"""You can define a path with a list of points combined with a cross-section.
A path can be extruded using any CrossSection returning a Component
The CrossSection defines the layer numbers, widths and offsets
Adapted from PHIDL https://github.com/amccaugh/phidl/ by Adam McCaughan
"""
from __future__ import annotations
import hashlib
import math
import warnings
from collections.abc import Callable, Iterable
import numpy as np
from numpy import mod, pi
from gdsfactory.cell import cell
from gdsfactory.component import Component
from gdsfactory.component_layout import (
_GeometryHelper,
_parse_move,
_reflect_points,
_rotate_points,
)
from gdsfactory.config import CONF
from gdsfactory.cross_section import CrossSection, Section, Transition
from gdsfactory.port import Port
from gdsfactory.snap import snap_to_grid2x
from gdsfactory.typings import (
ComponentSpec,
Coordinates,
CrossSectionSpec,
Float2,
LayerSpec,
WidthTypes,
)
def _simplify(points, tolerance):
import shapely.geometry as sg
ls = sg.LineString(points)
ls_simple = ls.simplify(tolerance=tolerance)
return np.asarray(ls_simple.coords)
[docs]
class Path(_GeometryHelper):
"""Path object for smooth Paths. You can extrude a Path with a CrossSection \
to create a Component.
Parameters:
path: array-like[N][2], Path, or list of Paths. Points or Paths to append() initially.
"""
[docs]
def __init__(self, path=None) -> None:
"""Creates an empty path."""
self.points = np.array([[0, 0]], dtype=np.float64)
self.start_angle = 0
self.end_angle = 0
self.info = {}
if path is not None:
# If array[N][2]
if (
(np.asarray(path, dtype=object).ndim == 2)
and np.issubdtype(np.array(path).dtype, np.number)
and (np.shape(path)[1] == 2)
):
self.points = np.array(path, dtype=np.float64)
nx1, ny1 = self.points[1] - self.points[0]
self.start_angle = np.arctan2(ny1, nx1) / np.pi * 180
nx2, ny2 = self.points[-1] - self.points[-2]
self.end_angle = np.arctan2(ny2, nx2) / np.pi * 180
elif isinstance(path, Path):
self.points = np.array(path.points, dtype=np.float64)
self.start_angle = path.start_angle
self.end_angle = path.end_angle
self.info = {}
elif np.asarray(path, dtype=object).size > 1:
self.append(path)
else:
raise ValueError(
"Path() the `path` argument must be either blank, a path Object, "
"an array-like[N][2] list of points, or a list of these"
)
def __repr__(self) -> str:
"""Returns path points."""
return (
f"Path(start_angle={self.start_angle}, "
f"end_angle={self.end_angle}, "
f"points={self.points})"
)
def __len__(self) -> int:
"""Returns path points."""
return len(self.points)
def __iadd__(self, path_or_points) -> Path:
"""Adds points to current path."""
return self.append(path_or_points)
def __add__(self, path) -> Path:
"""Returns new path concatenating current and new path."""
new = self.copy()
return new.append(path)
@property
def bbox(self):
"""Returns the bounding box of the Path."""
bbox = [
(np.min(self.points[:, 0]), np.min(self.points[:, 1])),
(np.max(self.points[:, 0]), np.max(self.points[:, 1])),
]
return np.array(bbox)
def append(self, path):
"""Attach Path to the end of this Path.
The input path automatically rotates and translates such that it continues
smoothly from the previous segment.
Args:
path: Path, array-like[N][2], or list of Paths. The input path that will be appended.
"""
# If appending another Path, load relevant variables
if isinstance(path, Path):
start_angle = path.start_angle
end_angle = path.end_angle
points = path.points
# If array[N][2]
elif (
(np.asarray(path, dtype=object).ndim == 2)
and np.issubdtype(np.array(path).dtype, np.number)
and (np.shape(path)[1] == 2)
):
points = np.asfarray(path)
nx1, ny1 = points[1] - points[0]
start_angle = np.arctan2(ny1, nx1) / np.pi * 180
nx2, ny2 = points[-1] - points[-2]
end_angle = np.arctan2(ny2, nx2) / np.pi * 180
# If list of Paths or arrays
elif isinstance(path, list | tuple):
for p in path:
self.append(p)
return self
else:
raise ValueError(
"Path.append() the `path` argument must be either "
"a Path object, an array-like[N][2] list of points, or a list of these"
)
# Connect beginning of new points with old points
points = _rotate_points(points, angle=self.end_angle - start_angle)
points += self.points[-1, :] - points[0, :]
# Update end angle
self.end_angle = mod(end_angle + self.end_angle - start_angle, 360)
# Concatenate old points + new points
self.points = np.vstack([self.points, points[1:]])
return self
def offset(self, offset: float | Callable[..., float] = 0):
"""Offsets Path so that it follows the Path centerline plus an offset.
The offset can either be a fixed value, or a function
of the form my_offset(t) where t goes from 0->1
Args:
offset: int or float, callable. Magnitude of the offset
"""
if offset == 0:
points = self.points
start_angle = self.start_angle
end_angle = self.end_angle
elif callable(offset):
# Compute lengths
dx = np.diff(self.points[:, 0])
dy = np.diff(self.points[:, 1])
lengths = np.cumsum(np.sqrt((dx) ** 2 + (dy) ** 2))
lengths = np.concatenate([[0], lengths])
# Create list of offset points and perform offset
points = self._centerpoint_offset_curve(
self.points,
offset_distance=offset(lengths / lengths[-1]),
start_angle=self.start_angle,
end_angle=self.end_angle,
)
# Numerically compute start and end angles
tol = 1e-6
ds = tol / lengths[-1]
ny1 = offset(ds) - offset(0)
start_angle = np.arctan2(-ny1, tol) / np.pi * 180 + self.start_angle
# start_angle = np.round(start_angle, decimals=6)
ny2 = offset(1) - offset(1 - ds)
end_angle = np.arctan2(-ny2, tol) / np.pi * 180 + self.end_angle
# end_angle = np.round(end_angle, decimals=6)
else: # Offset is just a number
points = self._centerpoint_offset_curve(
self.points,
offset_distance=offset,
start_angle=self.start_angle,
end_angle=self.end_angle,
)
start_angle = self.start_angle
end_angle = self.end_angle
self.points = points
self.start_angle = start_angle
self.end_angle = end_angle
return self
def move(self, origin=(0, 0), destination=None, axis=None):
"""Moves the Path from the origin point to the destination.
