gdstk.FlexPath

class gdstk.FlexPath(points, width, offset=0, joins='natural', ends='flush', bend_radius=0, bend_function=None, tolerance=1e-2, simple_path=False, scale_width=True, layer=0, datatype=0)

Flexible path creation.

FlexPath can be used to create single and multiple parallel paths with controlled widths and offsets. Joins and end caps can be customized freely and, if desired, bends can be automatically created to join path segments continuously.

Adjacent sections are expected to be joined smoothly when at least one of them is curved. If that condition cannot be met, gdstk.RobustPath should be used instead.

Parameters:

points – Single point or sequence of points that make up the path. Each point can be a pair of coordinates or a complex value.
width (number or sequence) – Width of the paths. If this is a sequence, its length defines the number of paths created.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path.
joins – Definition for the joins. One of “natural”, “miter”, “bevel”, “round”, “smooth”, or a callable. A callable must accept 6 arguments (end point and direction vector for each edge adjacent to the join, the center of the join, and the path width) and return a sequence of points that define the join shape.
ends – Definition for the end caps. One of “flush”, “extended”, “round”, “smooth”, a 2-tuple, or a callable. A 2-tuple defines the extension length on both ends of the path. A callable must accept 4 arguments (cap end point and direction for both path sides) and return a sequence of points that define the cap shape.
bend_radius (number or sequence) – If a positive number, path segments are joined by a bend shape (defaults to a circular arc) when possible.
bend_function (callable) – A callable that takes 4 arguments (radius, initial and final angles, and the bend center) and returns a sequence of points defining the bend shape.
tolerance – Tolerance used for calculating the polygonal approximation of the paths.
simple_path – If True, the paths will be stored as GDSII path elements. They require less memory, but do not support “smooth” or callable joins and end caps, or width changes along the path.
scale_width – If False, the path widths are not scaled when transforming this path.
layer – layer number assigned to this path.
datatype – data type number assigned to this path.

Notes

If width is a number and offset a sequence, the number of parallel paths is defined by the latter.

Arguments joins, ends, bend_radius, bend_function, layer, and datatype can also be lists with one definition for each path created.

Examples

>>> path = gdstk.FlexPath(
...     [(0, 5), (0, 0), (5, 0), (15, 10), (15, -5)],
...     [0.8, 0.8, 0.8, 0.8],
...     1.0,
...     joins=["natural", "bevel", "miter", "round"],
...     ends=["flush", "extended", (0.4, 0.8), "round"],
...     layer=[0, 1, 2, 3],
... )

>>> points = [(0, 8), (0, 0), (8, 0), (18, 13), (18, -8)]
>>> path_1 = gdstk.FlexPath(points , 1, datatype=1)
>>> path_2 = gdstk.FlexPath(points , 1, bend_radius=3)

>>> def custom_broken_join(p0, v0, p1, v1, center, width):
...     p0 = numpy.array(p0)
...     v0 = numpy.array(v0)
...     p1 = numpy.array(p1)
...     v1 = numpy.array(v1)
...     center = numpy.array(center)
...     # Calculate intersection point p between lines defined by
...     # p0 + u0 * v0 (for all u0) and p1 + u1 * v1 (for all u1)
...     den = v1[1] * v0[0] - v1[0] * v0[1]
...     lim = 1e-12 * ((v0[0] ** 2 + v0[1] ** 2) *
...                    (v1[0] ** 2 + v1[1] ** 2))
...     if den ** 2 < lim:
...         # Lines are parallel: use mid-point
...         u0 = u1 = 0
...         p = 0.5 * (p0 + p1)
...     else:
...         dx = p1[0] - p0[0]
...         dy = p1[1] - p0[1]
...         u0 = (v1[1] * dx - v1[0] * dy) / den
...         u1 = (v0[1] * dx - v0[0] * dy) / den
...         p = 0.5 * (p0 + v0 * u0 + p1 + v1 * u1)
...     if u0 <= 0 and u1 >= 0:
...         # Inner corner
...         return [p]
...     # Outer corner
...     return [p0, center, p1]
>>> def custom_pointy_end(p0, v0, p1, v1):
...     p0 = numpy.array(p0)
...     v0 = numpy.array(v0)
...     p1 = numpy.array(p1)
...     v1 = numpy.array(v1)
...     r = 0.5 * numpy.sqrt(numpy.sum((p0 - p1) ** 2))
...     v0 /= numpy.sqrt(numpy.sum(v0 ** 2))
...     v1 /= numpy.sqrt(numpy.sum(v1 ** 2))
...     return [p0, 0.5 * (p0 + p1) + 0.5 * (v0 - v1) * r, p1]
>>> path = gdstk.FlexPath(
...     [(0, 5), (0, 0), (5, 0), (15, 10), (15, -5)],
...     3,
...     joins=custom_broken_join,
...     ends=custom_pointy_end,
... )

