of route_single.

route_bundle uses a river/bundle/bus router.

At the moment it works only when each group of ports have the same orientation.

ys_right = [0, 10, 20, 40, 50, 80]
pitch = 127.0
N = len(ys_right)
ys_left = [(i - N / 2) * pitch for i in range(N)]
layer = (1, 0)

right_ports = [
    gf.Port(f"R_{i}", center=(0, ys_right[i]), width=0.5, orientation=180, layer=layer)
    for i in range(N)
]
left_ports = [
    gf.Port(f"L_{i}", center=(-200, ys_left[i]), width=0.5, orientation=0, layer=layer)
    for i in range(N)
]

# you can also mess up the port order and it will sort them by default
left_ports.reverse()

c = gf.Component()
routes = gf.routing.route_bundle(
    c, left_ports, right_ports, start_straight_length=50, sort_ports=True
)
c.add_ports(left_ports)
c.add_ports(right_ports)
c
../_images/1aaa69df4471612c1e1408adc136eebe94efdb7987de5d3cbca5f1af13bc807d.png
xs_top = [0, 10, 20, 40, 50, 80]
pitch = 127.0
N = len(xs_top)
xs_bottom = [(i - N / 2) * pitch for i in range(N)]
layer = (1, 0)

top_ports = [
    gf.Port(f"top_{i}", center=(xs_top[i], 0), width=0.5, orientation=270, layer=layer)
    for i in range(N)
]

bot_ports = [
    gf.Port(
        f"bot_{i}",
        center=(xs_bottom[i], -300),
        width=0.5,
        orientation=90,
        layer=layer,
    )
    for i in range(N)
]

c = gf.Component()
routes = gf.routing.route_bundle(
    c, top_ports, bot_ports, separation=5.0, end_straight_length=100
)
c
../_images/4e420bacab2cf9650701dfdba7019d24d4769805c0e093892ea7ae5cfd3383df.png

route_bundle can also route bundles through corners

@gf.cell(cache={})
def test_connect_corner(N=6, config="A"):
    d = 10.0
    sep = 5.0
    c = gf.Component()
    layer = (1, 0)

    if config in ["A", "B"]:
        a = 100.0
        ports_A_TR = [
            Port(
                f"A_TR_{i}",
                center=(d, a / 2 + i * sep),
                width=0.5,
                orientation=0,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_A_TL = [
            Port(
                f"A_TL_{i}",
                center=(-d, a / 2 + i * sep),
                width=0.5,
                orientation=180,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_A_BR = [
            Port(
                f"A_BR_{i}",
                center=(d, -a / 2 - i * sep),
                width=0.5,
                orientation=0,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_A_BL = [
            Port(
                f"A_BL_{i}",
                center=(-d, -a / 2 - i * sep),
                width=0.5,
                orientation=180,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_A = [ports_A_TR, ports_A_TL, ports_A_BR, ports_A_BL]

        ports_B_TR = [
            Port(
                f"B_TR_{i}",
                center=(a / 2 + i * sep, d),
                width=0.5,
                orientation=90,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_B_TL = [
            Port(
                f"B_TL_{i}",
                center=(-a / 2 - i * sep, d),
                width=0.5,
                orientation=90,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_B_BR = [
            Port(
                f"B_BR_{i}",
                center=(a / 2 + i * sep, -d),
                width=0.5,
                orientation=270,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_B_BL = [
            Port(
                f"B_BL_{i}",
                center=(-a / 2 - i * sep, -d),
                width=0.5,
                orientation=270,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_B = [ports_B_TR, ports_B_TL, ports_B_BR, ports_B_BL]

    elif config in ["C", "D"]:
        a = N * sep + 2 * d
        ports_A_TR = [
            Port(
                f"A_TR_{i}",
                center=(a, d + i * sep),
                width=0.5,
                orientation=0,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_A_TL = [
            Port(
                f"A_TL_{i}",
                center=(-a, d + i * sep),
                width=0.5,
                orientation=180,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_A_BR = [
            Port(
                f"A_BR_{i}",
                center=(a, -d - i * sep),
                width=0.5,
                orientation=0,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_A_BL = [
            Port(
                f"A_BL_{i}",
                center=(-a, -d - i * sep),
                width=0.5,
                orientation=180,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_A = [ports_A_TR, ports_A_TL, ports_A_BR, ports_A_BL]