Both origin and destination can be 1x2 array-like or a Port.
Args:
origin : array-like[2], Port Origin point of the move.
destination : array-like[2], Port Destination point of the move.
axis : {'x', 'y'} Direction of move.
"""
dx, dy = _parse_move(origin, destination, axis)
self.points += np.array([dx, dy])
return self
def rotate(self, angle: float = 45, center: Float2 | None = (0, 0)):
"""Rotates all Polygons in the Component around the specified center point.
If no center point specified will rotate around (0,0).
Args:
angle: Angle to rotate the Component in degrees.
center: array-like[2] or None. component of the Component.
"""
if angle == 0:
return self
self.points = _rotate_points(self.points, angle, center)
if self.start_angle is not None:
self.start_angle = mod(self.start_angle + angle, 360)
if self.end_angle is not None:
self.end_angle = mod(self.end_angle + angle, 360)
return self
def mirror(self, p1: Float2 = (0, 1), p2: Float2 = (0, 0)):
"""Mirrors the Path across the line formed between the two specified points.
``points`` may be input as either single points [1,2]
or array-like[N][2], and will return in kind.
Args:
p1: First point of the line.
p2: Second point of the line.
"""
self.points = _reflect_points(self.points, p1, p2)
angle = np.arctan2((p2[1] - p1[1]), (p2[0] - p1[0])) * 180 / pi
if self.start_angle is not None:
self.start_angle = mod(2 * angle - self.start_angle, 360)
if self.end_angle is not None:
self.end_angle = mod(2 * angle - self.end_angle, 360)
return self
def _centerpoint_offset_curve(
self, points, offset_distance, start_angle, end_angle
):
"""Creates a offset curve (but does not account for cusps etc)\
by computing the centerpoint offset of the supplied x and y points."""
new_points = np.array(points, dtype=np.float64)
dx = np.diff(points[:, 0])
dy = np.diff(points[:, 1])
theta = np.arctan2(dy, dx)
theta = np.concatenate([theta[:1], theta, theta[-1:]])
theta_mid = (np.pi + theta[1:] + theta[:-1]) / 2 # Mean angle between segments
dtheta_int = np.pi + theta[:-1] - theta[1:] # Internal angle between segments
offset_distance = offset_distance / np.sin(dtheta_int / 2)
new_points[:, 0] -= offset_distance * np.cos(theta_mid)
new_points[:, 1] -= offset_distance * np.sin(theta_mid)
if start_angle is not None:
new_points[0, :] = points[0, :] + (
np.sin(start_angle * np.pi / 180) * offset_distance[0],
-np.cos(start_angle * np.pi / 180) * offset_distance[0],
)
if end_angle is not None:
new_points[-1, :] = points[-1, :] + (
np.sin(end_angle * np.pi / 180) * offset_distance[-1],
-np.cos(end_angle * np.pi / 180) * offset_distance[-1],
)
return new_points
def _parametric_offset_curve(self, points, offset_distance, start_angle, end_angle):
"""Creates a parametric offset (does not account for cusps etc) \
by using gradient of the supplied x and y points."""
x = points[:, 0]
y = points[:, 1]
dxdt = np.gradient(x)
dydt = np.gradient(y)
if start_angle is not None:
dxdt[0] = np.cos(start_angle * np.pi / 180)
dydt[0] = np.sin(start_angle * np.pi / 180)
if end_angle is not None:
dxdt[-1] = np.cos(end_angle * np.pi / 180)
dydt[-1] = np.sin(end_angle * np.pi / 180)
x_offset = x + offset_distance * dydt / np.sqrt(dxdt**2 + dydt**2)
y_offset = y - offset_distance * dxdt / np.sqrt(dydt**2 + dxdt**2)
return np.array([x_offset, y_offset]).T
def length(self) -> float:
"""Return cumulative length."""
x = self.points[:, 0]
y = self.points[:, 1]
dx = np.diff(x)
dy = np.diff(y)
return np.sum(np.sqrt((dx) ** 2 + (dy) ** 2))
def curvature(self):
"""Calculates Path curvature.
The curvature is numerically computed so areas where the curvature
jumps instantaneously (such as between an arc and a straight segment)
will be slightly interpolated, and sudden changes in point density
along the curve can cause discontinuities.
Returns:
s: array-like[N] The arc-length of the Path
K: array-like[N] The curvature of the Path
"""
x = self.points[:, 0]
y = self.points[:, 1]
dx = np.diff(x)
dy = np.diff(y)
ds = np.sqrt((dx) ** 2 + (dy) ** 2)
s = np.cumsum(ds)
theta = np.arctan2(dy, dx)
# Fix discontinuities arising from np.arctan2
dtheta = np.diff(theta)
dtheta[np.where(dtheta > np.pi)] += -2 * np.pi
dtheta[np.where(dtheta < -np.pi)] += 2 * np.pi
theta = np.concatenate([[0], np.cumsum(dtheta)]) + theta[0]
K = np.gradient(theta, s, edge_order=2)
return s, K
def hash_geometry(self, precision: float = 1e-4) -> str:
"""Computes an SHA1 hash of the points in the Path and the start_angle and end_angle.
Args:
precision: Rounding precision for the the objects in the Component. For instance, \
a precision of 1e-2 will round a point at (0.124, 1.748) to (0.12, 1.75)
Returns:
str Hash result in the form of an SHA1 hex digest string.