Methods

`apply_repetition`()	Create new flexpaths based on this object's `repetition` attribute.
`arc`(radius, initial_angle, final_angle[, ...])	Append an elliptical arc to this path.
`bezier`(xy[, width, offset, relative])	Append a Bézier curve to this path.
`commands`(path_commands...)	Append sections to this path according to commands.
`copy`()	Create a copy this flexpath.
`cubic`(xy[, width, offset, relative])	Append cubic Bézier curves to this path.
`cubic_smooth`(xy[, width, offset, relative])	Append smooth cubic Bézier curves to this path.
`delete_gds_property`(attr)	Delete a GDSII property of this element.
`delete_property`(name)	Delete the first property of this element matching a name.
`get_gds_property`(attr)	Return a GDSII property of this element.
`get_property`(name)	Return the values of the first property of this element matching a name.
`horizontal`(x[, width, offset, relative])	Append horizontal segments to this path.
`interpolation`(points[, angles, tension_in, ...])	Append a smooth interpolating curve through the given points.
`mirror`(p1[, p2])	Mirror this path across the line through p1 and p2.
`offsets`()	Offsets of all paths at every point.
`parametric`(path_function[, width, offset, ...])	Append a parametric curve to this path.
`path_spines`()	Central spines of each parallel path.
`quadratic`(xy[, width, offset, relative])	Append quadratic Bézier curves to this path.
`quadratic_smooth`(xy[, width, offset, relative])	Append smooth quadratic Bézier curves to this path.
`rotate`(angle[, center])	Rotate this path.
`scale`(s[, center])	Scale this path.
`segment`(xy[, width, offset, relative])	Append straight segments to this path.
`set_bend_function`(*functions)	Set the bend function for all paths.
`set_bend_radius`(*radii)	Set the bend radius for all paths.
`set_datatypes`(*datatypes)	Set the datatypes for all paths.
`set_ends`(*ends)	Set the end types for all paths.
`set_gds_property`(attr, value)	Set a GDSII property for this element.
`set_joins`(*joins)	Set the end types for all paths.
`set_layers`(*layers)	Set the layers for all paths.
`set_property`(name, value)	Set a property for this element.
`spine`()	Central path spine.
`to_polygons`()	Calculate the polygonal representations of this path.
`translate`(dx[, dy])	Translate this path.
`turn`(radius, angle[, width, offset])	Append a circular turn to this path.
`vertical`(y[, width, offset, relative])	Append vertical segments to this path.
`widths`()	Widths of all paths at every point.

Attributes

`bend_function`	Bend function for each path.
`bend_radius`	Bend radius for each path.
`datatypes`	FlexPath data type.
`ends`	End types for each path.
`joins`	Join types for each path.
`layers`	FlexPath layer.
`num_paths`	Number of paths.
`properties`	Properties of this element.
`raith_data`	Raith electron beam lithography data.
`repetition`	Repetition associated with this element.
`scale_width`	Scale width flag.
`simple_path`	Simple path flag.
`size`	Number of points in the path spine.
`tolerance`	Path tolerance.

apply_repetition() → list

Create new flexpaths based on this object’s repetition attribute.

After the repetition is applied, the original attribute is set to None.

Returns:: Newly created objects.

arc(radius, initial_angle, final_angle, rotation=0, width=None, offset=None) → self

Append an elliptical arc to this path.

Parameters:

radius (number or sequence[2]) – Circular arc radius or elliptical arc radii.
initial_angle – Starting angle (in radians).
final_angle – Ending angle (in radians).
rotation – Arc rotation.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.

Examples

>>> path = gdstk.FlexPath((0, 0), [0.2, 0.3], 0.4, tolerance=1e-3)
>>> path.vertical(5)
>>> path.arc(2.5, numpy.pi, 0)
>>> path.arc(5, -numpy.pi, -numpy.pi / 2)

bend_function: Bend function for each path.

Notes

This attribute is read-only.

See also

gdstk.FlexPath.set_bend_function()

bend_radius: Bend radius for each path.

