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Source code for matplotlib.path

r"""
A module for dealing with the polylines used throughout Matplotlib.

The primary class for polyline handling in Matplotlib is Path.  Almost all
vector drawing makes use of Path\s somewhere in the drawing pipeline.

Whilst a Path instance itself cannot be drawn, some .Artist subclasses,
such as .PathPatch and .PathCollection, can be used for convenient Path
visualisation.
"""

from functools import lru_cache
from weakref import WeakValueDictionary

import numpy as np

from . import _path, cbook, rcParams

[docs]class Path(object):
"""
:class:Path represents a series of possibly disconnected,
possibly closed, line and curve segments.

The underlying storage is made up of two parallel numpy arrays:
- *vertices*: an Nx2 float array of vertices
- *codes*: an N-length uint8 array of vertex types

These two arrays always have the same length in the first
dimension.  For example, to represent a cubic curve, you must
provide three vertices as well as three codes CURVE3.

The code types are:

- STOP   :  1 vertex (ignored)
A marker for the end of the entire path (currently not
required and ignored)

- MOVETO :  1 vertex
Pick up the pen and move to the given vertex.

- LINETO :  1 vertex
Draw a line from the current position to the given vertex.

- CURVE3 :  1 control point, 1 endpoint
Draw a quadratic Bezier curve from the current position,
with the given control point, to the given end point.

- CURVE4 :  2 control points, 1 endpoint
Draw a cubic Bezier curve from the current position, with
the given control points, to the given end point.

- CLOSEPOLY : 1 vertex (ignored)
Draw a line segment to the start point of the current
polyline.

Users of Path objects should not access the vertices and codes
arrays directly.  Instead, they should use :meth:iter_segments
or :meth:cleaned to get the vertex/code pairs.  This is important,
since many :class:Path objects, as an optimization, do not store a
*codes* at all, but have a default one provided for them by
:meth:iter_segments.

Some behavior of Path objects can be controlled by rcParams. See
the rcParams whose keys contain 'path.'.

.. note::

The vertices and codes arrays should be treated as
immutable -- there are a number of optimizations and assumptions
made up front in the constructor that will not change when the
data changes.

"""

code_type = np.uint8

# Path codes
STOP = code_type(0)         # 1 vertex
MOVETO = code_type(1)       # 1 vertex
LINETO = code_type(2)       # 1 vertex
CURVE3 = code_type(3)       # 2 vertices
CURVE4 = code_type(4)       # 3 vertices
CLOSEPOLY = code_type(79)   # 1 vertex

#: A dictionary mapping Path codes to the number of vertices that the
#: code expects.
NUM_VERTICES_FOR_CODE = {STOP: 1,
MOVETO: 1,
LINETO: 1,
CURVE3: 2,
CURVE4: 3,
CLOSEPOLY: 1}

def __init__(self, vertices, codes=None, _interpolation_steps=1,
"""
Create a new path with the given vertices and codes.

Parameters
----------
vertices : array_like
The (n, 2) float array, masked array or sequence of pairs
representing the vertices of the path.

If *vertices* contains masked values, they will be converted
to NaNs which are then handled correctly by the Agg
PathIterator and other consumers of path data, such as
:meth:iter_segments.
codes : {None, array_like}, optional
n-length array integers representing the codes of the path.
If not None, codes must be the same length as vertices.
If None, *vertices* will be treated as a series of line segments.
_interpolation_steps : int, optional
Used as a hint to certain projections, such as Polar, that this
path should be linearly interpolated immediately before drawing.
This attribute is primarily an implementation detail and is not
intended for public use.
closed : bool, optional
If *codes* is None and closed is True, vertices will be treated as
line segments of a closed polygon.
Makes the path behave in an immutable way and sets the vertices
"""
if vertices.ndim != 2 or vertices.shape != 2:
raise ValueError(
"'vertices' must be a 2D list or array with shape Nx2")

if codes is not None:
codes = np.asarray(codes, self.code_type)
if codes.ndim != 1 or len(codes) != len(vertices):
raise ValueError("'codes' must be a 1D list or array with the "
"same length of 'vertices'")
if len(codes) and codes != self.MOVETO:
raise ValueError("The first element of 'code' must be equal "
"to 'MOVETO' ({})".format(self.MOVETO))
elif closed and len(vertices):
codes = np.empty(len(vertices), dtype=self.code_type)
codes = self.MOVETO
codes[1:-1] = self.LINETO
codes[-1] = self.CLOSEPOLY

self._vertices = vertices
self._codes = codes
self._interpolation_steps = _interpolation_steps
self._update_values()

self._vertices.flags.writeable = False
if self._codes is not None:
self._codes.flags.writeable = False
else:

@classmethod
def _fast_from_codes_and_verts(cls, verts, codes, internals_from=None):
"""
Creates a Path instance without the expense of calling the constructor.

