<gh_stars>100-1000
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy import sqrt, pi, cos, sin, log, exp, sinh, mod
from numpy.linalg import norm
from phidl.device_layout import Device, CrossSection, Port
from phidl.device_layout import _parse_layer
from phidl.geometry import turn
import phidl.path as pp
from phidl import Path
import gdspy
import warnings


def _get_rotated_basis(theta):
    """Returns basis vectors rotated CCW by theta (in degrees)
    """
    theta = np.radians(theta)
    e1 = np.array([np.cos(theta), np.sin(theta)])
    e2 = np.array([-1*np.sin(theta), np.cos(theta)])
    return e1, e2

def _arc(radius = 10, width = 0.5, theta = 45, start_angle = 0, angle_resolution = 2.5, layer = 0):
    """ Creates an arc of arclength ``theta`` starting at angle ``start_angle`` """
    inner_radius = radius-width/2
    outer_radius = radius+width/2
    angle1 = (start_angle)*pi/180
    angle2 = (start_angle + theta)*pi/180
    t = np.linspace(angle1, angle2, int(np.ceil(abs(theta)/angle_resolution)))
    inner_points_x = (inner_radius*cos(t)).tolist()
    inner_points_y = (inner_radius*sin(t)).tolist()
    outer_points_x = (outer_radius*cos(t)).tolist()
    outer_points_y = (outer_radius*sin(t)).tolist()
    xpts = inner_points_x + outer_points_x[::-1]
    ypts = inner_points_y + outer_points_y[::-1]

    D = Device('arc')
    D.add_polygon(points = (xpts,ypts), layer = layer)
    D.add_port(name = 1, midpoint = (radius*cos(angle1), radius*sin(angle1)),  width = width, orientation = start_angle - 90 + 180*(theta<0))
    D.add_port(name = 2, midpoint = (radius*cos(angle2), radius*sin(angle2)),  width = width, orientation = start_angle + theta + 90 - 180*(theta<0))
    D.info['length'] = (abs(theta)*pi/180)*radius
    return D



def _gradual_bend(
    radius = 20,
    width = 1.0,
    angular_coverage=15,
    num_steps=10,
    angle_resolution=0.1,
    start_angle=0,
    direction='ccw',
    layer=0,
    ):

    """
    creates a 90-degree bent waveguide
    the bending radius is gradually increased until it reaches the minimum
    value of the radius at the "angular coverage" angle.
    it essentially creates a smooth transition to a bent waveguide mode.
    user can control number of steps provided.
    direction determined by start angle and cw or ccw switch
    ############
    with the default 10 "num_steps" and 15 degree coverage, effective radius is about 1.5*radius.
    """
    angular_coverage=np.deg2rad(angular_coverage)
    D = Device()

    #determines the increment in radius through its inverse from 0 to 1/r
    inc_rad =(radius**-1)/(num_steps)
    angle_step = angular_coverage/num_steps

    #construct a series of sub-arcs with equal angles but gradually decreasing bend radius
    arcs = []
    for x in range(num_steps):
        A = _arc(radius=1/((x+1)*inc_rad),width=width,theta=np.rad2deg(angle_step),start_angle=x*np.rad2deg(angle_step),angle_resolution=angle_resolution,layer=layer)
        a = D.add_ref(A)
        arcs.append(a)
        if x>0:
            a.connect(port=1,destination=prevPort)
        prevPort=a.ports[2]
    D.add_port(name=1,port=arcs[0].ports[1])

    #now connect a regular bend for the normal curved portion
    B = _arc(radius=radius,width=width,theta=45-np.rad2deg(angular_coverage),start_angle=angular_coverage,angle_resolution=angle_resolution,layer=layer)
    b = D.add_ref(B)
    b.connect(port=1,destination=prevPort)
    prevPort=b.ports[2]
    D.add_port(name=2,port=prevPort)

    #now create the overall structure
    Total = Device()

    #clone the half-curve into two objects and connect for a 90 deg bend.
    D1 = Total.add_ref(D)
    D2 = Total.add_ref(D)
    D2.mirror(p1=[0,0],p2=[1,1])
    D2.connect(port=2,destination=D1.ports[2])
    Total.xmin=0
    Total.ymin=0

    #orient to default settings...
    Total.mirror(p1=[0,0],p2=[1,1])
    Total.mirror(p1=[0,0],p2=[1,0])

    #orient to user-provided settings
    if direction == 'cw':
        Total.mirror(p1=[0,0],p2=[1,0])
    Total.rotate(angle=start_angle,center=Total.center)
    Total.center=[0,0]
    Total.add_port(name=1,port=D1.ports[1])
    Total.add_port(name=2,port=D2.ports[1])

    return Total


def route_basic(port1, port2, path_type = 'sine', width_type = 'straight', width1 = None, width2 = None, num_path_pts = 99, layer = 0):
    """
    .. deprecated:: 1.6.0
        `route_basic` will be removed in August 2022, please replace with
        `route_quad()` or `route_smooth()`.
    """
    warnings.warn("""[PHIDL] Warning: route_basic() will be deprecated 
    in August 2022, please replace with `route_quad()` or `route_smooth()`""")
    # Assuming they're both Ports for now
    point_a = np.array(port1.midpoint)
    if width1 is None:  width1 = port1.width
    point_b = np.array(port2.midpoint)
    if width2 is None:  width2 = port2.width
    if round(abs(mod(port1.orientation - port2.orientation,360)),3) != 180:
        raise ValueError('[DEVICE] route() error: Ports do not face each other (orientations must be 180 apart)')
    orientation = port1.orientation

    separation = point_b - point_a  # Vector drawn from A to B
    distance = norm(separation) # Magnitude of vector from A to B
    rotation = np.arctan2(separation[1],separation[0])*180/pi # Rotation of vector from A to B
    angle = rotation - orientation   # If looking out along the normal of ``a``, the angle you would have to look to see ``b``
    forward_distance = distance*cos(angle*pi/180)
    lateral_distance = distance*sin(angle*pi/180)

    # Create a path assuming starting at the origin and setting orientation = 0
    # use the "connect" function later to move the path to the correct location
    xf = forward_distance
    yf = lateral_distance
    if path_type == 'straight':
        curve_fun = lambda t: [xf*t, yf*t]
        curve_deriv_fun = lambda t: [xf + t*0, t*0]
    if path_type == 'sine':
        curve_fun = lambda t: [xf*t, yf*(1-cos(t*pi))/2]
        curve_deriv_fun = lambda t: [xf  + t*0, yf*(sin(t*pi)*pi)/2]
    #if path_type == 'semicircle':
    #    def semicircle(t):
    #        t = np.array(t)
    #        x,y = np.zeros(t.shape), np.zeros(t.shape)
    #        ii = (0 <= t) & (t <= 0.5)
    #        jj = (0.5 < t) & (t <= 1)
    #        x[ii] = (cos(-pi/2 + t[ii]*pi/2))*xf
    #        y[ii] = (sin(-pi/2 + t[ii]*pi/2)+1)*yf*2
    #        x[jj] = (cos(pi*3/2 - t[jj]*pi)+2)*xf/2
    #        y[jj] = (sin(pi*3/2 - t[jj]*pi)+1)*yf/2
    #        return x,y
    #    curve_fun = semicircle
    #    curve_deriv_fun = None
    if width_type == 'straight':
        width_fun = lambda t: (width2 - width1)*t + width1
    if width_type == 'sine':
        width_fun = lambda t: (width2 - width1)*(1-cos(t*pi))/2 + width1

    route_path = gdspy.Path(width = width1, initial_point = (0,0))
    route_path.parametric(curve_fun, curve_deriv_fun, number_of_evaluations=num_path_pts,
            max_points=199, final_width=width_fun, final_distance=None)
    route_path_polygons = route_path.polygons

    # Make the route path into a Device with ports, and use "connect" to move it
    # into the proper location
    D = Device()
    D.add_polygon(route_path_polygons, layer = layer)
    p1 = D.add_port(name = 1, midpoint = (0,0), width = width1, orientation = 180)
    p2 = D.add_port(name = 2, midpoint = [forward_distance,lateral_distance], width = width2, orientation = 0)
    D.info['length'] = route_path.length

    D.rotate(angle =  180 + port1.orientation - p1.orientation, center = p1.midpoint)
    D.move(origin = p1, destination = port1)
    return D


def route_quad(port1, port2, width1=None, width2=None, layer=0):
    """Routes a basic quadrilateral polygon directly between two ports.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    width1, width2 : int, float or None
        Width of quadrilateral at ports. If None, uses port widths.
    layer : int or array-like[2]
        Layer to put the route on.

    Returns
    ---------
    D : Device
        A Device containing the route and two ports (`1` and `2`) on either end.
    """
    def get_port_edges(port, width):
        _, e1 = _get_rotated_basis(port.orientation)
        pt1 = port.midpoint + e1*width/2
        pt2 = port.midpoint - 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])]
    D = Device()
    D.add_polygon(points=vertices, layer=layer)
    D.add_port(name=1, midpoint=port1.midpoint, orientation=port1.orientation+180, width=width1)
    D.add_port(name=2, midpoint=port2.midpoint, orientation=port2.orientation+180, width=width2) 
    return D


def route_smooth(
        port1, 
        port2, 
        radius=5, 
        width=None,
        path_type='manhattan', 
        manual_path=None, 
        smooth_options={'corner_fun': pp.euler, 'use_eff': True}, 
        layer=np.nan, 
        **kwargs
        ):

    """ Convenience function that routes a path between ports using pp.smooth(),
    then immediately extrudes the path to create polygons. Has several waypoint
    path type options.  Equivalent to e.g.
        >>> pts = pr.path_manhattan(port1, port2, radius) 
        >>> P = pp.smooth(pts, radius)
        >>> D = P.extrude(width)

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    radius : int or float
        Bend radius passed to pp.smooth
    width : None, int, float, array-like[2], or CrossSection
        If None, the route linearly tapers between the widths the ports
        If set to a single number (e.g. `width=1.7`): makes a fixed-width route
        If set to a 2-element array (e.g. `width=[1.8,2.5]`): makes a route
            whose width varies linearly from width[0] to width[1]
        If set to a CrossSection: uses the CrossSection parameters for the route
    path_type : {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'}
        Method of waypoint path creation. Should be one of
            - 'manhattan' - automatic manhattan routing 
                    (see path_manhattan() ).
            - 'L' - L-shaped path for orthogonal ports that can be directly 
                    connected (see path_L() ).
            - 'U' - U-shaped path for parrallel or facing ports
                    (see path_U() ).
            - 'J' - J-shaped path for orthogonal ports that cannot be 
                    directly connected (see path_J() ).
            - 'C' - C-shaped path for ports that face away from each 
                    other (see path_C() ).
            - 'Z' - Z-shaped path with three segments for ports at any 
                    angles (see path_Z() ).
            - 'V' - V-shaped path with two segments for ports at any 
                    angles (see path_V() ).
            - 'straight' - straight path for ports that face each other 
                    see path_straight() ).
            - 'manual' - use an explicit waypoint path provided 
                    in manual_path.
    manual_path : array-like[N][2] or Path
        Waypoint path for creating a manual route
    smooth_options: dict
        Keyword arguments passed to pp.smooth
    layer : int or array-like[2]
        Layer to put route on. `layer=0` is used by default.  
    **kwargs :
        Keyword arguments passed to the waypoint path function.

    Returns
    ----------
    D : Device
        A Device containing the route and two ports (`1` and `2`) on either end.
    """
    if path_type == 'straight':
        P = path_straight(port1, port2)
    elif path_type == 'manual':
        if not isinstance(manual_path, Path):
            P = Path(manual_path)
        else:
            P = manual_path
    elif path_type == 'L':
        P = path_L(port1, port2)
    elif path_type == 'U':
        P = path_U(port1, port2, **kwargs)
    elif path_type == 'J':
        P = path_J(port1, port2, **kwargs)
    elif path_type == 'C':
        P = path_C(port1, port2, **kwargs)
    elif path_type == 'manhattan':
        if smooth_options['corner_fun'] == pp.euler:
            use_eff = smooth_options.get('use_eff')
            if use_eff is None or use_eff == False:
                raise ValueError("""[PHIDL] route_smooth(): when using manhattan path type with euler
                    bends, smooth_options['use_eff'] must be True.""")
        P = path_manhattan(port1, port2, radius=radius)
    elif path_type == 'Z':
        P = path_Z(port1, port2, **kwargs)
    elif path_type == 'V':
        P = path_V(port1, port2)
    else:
        raise ValueError("""[PHIDL] route_smooth() received an invalid path_type.  Must be one of
        {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'}""")

    P = pp.smooth(points=P, radius=radius, **smooth_options)
    if width is None:
        X1 = CrossSection().add(width=port1.width, ports=(1, 2), layer=layer, name='a')
        X2 = CrossSection().add(width=port2.width, ports=(1, 2), layer=layer, name='a')
        cross_section = pp.transition(cross_section1=X1, cross_section2=X2, width_type='linear')
        D = P.extrude(width=cross_section)
    else:
        D = P.extrude(width=width, layer=layer)
        if not isinstance(width, CrossSection):
            newport1 = D.add_port(port = port1, name = 1).rotate(180)
            newport2 = D.add_port(port = port2, name = 2).rotate(180)
            if np.size(width) == 1:
                newport1.width = width
                newport2.width = width
            if np.size(width) == 2:
                newport1.width = width[0]
                newport2.width = width[1]
    return D


def route_sharp(
        port1, 
        port2, 
        width=None,
        path_type='manhattan', 
        manual_path=None, 
        layer=np.nan, 
        **kwargs
        ):

    """ Convenience function that routes a path between ports and immediately 
    extrudes the path to create polygons. Has several waypoint path type 
    options.  Equivalent to e.g.
        >>> P = pr.path_manhattan(port1, port2, radius) 
        >>> D = P.extrude(width)

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    width : None, int, float, array-like[2], or CrossSection
        If None, the route linearly tapers between the widths the ports
        If set to a single number (e.g. `width=1.7`): makes a fixed-width route
        If set to a 2-element array (e.g. `width=[1.8,2.5]`): makes a route
            whose width varies linearly from width[0] to width[1]
        If set to a CrossSection: uses the CrossSection parameters for the route
    path_type : {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'}
        Method of waypoint path creation. Should be one of
            - 'manhattan' - automatic manhattan routing 
                    (see path_manhattan() ).
            - 'L' - L-shaped path for orthogonal ports that can be directly 
                    connected (see path_L() ).
            - 'U' - U-shaped path for parrallel or facing ports
                    (see path_U() ).
            - 'J' - J-shaped path for orthogonal ports that cannot be 
                    directly connected (see path_J() ).
            - 'C' - C-shaped path for ports that face away from each 
                    other (see path_C() ).
            - 'Z' - Z-shaped path with three segments for ports at any 
                    angles (see path_Z() ).
            - 'V' - V-shaped path with two segments for ports at any 
                    angles (see path_V() ).
            - 'straight' - straight path for ports that face each other 
                    see path_straight() ).
            - 'manual' - use an explicit waypoint path provided 
                    in manual_path.
    manual_path : array-like[N][2] or Path
        Waypoint path for creating a manual route
    layer : int or array-like[2]
        Layer to put route on. `layer=0` is used by default. 
    **kwargs :
        Keyword arguments passed to the waypoint path function.