Notes

This attribute is read-only.

See also

gdstk.FlexPath.set_bend_radius()

bezier(xy, width=None, offset=None, relative=False) → self

Append a Bézier curve to this path.

Parameters:

xy (sequence of points) – Curve control points.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.
relative – If True, coordinates are relative to the last point.

Examples

>>> path = gdstk.FlexPath((0, 0), 0.2, tolerance=1e-3)
>>> path.bezier([(4, 1), (4, 3), (0, 5),
...              (-4, 3), (-4, -2), (0, -4)])

commands(path_commands...) → self

Append sections to this path according to commands.

Commands are single characters followed by a pre-defined number of numerical arguments, according to the table below:

Command	Primitive	Arguments
L/l	Line segment	x, y
H/h	Horizontal segment	x
V/v	Vertical segment	y
C/c	Cubic Bézier	x0, y0, x1, y1, x2, y2
S/s	Smooth cubic Bézier	x0, y0, x1, y1
Q/q	Quadratic Bézier	x0, y0, x1, y1
T/t	Smooth quadratic Bézier	x, y
a	Circular turn	rad, ang
A	Circular arc	rad, ang0, ang1
E	Elliptical arc	rad0, rad1, ang0, ang1, rot

Uppercase commands assume that coordinates are absolute, whereas the lowercase versions assume they are relative to the previous endpoint.

Notes

The meaning and order of the arguments of all commands are identical to the corresponding method.

Examples

>>> path = gdstk.FlexPath((0, 0), [0.2, 0.4, 0.2], 0.5,
...                       tolerance=1e-3)
>>> path.commands("l", 3, 4,
...               "A", 2, numpy.arctan2(3, -4), numpy.pi / 2,
...               "h", 0.5,
...               "a", 3, -numpy.pi)

copy() → gdstk.FlexPath

Create a copy this flexpath.

Returns:: Copy of this flexpath.

cubic(xy, width=None, offset=None, relative=False) → self

Append cubic Bézier curves to this path.

Parameters:

xy (sequence of points) – Each set of 3 consecutive points is interpreted as 2 control points and an end point.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.
relative – If True, coordinates are relative to the last point.

Notes

Changes in width and offset are split equally among curve parts defined by xy.

Examples

>>> path = gdstk.FlexPath((0, 0), 0.2, tolerance=1e-3)
>>> path.cubic([(0, 1), (1, 1), (1, 0)])
>>> path.cubic([(1, -1), (2, -1), (2.5, -0.5),
...             (3, 0), (3, 1), (2, 1)], width=0.5)

cubic_smooth(xy, width=None, offset=None, relative=False) → self

Append smooth cubic Bézier curves to this path.

The first control point is assumed to be the reflection of the last control point of this path with respect to its end point.

Parameters:

xy (sequence of points) – Each set of 2 consecutive points is interpreted as the second control points and an end point.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.
relative – If True, coordinates are relative to the last point.

Notes

Changes in width and offset are split equally among curve parts defined by xy.

Examples

>>> path = gdstk.FlexPath((0, 0), 0.2, tolerance=1e-3)
>>> path.cubic([(0, 1), (1, 1), (1, 0)])
>>> path.cubic_smooth([(2, -1), (2.5, -0.5), (3, 1), (2, 1)],
...                   width=0.5)

datatypes: FlexPath data type.

Notes

This attribute is read-only.

See also

gdstk.FlexPath.set_datatypes()

delete_gds_property(attr) → self

Delete a GDSII property of this element.

Parameters:: attr (number) – Property number.

delete_property(name) → self

Delete the first property of this element matching a name.

Parameters:: name (str) – Property name.

ends: End types for each path.

Notes

This attribute is read-only.

See also

gdstk.FlexPath.set_ends()

get_gds_property(attr) → str

Return a GDSII property of this element.

Parameters:: attr (number) – Property number.
Returns:: Property value. If the property number does not exist, None is returned.
Return type:: str or None

get_property(name) → list

Return the values of the first property of this element matching a name.

Parameters:: name (str) – Property name.
Returns:: List of property values. If no property is found, None is returned.
Return type:: list or None

horizontal(x, width=None, offset=None, relative=False) → self

Append horizontal segments to this path.

Parameters:

x (number or sequence) – End point x coordinates.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.
relative – If True, coordinates are relative to the last point.

Notes

If x is a sequence, changes in width and offset are split equally among segments.