Parameters
----------
verts : numpy array
codes : numpy array
internals_from : Path or None
If not None, another Path from which the attributes
should_simplify, simplify_threshold, and
interpolation_steps will be copied.  Note that readonly is
never copied, and always set to False by this constructor.
"""
pth = cls.__new__(cls)
pth._codes = codes
if internals_from is not None:
pth._should_simplify = internals_from._should_simplify
pth._simplify_threshold = internals_from._simplify_threshold
pth._interpolation_steps = internals_from._interpolation_steps
else:
pth._should_simplify = True
pth._simplify_threshold = rcParams['path.simplify_threshold']
pth._interpolation_steps = 1
return pth

def _update_values(self):
self._simplify_threshold = rcParams['path.simplify_threshold']
self._should_simplify = (
self._simplify_threshold > 0 and
rcParams['path.simplify'] and
len(self._vertices) >= 128 and
(self._codes is None or np.all(self._codes <= Path.LINETO))
)

@property
def vertices(self):
"""
The list of vertices in the Path as an Nx2 numpy array.
"""
return self._vertices

@vertices.setter
def vertices(self, vertices):
raise AttributeError("Can't set vertices on a readonly Path")
self._vertices = vertices
self._update_values()

@property
def codes(self):
"""
The list of codes in the Path as a 1-D numpy array.  Each
code is one of STOP, MOVETO, LINETO, CURVE3, CURVE4
or CLOSEPOLY.  For codes that correspond to more than one
vertex (CURVE3 and CURVE4), that code will be repeated so
that the length of self.vertices and self.codes is always
the same.
"""
return self._codes

@codes.setter
def codes(self, codes):
raise AttributeError("Can't set codes on a readonly Path")
self._codes = codes
self._update_values()

@property
def simplify_threshold(self):
"""
The fraction of a pixel difference below which vertices will
be simplified out.
"""
return self._simplify_threshold

@simplify_threshold.setter
def simplify_threshold(self, threshold):
self._simplify_threshold = threshold

@cbook.deprecated(
"3.1", alternative="not np.isfinite(self.vertices).all()")
@property
def has_nonfinite(self):
"""
True if the vertices array has nonfinite values.
"""
return not np.isfinite(self._vertices).all()

@property
def should_simplify(self):
"""
True if the vertices array should be simplified.
"""
return self._should_simplify

@should_simplify.setter
def should_simplify(self, should_simplify):
self._should_simplify = should_simplify

@property
"""
True if the Path is read-only.
"""

def __copy__(self):
"""
Returns a shallow copy of the Path, which will share the
vertices and codes with the source Path.
"""
import copy
return copy.copy(self)

copy = __copy__

def __deepcopy__(self, memo=None):
"""
Returns a deepcopy of the Path.  The Path will not be
readonly, even if the source Path is.
"""
try:
codes = self.codes.copy()
except AttributeError:
codes = None
return self.__class__(
self.vertices.copy(), codes,
_interpolation_steps=self._interpolation_steps)

deepcopy = __deepcopy__

[docs]    @classmethod
def make_compound_path_from_polys(cls, XY):
"""
Make a compound path object to draw a number
of polygons with equal numbers of sides XY is a (numpolys x
numsides x 2) numpy array of vertices.  Return object is a
:class:Path

.. plot:: gallery/misc/histogram_path.py

"""