    Returns
    ----------
    D : Device
        A Device containing the route and two ports (`1` and `2`) on either end.
    """
    if path_type == 'straight':
        P = path_straight(port1, port2)
    elif path_type == 'manual':
        if not isinstance(manual_path, Path):
            P = Path(manual_path)
        else:
            P = manual_path
    elif path_type == 'L':
        P = path_L(port1, port2)
    elif path_type == 'U':
        P = path_U(port1, port2, **kwargs)
    elif path_type == 'J':
        P = path_J(port1, port2, **kwargs)
    elif path_type == 'C':
        P = path_C(port1, port2, **kwargs)
    elif path_type == 'manhattan':
        radius = max(port1.width, port2.width)
        P = path_manhattan(port1, port2, radius=radius)
    elif path_type == 'Z':
        P = path_Z(port1, port2, **kwargs)
    elif path_type == 'V':
        P = path_V(port1, port2)
    else:
        raise ValueError("""[PHIDL] route_sharp() received an invalid path_type.  Must be one of
        {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'}""")
    if width is None:
        X1 = CrossSection().add(width=port1.width, ports=(1, 2), layer=layer, name='a')
        X2 = CrossSection().add(width=port2.width, ports=(1, 2), layer=layer, name='a')
        cross_section = pp.transition(cross_section1=X1, cross_section2=X2, width_type='linear')
        D = P.extrude(width=cross_section)
    else:
        D = P.extrude(width=width, layer=layer)
        if not isinstance(width, CrossSection):
            newport1 = D.add_port(port = port1, name = 1).rotate(180)
            newport2 = D.add_port(port = port2, name = 2).rotate(180)
            if np.size(width) == 1:
                newport1.width = width
                newport2.width = width
            if np.size(width) == 2:
                newport1.width = width[0]
                newport2.width = width[1]
    return D


def path_straight(port1, port2):
    """Return waypoint path between port1 and port2 in a straight line. 
    Useful when ports point directly at each other.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.

    Returns
    ----------
    points : array[2][2]
        Waypoints for the route path to follow.
    """
    delta_orientation = np.round(np.abs(np.mod(port1.orientation - port2.orientation, 360)), 3)
    e1, e2 = _get_rotated_basis(port1.orientation)
    displacement = port2.midpoint - port1.midpoint
    xrel = np.round(np.dot(displacement, e1), 3)  # relative position of port 2, forward/backward
    yrel = np.round(np.dot(displacement, e2), 3)  # relative position of port 2, left/right
    if (delta_orientation not in (0, 180, 360)) or (yrel != 0) or (xrel <= 0):
        raise ValueError('[PHIDL] path_straight(): ports must point directly at each other.')
    return Path(np.array([port1.midpoint, port2.midpoint]))


def path_L(port1, port2):
    """Return waypoint path between port1 and port2 in an L shape. Useful 
    when orthogonal ports can be directly connected with one turn.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    delta_orientation = np.round(np.abs(np.mod(port1.orientation - port2.orientation, 360)), 3)
    if delta_orientation not in (90, 270):
        raise ValueError('[PHIDL] path_L(): ports must be orthogonal.')
    e1, e2 = _get_rotated_basis(port1.orientation)
    # assemble waypoints
    pt1 = port1.midpoint
    pt3 = port2.midpoint
    delta_vec = pt3-pt1
    pt2 = pt1 + np.dot(delta_vec, e1)*e1
    return Path(np.array([pt1, pt2, pt3]))


def path_U(port1, port2, length1=200):
    """Return waypoint path between port1 and port2 in a U shape. Useful 
    when ports face the same direction or toward each other.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    length1 : int or float
        Length of segment exiting port1. Should be larger than bend radius.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    delta_orientation = np.round(np.abs(np.mod(port1.orientation - port2.orientation, 360)), 3)
    if delta_orientation not in (0, 180, 360):
        raise ValueError('[PHIDL] path_U(): ports must be parrallel.')
    theta = np.radians(port1.orientation)
    e1 = np.array([np.cos(theta), np.sin(theta)])
    e2 = np.array([-1*np.sin(theta), np.cos(theta)])
    # assemble waypoints
    pt1 = port1.midpoint
    pt4 = port2.midpoint
    pt2 = pt1 + length1*e1  # outward by length1 distance
    delta_vec = pt4-pt2
    pt3 = pt2 + np.dot(delta_vec, e2)*e2
    return Path(np.array([pt1, pt2, pt3, pt4]))


def path_J(port1, port2, length1=200, length2=200):
    """Return waypoint path between port1 and port2 in a J shape. Useful 
    when orthogonal ports cannot be connected directly with an L shape.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    length1 : int or float
        Length of segment exiting port1. Should be larger than bend radius.
    length2 : int or float
        Length of segment exiting port2. Should be larger than bend radius.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    delta_orientation = np.round(np.abs(np.mod(port1.orientation - port2.orientation, 360)), 3)
    if delta_orientation not in (90, 270):
        raise ValueError('[PHIDL] path_J(): ports must be orthogonal.')
    e1, _ = _get_rotated_basis(port1.orientation)
    e2, _ = _get_rotated_basis(port2.orientation)
    # assemble waypoints
    pt1 = port1.midpoint 
    pt2 = pt1 + length1*e1  # outward from port1 by length1
    pt5 = port2.midpoint
    pt4 = pt5 + length2*e2  # outward from port2 by length2
    delta_vec = pt4-pt2 
    pt3 = pt2 + np.dot(delta_vec, e2)*e2  # move orthogonally in e2 direction
    return Path(np.array([pt1, pt2, pt3, pt4, pt5]))


def path_C(port1, port2, length1=100, left1=100, length2=100):
    """Return waypoint path between port1 and port2 in a C shape. Useful 
    when ports are parrallel and face away from each other.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    length1 : int or float
        Length of route segment coming out of port1. Should be at larger
        than bend radius.
    left1 : int or float
        Length of route segment that turns left (or right if negative) 
        from port1. Should be larger than twice the bend radius.
    length2 : int or float
        Length of route segment coming out of port2. Should be larger
        than bend radius.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    delta_orientation = np.round(np.abs(np.mod(port1.orientation - port2.orientation, 360)), 3)
    if delta_orientation not in (0, 180, 360):
        raise ValueError('[PHIDL] path_C(): ports must be parrallel.')
    e1, e_left = _get_rotated_basis(port1.orientation)
    e2, _ = _get_rotated_basis(port2.orientation)
    # assemble route points
    pt1 = port1.midpoint 
    pt2 = pt1 + length1*e1  # outward from port1 by length1
    pt3 = pt2 + left1*e_left  # leftward by left1
    pt6 = port2.midpoint
    pt5 = pt6 + length2*e2  # outward from port2 by length2
    delta_vec = pt5-pt3 
    pt4 = pt3 + np.dot(delta_vec, e1)*e1  # move orthogonally in e1 direction
    return Path(np.array([pt1, pt2, pt3, pt4, pt5, pt6]))


def path_manhattan(port1, port2, radius):
    """Return waypoint path between port1 and port2 using manhattan routing.
    Routing is performed using straight, L, U, J, or C  waypoint path
    as needed. Ports must face orthogonal or parallel directions. 

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    radius : float or int
        Bend radius for 90 degree bend.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    radius = radius + 0.1  # ensure space for bend radius
    e1, e2 = _get_rotated_basis(port1.orientation)
    displacement = port2.midpoint - port1.midpoint
    xrel = np.round(np.dot(displacement, e1), 3)  # port2 position, forward(+)/backward(-) from port 1
    yrel = np.round(np.dot(displacement, e2), 3)  # port2 position, left(+)/right(-) from port1 
    orel = np.round(np.abs(np.mod(port2.orientation - port1.orientation, 360)), 3)  # relative orientation
    if orel not in (0, 90, 180, 270, 360):
        raise ValueError('[PHIDL] path_manhattan(): ports must face parrallel or orthogonal directions.')
    if orel in (90, 270): 
        # Orthogonal case
        if ((orel == 90 and yrel < -1*radius) or (orel == 270 and yrel > radius)) and xrel > radius:
            pts = path_L(port1, port2)
        else:
            # Adjust length1 and length2 to ensure intermediate segments fit bend radius
            direction = -1 if (orel == 270) else 1
            length2 = 2*radius-direction*yrel if (np.abs(radius+direction*yrel) < 2*radius) else radius
            length1 = 2*radius+xrel if (np.abs(radius-xrel) < 2*radius) else radius
            pts = path_J(port1, port2, length1=length1, length2=length2)
    else: 
        # Parrallel case
        if orel == 180 and yrel == 0 and xrel > 0:
            pts = path_straight(port1, port2)
        elif (orel == 180 and xrel <= 2*radius) or (np.abs(yrel) < 2*radius):
            # Adjust length1 and left1 to ensure intermediate segments fit bend radius
            left1 = np.abs(yrel)+2*radius if (np.abs(yrel) < 4*radius) else 2*radius
            y_direction = -1 if (yrel < 0) else 1
            left1 = y_direction*left1
            length2 = radius
            x_direction = -1 if (orel == 180) else 1
            segmentx_length = np.abs(xrel+x_direction*length2-radius)
            if segmentx_length < 2*radius:
                length1 = xrel+x_direction*length2+2*radius
            else:
                length1 = radius
            pts = path_C(port1, port2, length1=length1, length2=length2, left1=left1)
        else:
            # Adjust length1 to ensure segment comes out of port2
            length1 = radius+xrel if (orel == 0 and xrel > 0) else radius
            pts = path_U(port1, port2, length1=length1)
    return pts


def path_Z(port1, port2, length1=100, length2=100):
    """Return waypoint path between port1 and port2 in a Z shape. Ports can have any relative
    orientation.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    length1 : int or float
        Length of route segment coming out of port1.
    length2 : int or float
        Length of route segment coming out of port2.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    # get basis vectors in port directions
    e1, _ = _get_rotated_basis(port1.orientation)
    e2, _ = _get_rotated_basis(port2.orientation)
    # assemble route  points
    pt1 = port1.midpoint 
    pt2 = pt1 + length1*e1  # outward from port1 by length1
    pt4 = port2.midpoint
    pt3 = pt4 + length2*e2  # outward from port2 by length2
    return Path(np.array([pt1, pt2, pt3, pt4]))


def path_V(port1, port2):
    """Return waypoint path between port1 and port2 in a V shape. Useful when
    ports point to a single connecting point

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    # get basis vectors in port directions
    e1, _ = _get_rotated_basis(port1.orientation)
    e2, _ = _get_rotated_basis(port2.orientation)
    # assemble route  points
    pt1 = port1.midpoint 
    pt3 = port2.midpoint
    # solve for intersection
    E = np.column_stack((e1, -1*e2))
    pt2 = np.matmul(np.linalg.inv(E), pt3-pt1)[0]*e1 + pt1
    return Path(np.array([pt1, pt2, pt3]))



def path_xy(port1, port2, directions = 'xxyx'):
    """ Creates a Path that travels only in x and y directions (manhattan) from
    one point (or Port) to another. The `directions` string determines the order
    of the x/y steps. Example: `directions = 'xyx'` will travel
        1/2 the distance in x from p1 to p2
        The whole distance in y from p1 to p2
        1/2 of the distance in x from p1 to p2

    Parameters
    ----------
    p1, p2 : array-like[2] points or Port objects
        Points to route between.
    directions : string of {'x','y'} characters
        Directions the Path will be routed along

    Returns
    ----------
    Path
        Waypoints for the route path to follow.
    """
    if isinstance(port1, Port): p1 = port1.midpoint
    elif np.size(port1) == 2:   p1 = port1
    if isinstance(port2, Port): p2 = port2.midpoint
    elif np.size(port2) == 2:   p2 = port2

    directions = directions.lower()
    num_x = sum([xy == 'x' for xy in directions])
    num_y = sum([xy == 'y' for xy in directions])
    distance = np.asarray(p2)-p1

    points = [p1]
    for xy in directions:
        if xy == 'x':
            travel = np.array([distance[0]/num_x, 0])
            new_point = points[-1] + travel
        elif xy == 'y':
            travel = np.array([0, distance[1]/num_y])
            new_point = points[-1] + travel
        else:
            raise ValueError('[PHIDL] path_xy() directions argument must be string with only "x" or "y" characters')
        if np.abs(np.sum(travel)) > 1e-6: # Only add point if traveling some significant distance
            points.append(new_point)

    return Path(np.array(points))

def route_xy(port1, port2, directions = 'xxyx', width = None, layer = np.nan):
    """ Routes a path in x and y directions (manhattan) from one point (or Port)
    to another. The `directions` string determines the order of the x/y steps.
    Example: `directions = 'xyx'` will travel
        1/2 the distance in x from p1 to p2
        The whole distance in y from p1 to p2
        1/2 of the distance in x from p1 to p2

    Parameters
    ----------
    port1, port2 : Ports pr array-like[2] points or Port objects
        Points to route between.
    directions : string of {'x','y'} characters
        Directions the Path will be routed along

    Returns
    ----------
    D : Device
        A Device containing the route and two ports (`1` and `2`) on either end.
    """

    P = path_xy(port1, port2, directions = directions)
    if width is None:
        X1 = CrossSection().add(width=port1.width, ports=(1, 2), layer=layer, name='a')
        X2 = CrossSection().add(width=port2.width, ports=(1, 2), layer=layer, name='a')
        cross_section = pp.transition(cross_section1=X1, cross_section2=X2, width_type='linear')
        D = P.extrude(width=cross_section)
    else:
        D = P.extrude(width=width, layer=layer)
        if not isinstance(width, CrossSection):
            newport1 = D.add_port(port = port1, name = 1).rotate(180)
            newport2 = D.add_port(port = port2, name = 2).rotate(180)
            if np.size(width) == 1:
                newport1.width = width
                newport2.width = width
            if np.size(width) == 2:
                newport1.width = width[0]
                newport2.width = width[1]
    # D = P.extrude(width, layer = layer)
    return D

# ################
# gradual_bend() - variable radius-of-curvature bends for low-loss routing
# note - these are not bezier spline curves, but are instead constructed by
# subdividing the coverage angle into equal segments and implementing a gradual
# decrease in bending radius until the minimum is reached. """

# ################
# route_manhattan() - routing between any two ports rotated in 90 degree increments
# note - ports must be located diagonally from each other and oriented along
# cardinal directions.  Routing can be done with circular or gradual bends.
# Waveguide width is set by the width parameter of the first port.