Examples

>>> path = gdstk.FlexPath([(0, 0)], 0.2)
>>> path.horizontal(2, width=0.4, relative=True)
>>> path.horizontal(2, offset=[0.4], relative=True)
>>> path.horizontal(2, relative=True)
>>> print(path.spine())
... [[0. 0.]
...  [2. 0.]
...  [4. 0.]
...  [6. 0.]]

See also

gdstk.FlexPath.segment()

interpolation(points, angles=None, tension_in=1, tension_out=1, initial_curl=1, final_curl=1, cycle=False, width=None, offset=None, relative=True) → self

Append a smooth interpolating curve through the given points.

Use the Hobby algorithm [1] to calculate a smooth interpolating path made of cubic Bézier segments between each pair of points. Angle and tension parameters can be specified at each point, and the path can be open or closed.

Parameters:

points (sequence[N] of points) – Vertices in the interpolating path.
angles (None or sequence[N + 1]) – Tangent angles at each point (in radians). Angles defined as None are automatically calculated.
tension_in (number or sequence[N + 1]) – Tension parameter when arriving at each point. One value per point or a single value used for all points.
tension_out (number or sequence[N + 1]) – Tension parameter when leaving each point. One value per point or a single value used for all points.
initial_curl – Ratio between the mock curvatures at the first point and at its neighbor. A value of 1 renders the first segment a good approximation for a circular arc. A value of 0 will better approximate a straight segment. It has no effect for closed paths or when an angle is defined for the first point.
final_curl – Ratio between the mock curvatures at the last point and at its neighbor. It has no effect for closed paths or when an angle is defined for the first point.
cycle – If True, calculates control points for a closed path, with an additional segment connecting the first and last points.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.
relative – If True, coordinates are relative to the last point.

Examples

>>> half_pi = numpy.pi / 2
>>> points = [(4, 1), (4, 3), (0, 5), (-4, 3), (-4, -2), (0, -4)]
>>> angles = [half_pi, None, None, None, -half_pi, -half_pi, None]
>>> path_1 = gdstk.FlexPath((0, 0), 0.2, tolerance=1e-3)
>>> path_1.interpolation(points, cycle=True)
>>> path_2 = gdstk.FlexPath((6, -8), 0.2, tolerance=1e-3)
>>> path_2.interpolation(points, angles, cycle=True, relative=True)

joins: Join types for each path.

Notes

This attribute is read-only.

See also

gdstk.FlexPath.set_joins()

layers: FlexPath layer.

Notes

This attribute is read-only.

See also

gdstk.FlexPath.set_layers()

mirror(p1, p2=(0, 0)) → self

Mirror this path across the line through p1 and p2.

Parameters:

p1 (coordinate pair or complex) – First point in the mirror line.
p2 (coordinate pair or complex) – Second point in the mirror line.

num_paths: Number of paths.

Notes

This attribute is read-only.

offsets() → numpy.ndarray

Offsets of all paths at every point.

Returns:: The offsets of each path at each point.

parametric(path_function, width=None, offset=None, relative=True) → self

Append a parametric curve to this path.

Parameters:

path_function (callable) – Function that defines the path. Must be a function of one argument (that varies from 0 to 1) that returns a 2-element sequence or complex with the coordinates of the path.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.
relative – If True, the return values of path_function are used as offsets from the current path position, i.e., to ensure a continuous path, path_function(0) must be (0, 0). Otherwise, they are used as absolute coordinates.

Examples

>>> def spiral(u):
...     rad = 2 * u ** 0.5
...     ang = 3 * numpy.pi * u
...     return (rad * numpy.cos(ang), rad * numpy.sin(ang))
>>> path = gdstk.FlexPath((0, 0), 0.2, tolerance=1e-3)
>>> path.parametric(spiral)

path_spines() → list

Central spines of each parallel path.

Returns:: Copy of the points that make up each parallel path.

properties

Properties of this element.

Properties are represented as a list of lists, each containing the property name followed by its values.

quadratic(xy, width=None, offset=None, relative=False) → self

Append quadratic Bézier curves to this path.

Parameters:

xy (sequence of points) – Each set of 2 consecutive points is interpreted as control point and an end point.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.
relative – If True, coordinates are relative to the last point.

Notes

Changes in width and offset are split equally among curve parts defined by xy.

See also

gdstk.FlexPath.cubic()

quadratic_smooth(xy, width=None, offset=None, relative=False) → self

Append smooth quadratic Bézier curves to this path.