# for each poly: 1 for the MOVETO, (numsides-1) for the LINETO, 1 for
# the CLOSEPOLY; the vert for the closepoly is ignored but we still
# need it to keep the codes aligned with the vertices
numpolys, numsides, two = XY.shape
if two != 2:
raise ValueError("The third dimension of 'XY' must be 2")
stride = numsides + 1
nverts = numpolys * stride
verts = np.zeros((nverts, 2))
codes = np.full(nverts, cls.LINETO, dtype=cls.code_type)
codes[0::stride] = cls.MOVETO
codes[numsides::stride] = cls.CLOSEPOLY
for i in range(numsides):
verts[i::stride] = XY[:, i]

return cls(verts, codes)

[docs]    @classmethod
def make_compound_path(cls, *args):
"""Make a compound path from a list of Path objects."""
# Handle an empty list in args (i.e. no args).
if not args:
return Path(np.empty([0, 2], dtype=np.float32))

lengths = [len(x) for x in args]
total_length = sum(lengths)

vertices = np.vstack([x.vertices for x in args])
vertices.reshape((total_length, 2))

codes = np.empty(total_length, dtype=cls.code_type)
i = 0
for path in args:
if path.codes is None:
codes[i] = cls.MOVETO
codes[i + 1:i + len(path.vertices)] = cls.LINETO
else:
codes[i:i + len(path.codes)] = path.codes
i += len(path.vertices)

return cls(vertices, codes)

def __repr__(self):
return "Path(%r, %r)" % (self.vertices, self.codes)

def __len__(self):
return len(self.vertices)

[docs]    def iter_segments(self, transform=None, remove_nans=True, clip=None,
snap=False, stroke_width=1.0, simplify=None,
curves=True, sketch=None):
"""
Iterates over all of the curve segments in the path.  Each iteration
returns a 2-tuple (vertices, code), where vertices is a
sequence of 1-3 coordinate pairs, and code is a Path code.

Additionally, this method can provide a number of standard cleanups and
conversions to the path.

Parameters
----------
transform : None or :class:~matplotlib.transforms.Transform
If not None, the given affine transformation will be applied to the
path.
remove_nans : bool, optional
Whether to remove all NaNs from the path and skip over them using
MOVETO commands.
clip : None or (float, float, float, float), optional
If not None, must be a four-tuple (x1, y1, x2, y2)
defining a rectangle in which to clip the path.
snap : None or bool, optional
If True, snap all nodes to pixels; if False, don't snap them.
If None, perform snapping if the path contains only segments
parallel to the x or y axes, and no more than 1024 of them.
stroke_width : float, optional
The width of the stroke being drawn (used for path snapping).
simplify : None or bool, optional
Whether to simplify the path by removing vertices
that do not affect its appearance.  If None, use the
:attr:should_simplify attribute.  See also :rc:path.simplify
and :rc:path.simplify_threshold.
curves : bool, optional
If True, curve segments will be returned as curve segments.
If False, all curves will be converted to line segments.
sketch : None or sequence, optional
If not None, must be a 3-tuple of the form
(scale, length, randomness), representing the sketch parameters.
"""
if not len(self):
return

cleaned = self.cleaned(transform=transform,
remove_nans=remove_nans, clip=clip,
snap=snap, stroke_width=stroke_width,
simplify=simplify, curves=curves,
sketch=sketch)

# Cache these object lookups for performance in the loop.
NUM_VERTICES_FOR_CODE = self.NUM_VERTICES_FOR_CODE
STOP = self.STOP

vertices = iter(cleaned.vertices)
codes = iter(cleaned.codes)
for curr_vertices, code in zip(vertices, codes):
if code == STOP:
break
extra_vertices = NUM_VERTICES_FOR_CODE[code] - 1
if extra_vertices:
for i in range(extra_vertices):
next(codes)
curr_vertices = np.append(curr_vertices, next(vertices))
yield curr_vertices, code

[docs]    def cleaned(self, transform=None, remove_nans=False, clip=None,
quantize=False, simplify=False, curves=False,
stroke_width=1.0, snap=False, sketch=None):
"""
Return a new Path with vertices and codes cleaned according to the
parameters.

--------
Path.iter_segments : for details of the keyword arguments.
"""
vertices, codes = _path.cleanup_path(
self, transform, remove_nans, clip, snap, stroke_width, simplify,
curves, sketch)
pth = Path._fast_from_codes_and_verts(vertices, codes, self)
if not simplify:
pth._should_simplify = False
return pth

[docs]    def transformed(self, transform):
"""
Return a transformed copy of the path.