.. code::
hash(
hash(First layer information: [layer1, datatype1]),
hash(Polygon 1 on layer 1 points: [(x1,y1),(x2,y2),(x3,y3)] ),
hash(Polygon 2 on layer 1 points: [(x1,y1),(x2,y2),(x3,y3),(x4,y4)] ),
hash(Polygon 3 on layer 1 points: [(x1,y1),(x2,y2),(x3,y3)] ),
hash(Second layer information: [layer2, datatype2]),
hash(Polygon 1 on layer 2 points: [(x1,y1),(x2,y2),(x3,y3),(x4,y4)] ),
hash(Polygon 2 on layer 2 points: [(x1,y1),(x2,y2),(x3,y3)] ),
)
"""
# A random offset which fixes common rounding errors intrinsic
# to floating point math. Example: with a precision of 0.1, the
# floating points 7.049999 and 7.050001 round to different values
# (7.0 and 7.1), but offset values (7.220485 and 7.220487) don't
magic_offset = 0.17048614
final_hash = hashlib.sha1()
points = (
np.ascontiguousarray(
(self.points / precision) + magic_offset, dtype=np.float64
)
.round()
.astype(np.int64)
)
final_hash.update(points)
angles = (
(
np.ascontiguousarray(
(self.start_angle, self.end_angle), dtype=np.float64
)
/ precision
)
.round()
.astype(np.int64)
)
final_hash.update(angles)
return final_hash.hexdigest()
@classmethod
def __get_validators__(cls):
"""For pydantic."""
yield cls._validate
@classmethod
def _validate(cls, v, validation_info):
"""Pydantic Path validator."""
assert isinstance(v, Path), f"TypeError, Got {type(v)}, expecting Path"
return v
def to_dict(self) -> dict[str, str]:
return dict(hash=self.hash_geometry())
def plot(self) -> None:
"""Plot path in matplotlib.
.. plot::
:include-source:
import gdsfactory as gf
p = gf.path.euler(radius=10)
p.plot()
"""
from gdsfactory.quickplotter import quickplot
return quickplot(self)
def extrude(
self,
cross_section: CrossSectionSpec | None = None,
layer: LayerSpec | None = None,
width: float | None = None,
simplify: float | None = None,
shear_angle_start: float | None = None,
shear_angle_end: float | None = None,
**kwargs,
) -> Component:
"""Returns Component by extruding a Path with a CrossSection.
A path can be extruded using any CrossSection returning a Component
The CrossSection defines the layer numbers, widths and offsets.
Args:
cross_section: to extrude.
layer: optional layer.
width: optional width in um.
simplify: Tolerance value for the simplification algorithm. \
All points that can be removed without changing the resulting polygon\
by more than the value listed here will be removed.
shear_angle_start: an optional angle to shear the starting face by (in degrees).
shear_angle_end: an optional angle to shear the ending face by (in degrees).
Keyword Args:
Supplied to :func:`gf.cell`.
.. plot::
:include-source:
import gdsfactory as gf
p = gf.path.euler(radius=10)
c = p.extrude(layer=(1, 0), width=0.5)
c.plot()
"""
return extrude(
p=self,
cross_section=cross_section,
layer=layer,
width=width,
simplify=simplify,
shear_angle_start=shear_angle_start,
shear_angle_end=shear_angle_end,
**kwargs,
)
def copy(self):
"""Returns a copy of the Path."""
p = Path()
p.info = self.info.copy()
p.points = np.array(self.points)
p.start_angle = self.start_angle
p.end_angle = self.end_angle
return p
PathFactory = Callable[..., Path]
def _sinusoidal_transition(y1, y2):
dy = y2 - y1
def sine(t):
return y1 + (1 - np.cos(np.pi * t)) / 2 * dy
return sine
def _parabolic_transition(y1, y2):
dy = y2 - y1
def parabolic(t):
return y1 + np.sqrt(t) * dy
return parabolic
def _linear_transition(y1, y2):
dy = y2 - y1
def linear(t):
return y1 + t * dy
return linear
def transition_exponential(y1, y2, exp=0.5):
"""Returns the function for an exponential transition.
Args:
y1: start width in um.
y2: end width in um.
exp: exponent.
"""
def exponential(t):
return y1 + (y2 - y1) * t**exp
return exponential
adiabatic_polyfit_TE1550SOI_220nm = np.array(
[
1.02478963e-09,
-8.65556534e-08,
3.32415694e-06,
-7.68408985e-05,
1.19282177e-03,
-1.31366332e-02,
1.05721429e-01,
-6.31057637e-01,
2.80689677e00,
-9.26867694e00,
2.24535191e01,
-3.90664800e01,
4.71899278e01,
-3.74726005e01,
1.77381560e01,
-1.12666286e00,
]
)
def transition_adiabatic(
w1: float,
w2: float,
neff_w,
wavelength: float = 1.55,
alpha: float = 1,
max_length: float = 200,
num_points_ODE: int = 2000,
):
"""Returns the points for an optimal adiabatic transition for well-guided modes.
Args:
w1: start width in um.
w2: end width in um.
neff_w: a callable that returns the effective index as a function of width. \
By default, use a compact model of neff(y) for fundamental 1550 nm TE \
mode of 220nm-thick core with 3.45 index, fully clad with 1.44 index.\
Many coefficients are needed to capture the behaviour.
wavelength: wavelength, in same units as widths
alpha: parameter that scales the rate of width change
- closer to 0 means longer and more adiabatic;
- 1 is the intuitive limit beyond which higher order modes are excited;
- [2] reports good performance up to 1.4 for fundamental TE in SOI (for multiple core thicknesses)
max_length: maximum length in um.
num_points_ODE: number of samplings points for the ODE solve.
References:
[1] Burns, W. K., et al. "Optical waveguide parabolic coupling horns."
Appl. Phys. Lett., vol. 30, no. 1, 1 Jan. 1977, pp. 28-30, doi:10.1063/1.89199.
[2] Fu, Yunfei, et al. "Efficient adiabatic silicon-on-insulator waveguide taper."
Photonics Res., vol. 2, no. 3, 1 June 2014, pp. A41-A44, doi:10.1364/PRJ.2.000A41.
"""
from scipy.integrate import odeint
# Define ODE
def dWdx(w, x, neff_w, wavelength, alpha):
return alpha * wavelength / (neff_w(w) * w)
# Parse input
if w2 < w1:
wmin = w2
wmax = w1
order = -1
else:
wmin = w1
wmax = w2
order = 1
# Solve ODE
x = np.linspace(0, max_length, num_points_ODE)
sol = odeint(dWdx, wmin, x, args=(neff_w, wavelength, alpha))
# Extract optimal curve
xs = x[np.where(sol[:, 0] < wmax)]
ws = sol[:, 0][np.where(sol[:, 0] < wmax)]
return xs, ws[::order]
[docs]
def transition(
cross_section1: CrossSectionSpec,
cross_section2: CrossSectionSpec,
width_type: WidthTypes | Callable = "sine",
) -> Transition:
"""Returns a smoothly-transitioning between two CrossSections.