# ################
# route_manhattan_auto() - handy routine which performs route_manhattan() on a
# vector of ports provided to it, allowing easy connecting of many objects.


class RoutingError(ValueError):
    pass


def route_manhattan(
    port1,
    port2,
    bendType='circular',
    layer=0,
    radius=20
    ):
    """
    .. deprecated:: 1.6.0
        `route_manhattan` will be removed in August 2022, please replace with
        `route_smooth()`.
    """
    warnings.warn("""[PHIDL] Warning: route_manhattan() will be deprecated 
    in August 2022, please replace with `route_smooth()`""")
    #route along cardinal directions between any two ports placed diagonally
    #from each other

    valid_bend_types = ["circular", "gradual"]

    if bendType not in valid_bend_types:
        raise ValueError("bendType%s= not in %s" % (bendType, valid_bend_types))

    if bendType == "gradual":
        b = _gradual_bend(radius=radius)
        radius_eff = b.xsize
    else:
        radius_eff = radius

    if (
        abs(port1.midpoint[0] - port2.midpoint[0]) < 2 * radius_eff
        or abs(port1.midpoint[1] - port2.midpoint[1]) < 2 * radius_eff
    ):
        raise RoutingError(
            "bend does not fit (radius = %s) you need radius <" % radius_eff,
            min(
                [
                    abs(port1.midpoint[0] - port2.midpoint[0]) / 2,
                    abs(port1.midpoint[1] - port2.midpoint[1]) / 2,
                ]
            ),
        )

    Total = Device()
    width=port1.width
    #first map into uniform plane with normal x,y coords
    #allows each situation to be put into uniform cases of quadrants for routing.
    #this is because bends change direction and positioning.
    if port1.orientation==0:
        p2=[port2.midpoint[0],port2.midpoint[1]]
        p1=[port1.midpoint[0],port1.midpoint[1]]
    if port1.orientation==90:
        p2=[port2.midpoint[1],-port2.midpoint[0]]
        p1=[port1.midpoint[1],-port1.midpoint[0]]
    if port1.orientation==180:
        p2=[-port2.midpoint[0],-port2.midpoint[1]]
        p1=[-port1.midpoint[0],-port1.midpoint[1]]
    if port1.orientation==270:
        p2=[-port2.midpoint[1],port2.midpoint[0]]
        p1=[-port1.midpoint[1],port1.midpoint[0]]

    Total.add_port(name=1,port=port1)
    Total.add_port(name=2,port=port2)

    if p2[1] == p1[1] or p2[0] == p1[0]:
        raise ValueError('Error - ports must be at different x AND y values.')

    #if it is parallel or anti-parallel, route with 180 option
    if (np.round(np.abs(np.mod(port1.orientation - port2.orientation,360)),3) == 180) or (np.round(np.abs(np.mod(port1.orientation - port2.orientation,360)),3) == 0):
        R1 = _route_manhattan180(port1=port1,port2=port2,bendType=bendType,layer=layer,radius=radius)
        r1 = Total.add_ref(R1)

    else:
        #first quadrant case
        if (p2[1] > p1[1]) & (p2[0] > p1[0]):
            #simple 90 degree single-bend case
            if port2.orientation == port1.orientation-90 or port2.orientation == port1.orientation+270:
                R1 = _route_manhattan90(port1=port1,port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
            elif port2.orientation == port1.orientation+90 or port2.orientation == port1.orientation-270:
                if bendType == 'circular':
                    B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=port1.orientation,theta=90)
                    radiusEff=radius
                if bendType == 'gradual':
                    B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=port1.orientation,direction='ccw')
                    radiusEff=B1.xsize-width/2
                b1=Total.add_ref(B1)
                b1.connect(port=1,destination=port1)

                R1 = _route_manhattan180(port1=b1.ports[2],port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
        #second quadrant case
        if (p2[1] > p1[1]) & (p2[0] < p1[0]):
            if np.abs(port1.orientation-port2.orientation) == 90 or np.abs(port1.orientation-port2.orientation) == 270:
                if bendType == 'circular':
                    B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=port1.orientation,theta=90)
                    radiusEff=radius
                if bendType == 'gradual':
                    B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=port1.orientation,direction='ccw')
                    radiusEff=B1.xsize-width/2
                b1=Total.add_ref(B1)
                b1.connect(port=1,destination=port1)
                R1 = _route_manhattan180(port1=b1.ports[2],port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
        #third quadrant case
        if (p2[1] < p1[1]) & (p2[0] < p1[0]):
            if np.abs(port1.orientation-port2.orientation) == 90 or np.abs(port1.orientation-port2.orientation) == 270:
                if bendType == 'circular':
                    B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=port1.orientation,theta=-90)
                    radiusEff=radius
                if bendType == 'gradual':
                    B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=port1.orientation,direction='cw')
                    radiusEff=B1.xsize-width/2
                b1=Total.add_ref(B1)
                b1.connect(port=1,destination=port1)
                R1 = _route_manhattan180(port1=b1.ports[2],port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
        #fourth quadrant case
        if (p2[1] < p1[1]) & (p2[0] > p1[0]):
            #simple 90 degree single-bend case
            if port2.orientation == port1.orientation+90 or port2.orientation == port1.orientation-270:
                R1 = _route_manhattan90(port1=port1,port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
            elif port2.orientation == port1.orientation-90 or port2.orientation == port1.orientation+270:
                if bendType == 'circular':
                    B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=port1.orientation,theta=-90)
                    radiusEff=radius
                if bendType == 'gradual':
                    B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=port1.orientation,direction='cw')
                    radiusEff=B1.xsize-width/2
                b1=Total.add_ref(B1)
                b1.connect(port=1,destination=port1)
                R1 = _route_manhattan180(port1=b1.ports[2],port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
    return Total

def _route_manhattan180(
    port1,
    port2,
    bendType='circular',
    layer=0,
    radius=20
    ):
    #this is a subroutine of route_manhattan() and should not be used by itself.
    Total = Device()
    width=port1.width
    #first map into uniform plane with normal x,y coords
    #allows each situation to be put into uniform cases of quadrants for routing.
    #this is because bends change direction and positioning.
    if port1.orientation==0:
        p2=[port2.midpoint[0],port2.midpoint[1]]
        p1=[port1.midpoint[0],port1.midpoint[1]]
    if port1.orientation==90:
        p2=[port2.midpoint[1],-port2.midpoint[0]]
        p1=[port1.midpoint[1],-port1.midpoint[0]]
    if port1.orientation==180:
        p2=[-port2.midpoint[0],-port2.midpoint[1]]
        p1=[-port1.midpoint[0],-port1.midpoint[1]]
    if port1.orientation==270:
        p2=[-port2.midpoint[1],port2.midpoint[0]]
        p1=[-port1.midpoint[1],port1.midpoint[0]]

    #create placeholder ports based on the imaginary coordinates we created
    Total.add_port(name='t1',midpoint=[0,0],orientation=0,width=width)
    if(port1.orientation!=port2.orientation):
        Total.add_port(name='t2',midpoint=list(np.subtract(p2,p1)),orientation=180,width=width)
    else:
        Total.add_port(name='t2',midpoint=list(np.subtract(p2,p1)),orientation=0,width=width)

    if port1.orientation==port2.orientation:
        #first quadrant target
        if (p2[1] > p1[1]) & (p2[0] > p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=90,theta=90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='ccw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=90,direction='ccw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
            b1.move([p2[0]-p1[0],0])
            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]-radiusEff*2])
            R1=route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b2.ports[2])
        #second quadrant target
        if (p2[1] > p1[1]) & (p2[0] < p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=90,theta=90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='ccw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=90,direction='ccw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)
            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])

            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]-radiusEff*2])
            R1=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b2.ports[2],port2=Total.ports['t2'],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=b1.ports[1])
            Total.add_port(name=2,port=r2.ports[2])
        #third quadrant target
        if (p2[1] < p1[1]) & (p2[0] < p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=-90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-90,theta=-90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='cw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-90,direction='cw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)
            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])

            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]+radiusEff*2])
            R1=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b2.ports[2],port2=Total.ports['t2'],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=b1.ports[1])
            Total.add_port(name=2,port=r2.ports[2])
        #fourth quadrant target
        if (p2[1] < p1[1]) & (p2[0] > p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=-90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-90,theta=-90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='cw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-90,direction='cw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
            b1.move([p2[0]-p1[0],0])
            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]+radiusEff*2])
            R1=route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b2.ports[2])

    #other port orientations are not supported:
    elif np.round(np.abs(np.mod(port1.orientation - port2.orientation,360)),3) != 180:
        raise ValueError('[DEVICE] route() error: Ports do not face each other (orientations must be 180 apart)')
    #otherwise, they are 180 degrees apart:
    else:
        #first quadrant target
        if (p2[1] > p1[1]) & (p2[0] > p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=90,theta=-90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='ccw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=90,direction='cw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
            b1.move([p2[0]-p1[0]-radiusEff*2,0])
            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]-radiusEff*2])
            R1=route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b2.ports[2])
        #second quadrant target
        if (p2[1] > p1[1]) & (p2[0] < p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=90,theta=90)
                B3=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=180,theta=-90)
                B4=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=90,theta=-90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='ccw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=90,direction='ccw')
                B3=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=180,direction='cw')
                B4=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=90,direction='cw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)
            b3=Total.add_ref(B3)
            b4=Total.add_ref(B4)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])

            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]-radiusEff*4])
            R1=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            b3.connect(port=b3.ports[1],destination=b2.ports[2])
            b3.move([p2[0]-p1[0],0])
            R2=route_basic(port1=b2.ports[2],port2=b3.ports[1],layer=layer)
            r2=Total.add_ref(R2)

            b4.connect(port=b4.ports[1],destination=b3.ports[2])

            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b4.ports[2])
         #third quadrant target
        if (p2[1] < p1[1]) & (p2[0] < p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=-90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-90,theta=-90)
                B3=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-180,theta=90)
                B4=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-90,theta=90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='cw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-90,direction='cw')
                B3=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-180,direction='ccw')
                B4=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-90,direction='ccw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)
            b3=Total.add_ref(B3)
            b4=Total.add_ref(B4)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])

            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]+radiusEff*4])
            R1=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            b3.connect(port=b3.ports[1],destination=b2.ports[2])
            b3.move([p2[0]-p1[0],0])
            R2=route_basic(port1=b2.ports[2],port2=b3.ports[1],layer=layer)
            r2=Total.add_ref(R2)

            b4.connect(port=b4.ports[1],destination=b3.ports[2])

            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b4.ports[2])
        #fourth quadrant target
        if (p2[1] < p1[1]) & (p2[0] > p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=-90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-90,theta=90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='cw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-90,direction='ccw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
            b1.move([p2[0]-p1[0]-radiusEff*2,0])
            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]+radiusEff*2])
            R1=route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b2.ports[2])

    Total.rotate(angle =  port1.orientation, center = p1)
    Total.move(origin = Total.ports['t1'], destination = port1)
    return Total

def _route_manhattan90(
    port1,
    port2,
    bendType='circular',
    layer=0,
    radius=20
    ):
    #this is a subroutine of route_manhattan() and should not be used by itself.
    Total = Device()
    width=port1.width
    #first map into uniform plane with normal x,y coords
    #allows each situation to be put into uniform cases of quadrants for routing.
    #this is because bends change direction and positioning.
    if port1.orientation==0:
        p2=[port2.midpoint[0],port2.midpoint[1]]
        p1=[port1.midpoint[0],port1.midpoint[1]]
    if port1.orientation==90:
        p2=[port2.midpoint[1],-port2.midpoint[0]]
        p1=[port1.midpoint[1],-port1.midpoint[0]]
    if port1.orientation==180:
        p2=[-port2.midpoint[0],-port2.midpoint[1]]
        p1=[-port1.midpoint[0],-port1.midpoint[1]]
    if port1.orientation==270:
        p2=[-port2.midpoint[1],port2.midpoint[0]]
        p1=[-port1.midpoint[1],port1.midpoint[0]]