--------
matplotlib.transforms.TransformedPath
A specialized path class that will cache the transformed result and
automatically update when the transform changes.
"""
return Path(transform.transform(self.vertices), self.codes,
self._interpolation_steps)

[docs]    def contains_point(self, point, transform=None, radius=0.0):
"""
Returns whether the (closed) path contains the given point.

If *transform* is not None, the path will be transformed before
performing the test.

"""
if transform is not None:
transform = transform.frozen()
# point_in_path does not handle nonlinear transforms, so we
# transform the path ourselves.  If transform is affine, letting
# point_in_path handle the transform avoids allocating an extra
# buffer.
if transform and not transform.is_affine:
self = transform.transform_path(self)
transform = None
return _path.point_in_path(point, point, radius, self, transform)

[docs]    def contains_points(self, points, transform=None, radius=0.0):
"""
Returns a bool array which is True if the (closed) path contains
the corresponding point.

If *transform* is not None, the path will be transformed before
performing the test.

"""
if transform is not None:
transform = transform.frozen()
result = _path.points_in_path(points, radius, self, transform)
return result.astype('bool')

[docs]    def contains_path(self, path, transform=None):
"""
Returns whether this (closed) path completely contains the given path.

If *transform* is not None, the path will be transformed before
performing the test.
"""
if transform is not None:
transform = transform.frozen()
return _path.path_in_path(self, None, path, transform)

[docs]    def get_extents(self, transform=None):
"""
Returns the extents (*xmin*, *ymin*, *xmax*, *ymax*) of the
path.

Unlike computing the extents on the *vertices* alone, this
algorithm will take into account the curves and deal with
control points appropriately.
"""
from .transforms import Bbox
path = self
if transform is not None:
transform = transform.frozen()
if not transform.is_affine:
path = self.transformed(transform)
transform = None
return Bbox(_path.get_path_extents(path, transform))

[docs]    def intersects_path(self, other, filled=True):
"""
Returns *True* if this path intersects another given path.

*filled*, when True, treats the paths as if they were filled.
That is, if one path completely encloses the other,
:meth:intersects_path will return True.
"""
return _path.path_intersects_path(self, other, filled)

[docs]    def intersects_bbox(self, bbox, filled=True):
"""
Returns *True* if this path intersects a given
:class:~matplotlib.transforms.Bbox.

*filled*, when True, treats the path as if it was filled.
That is, if the path completely encloses the bounding box,
:meth:intersects_bbox will return True.

The bounding box is always considered filled.
"""
return _path.path_intersects_rectangle(self,
bbox.x0, bbox.y0, bbox.x1, bbox.y1, filled)

[docs]    def interpolated(self, steps):
"""
Returns a new path resampled to length N x steps.  Does not
currently handle interpolating curves.
"""
if steps == 1:
return self

vertices = simple_linear_interpolation(self.vertices, steps)
codes = self.codes
if codes is not None:
new_codes = np.full((len(codes) - 1) * steps + 1, Path.LINETO,
dtype=self.code_type)
new_codes[0::steps] = codes
else:
new_codes = None
return Path(vertices, new_codes)

[docs]    def to_polygons(self, transform=None, width=0, height=0, closed_only=True):
"""
Convert this path to a list of polygons or polylines.  Each
polygon/polyline is an Nx2 array of vertices.  In other words,
each polygon has no MOVETO instructions or curves.  This
is useful for displaying in backends that do not support
compound paths or Bezier curves.

If *width* and *height* are both non-zero then the lines will
be simplified so that vertices outside of (0, 0), (width,
height) will be clipped.