Only cross-sectional elements that have the `name` (as in X.add(..., name = 'wg') )
parameter specified in both input CrossSections will be created.
Port names will be cloned from the input CrossSections in reverse.
Args:
cross_section1: First CrossSection.
cross_section2: Second CrossSection.
width_type: sine or linear. type of width transition used if any widths \
are different between the two input CrossSections.
"""
from gdsfactory.pdk import get_cross_section, get_layer
X1 = get_cross_section(cross_section1)
X2 = get_cross_section(cross_section2)
layers1 = {get_layer(section.layer) for section in X1.sections}
layers2 = {get_layer(section.layer) for section in X2.sections}
layers1.add(get_layer(X1.layer))
layers2.add(get_layer(X2.layer))
has_common_layers = bool(layers1.intersection(layers2))
if not has_common_layers:
raise ValueError(
f"transition() found no common layers X1 {layers1} and X2 {layers2}"
)
return Transition(
cross_section1=X1,
cross_section2=X2,
width_type=width_type,
)
@cell
def along_path(
p: Path,
component: ComponentSpec,
spacing: float,
padding: float,
) -> Component:
"""Returns Component containing many copies of `component` along `p`.
Places as many copies of `component` along each segment of `p` as possible
under the given constraints. `spacing` is always followed precisely, but
actual `padding` may exceed the provided value to place components evenly.
Args:
p: Path to place components along.
component: Component to repeat along the path. The unrotated version of \
this object should be oriented for placement on a horizontal line.
spacing: distance between component placements.
padding: minimum distance from the path start to the first component.
"""
from gdsfactory.pdk import get_component
component = get_component(component)
length = p.length()
number = (length - 2 * padding) // spacing + 1
c = Component()
cum_dist = 0
next_component = (length - (number - 1) * spacing) / 2
stop = length - next_component
# Prepare in advance the rotation angle for each segment
angle_list = [
np.rad2deg(
np.arctan2(
(p.points[i + 1] - p.points[i])[1], (p.points[i + 1] - p.points[i])[0]
)
)
for i in range(len(p.points) - 1)
]
for i, start_pt in enumerate(p.points[:-1]):
end_pt = p.points[i + 1]
segment_vector = end_pt - start_pt
segment_length = np.linalg.norm(segment_vector)
unit_vector = segment_vector / segment_length
# Get the pre-calculated angle for this segment
angle = angle_list[i]
while next_component <= cum_dist + segment_length and next_component <= stop:
added_dist = next_component - cum_dist
offset = added_dist * unit_vector
component_ref = c << component
component_ref.rotate(angle).move(start_pt + offset)
next_component += spacing
cum_dist += segment_length
return c
@cell
def extrude(
p: Path,
cross_section: CrossSectionSpec | None = None,
layer: LayerSpec | None = None,
width: float | None = None,
simplify: float | None = None,
shear_angle_start: float | None = None,
shear_angle_end: float | None = None,
allow_offgrid: bool | None = None,
snap_to_grid: bool = False,
add_bbox: bool = True,
) -> Component:
"""Returns Component extruding a Path with a cross_section.
A path can be extruded using any CrossSection returning a Component
The CrossSection defines the layer numbers, widths and offsets
Args:
p: a path is a list of points (arc, straight, euler).
cross_section: to extrude.
layer: optional layer to extrude.
width: optional width to extrude.
simplify: Tolerance value for the simplification algorithm. \
All points that can be removed without changing the resulting polygon \
by more than the value listed here will be removed.
shear_angle_start: an optional angle to shear the starting face by (in degrees).
shear_angle_end: an optional angle to shear the ending face by (in degrees).
add_pins: if True adds pins to the ports of the component according to `cross_section`.
add_bbox: if True adds a bounding box to the component.
"""
from gdsfactory.pdk import (
get_cross_section,
get_layer,
)
if allow_offgrid is None:
allow_offgrid = CONF.allow_offgrid
if cross_section is None and layer is None:
raise ValueError("CrossSection or layer needed")
if cross_section is not None and layer is not None:
raise ValueError("Define only CrossSection or layer")
if layer is not None and width is None:
raise ValueError("Need to define layer width")
elif width:
s = Section(
width=width,
layer=layer,
port_names=("o1", "o2"),
port_types=("optical", "optical"),
)
cross_section = CrossSection(sections=(s,))
xsection_points = []
c = Component()
x = get_cross_section(cross_section)
if isinstance(x, Transition):
return extrude_transition(
p,
transition=x,
shear_angle_start=shear_angle_start,
shear_angle_end=shear_angle_end,
)
for section in x.sections:
p_sec = p.copy()
width = snap_to_grid2x(section.width)
offset = section.offset
layer = get_layer(section.layer)
port_names = section.port_names
port_types = section.port_types
hidden = section.hidden
width_function = section.width_function
offset_function = section.offset_function
if isinstance(width, int | float) and isinstance(offset, int | float):
xsection_points.append([width, offset])
if isinstance(layer, int):
layer = (layer, 0)
if (
isinstance(layer, Iterable)
and len(layer) == 2
and isinstance(layer[0], int)
and isinstance(layer[1], int)
):
xsection_points.append([layer[0], layer[1]])
if section.insets and section.insets != (0, 0):
p_pts = p_sec.points
new_x_start = p.xmin + section.insets[0]
new_x_stop = p.xmax - section.insets[1]
if new_x_start > np.max(p_pts[:, 0]) or new_x_stop < np.min(p_pts[:, 0]):
warnings.warn(
f"Cannot apply delay to Section '{section.name}', delay results in points outside of original path.",
stacklevel=3,
)
continue
new_start_idx = np.argwhere(p_pts[:, 0] > new_x_start)[0, 0]
new_stop_idx = np.argwhere(p_pts[:, 0] < new_x_stop)[-1, 0]
new_start_point = [new_x_start, p_pts[new_start_idx, 1]]
new_stop_point = [new_x_stop, p_pts[new_stop_idx, 1]]
p_sec = Path(
[new_start_point, *p_pts[new_start_idx:new_stop_idx], new_stop_point]
)
if callable(offset_function):
p_sec.offset(offset_function)
offset = 0
end_angle = p_sec.end_angle