    #create placeholder ports based on the imaginary coordinates we created
    Total.add_port(name='t1',midpoint=[0,0],orientation=0,width=width)

    #CHECK THIS


    #first quadrant target, route upward
    if (p2[1] > p1[1]) & (p2[0] > p1[0]):
        Total.add_port(name='t2',midpoint=list(np.subtract(p2,p1)),orientation=-90,width=width)
        if bendType == 'circular':
            B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=90)
            radiusEff=radius
        if bendType == 'gradual':
            B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='ccw')
            radiusEff=B1.xsize-width/2
        b1=Total.add_ref(B1)
        b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
        b1.move([p2[0]-p1[0]-radiusEff,0])

        R1 = route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
        R2 = route_basic(port1=b1.ports[2],port2=Total.ports['t2'],layer=layer)
        r1 = Total.add_ref(R1)
        r2 = Total.add_ref(R2)
        Total.add_port(name=1,port=r1.ports[1])
        Total.add_port(name=2,port=r2.ports[2])

    #fourth quadrant target, route downward
    if (p2[1] < p1[1]) & (p2[0] > p1[0]):
        Total.add_port(name='t2',midpoint=list(np.subtract(p2,p1)),orientation=90,width=width)
        if bendType == 'circular':
            B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=-90)
            radiusEff=radius
        if bendType == 'gradual':
            B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='cw')
            radiusEff=B1.xsize-width/2
        b1=Total.add_ref(B1)
        b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
        b1.move([p2[0]-p1[0]-radiusEff,0])
        R1 = route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
        R2 = route_basic(port1=b1.ports[2],port2=Total.ports['t2'],layer=layer)
        r1 = Total.add_ref(R1)
        r2 = Total.add_ref(R2)
        Total.add_port(name=1,port=r1.ports[1])
        Total.add_port(name=2,port=r2.ports[2])
    Total.rotate(angle =  port1.orientation, center = p1)
    Total.move(origin = Total.ports['t1'], destination = port1)

    return Total


def route_manhattan_auto(
    ports,
    bendType='circular',
    layer=0,
    radius=20
    ):
    """ routes a one-dimensional array of ports using manhattan algorithm
    and give it a series of ports to route to in a continuous list.
    accepts same parameters as ordinary route_manhattan to determine bending """
    Total=Device()
    for x in range(int(np.floor(len(ports)/2))+1):
        R = route_manhattan(port1=ports[x],port2=ports[x+1],bendType=bendType,layer=layer,radius=radius)
        r = Total.add_ref(R)

    return Total

def route_turn_manhattan(
    port1,
    port2,
    layer=0,
    radius=20
    ):
    """
    Mahattan routing between two ports. If directions are not cardinal, adds a
    turn to make cardinal and then routes.

    Parameters
    ----------
    port1, port2: Port objects
        Ports to route to and from
    layer: int (default: 0)
        Layer to use for the routes
    radius: float (default: 20)
        Curve radius for bends

    Returns
    ----------
    Device object

    Notes
    ----------
    If direction is not cardinal, will route to nearest cardinal, then call
    route_manhattan.
    """

    D = Device()
    new_ports = []
    for port in (port1, port2):
        if port.orientation % 90 == 0:
            new_ports.append(port)
        else:
            turn_angle = _get_turn_angle(port.orientation, _to_cardinal(port.orientation))
            turn_route = turn(port, radius=radius, angle=turn_angle, layer=layer)
            D.add_ref(turn_route)
            new_ports.append(turn_route.ports[2])

    #Manhattan on new ports
    route = route_manhattan(new_ports[0], new_ports[1], bendType='circular', layer=layer,
                       radius=radius)

    D.add_ref(route)

    return D


def _to_cardinal(angle):
    """
    Determines which cardinal direction is closest to input angle

    Parameters
    ----------
    angle : float

    Returns
    -------
    angle : [-180, -90, 0, 90]
        Which cardinal direction is closest to the input angle
    """

    angle = _map_to_pm180(angle)

    cardinals = np.array([-180, -90, 0, 90])

    arg = np.argmin(np.abs(angle - cardinals))

    return cardinals[arg]


def _map_to_pm180(angle):
    """converts an angle to an angle between -180 (inclusive) to +180 (exclusive)"""
    return np.mod(angle + 180,360)-180

def _get_turn_angle(start_angle, target_angle):
    """
    Difference in angle in the range -180 to +180 (where negative is counter clockwise)

    Parameters
    ----------
    start_angle, target_angle : float

    Returns
    -------
    float
        difference in angle.
    """
    return _map_to_pm180(target_angle - start_angle)


#==============================================================================
# Test code for route_manhattan
#==============================================================================

# D=Device()
# A=pg.compass()
# A.add_port(name=1,port=A.ports['N'])
# A.add_port(name=2,port=A.ports['E'])
# A.add_port(name=3,port=A.ports['S'])
# A.add_port(name=4,port=A.ports['W'])
# points=[]
# points.append((300,300))
# points.append((-300,300))
# points.append((-300,-300))
# points.append((300,-300))

# xoff=0
# yoff=0
# for x in range(4):
#     for y in range(4):
#         for z in range(4):
#             a = D.add_ref(A)
#             b = D.add_ref(A)
#             a.center=(xoff,yoff)
#             b.center=(xoff+(points[y])[0],yoff+(points[y])[1])
#             C = route_manhattan(bendType='gradual',port1=a.ports[z+1],port2=b.ports[x+1])
#             c=D.add_ref(C)
#             yoff+=600
#         yoff+=600
#     xoff+=600
#     yoff=0

# quickplot(D)



from __future__ import division, print_function, absolute_import
import numpy as np
from numpy import sqrt, pi, cos, sin, log, exp, sinh, mod
from numpy.linalg import norm
from phidl.device_layout import Device, CrossSection, Port
from phidl.device_layout import _parse_layer
from phidl.geometry import turn
import phidl.path as pp
from phidl import Path
import gdspy
import warnings


def _get_rotated_basis(theta):
    """Returns basis vectors rotated CCW by theta (in degrees)
    """
    theta = np.radians(theta)
    e1 = np.array([np.cos(theta), np.sin(theta)])
    e2 = np.array([-1*np.sin(theta), np.cos(theta)])
    return e1, e2

def _arc(radius = 10, width = 0.5, theta = 45, start_angle = 0, angle_resolution = 2.5, layer = 0):
    """ Creates an arc of arclength ``theta`` starting at angle ``start_angle`` """
    inner_radius = radius-width/2
    outer_radius = radius+width/2
    angle1 = (start_angle)*pi/180
    angle2 = (start_angle + theta)*pi/180
    t = np.linspace(angle1, angle2, int(np.ceil(abs(theta)/angle_resolution)))
    inner_points_x = (inner_radius*cos(t)).tolist()
    inner_points_y = (inner_radius*sin(t)).tolist()
    outer_points_x = (outer_radius*cos(t)).tolist()
    outer_points_y = (outer_radius*sin(t)).tolist()
    xpts = inner_points_x + outer_points_x[::-1]
    ypts = inner_points_y + outer_points_y[::-1]

    D = Device('arc')
    D.add_polygon(points = (xpts,ypts), layer = layer)
    D.add_port(name = 1, midpoint = (radius*cos(angle1), radius*sin(angle1)),  width = width, orientation = start_angle - 90 + 180*(theta<0))
    D.add_port(name = 2, midpoint = (radius*cos(angle2), radius*sin(angle2)),  width = width, orientation = start_angle + theta + 90 - 180*(theta<0))
    D.info['length'] = (abs(theta)*pi/180)*radius
    return D



def _gradual_bend(
    radius = 20,
    width = 1.0,
    angular_coverage=15,
    num_steps=10,
    angle_resolution=0.1,
    start_angle=0,
    direction='ccw',
    layer=0,
    ):

    """
    creates a 90-degree bent waveguide
    the bending radius is gradually increased until it reaches the minimum
    value of the radius at the "angular coverage" angle.
    it essentially creates a smooth transition to a bent waveguide mode.
    user can control number of steps provided.
    direction determined by start angle and cw or ccw switch
    ############
    with the default 10 "num_steps" and 15 degree coverage, effective radius is about 1.5*radius.
    """
    angular_coverage=np.deg2rad(angular_coverage)
    D = Device()

    #determines the increment in radius through its inverse from 0 to 1/r
    inc_rad =(radius**-1)/(num_steps)
    angle_step = angular_coverage/num_steps

    #construct a series of sub-arcs with equal angles but gradually decreasing bend radius
    arcs = []
    for x in range(num_steps):
        A = _arc(radius=1/((x+1)*inc_rad),width=width,theta=np.rad2deg(angle_step),start_angle=x*np.rad2deg(angle_step),angle_resolution=angle_resolution,layer=layer)
        a = D.add_ref(A)
        arcs.append(a)
        if x>0:
            a.connect(port=1,destination=prevPort)
        prevPort=a.ports[2]
    D.add_port(name=1,port=arcs[0].ports[1])

    #now connect a regular bend for the normal curved portion
    B = _arc(radius=radius,width=width,theta=45-np.rad2deg(angular_coverage),start_angle=angular_coverage,angle_resolution=angle_resolution,layer=layer)
    b = D.add_ref(B)
    b.connect(port=1,destination=prevPort)
    prevPort=b.ports[2]
    D.add_port(name=2,port=prevPort)

    #now create the overall structure
    Total = Device()

    #clone the half-curve into two objects and connect for a 90 deg bend.
    D1 = Total.add_ref(D)
    D2 = Total.add_ref(D)
    D2.mirror(p1=[0,0],p2=[1,1])
    D2.connect(port=2,destination=D1.ports[2])
    Total.xmin=0
    Total.ymin=0

    #orient to default settings...
    Total.mirror(p1=[0,0],p2=[1,1])
    Total.mirror(p1=[0,0],p2=[1,0])

    #orient to user-provided settings
    if direction == 'cw':
        Total.mirror(p1=[0,0],p2=[1,0])
    Total.rotate(angle=start_angle,center=Total.center)
    Total.center=[0,0]
    Total.add_port(name=1,port=D1.ports[1])
    Total.add_port(name=2,port=D2.ports[1])

    return Total


def route_basic(port1, port2, path_type = 'sine', width_type = 'straight', width1 = None, width2 = None, num_path_pts = 99, layer = 0):
    """
    .. deprecated:: 1.6.0
        `route_basic` will be removed in August 2022, please replace with
        `route_quad()` or `route_smooth()`.
    """
    warnings.warn("""[PHIDL] Warning: route_basic() will be deprecated 
    in August 2022, please replace with `route_quad()` or `route_smooth()`""")
    # Assuming they're both Ports for now
    point_a = np.array(port1.midpoint)
    if width1 is None:  width1 = port1.width
    point_b = np.array(port2.midpoint)
    if width2 is None:  width2 = port2.width
    if round(abs(mod(port1.orientation - port2.orientation,360)),3) != 180:
        raise ValueError('[DEVICE] route() error: Ports do not face each other (orientations must be 180 apart)')
    orientation = port1.orientation

    separation = point_b - point_a  # Vector drawn from A to B
    distance = norm(separation) # Magnitude of vector from A to B
    rotation = np.arctan2(separation[1],separation[0])*180/pi # Rotation of vector from A to B
    angle = rotation - orientation   # If looking out along the normal of ``a``, the angle you would have to look to see ``b``
    forward_distance = distance*cos(angle*pi/180)
    lateral_distance = distance*sin(angle*pi/180)

    # Create a path assuming starting at the origin and setting orientation = 0
    # use the "connect" function later to move the path to the correct location
    xf = forward_distance
    yf = lateral_distance
    if path_type == 'straight':
        curve_fun = lambda t: [xf*t, yf*t]
        curve_deriv_fun = lambda t: [xf + t*0, t*0]
    if path_type == 'sine':
        curve_fun = lambda t: [xf*t, yf*(1-cos(t*pi))/2]
        curve_deriv_fun = lambda t: [xf  + t*0, yf*(sin(t*pi)*pi)/2]
    #if path_type == 'semicircle':
    #    def semicircle(t):
    #        t = np.array(t)
    #        x,y = np.zeros(t.shape), np.zeros(t.shape)
    #        ii = (0 <= t) & (t <= 0.5)
    #        jj = (0.5 < t) & (t <= 1)
    #        x[ii] = (cos(-pi/2 + t[ii]*pi/2))*xf
    #        y[ii] = (sin(-pi/2 + t[ii]*pi/2)+1)*yf*2
    #        x[jj] = (cos(pi*3/2 - t[jj]*pi)+2)*xf/2
    #        y[jj] = (sin(pi*3/2 - t[jj]*pi)+1)*yf/2
    #        return x,y
    #    curve_fun = semicircle
    #    curve_deriv_fun = None
    if width_type == 'straight':
        width_fun = lambda t: (width2 - width1)*t + width1
    if width_type == 'sine':
        width_fun = lambda t: (width2 - width1)*(1-cos(t*pi))/2 + width1

    route_path = gdspy.Path(width = width1, initial_point = (0,0))
    route_path.parametric(curve_fun, curve_deriv_fun, number_of_evaluations=num_path_pts,
            max_points=199, final_width=width_fun, final_distance=None)
    route_path_polygons = route_path.polygons

    # Make the route path into a Device with ports, and use "connect" to move it
    # into the proper location
    D = Device()
    D.add_polygon(route_path_polygons, layer = layer)
    p1 = D.add_port(name = 1, midpoint = (0,0), width = width1, orientation = 180)
    p2 = D.add_port(name = 2, midpoint = [forward_distance,lateral_distance], width = width2, orientation = 0)
    D.info['length'] = route_path.length

    D.rotate(angle =  180 + port1.orientation - p1.orientation, center = p1.midpoint)
    D.move(origin = p1, destination = port1)
    return D


def route_quad(port1, port2, width1=None, width2=None, layer=0):
    """Routes a basic quadrilateral polygon directly between two ports.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    width1, width2 : int, float or None
        Width of quadrilateral at ports. If None, uses port widths.
    layer : int or array-like[2]
        Layer to put the route on.