If *closed_only* is True (default), only closed polygons,
with the last point being the same as the first point, will be
returned.  Any unclosed polylines in the path will be
explicitly closed.  If *closed_only* is False, any unclosed
polygons in the path will be returned as unclosed polygons,
and the closed polygons will be returned explicitly closed by
setting the last point to the same as the first point.
"""
if len(self.vertices) == 0:
return []

if transform is not None:
transform = transform.frozen()

if self.codes is None and (width == 0 or height == 0):
vertices = self.vertices
if closed_only:
if len(vertices) < 3:
return []
elif np.any(vertices != vertices[-1]):
vertices = [*vertices, vertices]

if transform is None:
return [vertices]
else:
return [transform.transform(vertices)]

# Deal with the case where there are curves and/or multiple
# subpaths (using extension code)
return _path.convert_path_to_polygons(
self, transform, width, height, closed_only)

_unit_rectangle = None

[docs]    @classmethod
def unit_rectangle(cls):
"""
Return a Path instance of the unit rectangle from (0, 0) to (1, 1).
"""
if cls._unit_rectangle is None:
cls._unit_rectangle = \
cls([[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0],
[0.0, 0.0]],
[cls.MOVETO, cls.LINETO, cls.LINETO, cls.LINETO,
cls.CLOSEPOLY],
return cls._unit_rectangle

_unit_regular_polygons = WeakValueDictionary()

[docs]    @classmethod
def unit_regular_polygon(cls, numVertices):
"""
Return a :class:Path instance for a unit regular polygon with the
given *numVertices* and radius of 1.0, centered at (0, 0).
"""
if numVertices <= 16:
path = cls._unit_regular_polygons.get(numVertices)
else:
path = None
if path is None:
theta = ((2 * np.pi / numVertices) * np.arange(numVertices + 1)
# This initial rotation is to make sure the polygon always
# "points-up".
+ np.pi / 2)
verts = np.column_stack((np.cos(theta), np.sin(theta)))
codes = np.empty(numVertices + 1)
codes = cls.MOVETO
codes[1:-1] = cls.LINETO
codes[-1] = cls.CLOSEPOLY
if numVertices <= 16:
cls._unit_regular_polygons[numVertices] = path
return path

_unit_regular_stars = WeakValueDictionary()

[docs]    @classmethod
def unit_regular_star(cls, numVertices, innerCircle=0.5):
"""
Return a :class:Path for a unit regular star with the given
numVertices and radius of 1.0, centered at (0, 0).
"""
if numVertices <= 16:
path = cls._unit_regular_stars.get((numVertices, innerCircle))
else:
path = None
if path is None:
ns2 = numVertices * 2
theta = (2*np.pi/ns2 * np.arange(ns2 + 1))
# This initial rotation is to make sure the polygon always
# "points-up"
theta += np.pi / 2.0
r = np.ones(ns2 + 1)
r[1::2] = innerCircle
verts = np.vstack((r*np.cos(theta), r*np.sin(theta))).transpose()
codes = np.empty((ns2 + 1,))
codes = cls.MOVETO
codes[1:-1] = cls.LINETO
codes[-1] = cls.CLOSEPOLY
if numVertices <= 16:
cls._unit_regular_stars[(numVertices, innerCircle)] = path
return path

[docs]    @classmethod
def unit_regular_asterisk(cls, numVertices):
"""
Return a :class:Path for a unit regular asterisk with the given
numVertices and radius of 1.0, centered at (0, 0).
"""
return cls.unit_regular_star(numVertices, 0.0)

_unit_circle = None

[docs]    @classmethod
def unit_circle(cls):
"""
Return the readonly :class:Path of the unit circle.

For most cases, :func:Path.circle will be what you want.
"""
if cls._unit_circle is None:
return cls._unit_circle

[docs]    @classmethod
"""
Return a Path representing a circle of a given radius and center.

Parameters
----------
center : pair of floats
The center of the circle. Default (0, 0).
The radius of the circle. Default is 1.
Whether the created path should have the "readonly" argument
set when creating the Path instance.

Notes
-----
The circle is approximated using 8 cubic Bezier curves, as described in