        ports_B_TR = [
            Port(
                f"B_TR_{i}",
                center=(d + i * sep, a),
                width=0.5,
                orientation=90,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_B_TL = [
            Port(
                f"B_TL_{i}",
                center=(-d - i * sep, a),
                width=0.5,
                orientation=90,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_B_BR = [
            Port(
                f"B_BR_{i}",
                center=(d + i * sep, -a),
                width=0.5,
                orientation=270,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_B_BL = [
            Port(
                f"B_BL_{i}",
                center=(-d - i * sep, -a),
                width=0.5,
                orientation=270,
                layer=layer,
            )
            for i in range(N)
        ]

        ports_B = [ports_B_TR, ports_B_TL, ports_B_BR, ports_B_BL]

    if config in ["A", "C"]:
        for ports1, ports2 in zip(ports_A, ports_B):
            gf.routing.route_bundle(c, ports1, ports2, radius=5, sort_ports=True)

    elif config in ["B", "D"]:
        for ports1, ports2 in zip(ports_A, ports_B):
            gf.routing.route_bundle(c, ports2, ports1, radius=5, sort_ports=True)

    return c


c = test_connect_corner(config="A")
c
../_images/ba2372586e73e4c7a3209ff34f6f415ae6ceee8be5083765dcab920ad49d43fe.png
c = test_connect_corner(config="C")
c
../_images/d168e50521cd5e74537049d0a8d38c26ea15bd4d4087725b9a141a13ceeedc30.png
@gf.cell(cache={})
def test_connect_bundle_udirect(dy=200, orientation=270, layer=(1, 0)):
    xs1 = [-100, -90, -80, -55, -35, 24, 0] + [200, 210, 240]
    axis = "X" if orientation in [0, 180] else "Y"
    pitch = 10.0
    N = len(xs1)
    xs2 = [70 + i * pitch for i in range(N)]

    if axis == "X":
        ports1 = [
            Port(
                f"top_{i}",
                center=(0, xs1[i]),
                width=0.5,
                orientation=orientation,
                layer=layer,
            )
            for i in range(N)
        ]

        ports2 = [
            Port(
                f"bottom_{i}",
                center=(dy, xs2[i]),
                width=0.5,
                orientation=orientation,
                layer=layer,
            )
            for i in range(N)
        ]

    else:
        ports1 = [
            Port(
                f"top_{i}",
                center=(xs1[i], 0),
                width=0.5,
                orientation=orientation,
                layer=layer,
            )
            for i in range(N)
        ]

        ports2 = [
            Port(
                f"bottom_{i}",
                center=(xs2[i], dy),
                width=0.5,
                orientation=orientation,
                layer=layer,
            )
            for i in range(N)
        ]

    c = Component()
    gf.routing.route_bundle(c, ports1, ports2, radius=10.0, sort_ports=True)
    return c


c = test_connect_bundle_udirect()
c
../_images/36a18b2a7002ec030d46313f133572e7455ef70a15bcb96fb3911aec9055c5c3.png
@gf.cell
def test_connect_bundle_u_indirect(dy=-200, orientation=180, layer=(1, 0)):
    xs1 = [-100, -90, -80, -55, -35] + [200, 210, 240]
    axis = "X" if orientation in [0, 180] else "Y"
    pitch = 10.0
    N = len(xs1)
    xs2 = [50 + i * pitch for i in range(N)]

    a1 = orientation
    a2 = a1 + 180

    if axis == "X":
        ports1 = [
            Port(f"top_{i}", center=(0, xs1[i]), width=0.5, orientation=a1, layer=layer)
            for i in range(N)
        ]

        ports2 = [
            Port(
                f"bot_{i}",
                center=(dy, xs2[i]),
                width=0.5,
                orientation=a2,
                layer=layer,
            )
            for i in range(N)
        ]

    else:
        ports1 = [
            Port(f"top_{i}", center=(xs1[i], 0), width=0.5, orientation=a1, layer=layer)
            for i in range(N)
        ]

        ports2 = [
            Port(
                f"bot_{i}",
                center=(xs2[i], dy),
                width=0.5,
                orientation=a2,
                layer=layer,
            )
            for i in range(N)
        ]

    c = Component()
    gf.routing.route_bundle(
        c,
        ports1,
        ports2,
        bend=gf.components.bend_euler,
        radius=5,
    )

    return c


c = test_connect_bundle_u_indirect(orientation=0)
c
../_images/693a08244702208c77299e7c6c51919c7872595fc1a5daf6f595517d9fb12b7f.png
@gf.cell
def test_north_to_south(layer=(1, 0)):
    dy = 200.0
    xs1 = [-500, -300, -100, -90, -80, -55, -35, 200, 210, 240, 500, 650]