    Returns
    ---------
    D : Device
        A Device containing the route and two ports (`1` and `2`) on either end.
    """
    def get_port_edges(port, width):
        _, e1 = _get_rotated_basis(port.orientation)
        pt1 = port.midpoint + e1*width/2
        pt2 = port.midpoint - 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])]
    D = Device()
    D.add_polygon(points=vertices, layer=layer)
    D.add_port(name=1, midpoint=port1.midpoint, orientation=port1.orientation+180, width=width1)
    D.add_port(name=2, midpoint=port2.midpoint, orientation=port2.orientation+180, width=width2) 
    return D


def route_smooth(
        port1, 
        port2, 
        radius=5, 
        width=None,
        path_type='manhattan', 
        manual_path=None, 
        smooth_options={'corner_fun': pp.euler, 'use_eff': True}, 
        layer=np.nan, 
        **kwargs
        ):

    """ Convenience function that routes a path between ports using pp.smooth(),
    then immediately extrudes the path to create polygons. Has several waypoint
    path type options.  Equivalent to e.g.
        >>> pts = pr.path_manhattan(port1, port2, radius) 
        >>> P = pp.smooth(pts, radius)
        >>> D = P.extrude(width)

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    radius : int or float
        Bend radius passed to pp.smooth
    width : None, int, float, array-like[2], or CrossSection
        If None, the route linearly tapers between the widths the ports
        If set to a single number (e.g. `width=1.7`): makes a fixed-width route
        If set to a 2-element array (e.g. `width=[1.8,2.5]`): makes a route
            whose width varies linearly from width[0] to width[1]
        If set to a CrossSection: uses the CrossSection parameters for the route
    path_type : {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'}
        Method of waypoint path creation. Should be one of
            - 'manhattan' - automatic manhattan routing 
                    (see path_manhattan() ).
            - 'L' - L-shaped path for orthogonal ports that can be directly 
                    connected (see path_L() ).
            - 'U' - U-shaped path for parrallel or facing ports
                    (see path_U() ).
            - 'J' - J-shaped path for orthogonal ports that cannot be 
                    directly connected (see path_J() ).
            - 'C' - C-shaped path for ports that face away from each 
                    other (see path_C() ).
            - 'Z' - Z-shaped path with three segments for ports at any 
                    angles (see path_Z() ).
            - 'V' - V-shaped path with two segments for ports at any 
                    angles (see path_V() ).
            - 'straight' - straight path for ports that face each other 
                    see path_straight() ).
            - 'manual' - use an explicit waypoint path provided 
                    in manual_path.
    manual_path : array-like[N][2] or Path
        Waypoint path for creating a manual route
    smooth_options: dict
        Keyword arguments passed to pp.smooth
    layer : int or array-like[2]
        Layer to put route on. `layer=0` is used by default.  
    **kwargs :
        Keyword arguments passed to the waypoint path function.

    Returns
    ----------
    D : Device
        A Device containing the route and two ports (`1` and `2`) on either end.
    """
    if path_type == 'straight':
        P = path_straight(port1, port2)
    elif path_type == 'manual':
        if not isinstance(manual_path, Path):
            P = Path(manual_path)
        else:
            P = manual_path
    elif path_type == 'L':
        P = path_L(port1, port2)
    elif path_type == 'U':
        P = path_U(port1, port2, **kwargs)
    elif path_type == 'J':
        P = path_J(port1, port2, **kwargs)
    elif path_type == 'C':
        P = path_C(port1, port2, **kwargs)
    elif path_type == 'manhattan':
        if smooth_options['corner_fun'] == pp.euler:
            use_eff = smooth_options.get('use_eff')
            if use_eff is None or use_eff == False:
                raise ValueError("""[PHIDL] route_smooth(): when using manhattan path type with euler
                    bends, smooth_options['use_eff'] must be True.""")
        P = path_manhattan(port1, port2, radius=radius)
    elif path_type == 'Z':
        P = path_Z(port1, port2, **kwargs)
    elif path_type == 'V':
        P = path_V(port1, port2)
    else:
        raise ValueError("""[PHIDL] route_smooth() received an invalid path_type.  Must be one of
        {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'}""")

    P = pp.smooth(points=P, radius=radius, **smooth_options)
    if width is None:
        X1 = CrossSection().add(width=port1.width, ports=(1, 2), layer=layer, name='a')
        X2 = CrossSection().add(width=port2.width, ports=(1, 2), layer=layer, name='a')
        cross_section = pp.transition(cross_section1=X1, cross_section2=X2, width_type='linear')
        D = P.extrude(width=cross_section)
    else:
        D = P.extrude(width=width, layer=layer)
        if not isinstance(width, CrossSection):
            newport1 = D.add_port(port = port1, name = 1).rotate(180)
            newport2 = D.add_port(port = port2, name = 2).rotate(180)
            if np.size(width) == 1:
                newport1.width = width
                newport2.width = width
            if np.size(width) == 2:
                newport1.width = width[0]
                newport2.width = width[1]
    return D


def route_sharp(
        port1, 
        port2, 
        width=None,
        path_type='manhattan', 
        manual_path=None, 
        layer=np.nan, 
        **kwargs
        ):

    """ Convenience function that routes a path between ports and immediately 
    extrudes the path to create polygons. Has several waypoint path type 
    options.  Equivalent to e.g.
        >>> P = pr.path_manhattan(port1, port2, radius) 
        >>> D = P.extrude(width)

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    width : None, int, float, array-like[2], or CrossSection
        If None, the route linearly tapers between the widths the ports
        If set to a single number (e.g. `width=1.7`): makes a fixed-width route
        If set to a 2-element array (e.g. `width=[1.8,2.5]`): makes a route
            whose width varies linearly from width[0] to width[1]
        If set to a CrossSection: uses the CrossSection parameters for the route
    path_type : {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'}
        Method of waypoint path creation. Should be one of
            - 'manhattan' - automatic manhattan routing 
                    (see path_manhattan() ).
            - 'L' - L-shaped path for orthogonal ports that can be directly 
                    connected (see path_L() ).
            - 'U' - U-shaped path for parrallel or facing ports
                    (see path_U() ).
            - 'J' - J-shaped path for orthogonal ports that cannot be 
                    directly connected (see path_J() ).
            - 'C' - C-shaped path for ports that face away from each 
                    other (see path_C() ).
            - 'Z' - Z-shaped path with three segments for ports at any 
                    angles (see path_Z() ).
            - 'V' - V-shaped path with two segments for ports at any 
                    angles (see path_V() ).
            - 'straight' - straight path for ports that face each other 
                    see path_straight() ).
            - 'manual' - use an explicit waypoint path provided 
                    in manual_path.
    manual_path : array-like[N][2] or Path
        Waypoint path for creating a manual route
    layer : int or array-like[2]
        Layer to put route on. `layer=0` is used by default. 
    **kwargs :
        Keyword arguments passed to the waypoint path function.

    Returns
    ----------
    D : Device
        A Device containing the route and two ports (`1` and `2`) on either end.
    """
    if path_type == 'straight':
        P = path_straight(port1, port2)
    elif path_type == 'manual':
        if not isinstance(manual_path, Path):
            P = Path(manual_path)
        else:
            P = manual_path
    elif path_type == 'L':
        P = path_L(port1, port2)
    elif path_type == 'U':
        P = path_U(port1, port2, **kwargs)
    elif path_type == 'J':
        P = path_J(port1, port2, **kwargs)
    elif path_type == 'C':
        P = path_C(port1, port2, **kwargs)
    elif path_type == 'manhattan':
        radius = max(port1.width, port2.width)
        P = path_manhattan(port1, port2, radius=radius)
    elif path_type == 'Z':
        P = path_Z(port1, port2, **kwargs)
    elif path_type == 'V':
        P = path_V(port1, port2)
    else:
        raise ValueError("""[PHIDL] route_sharp() received an invalid path_type.  Must be one of
        {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'}""")
    if width is None:
        X1 = CrossSection().add(width=port1.width, ports=(1, 2), layer=layer, name='a')
        X2 = CrossSection().add(width=port2.width, ports=(1, 2), layer=layer, name='a')
        cross_section = pp.transition(cross_section1=X1, cross_section2=X2, width_type='linear')
        D = P.extrude(width=cross_section)
    else:
        D = P.extrude(width=width, layer=layer)
        if not isinstance(width, CrossSection):
            newport1 = D.add_port(port = port1, name = 1).rotate(180)
            newport2 = D.add_port(port = port2, name = 2).rotate(180)
            if np.size(width) == 1:
                newport1.width = width
                newport2.width = width
            if np.size(width) == 2:
                newport1.width = width[0]
                newport2.width = width[1]
    return D


def path_straight(port1, port2):
    """Return waypoint path between port1 and port2 in a straight line. 
    Useful when ports point directly at each other.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.

    Returns
    ----------
    points : array[2][2]
        Waypoints for the route path to follow.
    """
    delta_orientation = np.round(np.abs(np.mod(port1.orientation - port2.orientation, 360)), 3)
    e1, e2 = _get_rotated_basis(port1.orientation)
    displacement = port2.midpoint - port1.midpoint
    xrel = np.round(np.dot(displacement, e1), 3)  # relative position of port 2, forward/backward
    yrel = np.round(np.dot(displacement, e2), 3)  # relative position of port 2, left/right
    if (delta_orientation not in (0, 180, 360)) or (yrel != 0) or (xrel <= 0):
        raise ValueError('[PHIDL] path_straight(): ports must point directly at each other.')
    return Path(np.array([port1.midpoint, port2.midpoint]))


def path_L(port1, port2):
    """Return waypoint path between port1 and port2 in an L shape. Useful 
    when orthogonal ports can be directly connected with one turn.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    delta_orientation = np.round(np.abs(np.mod(port1.orientation - port2.orientation, 360)), 3)
    if delta_orientation not in (90, 270):
        raise ValueError('[PHIDL] path_L(): ports must be orthogonal.')
    e1, e2 = _get_rotated_basis(port1.orientation)
    # assemble waypoints
    pt1 = port1.midpoint
    pt3 = port2.midpoint
    delta_vec = pt3-pt1
    pt2 = pt1 + np.dot(delta_vec, e1)*e1
    return Path(np.array([pt1, pt2, pt3]))


def path_U(port1, port2, length1=200):
    """Return waypoint path between port1 and port2 in a U shape. Useful 
    when ports face the same direction or toward each other.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    length1 : int or float
        Length of segment exiting port1. Should be larger than bend radius.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    delta_orientation = np.round(np.abs(np.mod(port1.orientation - port2.orientation, 360)), 3)
    if delta_orientation not in (0, 180, 360):
        raise ValueError('[PHIDL] path_U(): ports must be parrallel.')
    theta = np.radians(port1.orientation)
    e1 = np.array([np.cos(theta), np.sin(theta)])
    e2 = np.array([-1*np.sin(theta), np.cos(theta)])
    # assemble waypoints
    pt1 = port1.midpoint
    pt4 = port2.midpoint
    pt2 = pt1 + length1*e1  # outward by length1 distance
    delta_vec = pt4-pt2
    pt3 = pt2 + np.dot(delta_vec, e2)*e2
    return Path(np.array([pt1, pt2, pt3, pt4]))


def path_J(port1, port2, length1=200, length2=200):
    """Return waypoint path between port1 and port2 in a J shape. Useful 
    when orthogonal ports cannot be connected directly with an L shape.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    length1 : int or float
        Length of segment exiting port1. Should be larger than bend radius.
    length2 : int or float
        Length of segment exiting port2. Should be larger than bend radius.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    delta_orientation = np.round(np.abs(np.mod(port1.orientation - port2.orientation, 360)), 3)
    if delta_orientation not in (90, 270):
        raise ValueError('[PHIDL] path_J(): ports must be orthogonal.')
    e1, _ = _get_rotated_basis(port1.orientation)
    e2, _ = _get_rotated_basis(port2.orientation)
    # assemble waypoints
    pt1 = port1.midpoint 
    pt2 = pt1 + length1*e1  # outward from port1 by length1
    pt5 = port2.midpoint
    pt4 = pt5 + length2*e2  # outward from port2 by length2
    delta_vec = pt4-pt2 
    pt3 = pt2 + np.dot(delta_vec, e2)*e2  # move orthogonally in e2 direction
    return Path(np.array([pt1, pt2, pt3, pt4, pt5]))


def path_C(port1, port2, length1=100, left1=100, length2=100):
    """Return waypoint path between port1 and port2 in a C shape. Useful 
    when ports are parrallel and face away from each other.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    length1 : int or float
        Length of route segment coming out of port1. Should be at larger
        than bend radius.
    left1 : int or float
        Length of route segment that turns left (or right if negative) 
        from port1. Should be larger than twice the bend radius.
    length2 : int or float
        Length of route segment coming out of port2. Should be larger
        than bend radius.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    delta_orientation = np.round(np.abs(np.mod(port1.orientation - port2.orientation, 360)), 3)
    if delta_orientation not in (0, 180, 360):
        raise ValueError('[PHIDL] path_C(): ports must be parrallel.')
    e1, e_left = _get_rotated_basis(port1.orientation)
    e2, _ = _get_rotated_basis(port2.orientation)
    # assemble route points
    pt1 = port1.midpoint 
    pt2 = pt1 + length1*e1  # outward from port1 by length1
    pt3 = pt2 + left1*e_left  # leftward by left1
    pt6 = port2.midpoint
    pt5 = pt6 + length2*e2  # outward from port2 by length2
    delta_vec = pt5-pt3 
    pt4 = pt3 + np.dot(delta_vec, e1)*e1  # move orthogonally in e1 direction
    return Path(np.array([pt1, pt2, pt3, pt4, pt5, pt6]))


def path_manhattan(port1, port2, radius):
    """Return waypoint path between port1 and port2 using manhattan routing.
    Routing is performed using straight, L, U, J, or C  waypoint path
    as needed. Ports must face orthogonal or parallel directions. 