start_angle = p_sec.start_angle
points = p_sec.points
if callable(width_function):
# Compute lengths
dx = np.diff(p_sec.points[:, 0])
dy = np.diff(p_sec.points[:, 1])
lengths = np.cumsum(np.sqrt(dx**2 + dy**2))
lengths = np.concatenate([[0], lengths])
width = width_function(lengths / lengths[-1])
dy = offset + width / 2
# _points = _shear_face(points, dy, shear_angle_start, shear_angle_end)
points1 = p_sec._centerpoint_offset_curve(
points,
offset_distance=dy,
start_angle=start_angle,
end_angle=end_angle,
)
dy = offset - width / 2
# _points = _shear_face(points, dy, shear_angle_start, shear_angle_end)
points2 = p_sec._centerpoint_offset_curve(
points,
offset_distance=dy,
start_angle=start_angle,
end_angle=end_angle,
)
if shear_angle_start or shear_angle_end:
_face_angle_start = (
start_angle + shear_angle_start - 90 if shear_angle_start else None
)
_face_angle_end = (
end_angle + shear_angle_end + 90 if shear_angle_end else None
)
points1 = _cut_path_with_ray(
start_point=points[0],
start_angle=_face_angle_start,
end_point=points[-1],
end_angle=_face_angle_end,
path=points1,
)
points2 = _cut_path_with_ray(
start_point=points[0],
start_angle=_face_angle_start,
end_point=points[-1],
end_angle=_face_angle_end,
path=points2,
)
# angle = start_angle + shear_angle_start + 90
# points2 = _cut_path_with_ray(points[0], angle, points2, start=True)
# Simplify lines using the Ramer–Douglas–Peucker algorithm
if isinstance(simplify, bool):
raise ValueError("simplify argument must be a number (e.g. 1e-3) or None")
with_simplify = section.simplify or simplify
if with_simplify:
points1 = _simplify(points1, tolerance=with_simplify)
points2 = _simplify(points2, tolerance=with_simplify)
# Join points together
points_poly = np.concatenate([points1, points2[::-1, :]])
if snap_to_grid:
points_poly = np.round(points_poly, 3)
layers = layer if hidden else [layer, layer]
if not hidden and p_sec.length() >= 1e-3:
c.add_polygon(points_poly, layer=layer)
# Add port_names if they were specified
if port_names[0] is not None:
port_width = width if np.isscalar(width) else width[0]
port_orientation = (p_sec.start_angle + 180) % 360
center = np.average([points1[0], points2[0]], axis=0)
face = [points1[0], points2[0]]
face = [_rotated_delta(point, center, port_orientation) for point in face]
c.add_port(
port=Port(
name=port_names[0],
layer=get_layer(layers[0]),
port_type=port_types[0],
width=port_width,
orientation=port_orientation,
center=center,
cross_section=x,
shear_angle=shear_angle_start,
allow_offgrid=allow_offgrid,
)
)
# port1.info["face"] = face
if port_names[1] is not None:
port_width = width if np.isscalar(width) else width[-1]
port_orientation = (p_sec.end_angle) % 360
center = np.average([points1[-1], points2[-1]], axis=0)
face = [points1[-1], points2[-1]]
face = [_rotated_delta(point, center, port_orientation) for point in face]
c.add_port(
port=Port(
name=port_names[1],
layer=get_layer(layers[1]),
port_type=port_types[1],
width=port_width,
center=center,
orientation=port_orientation,
cross_section=x,
shear_angle=shear_angle_end,
allow_offgrid=allow_offgrid,
)
)
# port2.info["face"] = face
c.info["length"] = float(np.round(p.length(), 3))
for via in x.components_along_path:
if via.offset:
points_offset = p._centerpoint_offset_curve(
points,
offset_distance=via.offset,
start_angle=start_angle,
end_angle=end_angle,
)
_p = Path(points_offset)
else:
_p = p
_ = c << along_path(
p=_p, component=via.component, spacing=via.spacing, padding=via.padding
)
if add_bbox:
x.add_bbox(c)
return c
def _get_named_sections(sections: tuple[Section, ...]) -> dict[str, Section]:
from gdsfactory.pdk import get_layer
named_sections = {}
for section in sections:
name = section.name or get_layer(section.layer)
if name in named_sections:
raise ValueError(
f"Duplicate name or layer '{name}' of section used for cross-section in transition. Cross-sections with multiple Sections for a single layer must have unique names for each section"
)
named_sections[name] = section
return named_sections
@cell
def extrude_transition(
p: Path,
transition: Transition,
shear_angle_start: float | None = None,
shear_angle_end: float | None = None,
) -> Component:
"""Extrudes a path along a transition.
Args:
p: path to extrude.
transition: transition to extrude along.
shear_angle_start: angle to shear the start of the path.
shear_angle_end: angle to shear the end of the path.
"""
from gdsfactory.pdk import get_cross_section, get_layer
c = Component()
x1 = get_cross_section(transition.cross_section1)
x2 = get_cross_section(transition.cross_section2)
width_type = transition.width_type
# if named, prefer name over layer
named_sections1 = _get_named_sections(x1.sections)
named_sections2 = _get_named_sections(x2.sections)
names1 = list(named_sections1.keys())
names2 = list(named_sections2.keys())
common_sections = set(names1).intersection(names2)
if len(common_sections) == 0:
raise ValueError(
f"transition() found no common layers X1 {names1} and X2 {names2}"
)
for section_name in common_sections:
section1 = named_sections1[section_name]
section2 = named_sections2[section_name]
port_names = section1.port_names
port_types = section1.port_types
p_sec = p.copy()
offset1 = section1.offset
offset2 = section2.offset
width1 = section1.width
width2 = section2.width
section1_layer = get_layer(section1.layer)
section2_layer = get_layer(section2.layer)
if callable(offset1):
offset1 = offset1(1)
if callable(offset2):
offset2 = offset2(0)
if callable(width1):
width1 = width1(1)
if callable(width2):
width2 = width2(0)
offset = _sinusoidal_transition(offset1, offset2)
if width_type == "linear":
width = _linear_transition(width1, width2)
elif width_type == "sine":
width = _sinusoidal_transition(width1, width2)
elif width_type == "parabolic":
width = _parabolic_transition(width1, width2)
elif callable(width_type):
def width_func(t):
return width_type(t, width1, width2) # noqa: B023
width = width_func
else:
raise ValueError(
f"width_type={width_type!r} must be {'sine','linear','parabolic'}, or a Callable w(t, width1, width2) returning the transition profile as a function of path position t."