    pitch = 10.0
    N = len(xs1)
    xs2 = [-20 + i * pitch for i in range(N // 2)]
    xs2 += [400 + i * pitch for i in range(N // 2)]

    a1 = 90
    a2 = a1 + 180

    ports1 = [
        gf.Port(f"top_{i}", center=(xs1[i], 0), width=0.5, orientation=a1, layer=layer)
        for i in range(N)
    ]

    ports2 = [
        gf.Port(f"bot_{i}", center=(xs2[i], dy), width=0.5, orientation=a2, layer=layer)
        for i in range(N)
    ]

    c = gf.Component()
    gf.routing.route_bundle(c, ports1, ports2)
    return c


c = test_north_to_south()
c
../_images/cecb294a57a8efa296289ee99325269e14dafbfec6885c5e150b113eda680ce7.png
@gf.cell
def demo_connect_bundle():
    """Combines all the connect_bundle tests."""
    y = 400.0
    x = 500
    y0 = 900
    dy = 200.0
    c = gf.Component()
    for j, s in enumerate([-1, 1]):
        for i, orientation in enumerate([0, 90, 180, 270]):
            ref = c << test_connect_bundle_u_indirect(
                dy=s * dy, orientation=orientation
            )
            ref.dcenter = (i * x, j * y)

            ref = c << test_connect_bundle_udirect(dy=s * dy, orientation=orientation)
            ref.dcenter = (i * x, j * y + y0)

    for i, config in enumerate(["A", "B", "C", "D"]):
        ref = c << test_connect_corner(config=config)
        ref.dcenter = (i * x, 1700)

    return c


c = demo_connect_bundle()
c.show()
c
../_images/5287b412a88ba14824a3266c096634369ca38e84e3b2c265e384e3e108554b64.png
import gdsfactory as gf
c = gf.Component()
c1 = c << gf.components.mmi2x2()
c2 = c << gf.components.mmi2x2()

c2.dmove((100, 50))
routes = gf.routing.route_bundle(
    c, [c1.ports["o4"], c1.ports["o3"]], [c2.ports["o1"], c2.ports["o2"]], radius=5
)
c
../_images/1a9bebd477b930add24c400efb1cb0143d2a38dd34b1363b7aaa70662279e40f.png
c = gf.Component()
c1 = c << gf.components.pad()
c2 = c << gf.components.pad()
c2.dmove((200, 100))
routes = gf.routing.route_bundle_electrical(
    c,
    [c1.ports["e3"]],
    [c2.ports["e1"]],
    cross_section=gf.cross_section.metal1,
)
c
../_images/cafd1456c7761345d7162c96f3d72289b5e61211b38711fbb32a22757556012a.png

Problem

Sometimes 90 degrees routes do not have enough space for a Manhattan route

c = gf.Component()
c1 = c << gf.components.nxn(east=3, ysize=20)
c2 = c << gf.components.nxn(west=3)
c2.dmove((80, 0))
c
../_images/762cbecde0b99cdf3bf39edc962f992abb2e11d6bdbaecef5cc47553f7bfe697.png
c = gf.Component()
c1 = c << gf.components.nxn(east=3, ysize=20)
c2 = c << gf.components.nxn(west=3)
c2.dmove((80, 0))
routes = gf.routing.route_bundle(
    c,
    list(c1.ports.filter(orientation=0)),
    list(c2.ports.filter(orientation=180)),
    on_collision=None,
)
c
../_images/ddea434e2949fefa5269a29b8a0ddbe27457b6cd7f8f247254473e4e6b7122e0.png
c = gf.Component()
pitch = 2.0
ys_left = [0, 10, 20]
N = len(ys_left)
ys_right = [(i - N / 2) * pitch for i in range(N)]
layer = (1, 0)

right_ports = [
    gf.Port(f"R_{i}", center=(0, ys_right[i]), width=0.5, orientation=180, layer=layer)
    for i in range(N)
]
left_ports = [
    gf.Port(f"L_{i}", center=(-50, ys_left[i]), width=0.5, orientation=0, layer=layer)
    for i in range(N)
]
left_ports.reverse()
routes = gf.routing.route_bundle(
    c, right_ports, left_ports, radius=5, on_collision=None
)

c
../_images/f2708f560a997936fdcebd2e562370645b30394d6739bd7d35d46047c4b221de.png