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    radius : float or int
        Bend radius for 90 degree bend.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    radius = radius + 0.1  # ensure space for bend radius
    e1, e2 = _get_rotated_basis(port1.orientation)
    displacement = port2.midpoint - port1.midpoint
    xrel = np.round(np.dot(displacement, e1), 3)  # port2 position, forward(+)/backward(-) from port 1
    yrel = np.round(np.dot(displacement, e2), 3)  # port2 position, left(+)/right(-) from port1 
    orel = np.round(np.abs(np.mod(port2.orientation - port1.orientation, 360)), 3)  # relative orientation
    if orel not in (0, 90, 180, 270, 360):
        raise ValueError('[PHIDL] path_manhattan(): ports must face parrallel or orthogonal directions.')
    if orel in (90, 270): 
        # Orthogonal case
        if ((orel == 90 and yrel < -1*radius) or (orel == 270 and yrel > radius)) and xrel > radius:
            pts = path_L(port1, port2)
        else:
            # Adjust length1 and length2 to ensure intermediate segments fit bend radius
            direction = -1 if (orel == 270) else 1
            length2 = 2*radius-direction*yrel if (np.abs(radius+direction*yrel) < 2*radius) else radius
            length1 = 2*radius+xrel if (np.abs(radius-xrel) < 2*radius) else radius
            pts = path_J(port1, port2, length1=length1, length2=length2)
    else: 
        # Parrallel case
        if orel == 180 and yrel == 0 and xrel > 0:
            pts = path_straight(port1, port2)
        elif (orel == 180 and xrel <= 2*radius) or (np.abs(yrel) < 2*radius):
            # Adjust length1 and left1 to ensure intermediate segments fit bend radius
            left1 = np.abs(yrel)+2*radius if (np.abs(yrel) < 4*radius) else 2*radius
            y_direction = -1 if (yrel < 0) else 1
            left1 = y_direction*left1
            length2 = radius
            x_direction = -1 if (orel == 180) else 1
            segmentx_length = np.abs(xrel+x_direction*length2-radius)
            if segmentx_length < 2*radius:
                length1 = xrel+x_direction*length2+2*radius
            else:
                length1 = radius
            pts = path_C(port1, port2, length1=length1, length2=length2, left1=left1)
        else:
            # Adjust length1 to ensure segment comes out of port2
            length1 = radius+xrel if (orel == 0 and xrel > 0) else radius
            pts = path_U(port1, port2, length1=length1)
    return pts


def path_Z(port1, port2, length1=100, length2=100):
    """Return waypoint path between port1 and port2 in a Z shape. Ports can have any relative
    orientation.

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.
    length1 : int or float
        Length of route segment coming out of port1.
    length2 : int or float
        Length of route segment coming out of port2.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    # get basis vectors in port directions
    e1, _ = _get_rotated_basis(port1.orientation)
    e2, _ = _get_rotated_basis(port2.orientation)
    # assemble route  points
    pt1 = port1.midpoint 
    pt2 = pt1 + length1*e1  # outward from port1 by length1
    pt4 = port2.midpoint
    pt3 = pt4 + length2*e2  # outward from port2 by length2
    return Path(np.array([pt1, pt2, pt3, pt4]))


def path_V(port1, port2):
    """Return waypoint path between port1 and port2 in a V shape. Useful when
    ports point to a single connecting point

    Parameters
    ----------
    port1, port2 : Port objects
        Ports to route between.

    Returns
    ----------
    points : Path
        Waypoints for the route path to follow.
    """
    # get basis vectors in port directions
    e1, _ = _get_rotated_basis(port1.orientation)
    e2, _ = _get_rotated_basis(port2.orientation)
    # assemble route  points
    pt1 = port1.midpoint 
    pt3 = port2.midpoint
    # solve for intersection
    E = np.column_stack((e1, -1*e2))
    pt2 = np.matmul(np.linalg.inv(E), pt3-pt1)[0]*e1 + pt1
    return Path(np.array([pt1, pt2, pt3]))



def path_xy(port1, port2, directions = 'xxyx'):
    """ Creates a Path that travels only in x and y directions (manhattan) from
    one point (or Port) to another. The `directions` string determines the order
    of the x/y steps. Example: `directions = 'xyx'` will travel
        1/2 the distance in x from p1 to p2
        The whole distance in y from p1 to p2
        1/2 of the distance in x from p1 to p2

    Parameters
    ----------
    p1, p2 : array-like[2] points or Port objects
        Points to route between.
    directions : string of {'x','y'} characters
        Directions the Path will be routed along

    Returns
    ----------
    Path
        Waypoints for the route path to follow.
    """
    if isinstance(port1, Port): p1 = port1.midpoint
    elif np.size(port1) == 2:   p1 = port1
    if isinstance(port2, Port): p2 = port2.midpoint
    elif np.size(port2) == 2:   p2 = port2

    directions = directions.lower()
    num_x = sum([xy == 'x' for xy in directions])
    num_y = sum([xy == 'y' for xy in directions])
    distance = np.asarray(p2)-p1

    points = [p1]
    for xy in directions:
        if xy == 'x':
            travel = np.array([distance[0]/num_x, 0])
            new_point = points[-1] + travel
        elif xy == 'y':
            travel = np.array([0, distance[1]/num_y])
            new_point = points[-1] + travel
        else:
            raise ValueError('[PHIDL] path_xy() directions argument must be string with only "x" or "y" characters')
        if np.abs(np.sum(travel)) > 1e-6: # Only add point if traveling some significant distance
            points.append(new_point)

    return Path(np.array(points))

def route_xy(port1, port2, directions = 'xxyx', width = None, layer = np.nan):
    """ Routes a path in x and y directions (manhattan) from one point (or Port)
    to another. The `directions` string determines the order of the x/y steps.
    Example: `directions = 'xyx'` will travel
        1/2 the distance in x from p1 to p2
        The whole distance in y from p1 to p2
        1/2 of the distance in x from p1 to p2

    Parameters
    ----------
    port1, port2 : Ports pr array-like[2] points or Port objects
        Points to route between.
    directions : string of {'x','y'} characters
        Directions the Path will be routed along

    Returns
    ----------
    D : Device
        A Device containing the route and two ports (`1` and `2`) on either end.
    """

    P = path_xy(port1, port2, directions = directions)
    if width is None:
        X1 = CrossSection().add(width=port1.width, ports=(1, 2), layer=layer, name='a')
        X2 = CrossSection().add(width=port2.width, ports=(1, 2), layer=layer, name='a')
        cross_section = pp.transition(cross_section1=X1, cross_section2=X2, width_type='linear')
        D = P.extrude(width=cross_section)
    else:
        D = P.extrude(width=width, layer=layer)
        if not isinstance(width, CrossSection):
            newport1 = D.add_port(port = port1, name = 1).rotate(180)
            newport2 = D.add_port(port = port2, name = 2).rotate(180)
            if np.size(width) == 1:
                newport1.width = width
                newport2.width = width
            if np.size(width) == 2:
                newport1.width = width[0]
                newport2.width = width[1]
    # D = P.extrude(width, layer = layer)
    return D

# ################
# gradual_bend() - variable radius-of-curvature bends for low-loss routing
# note - these are not bezier spline curves, but are instead constructed by
# subdividing the coverage angle into equal segments and implementing a gradual
# decrease in bending radius until the minimum is reached. """

# ################
# route_manhattan() - routing between any two ports rotated in 90 degree increments
# note - ports must be located diagonally from each other and oriented along
# cardinal directions.  Routing can be done with circular or gradual bends.
# Waveguide width is set by the width parameter of the first port.

# ################
# route_manhattan_auto() - handy routine which performs route_manhattan() on a
# vector of ports provided to it, allowing easy connecting of many objects.


class RoutingError(ValueError):
    pass


def route_manhattan(
    port1,
    port2,
    bendType='circular',
    layer=0,
    radius=20
    ):
    """
    .. deprecated:: 1.6.0
        `route_manhattan` will be removed in August 2022, please replace with
        `route_smooth()`.
    """
    warnings.warn("""[PHIDL] Warning: route_manhattan() will be deprecated 
    in August 2022, please replace with `route_smooth()`""")
    #route along cardinal directions between any two ports placed diagonally
    #from each other

    valid_bend_types = ["circular", "gradual"]

    if bendType not in valid_bend_types:
        raise ValueError("bendType%s= not in %s" % (bendType, valid_bend_types))

    if bendType == "gradual":
        b = _gradual_bend(radius=radius)
        radius_eff = b.xsize
    else:
        radius_eff = radius

    if (
        abs(port1.midpoint[0] - port2.midpoint[0]) < 2 * radius_eff
        or abs(port1.midpoint[1] - port2.midpoint[1]) < 2 * radius_eff
    ):
        raise RoutingError(
            "bend does not fit (radius = %s) you need radius <" % radius_eff,
            min(
                [
                    abs(port1.midpoint[0] - port2.midpoint[0]) / 2,
                    abs(port1.midpoint[1] - port2.midpoint[1]) / 2,
                ]
            ),
        )

    Total = Device()
    width=port1.width
    #first map into uniform plane with normal x,y coords
    #allows each situation to be put into uniform cases of quadrants for routing.
    #this is because bends change direction and positioning.
    if port1.orientation==0:
        p2=[port2.midpoint[0],port2.midpoint[1]]
        p1=[port1.midpoint[0],port1.midpoint[1]]
    if port1.orientation==90:
        p2=[port2.midpoint[1],-port2.midpoint[0]]
        p1=[port1.midpoint[1],-port1.midpoint[0]]
    if port1.orientation==180:
        p2=[-port2.midpoint[0],-port2.midpoint[1]]
        p1=[-port1.midpoint[0],-port1.midpoint[1]]
    if port1.orientation==270:
        p2=[-port2.midpoint[1],port2.midpoint[0]]
        p1=[-port1.midpoint[1],port1.midpoint[0]]

    Total.add_port(name=1,port=port1)
    Total.add_port(name=2,port=port2)

    if p2[1] == p1[1] or p2[0] == p1[0]:
        raise ValueError('Error - ports must be at different x AND y values.')

    #if it is parallel or anti-parallel, route with 180 option
    if (np.round(np.abs(np.mod(port1.orientation - port2.orientation,360)),3) == 180) or (np.round(np.abs(np.mod(port1.orientation - port2.orientation,360)),3) == 0):
        R1 = _route_manhattan180(port1=port1,port2=port2,bendType=bendType,layer=layer,radius=radius)
        r1 = Total.add_ref(R1)

    else:
        #first quadrant case
        if (p2[1] > p1[1]) & (p2[0] > p1[0]):
            #simple 90 degree single-bend case
            if port2.orientation == port1.orientation-90 or port2.orientation == port1.orientation+270:
                R1 = _route_manhattan90(port1=port1,port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
            elif port2.orientation == port1.orientation+90 or port2.orientation == port1.orientation-270:
                if bendType == 'circular':
                    B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=port1.orientation,theta=90)
                    radiusEff=radius
                if bendType == 'gradual':
                    B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=port1.orientation,direction='ccw')
                    radiusEff=B1.xsize-width/2
                b1=Total.add_ref(B1)
                b1.connect(port=1,destination=port1)

                R1 = _route_manhattan180(port1=b1.ports[2],port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
        #second quadrant case
        if (p2[1] > p1[1]) & (p2[0] < p1[0]):
            if np.abs(port1.orientation-port2.orientation) == 90 or np.abs(port1.orientation-port2.orientation) == 270:
                if bendType == 'circular':
                    B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=port1.orientation,theta=90)
                    radiusEff=radius
                if bendType == 'gradual':
                    B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=port1.orientation,direction='ccw')
                    radiusEff=B1.xsize-width/2
                b1=Total.add_ref(B1)
                b1.connect(port=1,destination=port1)
                R1 = _route_manhattan180(port1=b1.ports[2],port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
        #third quadrant case
        if (p2[1] < p1[1]) & (p2[0] < p1[0]):
            if np.abs(port1.orientation-port2.orientation) == 90 or np.abs(port1.orientation-port2.orientation) == 270:
                if bendType == 'circular':
                    B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=port1.orientation,theta=-90)
                    radiusEff=radius
                if bendType == 'gradual':
                    B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=port1.orientation,direction='cw')
                    radiusEff=B1.xsize-width/2
                b1=Total.add_ref(B1)
                b1.connect(port=1,destination=port1)
                R1 = _route_manhattan180(port1=b1.ports[2],port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
        #fourth quadrant case
        if (p2[1] < p1[1]) & (p2[0] > p1[0]):
            #simple 90 degree single-bend case
            if port2.orientation == port1.orientation+90 or port2.orientation == port1.orientation-270:
                R1 = _route_manhattan90(port1=port1,port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
            elif port2.orientation == port1.orientation-90 or port2.orientation == port1.orientation+270:
                if bendType == 'circular':
                    B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=port1.orientation,theta=-90)
                    radiusEff=radius
                if bendType == 'gradual':
                    B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=port1.orientation,direction='cw')
                    radiusEff=B1.xsize-width/2
                b1=Total.add_ref(B1)
                b1.connect(port=1,destination=port1)
                R1 = _route_manhattan180(port1=b1.ports[2],port2=port2,bendType=bendType,layer=layer,radius=radius)
                r1 = Total.add_ref(R1)
    return Total

def _route_manhattan180(
    port1,
    port2,
    bendType='circular',
    layer=0,
    radius=20
    ):
    #this is a subroutine of route_manhattan() and should not be used by itself.
    Total = Device()
    width=port1.width
    #first map into uniform plane with normal x,y coords
    #allows each situation to be put into uniform cases of quadrants for routing.
    #this is because bends change direction and positioning.
    if port1.orientation==0:
        p2=[port2.midpoint[0],port2.midpoint[1]]
        p1=[port1.midpoint[0],port1.midpoint[1]]
    if port1.orientation==90:
        p2=[port2.midpoint[1],-port2.midpoint[0]]
        p1=[port1.midpoint[1],-port1.midpoint[0]]
    if port1.orientation==180:
        p2=[-port2.midpoint[0],-port2.midpoint[1]]
        p1=[-port1.midpoint[0],-port1.midpoint[1]]
    if port1.orientation==270:
        p2=[-port2.midpoint[1],port2.midpoint[0]]
        p1=[-port1.midpoint[1],port1.midpoint[0]]