)
if section1_layer != section2_layer:
hidden = True
layer1 = get_layer(section1_layer)
layer2 = get_layer(section2_layer)
layer = (layer1, layer2)
else:
hidden = False
layer = get_layer(section1_layer)
p_sec.offset(offset)
offset = 0
end_angle = p_sec.end_angle
start_angle = p_sec.start_angle
points = p_sec.points
if callable(width):
# Compute lengths
dx = np.diff(p_sec.points[:, 0])
dy = np.diff(p_sec.points[:, 1])
lengths = np.cumsum(np.sqrt(dx**2 + dy**2))
lengths = np.concatenate([[0], lengths])
width = width(lengths / lengths[-1])
dy = offset + width / 2
# _points = _shear_face(points, dy, shear_angle_start, shear_angle_end)
points1 = p_sec._centerpoint_offset_curve(
points,
offset_distance=dy,
start_angle=start_angle,
end_angle=end_angle,
)
dy = offset - width / 2
# _points = _shear_face(points, dy, shear_angle_start, shear_angle_end)
points2 = p_sec._centerpoint_offset_curve(
points,
offset_distance=dy,
start_angle=start_angle,
end_angle=end_angle,
)
if shear_angle_start or shear_angle_end:
_face_angle_start = (
start_angle + shear_angle_start - 90 if shear_angle_start else None
)
_face_angle_end = (
end_angle + shear_angle_end + 90 if shear_angle_end else None
)
points1 = _cut_path_with_ray(
start_point=points[0],
start_angle=_face_angle_start,
end_point=points[-1],
end_angle=_face_angle_end,
path=points1,
)
points2 = _cut_path_with_ray(
start_point=points[0],
start_angle=_face_angle_start,
end_point=points[-1],
end_angle=_face_angle_end,
path=points2,
)
with_simplify = section1.simplify and section2.simplify
if with_simplify:
tolerance = min([section1.simplify, section2.simplify])
points1 = _simplify(points1, tolerance=tolerance)
points2 = _simplify(points2, tolerance=tolerance)
# Join points together
points_poly = np.concatenate([points1, points2[::-1, :]])
layers = layer if hidden else [layer, layer]
if not hidden and p_sec.length() > 1e-3:
c.add_polygon(points_poly, layer=layer)
# Add port_names if they were specified
if port_names[0] is not None:
port_width = width1
port_orientation = (p_sec.start_angle + 180) % 360
center = points[0]
face = [points1[0], points2[0]]
face = [_rotated_delta(point, center, port_orientation) for point in face]
c.add_port(
port=Port(
name=port_names[0],
layer=get_layer(layers[0]),
port_type=port_types[0],
width=port_width,
orientation=port_orientation,
center=center,
cross_section=x1,
shear_angle=shear_angle_start,
)
)
# port1.info["face"] = face
if port_names[1] is not None:
port_width = width2
port_orientation = (p_sec.end_angle) % 360
center = points[-1]
face = [points1[-1], points2[-1]]
face = [_rotated_delta(point, center, port_orientation) for point in face]
c.add_port(
port=Port(
name=port_names[1],
layer=get_layer(layers[1]),
port_type=port_types[1],
width=port_width,
center=center,
orientation=port_orientation,
cross_section=x2,
shear_angle=shear_angle_end,
)
)
# port2.info["face"] = face
c.info["length"] = float(np.round(p.length(), 3))
return c
def _rotated_delta(
point: np.ndarray, center: np.ndarray, orientation: float
) -> np.ndarray:
"""Gets the rotated distance of a point from a center.
Args:
point: the initial point.
center: a center point to use as a reference.
orientation: the rotation, in degrees.
Returns: the normalized delta between the point and center, accounting for rotation
"""
ca = np.cos(orientation * np.pi / 180)
sa = np.sin(orientation * np.pi / 180)
rot_mat = np.array([[ca, -sa], [sa, ca]])
delta = point - center
return np.dot(delta, rot_mat)
def _cut_path_with_ray(
start_point: np.ndarray,
start_angle: float | None,
end_point: np.ndarray,
end_angle: float | None,
path: np.ndarray,
) -> np.ndarray:
"""Cuts or extends a path given a point and angle to project."""
import shapely.geometry as sg
import shapely.ops
# a distance to approximate infinity to find ray-segment intersections
far_distance = 10000
path_cmp = np.copy(path)
# pad start
dp = path[0] - path[1]
d_ext = far_distance / np.sqrt(np.sum(dp**2)) * np.array([dp[0], dp[1]])
path_cmp[0] += d_ext
# pad end
dp = path[-1] - path[-2]
d_ext = far_distance / np.sqrt(np.sum(dp**2)) * np.array([dp[0], dp[1]])
path_cmp[-1] += d_ext
intersections = [sg.Point(path[0]), sg.Point(path[-1])]
distances = []
ls = sg.LineString(path_cmp)
for i, angle, point in [(0, start_angle, start_point), (1, end_angle, end_point)]:
if angle:
# get intersection
angle_rad = np.deg2rad(angle)
dx_far = np.cos(angle_rad) * far_distance
dy_far = np.sin(angle_rad) * far_distance
d_far = np.array([dx_far, dy_far])
ls_ray = sg.LineString([point - d_far, point + d_far])
intersection = ls.intersection(ls_ray)
if not isinstance(intersection, sg.Point):
if not isinstance(intersection, sg.MultiPoint):
raise ValueError(
f"Expected intersection to be a point, but got {intersection}"
)
_, nearest = shapely.ops.nearest_points(sg.Point(point), intersection)
intersection = nearest
intersections[i] = intersection
else:
intersection = intersections[i]
distance = ls.project(intersection)
distances.append(distance)
# when trimming the start, start counting at the intersection point, then
# add all subsequent points
points = [np.array(intersections[0].coords[0])]
for point in path[1:-1]:
if distances[0] < ls.project(sg.Point(point)) < distances[1]:
points.append(point)
points.append(np.array(intersections[1].coords[0]))
return np.array(points)
[docs]
def arc(
radius: float = 10.0,
angle: float = 90,
npoints: int | None = None,
start_angle: float | None = -90,
) -> Path:
"""Returns a radial arc.