Solution

Add Sbend routes using route_bundle_sbend

c = gf.Component()
c1 = c << gf.components.nxn(east=3, ysize=20)
c2 = c << gf.components.nxn(west=3)
c2.dmove((80, 0))
routes = gf.routing.route_bundle_sbend(
    c,
    c1.ports.filter(orientation=0),
    c2.ports.filter(orientation=180),
    enforce_port_ordering=False,
)
c
../_images/6371082f3b63b4de45328d70bbf7d165573464c0c0d9810430b59b058b3c34fc.png
import gdsfactory as gf
from gdsfactory.samples.big_device import big_device

c = gf.Component()
c1 = big_device()
c2 = gf.routing.add_fiber_array(c1)
c2.plot()
../_images/cf1b5b01e6a2269abda1936245fd989b5b6b594965609b0bd6c582dc8182ecad.png

Collision#

You can navigate around bounding boxes when routing if you pass the bboxes of all the objects that you want to avoid.

Currently the router only respects any (merged) bounding boxes which overlap with start or end port bundles

import gdsfactory as gf

c = gf.Component()
columns = 2
ptop = c << gf.components.pad_array(columns=columns, port_orientation=270)
pbot = c << gf.components.pad_array(port_orientation=270, columns=columns)
ptop.dmovex(300)
ptop.dmovey(300)

obstacle = c << gf.c.rectangle(size=(300, 100), layer="M3")
obstacle.dymin = pbot.dymax - 10
obstacle.dxmin = pbot.dxmax - 10


routes = gf.routing.route_bundle_electrical(
    c,
    pbot.ports,
    ptop.ports,
    start_straight_length=100,
    separation=20,
    bboxes=[
        obstacle.bbox(),
        pbot.bbox(),
        ptop.bbox(),
    ],  # obstacles to avoid
    sort_ports=True,
)

c
../_images/06633a65e845fdc18da62681340f4dfde13c674548aa1a977bbdd81d152fa628.png
import gdsfactory as gf

c = gf.Component()
columns = 2
ptop = c << gf.components.pad_array(columns=columns, port_orientation=270)
pbot = c << gf.components.pad_array(port_orientation=270, columns=columns)
ptop.dmovex(300)
ptop.dmovey(300)

obstacle = c << gf.c.rectangle(size=(300, 100), layer="M3", centered=True)
obstacle.dymin = pbot.dymax - 10
obstacle.dxmin = pbot.dxmax + 10

c2 = gf.Component()  # create a dummy component to get the size of the obstacle
obstacle_sized = c2 << gf.c.rectangle(size=(340, 140), layer="M3", centered=True)
obstacle_sized.dcenter = obstacle.dcenter


routes = gf.routing.route_bundle_electrical(
    c,
    pbot.ports,
    ptop.ports,
    start_straight_length=100,
    separation=20,
    bboxes=[
        obstacle_sized.bbox(),
        pbot.bbox(),
        ptop.bbox(),
    ],  # obstacles to avoid
    sort_ports=True,
)

c
../_images/58017a7ae9ca62410f5ceb01e2374e64014e1d8583585e46b8b4ddcd0ac9e92b.png

route_bundle_all_angle#

You can also route using diagonal routes.

import gdsfactory as gf

c = gf.Component()
rows = 3
straight = gf.c.straight
w1 = c << gf.c.array(straight, spacing=(0, 10), rows=rows, columns=1)
w2 = c << gf.c.array(straight, spacing=(0, 10), rows=rows, columns=1)
w2.drotate(-30)
w2.dmovex(140)
p1 = list(w1.ports.filter(orientation=0))
p2 = list(w2.ports.filter(orientation=150))
p1.reverse()
p2.reverse()

gf.routing.route_bundle_all_angle(
    c,
    p1,
    p2,
    separation=3,
)
c
../_images/e4cef0383b70d5ec1bb51a5c66831c75a868d66350ce38da76d1f3b600c51a96.png

You can also use it to connect rotated components that do not have a manhattan orientation (0, 90, 180, 270)

c = gf.Component()

mmi = gf.components.mmi2x2(width_mmi=10, gap_mmi=3)
mmi1 = c.create_vinst(mmi)  # create a virtual instance
mmi2 = c.create_vinst(mmi)  # create a virtual instance

mmi2.dmove((100, 10))
mmi2.drotate(30)

routes = gf.routing.route_bundle_all_angle(
    c,
    mmi1.ports.filter(orientation=0),
    [mmi2.ports["o2"], mmi2.ports["o1"]],
)
c.show()
c
../_images/15a3f2538167bf954fa8c326137f40457216ae930fe22fcbdb05205ec591de19.png