    #create placeholder ports based on the imaginary coordinates we created
    Total.add_port(name='t1',midpoint=[0,0],orientation=0,width=width)
    if(port1.orientation!=port2.orientation):
        Total.add_port(name='t2',midpoint=list(np.subtract(p2,p1)),orientation=180,width=width)
    else:
        Total.add_port(name='t2',midpoint=list(np.subtract(p2,p1)),orientation=0,width=width)

    if port1.orientation==port2.orientation:
        #first quadrant target
        if (p2[1] > p1[1]) & (p2[0] > p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=90,theta=90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='ccw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=90,direction='ccw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
            b1.move([p2[0]-p1[0],0])
            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]-radiusEff*2])
            R1=route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b2.ports[2])
        #second quadrant target
        if (p2[1] > p1[1]) & (p2[0] < p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=90,theta=90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='ccw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=90,direction='ccw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)
            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])

            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]-radiusEff*2])
            R1=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b2.ports[2],port2=Total.ports['t2'],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=b1.ports[1])
            Total.add_port(name=2,port=r2.ports[2])
        #third quadrant target
        if (p2[1] < p1[1]) & (p2[0] < p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=-90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-90,theta=-90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='cw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-90,direction='cw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)
            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])

            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]+radiusEff*2])
            R1=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b2.ports[2],port2=Total.ports['t2'],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=b1.ports[1])
            Total.add_port(name=2,port=r2.ports[2])
        #fourth quadrant target
        if (p2[1] < p1[1]) & (p2[0] > p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=-90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-90,theta=-90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='cw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-90,direction='cw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
            b1.move([p2[0]-p1[0],0])
            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]+radiusEff*2])
            R1=route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b2.ports[2])

    #other port orientations are not supported:
    elif np.round(np.abs(np.mod(port1.orientation - port2.orientation,360)),3) != 180:
        raise ValueError('[DEVICE] route() error: Ports do not face each other (orientations must be 180 apart)')
    #otherwise, they are 180 degrees apart:
    else:
        #first quadrant target
        if (p2[1] > p1[1]) & (p2[0] > p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=90,theta=-90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='ccw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=90,direction='cw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
            b1.move([p2[0]-p1[0]-radiusEff*2,0])
            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]-radiusEff*2])
            R1=route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b2.ports[2])
        #second quadrant target
        if (p2[1] > p1[1]) & (p2[0] < p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=90,theta=90)
                B3=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=180,theta=-90)
                B4=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=90,theta=-90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='ccw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=90,direction='ccw')
                B3=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=180,direction='cw')
                B4=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=90,direction='cw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)
            b3=Total.add_ref(B3)
            b4=Total.add_ref(B4)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])

            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]-radiusEff*4])
            R1=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            b3.connect(port=b3.ports[1],destination=b2.ports[2])
            b3.move([p2[0]-p1[0],0])
            R2=route_basic(port1=b2.ports[2],port2=b3.ports[1],layer=layer)
            r2=Total.add_ref(R2)

            b4.connect(port=b4.ports[1],destination=b3.ports[2])

            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b4.ports[2])
         #third quadrant target
        if (p2[1] < p1[1]) & (p2[0] < p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=-90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-90,theta=-90)
                B3=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-180,theta=90)
                B4=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-90,theta=90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='cw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-90,direction='cw')
                B3=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-180,direction='ccw')
                B4=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-90,direction='ccw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)
            b3=Total.add_ref(B3)
            b4=Total.add_ref(B4)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])

            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]+radiusEff*4])
            R1=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            b3.connect(port=b3.ports[1],destination=b2.ports[2])
            b3.move([p2[0]-p1[0],0])
            R2=route_basic(port1=b2.ports[2],port2=b3.ports[1],layer=layer)
            r2=Total.add_ref(R2)

            b4.connect(port=b4.ports[1],destination=b3.ports[2])

            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b4.ports[2])
        #fourth quadrant target
        if (p2[1] < p1[1]) & (p2[0] > p1[0]):
            if bendType == 'circular':
                B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=-90)
                B2=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=-90,theta=90)
                radiusEff=radius
            if bendType == 'gradual':
                B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='cw')
                B2=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=-90,direction='ccw')
                radiusEff=B1.xsize-width/2
            b1=Total.add_ref(B1)
            b2=Total.add_ref(B2)


            b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
            b1.move([p2[0]-p1[0]-radiusEff*2,0])
            b2.connect(port=b2.ports[1],destination=b1.ports[2])
            b2.move([0,p2[1]-p1[1]+radiusEff*2])
            R1=route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
            r1=Total.add_ref(R1)
            R2=route_basic(port1=b1.ports[2],port2=b2.ports[1],layer=layer)
            r2=Total.add_ref(R2)
            Total.add_port(name=1,port=r1.ports[1])
            Total.add_port(name=2,port=b2.ports[2])

    Total.rotate(angle =  port1.orientation, center = p1)
    Total.move(origin = Total.ports['t1'], destination = port1)
    return Total

def _route_manhattan90(
    port1,
    port2,
    bendType='circular',
    layer=0,
    radius=20
    ):
    #this is a subroutine of route_manhattan() and should not be used by itself.
    Total = Device()
    width=port1.width
    #first map into uniform plane with normal x,y coords
    #allows each situation to be put into uniform cases of quadrants for routing.
    #this is because bends change direction and positioning.
    if port1.orientation==0:
        p2=[port2.midpoint[0],port2.midpoint[1]]
        p1=[port1.midpoint[0],port1.midpoint[1]]
    if port1.orientation==90:
        p2=[port2.midpoint[1],-port2.midpoint[0]]
        p1=[port1.midpoint[1],-port1.midpoint[0]]
    if port1.orientation==180:
        p2=[-port2.midpoint[0],-port2.midpoint[1]]
        p1=[-port1.midpoint[0],-port1.midpoint[1]]
    if port1.orientation==270:
        p2=[-port2.midpoint[1],port2.midpoint[0]]
        p1=[-port1.midpoint[1],port1.midpoint[0]]

    #create placeholder ports based on the imaginary coordinates we created
    Total.add_port(name='t1',midpoint=[0,0],orientation=0,width=width)

    #CHECK THIS


    #first quadrant target, route upward
    if (p2[1] > p1[1]) & (p2[0] > p1[0]):
        Total.add_port(name='t2',midpoint=list(np.subtract(p2,p1)),orientation=-90,width=width)
        if bendType == 'circular':
            B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=90)
            radiusEff=radius
        if bendType == 'gradual':
            B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='ccw')
            radiusEff=B1.xsize-width/2
        b1=Total.add_ref(B1)
        b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
        b1.move([p2[0]-p1[0]-radiusEff,0])

        R1 = route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
        R2 = route_basic(port1=b1.ports[2],port2=Total.ports['t2'],layer=layer)
        r1 = Total.add_ref(R1)
        r2 = Total.add_ref(R2)
        Total.add_port(name=1,port=r1.ports[1])
        Total.add_port(name=2,port=r2.ports[2])

    #fourth quadrant target, route downward
    if (p2[1] < p1[1]) & (p2[0] > p1[0]):
        Total.add_port(name='t2',midpoint=list(np.subtract(p2,p1)),orientation=90,width=width)
        if bendType == 'circular':
            B1=_arc(radius=radius,width=width,layer=layer,angle_resolution=1,start_angle=0,theta=-90)
            radiusEff=radius
        if bendType == 'gradual':
            B1=_gradual_bend(radius=radius,width=width,layer=layer,start_angle=0,direction='cw')
            radiusEff=B1.xsize-width/2
        b1=Total.add_ref(B1)
        b1.connect(port=b1.ports[1],destination=Total.ports['t1'])
        b1.move([p2[0]-p1[0]-radiusEff,0])
        R1 = route_basic(port1=Total.ports['t1'],port2=b1.ports[1],layer=layer)
        R2 = route_basic(port1=b1.ports[2],port2=Total.ports['t2'],layer=layer)
        r1 = Total.add_ref(R1)
        r2 = Total.add_ref(R2)
        Total.add_port(name=1,port=r1.ports[1])
        Total.add_port(name=2,port=r2.ports[2])
    Total.rotate(angle =  port1.orientation, center = p1)
    Total.move(origin = Total.ports['t1'], destination = port1)

    return Total


def route_manhattan_auto(
    ports,
    bendType='circular',
    layer=0,
    radius=20
    ):
    """ routes a one-dimensional array of ports using manhattan algorithm
    and give it a series of ports to route to in a continuous list.
    accepts same parameters as ordinary route_manhattan to determine bending """
    Total=Device()
    for x in range(int(np.floor(len(ports)/2))+1):
        R = route_manhattan(port1=ports[x],port2=ports[x+1],bendType=bendType,layer=layer,radius=radius)
        r = Total.add_ref(R)

    return Total

def route_turn_manhattan(
    port1,
    port2,
    layer=0,
    radius=20
    ):
    """
    Mahattan routing between two ports. If directions are not cardinal, adds a
    turn to make cardinal and then routes.

    Parameters
    ----------
    port1, port2: Port objects
        Ports to route to and from
    layer: int (default: 0)
        Layer to use for the routes
    radius: float (default: 20)
        Curve radius for bends

    Returns
    ----------
    Device object

    Notes
    ----------
    If direction is not cardinal, will route to nearest cardinal, then call
    route_manhattan.
    """

    D = Device()
    new_ports = []
    for port in (port1, port2):
        if port.orientation % 90 == 0:
            new_ports.append(port)
        else:
            turn_angle = _get_turn_angle(port.orientation, _to_cardinal(port.orientation))
            turn_route = turn(port, radius=radius, angle=turn_angle, layer=layer)
            D.add_ref(turn_route)
            new_ports.append(turn_route.ports[2])

    #Manhattan on new ports
    route = route_manhattan(new_ports[0], new_ports[1], bendType='circular', layer=layer,
                       radius=radius)

    D.add_ref(route)

    return D


def _to_cardinal(angle):
    """
    Determines which cardinal direction is closest to input angle

    Parameters
    ----------
    angle : float

    Returns
    -------
    angle : [-180, -90, 0, 90]
        Which cardinal direction is closest to the input angle
    """

    angle = _map_to_pm180(angle)

    cardinals = np.array([-180, -90, 0, 90])

    arg = np.argmin(np.abs(angle - cardinals))

    return cardinals[arg]


def _map_to_pm180(angle):
    """converts an angle to an angle between -180 (inclusive) to +180 (exclusive)"""
    return np.mod(angle + 180,360)-180

def _get_turn_angle(start_angle, target_angle):
    """
    Difference in angle in the range -180 to +180 (where negative is counter clockwise)

    Parameters
    ----------
    start_angle, target_angle : float

    Returns
    -------
    float
        difference in angle.
    """
    return _map_to_pm180(target_angle - start_angle)


#==============================================================================
# Test code for route_manhattan
#==============================================================================

# D=Device()
# A=pg.compass()
# A.add_port(name=1,port=A.ports['N'])
# A.add_port(name=2,port=A.ports['E'])
# A.add_port(name=3,port=A.ports['S'])
# A.add_port(name=4,port=A.ports['W'])
# points=[]
# points.append((300,300))
# points.append((-300,300))
# points.append((-300,-300))
# points.append((300,-300))

# xoff=0
# yoff=0
# for x in range(4):
#     for y in range(4):
#         for z in range(4):
#             a = D.add_ref(A)
#             b = D.add_ref(A)
#             a.center=(xoff,yoff)
#             b.center=(xoff+(points[y])[0],yoff+(points[y])[1])
#             C = route_manhattan(bendType='gradual',port1=a.ports[z+1],port2=b.ports[x+1])
#             c=D.add_ref(C)
#             yoff+=600
#         yoff+=600
#     xoff+=600
#     yoff=0