Args:
radius: minimum radius of curvature.
angle: total angle of the curve.
npoints: Number of points used per 360 degrees. Defaults to pdk.bend_points_distance.
start_angle: initial angle of the curve for drawing, default -90 degrees.
.. plot::
:include-source:
import gdsfactory as gf
p = gf.path.arc(radius=10, angle=45)
p.plot()
"""
from gdsfactory.pdk import get_active_pdk
PDK = get_active_pdk()
npoints = npoints or abs(int(angle / 360 * radius / PDK.bend_points_distance / 2))
npoints = max(int(npoints), int(360 / angle) + 1)
t = np.linspace(
start_angle * np.pi / 180, (angle + start_angle) * np.pi / 180, npoints
)
x = radius * np.cos(t)
y = radius * (np.sin(t) + 1)
points = np.array((x, y)).T * np.sign(angle)
P = Path()
# Manually add points & adjust start and end angles
P.points = points
P.start_angle = start_angle + 90
P.end_angle = start_angle + angle + 90
return P
def _cumtrapz(x):
"""Numpy-based implementation of the cumulative trapezoidal integration \
function usually found in scipy (scipy.integrate.cumtrapz)."""
return np.cumsum((x[1:] + x[:-1]) / 2)
def _fresnel(R0, s, num_pts, n_iter=8):
"""Fresnel integral using a series expansion."""
t = np.linspace(0, s / (np.sqrt(2) * R0), num_pts)
x = np.zeros(num_pts)
y = np.zeros(num_pts)
for n in range(n_iter):
x += (-1) ** n * t ** (4 * n + 1) / (math.factorial(2 * n) * (4 * n + 1))
y += (-1) ** n * t ** (4 * n + 3) / (math.factorial(2 * n + 1) * (4 * n + 3))
return np.array([np.sqrt(2) * R0 * x, np.sqrt(2) * R0 * y])
[docs]
def euler(
radius: float = 10,
angle: float = 90,
p: float = 0.5,
use_eff: bool = False,
npoints: int | None = None,
) -> Path:
"""Returns an euler bend that adiabatically transitions from straight to curved.
`radius` is the minimum radius of curvature of the bend.
However, if `use_eff` is set to True, `radius` corresponds to the effective
radius of curvature (making the curve a drop-in replacement for an arc).
If p < 1.0, will create a "partial euler" curve as described in Vogelbacher et. al.
https://dx.doi.org/10.1364/oe.27.031394
Args:
radius: minimum radius of curvature.
angle: total angle of the curve.
p: Proportion of the curve that is an Euler curve.
use_eff: If False: `radius` is the minimum radius of curvature of the bend. \
If True: The curve will be scaled such that the endpoints match an \
arc with parameters `radius` and `angle`.
npoints: Number of points used per 360 degrees.
.. plot::
:include-source:
import gdsfactory as gf
p = gf.path.euler(radius=10, angle=45, p=1, use_eff=True, npoints=720)
p.plot()
"""
from gdsfactory.pdk import get_active_pdk
if (p < 0) or (p > 1):
raise ValueError("euler requires argument `p` be between 0 and 1")
if p == 0:
P = arc(radius=radius, angle=angle, npoints=npoints)
P.info["Reff"] = radius
P.info["Rmin"] = radius
return P
if angle < 0:
mirror = True
angle = np.abs(angle)
else:
mirror = False
R0 = 1
alpha = np.radians(angle)
Rp = R0 / (np.sqrt(p * alpha))
sp = R0 * np.sqrt(p * alpha)
s0 = 2 * sp + Rp * alpha * (1 - p)
pdk = get_active_pdk()
npoints = npoints or abs(int(angle / 360 * radius / pdk.bend_points_distance / 2))
npoints = max(npoints, int(360 / angle) + 1)
num_pts_euler = int(np.round(sp / (s0 / 2) * npoints))
num_pts_arc = npoints - num_pts_euler
# Ensure a minimum of 2 points for each euler/arc section
if npoints <= 2:
num_pts_euler = 0
num_pts_arc = 2
if num_pts_euler > 0:
xbend1, ybend1 = _fresnel(R0, sp, num_pts_euler)
xp, yp = xbend1[-1], ybend1[-1]
dx = xp - Rp * np.sin(p * alpha / 2)
dy = yp - Rp * (1 - np.cos(p * alpha / 2))
else:
xbend1 = ybend1 = np.asfarray([])
dx = 0
dy = 0
s = np.linspace(sp, s0 / 2, num_pts_arc)
xbend2 = Rp * np.sin((s - sp) / Rp + p * alpha / 2) + dx
ybend2 = Rp * (1 - np.cos((s - sp) / Rp + p * alpha / 2)) + dy
x = np.concatenate([xbend1, xbend2[1:]])
y = np.concatenate([ybend1, ybend2[1:]])
points1 = np.array([x, y]).T
points2 = np.flipud(np.array([x, -y]).T)
points2 = _rotate_points(points2, angle - 180)
points2 += -points2[0, :] + points1[-1, :]
points = np.concatenate([points1[:-1], points2])
# Find y-axis intersection point to compute Reff
start_angle = 180 * (angle < 0)
end_angle = start_angle + angle
dy = np.tan(np.radians(end_angle - 90)) * points[-1][0]
Reff = points[-1][1] - dy
Rmin = Rp
# Fix degenerate condition at angle == 180
if np.abs(180 - angle) < 1e-3:
Reff = points[-1][1] / 2
# Scale curve to either match Reff or Rmin
scale = radius / Reff if use_eff else radius / Rmin
points *= scale
P = Path()
# Manually add points & adjust start and end angles
P.points = points
P.start_angle = start_angle
P.end_angle = end_angle
P.info["Reff"] = Reff * scale
P.info["Rmin"] = Rmin * scale
if mirror:
P.mirror((1, 0))
return P
[docs]
def straight(
length: float = 10.0, npoints: int = 2, snap_to_grid: bool = False
) -> Path:
"""Returns a straight path.