The control point is assumed to be the reflection of the last control point of this curve with respect to its end point.

Parameters:

xy (sequence of points) – Curve end points.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.
relative – If True, coordinates are relative to the last point.

Notes

Changes in width and offset are split equally among curve parts defined by xy.

See also

gdstk.FlexPath.cubic_smooth()

raith_data: Raith electron beam lithography data.

repetition: Repetition associated with this element.

rotate(angle, center=(0, 0)) → self

Rotate this path.

Parameters:

angle – Rotation angle (in radians).
center (coordinate pair or complex) – Center of the transformation.

scale(s, center=(0, 0)) → self

Scale this path.

Parameters:

s – Scaling factor.
center (coordinate pair or complex) – Center of the transformation.

scale_width: Scale width flag.

segment(xy, width=None, offset=None, relative=False) → self

Append straight segments to this path.

Parameters:

xy – Segment end point or sequence of end points. Each point can be a pair of coordinates or a complex value.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.
relative – If True, coordinates are relative to the last point.

Notes

If xy is a sequence, changes in width and offset are split equally among segments.

Examples

>>> points = [(1, 0), (1, 1), (-1, 1), (-1, -1), (1, -1)]
>>> path_1 = gdstk.FlexPath((0, 0), 0.2)
>>> path_1.segment(points, 0.6)
>>> path_2 = gdstk.FlexPath((3, 0), [0.1, 0.1], 0.2)
>>> path_2.segment(points, offset=0.6, relative=True)

set_bend_function(*functions) → self

Set the bend function for all paths.

Parameters:: functions – Sequence of callable or None.

See also

gdstk.FlexPath

set_bend_radius(*radii) → self

Set the bend radius for all paths.

Parameters:: radii – Sequence of floats.

See also

gdstk.FlexPath

set_datatypes(*datatypes) → self

Set the datatypes for all paths.

Parameters:: datatypes – data type numbers for all paths.

set_ends(*ends) → self

Set the end types for all paths.

Parameters:: ends – Sequence of “flush”, “extended”, “round”, “smooth”, a 2-tuple, or a callable.

See also

gdstk.FlexPath

set_gds_property(attr, value) → self

Set a GDSII property for this element.

GDSII properties are stored under the special name “S_GDS_PROPERTY”, as defined by the OASIS specification.

Parameters:

attr (number) – Property number.
value (str) – Property value.

set_joins(*joins) → self

Set the end types for all paths.

Parameters:: joins – Sequence of “natural”, “miter”, “bevel”, “round”, “smooth”, or a callable.

See also

gdstk.FlexPath

set_layers(*layers) → self

Set the layers for all paths.

Parameters:: layers – layer numbers for all paths.

set_property(name, value) → self

Set a property for this element.

The property name does not have to be unique. Multiple properties can have the same name.

Parameters:

name (str) – Property name.
value (str, bytes, number, or sequence of those) – Values associated with the property.

Notes

These properties can be used to associate custom metadata with an element, but general properties are not supported by GDSII files, only OASIS. Use the specific methods to access GDSII properties.

simple_path: Simple path flag.

size: Number of points in the path spine.

Notes

This attribute is read-only.

spine() → numpy.ndarray

Central path spine.

Returns:: Copy of the points that make up the path at zero offset.

to_polygons() → list

Calculate the polygonal representations of this path.

Returns:: The polygonal contours defined by this path.

tolerance: Path tolerance.

translate(dx, dy=None) → self

Translate this path.

Parameters:

dx – Translation in the x coordinate or translation vector.
dy – Translation in the y coordinate.

turn(radius, angle, width=None, offset=None) → self

Append a circular turn to this path.

Parameters:

radius – Circular arc radius.
angle – Turning angle. Positive values turn counter clockwise and negative values, clockwise.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.

vertical(y, width=None, offset=None, relative=False) → self

Append vertical segments to this path.

Parameters:

y (number or sequence) – End point y coordinates.
width (number or sequence) – Width at the end point(s). If this is a sequence, it must define the width for each path. The width is linearly tapered from its previous value.
offset (number or sequence) – If this is a number, it is treated as the distance between centers of adjacent paths. If it is a sequence, each number represents the absolute offset from the center of the path. The offsets are linearly tapered from their previous values.
relative – If True, coordinates are relative to the last point.

Notes

If y is a sequence, changes in width and offset are split equally among segments.

widths() → numpy.ndarray

Widths of all paths at every point.

Returns:: The widths of each path at each point.