# quickplot(D)
Returns basis vectors rotated CCW by theta (in degrees) Creates an arc of arclength ``theta`` starting at angle ``start_angle`` creates a 90-degree bent waveguide     the bending radius is gradually increased until it reaches the minimum     value of the radius at the "angular coverage" angle.     it essentially creates a smooth transition to a bent waveguide mode.     user can control number of steps provided.     direction determined by start angle and cw or ccw switch     ############     with the default 10 "num_steps" and 15 degree coverage, effective radius is about 1.5*radius. #determines the increment in radius through its inverse from 0 to 1/r #construct a series of sub-arcs with equal angles but gradually decreasing bend radius #now connect a regular bend for the normal curved portion #now create the overall structure #clone the half-curve into two objects and connect for a 90 deg bend. #orient to default settings... #orient to user-provided settings .. deprecated:: 1.6.0         `route_basic` will be removed in August 2022, please replace with         `route_quad()` or `route_smooth()`. [PHIDL] Warning: route_basic() will be deprecated      in August 2022, please replace with `route_quad()` or `route_smooth()` # Assuming they're both Ports for now # Vector drawn from A to B # Magnitude of vector from A to B # Rotation of vector from A to B # If looking out along the normal of ``a``, the angle you would have to look to see ``b`` # Create a path assuming starting at the origin and setting orientation = 0 # use the "connect" function later to move the path to the correct location #if path_type == 'semicircle': #    def semicircle(t): #        t = np.array(t) #        x,y = np.zeros(t.shape), np.zeros(t.shape) #        ii = (0 <= t) & (t <= 0.5) #        jj = (0.5 < t) & (t <= 1) #        x[ii] = (cos(-pi/2 + t[ii]*pi/2))*xf #        y[ii] = (sin(-pi/2 + t[ii]*pi/2)+1)*yf*2 #        x[jj] = (cos(pi*3/2 - t[jj]*pi)+2)*xf/2 #        y[jj] = (sin(pi*3/2 - t[jj]*pi)+1)*yf/2 #        return x,y #    curve_fun = semicircle #    curve_deriv_fun = None # Make the route path into a Device with ports, and use "connect" to move it # into the proper location Routes a basic quadrilateral polygon directly between two ports.      Parameters     ----------     port1, port2 : Port objects         Ports to route between.     width1, width2 : int, float or None         Width of quadrilateral at ports. If None, uses port widths.     layer : int or array-like[2]         Layer to put the route on.      Returns     ---------     D : Device         A Device containing the route and two ports (`1` and `2`) on either end. # sort vertices by angle from center of quadrilateral to make convex polygon Convenience function that routes a path between ports using pp.smooth(),     then immediately extrudes the path to create polygons. Has several waypoint     path type options.  Equivalent to e.g.         >>> pts = pr.path_manhattan(port1, port2, radius)          >>> P = pp.smooth(pts, radius)         >>> D = P.extrude(width)      Parameters     ----------     port1, port2 : Port objects         Ports to route between.     radius : int or float         Bend radius passed to pp.smooth     width : None, int, float, array-like[2], or CrossSection         If None, the route linearly tapers between the widths the ports         If set to a single number (e.g. `width=1.7`): makes a fixed-width route         If set to a 2-element array (e.g. `width=[1.8,2.5]`): makes a route             whose width varies linearly from width[0] to width[1]         If set to a CrossSection: uses the CrossSection parameters for the route     path_type : {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'}         Method of waypoint path creation. Should be one of             - 'manhattan' - automatic manhattan routing                      (see path_manhattan() ).             - 'L' - L-shaped path for orthogonal ports that can be directly                      connected (see path_L() ).             - 'U' - U-shaped path for parrallel or facing ports                     (see path_U() ).             - 'J' - J-shaped path for orthogonal ports that cannot be                      directly connected (see path_J() ).             - 'C' - C-shaped path for ports that face away from each                      other (see path_C() ).             - 'Z' - Z-shaped path with three segments for ports at any                      angles (see path_Z() ).             - 'V' - V-shaped path with two segments for ports at any                      angles (see path_V() ).             - 'straight' - straight path for ports that face each other                      see path_straight() ).             - 'manual' - use an explicit waypoint path provided                      in manual_path.     manual_path : array-like[N][2] or Path         Waypoint path for creating a manual route     smooth_options: dict         Keyword arguments passed to pp.smooth     layer : int or array-like[2]         Layer to put route on. `layer=0` is used by default.       **kwargs :         Keyword arguments passed to the waypoint path function.      Returns     ----------     D : Device         A Device containing the route and two ports (`1` and `2`) on either end. [PHIDL] route_smooth(): when using manhattan path type with euler                     bends, smooth_options['use_eff'] must be True. [PHIDL] route_smooth() received an invalid path_type.  Must be one of         {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'} Convenience function that routes a path between ports and immediately      extrudes the path to create polygons. Has several waypoint path type      options.  Equivalent to e.g.         >>> P = pr.path_manhattan(port1, port2, radius)          >>> D = P.extrude(width)      Parameters     ----------     port1, port2 : Port objects         Ports to route between.     width : None, int, float, array-like[2], or CrossSection         If None, the route linearly tapers between the widths the ports         If set to a single number (e.g. `width=1.7`): makes a fixed-width route         If set to a 2-element array (e.g. `width=[1.8,2.5]`): makes a route             whose width varies linearly from width[0] to width[1]         If set to a CrossSection: uses the CrossSection parameters for the route     path_type : {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'}         Method of waypoint path creation. Should be one of             - 'manhattan' - automatic manhattan routing                      (see path_manhattan() ).             - 'L' - L-shaped path for orthogonal ports that can be directly                      connected (see path_L() ).             - 'U' - U-shaped path for parrallel or facing ports                     (see path_U() ).             - 'J' - J-shaped path for orthogonal ports that cannot be                      directly connected (see path_J() ).             - 'C' - C-shaped path for ports that face away from each                      other (see path_C() ).             - 'Z' - Z-shaped path with three segments for ports at any                      angles (see path_Z() ).             - 'V' - V-shaped path with two segments for ports at any                      angles (see path_V() ).             - 'straight' - straight path for ports that face each other                      see path_straight() ).             - 'manual' - use an explicit waypoint path provided                      in manual_path.     manual_path : array-like[N][2] or Path         Waypoint path for creating a manual route     layer : int or array-like[2]         Layer to put route on. `layer=0` is used by default.      **kwargs :         Keyword arguments passed to the waypoint path function.      Returns     ----------     D : Device         A Device containing the route and two ports (`1` and `2`) on either end. [PHIDL] route_sharp() received an invalid path_type.  Must be one of         {'manhattan', 'L', 'U', 'J', 'C', 'V', 'Z', 'straight', 'manual'} Return waypoint path between port1 and port2 in a straight line.      Useful when ports point directly at each other.      Parameters     ----------     port1, port2 : Port objects         Ports to route between.      Returns     ----------     points : array[2][2]         Waypoints for the route path to follow. # relative position of port 2, forward/backward # relative position of port 2, left/right Return waypoint path between port1 and port2 in an L shape. Useful      when orthogonal ports can be directly connected with one turn.      Parameters     ----------     port1, port2 : Port objects         Ports to route between.      Returns     ----------     points : Path         Waypoints for the route path to follow. # assemble waypoints Return waypoint path between port1 and port2 in a U shape. Useful      when ports face the same direction or toward each other.      Parameters     ----------     port1, port2 : Port objects         Ports to route between.     length1 : int or float         Length of segment exiting port1. Should be larger than bend radius.      Returns     ----------     points : Path         Waypoints for the route path to follow. # assemble waypoints # outward by length1 distance Return waypoint path between port1 and port2 in a J shape. Useful      when orthogonal ports cannot be connected directly with an L shape.      Parameters     ----------     port1, port2 : Port objects         Ports to route between.     length1 : int or float         Length of segment exiting port1. Should be larger than bend radius.     length2 : int or float         Length of segment exiting port2. Should be larger than bend radius.      Returns     ----------     points : Path         Waypoints for the route path to follow. # assemble waypoints # outward from port1 by length1 # outward from port2 by length2 # move orthogonally in e2 direction Return waypoint path between port1 and port2 in a C shape. Useful      when ports are parrallel and face away from each other.      Parameters     ----------     port1, port2 : Port objects         Ports to route between.     length1 : int or float         Length of route segment coming out of port1. Should be at larger         than bend radius.     left1 : int or float         Length of route segment that turns left (or right if negative)          from port1. Should be larger than twice the bend radius.     length2 : int or float         Length of route segment coming out of port2. Should be larger         than bend radius.      Returns     ----------     points : Path         Waypoints for the route path to follow. # assemble route points # outward from port1 by length1 # leftward by left1 # outward from port2 by length2 # move orthogonally in e1 direction Return waypoint path between port1 and port2 using manhattan routing.     Routing is performed using straight, L, U, J, or C  waypoint path     as needed. Ports must face orthogonal or parallel directions.       Parameters     ----------     port1, port2 : Port objects         Ports to route between.     radius : float or int         Bend radius for 90 degree bend.      Returns     ----------     points : Path         Waypoints for the route path to follow. # ensure space for bend radius # port2 position, forward(+)/backward(-) from port 1 # port2 position, left(+)/right(-) from port1 # relative orientation # Orthogonal case # Adjust length1 and length2 to ensure intermediate segments fit bend radius # Parrallel case # Adjust length1 and left1 to ensure intermediate segments fit bend radius # Adjust length1 to ensure segment comes out of port2 Return waypoint path between port1 and port2 in a Z shape. Ports can have any relative     orientation.      Parameters     ----------     port1, port2 : Port objects         Ports to route between.     length1 : int or float         Length of route segment coming out of port1.     length2 : int or float         Length of route segment coming out of port2.      Returns     ----------     points : Path         Waypoints for the route path to follow. # get basis vectors in port directions # assemble route  points # outward from port1 by length1 # outward from port2 by length2 Return waypoint path between port1 and port2 in a V shape. Useful when     ports point to a single connecting point      Parameters     ----------     port1, port2 : Port objects         Ports to route between.      Returns     ----------     points : Path         Waypoints for the route path to follow. # get basis vectors in port directions # assemble route  points # solve for intersection Creates a Path that travels only in x and y directions (manhattan) from     one point (or Port) to another. The `directions` string determines the order     of the x/y steps. Example: `directions = 'xyx'` will travel         1/2 the distance in x from p1 to p2         The whole distance in y from p1 to p2         1/2 of the distance in x from p1 to p2      Parameters     ----------     p1, p2 : array-like[2] points or Port objects         Points to route between.     directions : string of {'x','y'} characters         Directions the Path will be routed along      Returns     ----------     Path         Waypoints for the route path to follow. # Only add point if traveling some significant distance Routes a path in x and y directions (manhattan) from one point (or Port)     to another. The `directions` string determines the order of the x/y steps.     Example: `directions = 'xyx'` will travel         1/2 the distance in x from p1 to p2         The whole distance in y from p1 to p2         1/2 of the distance in x from p1 to p2      Parameters     ----------     port1, port2 : Ports pr array-like[2] points or Port objects         Points to route between.     directions : string of {'x','y'} characters         Directions the Path will be routed along      Returns     ----------     D : Device         A Device containing the route and two ports (`1` and `2`) on either end. # D = P.extrude(width, layer = layer) # ################ # gradual_bend() - variable radius-of-curvature bends for low-loss routing # note - these are not bezier spline curves, but are instead constructed by # subdividing the coverage angle into equal segments and implementing a gradual # decrease in bending radius until the minimum is reached. """ # ################ # route_manhattan() - routing between any two ports rotated in 90 degree increments # note - ports must be located diagonally from each other and oriented along # cardinal directions.  Routing can be done with circular or gradual bends. # Waveguide width is set by the width parameter of the first port. # ################ # route_manhattan_auto() - handy routine which performs route_manhattan() on a # vector of ports provided to it, allowing easy connecting of many objects. .. deprecated:: 1.6.0         `route_manhattan` will be removed in August 2022, please replace with         `route_smooth()`. [PHIDL] Warning: route_manhattan() will be deprecated      in August 2022, please replace with `route_smooth()` #route along cardinal directions between any two ports placed diagonally #from each other #first map into uniform plane with normal x,y coords #allows each situation to be put into uniform cases of quadrants for routing. #this is because bends change direction and positioning. #if it is parallel or anti-parallel, route with 180 option #first quadrant case #simple 90 degree single-bend case #second quadrant case #third quadrant case #fourth quadrant case #simple 90 degree single-bend case #this is a subroutine of route_manhattan() and should not be used by itself. #first map into uniform plane with normal x,y coords #allows each situation to be put into uniform cases of quadrants for routing. #this is because bends change direction and positioning. #create placeholder ports based on the imaginary coordinates we created #first quadrant target #second quadrant target #third quadrant target #fourth quadrant target #other port orientations are not supported: #otherwise, they are 180 degrees apart: #first quadrant target #second quadrant target #third quadrant target #fourth quadrant target #this is a subroutine of route_manhattan() and should not be used by itself. #first map into uniform plane with normal x,y coords #allows each situation to be put into uniform cases of quadrants for routing. #this is because bends change direction and positioning. #create placeholder ports based on the imaginary coordinates we created #CHECK THIS #first quadrant target, route upward #fourth quadrant target, route downward routes a one-dimensional array of ports using manhattan algorithm     and give it a series of ports to route to in a continuous list.     accepts same parameters as ordinary route_manhattan to determine bending Mahattan routing between two ports. If directions are not cardinal, adds a     turn to make cardinal and then routes.      Parameters     ----------     port1, port2: Port objects         Ports to route to and from     layer: int (default: 0)         Layer to use for the routes     radius: float (default: 20)         Curve radius for bends      Returns     ----------     Device object      Notes     ----------     If direction is not cardinal, will route to nearest cardinal, then call     route_manhattan. #Manhattan on new ports Determines which cardinal direction is closest to input angle      Parameters     ----------     angle : float      Returns     -------     angle : [-180, -90, 0, 90]         Which cardinal direction is closest to the input angle converts an angle to an angle between -180 (inclusive) to +180 (exclusive) Difference in angle in the range -180 to +180 (where negative is counter clockwise)      Parameters     ----------     start_angle, target_angle : float      Returns     -------     float         difference in angle. #============================================================================== # Test code for route_manhattan #============================================================================== # D=Device() # A=pg.compass() # A.add_port(name=1,port=A.ports['N']) # A.add_port(name=2,port=A.ports['E']) # A.add_port(name=3,port=A.ports['S']) # A.add_port(name=4,port=A.ports['W']) # points=[] # points.append((300,300)) # points.append((-300,300)) # points.append((-300,-300)) # points.append((300,-300)) # xoff=0 # yoff=0 # for x in range(4): #     for y in range(4): #         for z in range(4): #             a = D.add_ref(A) #             b = D.add_ref(A) #             a.center=(xoff,yoff) #             b.center=(xoff+(points[y])[0],yoff+(points[y])[1]) #             C = route_manhattan(bendType='gradual',port1=a.ports[z+1],port2=b.ports[x+1]) #             c=D.add_ref(C) #             yoff+=600 #         yoff+=600 #     xoff+=600 #     yoff=0 # quickplot(D)