For transitions you should increase have at least 100 points
Args:
length: of straight.
npoints: number of points.
snap_to_grid: snap to grid.
"""
if snap_to_grid:
length = snap_to_grid2x(length)
if length < 0:
raise ValueError(f"length = {length} needs to be > 0")
x = np.linspace(0, length, npoints)
y = x * 0
points = np.array((x, y)).T
p = Path()
p.append(points)
return p
[docs]
def spiral_archimedean(
min_bend_radius: float, separation: float, number_of_loops: float, npoints: int
) -> Path:
"""Returns an Archimedean spiral.
Args:
min_bend_radius: Inner radius of the spiral.
separation: Separation between the loops in um.
number_of_loops: number of loops.
npoints: number of Points.
.. plot::
:include-source:
import gdsfactory as gf
p = gf.path.spiral_archimedean(min_bend_radius=5, separation=2, number_of_loops=3, npoints=200)
p.plot()
"""
return Path(
[
(separation / np.pi * theta + min_bend_radius)
* np.array((np.sin(theta), np.cos(theta)))
for theta in np.linspace(0, number_of_loops * 2 * np.pi, npoints)
]
)
def _compute_segments(points):
points = np.asfarray(points)
normals = np.diff(points, axis=0)
normals = (normals.T / np.linalg.norm(normals, axis=1)).T
dx = np.diff(points[:, 0])
dy = np.diff(points[:, 1])
ds = np.sqrt(dx**2 + dy**2)
theta = np.degrees(np.arctan2(dy, dx))
dtheta = np.diff(theta)
dtheta = dtheta - 360 * np.floor((dtheta + 180) / 360)
return points, normals, ds, theta, dtheta
[docs]
def smooth(
points: Coordinates,
radius: float = 4.0,
bend: PathFactory = euler,
**kwargs,
) -> Path:
"""Returns a smooth Path from a series of waypoints.
Args:
points: array-like[N][2] List of waypoints for the path to follow.
radius: radius of curvature, passed to `bend`.
bend: bend function that returns a path that round corners.
kwargs: Extra keyword arguments that will be passed to `bend`.
.. plot::
:include-source:
import gdsfactory as gf
p = gf.path.smooth(([0, 0], [0, 10], [10, 10]))
p.plot()
"""
if isinstance(points, Path):
points = points.points
points, normals, ds, theta, dtheta = _compute_segments(points)
colinear_elements = np.concatenate([[False], np.abs(dtheta) < 1e-6, [False]])
if np.any(colinear_elements):
new_points = points[~colinear_elements, :]
points, normals, ds, theta, dtheta = _compute_segments(new_points)
if np.any(np.abs(np.abs(dtheta) - 180) < 1e-6):
raise ValueError(
"smooth() received points which double-back on themselves"
"--turns cannot be computed when going forwards then exactly backwards."
)
# FIXME add caching
# Create arcs
paths = []
radii = []
for dt in dtheta:
P = bend(radius=radius, angle=dt, **kwargs)
chord = np.linalg.norm(P.points[-1, :] - P.points[0, :])
r = (chord / 2) / np.sin(np.radians(dt / 2))
r = np.abs(r)
radii.append(r)
paths.append(P)
d = np.abs(np.array(radii) / np.tan(np.radians(180 - dtheta) / 2))
encroachment = np.concatenate([[0], d]) + np.concatenate([d, [0]])
if np.any(encroachment > ds):
raise ValueError(
"smooth(): Not enough distance between points to to fit curves."
"Try reducing the radius or spacing the points out farther"
)
p1 = points[1:-1, :] - normals[:-1, :] * d[:, np.newaxis]
# Move arcs into position
new_points = []
new_points.append([points[0, :]])
for n in range(len(dtheta)):
P = paths[n]
P.rotate(theta[n] - 0)
P.move(p1[n])
new_points.append(P.points)
new_points.append([points[-1, :]])
new_points = np.concatenate(new_points)
P = Path()
P.rotate(theta[0])
P.append(new_points)
P.move(points[0, :])
return P
__all__ = [
"Path",
"arc",
"along_path",
"euler",
"extrude",
"extrude_transition",
"smooth",
"spiral_archimedean",
"straight",
"transition",
"transition_adiabatic",
]
if __name__ == "__main__":
import gdsfactory as gf
P = gf.path.straight(length=10)
s0 = gf.Section(
width=0.415, offset=0, layer=(1, 0), name="core", port_names=("o1", "o2")
)
s1 = gf.Section(width=3, offset=0, layer=(3, 0), name="slab")
X1 = gf.CrossSection(sections=(s0, s1))
s2 = gf.Section(
width=0.5, offset=0, layer=(1, 0), name="core", port_names=("o1", "o2")
)
s3 = gf.Section(width=2.0, offset=0, layer=(3, 0), name="slab")
X2 = gf.CrossSection(sections=(s2, s3))
def width_type_function(t, w1, w2):
return w1 + (w2 - w1) * (t + 1) / 2
# t = gf.path.transition(X1, X2, width_type=width_type_function)
# c = gf.path.extrude(P, t, shear_angle_start=10, shear_angle_end=45)
# c = gf.path.extrude(P, t)
w1 = 1
w2 = 5
x1 = gf.get_cross_section("xs_sc", width=w1)
x2 = gf.get_cross_section("xs_sc", width=w2)
trans = gf.path.transition(
x1, x2, width_type=lambda t: width_type_function(t, w1, w2)
)
c = gf.components.bend_euler(radius=10, cross_section=trans)
# xs = gf.cross_section.pn(slab_inset=-0.2)
# c = gf.c.straight(cross_section=xs)
c.show(show_ports=True)