Lancaster, Don.  Approximating a Circle or an Ellipse Using Four
Bezier Cubic Splines <http://www.tinaja.com/glib/ellipse4.pdf>_.
"""
MAGIC = 0.2652031
SQRTHALF = np.sqrt(0.5)
MAGIC45 = SQRTHALF * MAGIC

vertices = np.array([[0.0, -1.0],

[MAGIC, -1.0],
[SQRTHALF-MAGIC45, -SQRTHALF-MAGIC45],
[SQRTHALF, -SQRTHALF],

[SQRTHALF+MAGIC45, -SQRTHALF+MAGIC45],
[1.0, -MAGIC],
[1.0, 0.0],

[1.0, MAGIC],
[SQRTHALF+MAGIC45, SQRTHALF-MAGIC45],
[SQRTHALF, SQRTHALF],

[SQRTHALF-MAGIC45, SQRTHALF+MAGIC45],
[MAGIC, 1.0],
[0.0, 1.0],

[-MAGIC, 1.0],
[-SQRTHALF+MAGIC45, SQRTHALF+MAGIC45],
[-SQRTHALF, SQRTHALF],

[-SQRTHALF-MAGIC45, SQRTHALF-MAGIC45],
[-1.0, MAGIC],
[-1.0, 0.0],

[-1.0, -MAGIC],
[-SQRTHALF-MAGIC45, -SQRTHALF+MAGIC45],
[-SQRTHALF, -SQRTHALF],

[-SQRTHALF+MAGIC45, -SQRTHALF-MAGIC45],
[-MAGIC, -1.0],
[0.0, -1.0],

[0.0, -1.0]],
dtype=float)

codes = [cls.CURVE4] * 26
codes = cls.MOVETO
codes[-1] = cls.CLOSEPOLY

_unit_circle_righthalf = None

[docs]    @classmethod
def unit_circle_righthalf(cls):
"""
Return a Path of the right half of a unit circle.

See Path.circle for the reference on the approximation used.
"""
if cls._unit_circle_righthalf is None:
MAGIC = 0.2652031
SQRTHALF = np.sqrt(0.5)
MAGIC45 = SQRTHALF * MAGIC

vertices = np.array(
[[0.0, -1.0],

[MAGIC, -1.0],
[SQRTHALF-MAGIC45, -SQRTHALF-MAGIC45],
[SQRTHALF, -SQRTHALF],

[SQRTHALF+MAGIC45, -SQRTHALF+MAGIC45],
[1.0, -MAGIC],
[1.0, 0.0],

[1.0, MAGIC],
[SQRTHALF+MAGIC45, SQRTHALF-MAGIC45],
[SQRTHALF, SQRTHALF],

[SQRTHALF-MAGIC45, SQRTHALF+MAGIC45],
[MAGIC, 1.0],
[0.0, 1.0],

[0.0, -1.0]],

float)

codes = np.full(14, cls.CURVE4, dtype=cls.code_type)
codes = cls.MOVETO
codes[-1] = cls.CLOSEPOLY

return cls._unit_circle_righthalf

[docs]    @classmethod
def arc(cls, theta1, theta2, n=None, is_wedge=False):
"""
Return the unit circle arc from angles *theta1* to *theta2* (in
degrees).

*theta2* is unwrapped to produce the shortest arc within 360 degrees.
That is, if *theta2* > *theta1* + 360, the arc will be from *theta1* to
*theta2* - 360 and not a full circle plus some extra overlap.

If *n* is provided, it is the number of spline segments to make.
If *n* is not provided, the number of spline segments is
determined based on the delta between *theta1* and *theta2*.

Masionobe, L.  2003.  Drawing an elliptical arc using
polylines, quadratic or cubic Bezier curves
<http://www.spaceroots.org/documents/ellipse/index.html>_.
"""
halfpi = np.pi * 0.5

eta1 = theta1
eta2 = theta2 - 360 * np.floor((theta2 - theta1) / 360)
# Ensure 2pi range is not flattened to 0 due to floating-point errors,
# but don't try to expand existing 0 range.
if theta2 != theta1 and eta2 <= eta1:
eta2 += 360

# number of curve segments to make
if n is None:
n = int(2 ** np.ceil((eta2 - eta1) / halfpi))
if n < 1:
raise ValueError("n must be >= 1 or None")

deta = (eta2 - eta1) / n
t = np.tan(0.5 * deta)
alpha = np.sin(deta) * (np.sqrt(4.0 + 3.0 * t * t) - 1) / 3.0

steps = np.linspace(eta1, eta2, n + 1, True)
cos_eta = np.cos(steps)
sin_eta = np.sin(steps)

xA = cos_eta[:-1]
yA = sin_eta[:-1]
xA_dot = -yA
yA_dot = xA

xB = cos_eta[1:]
yB = sin_eta[1:]
xB_dot = -yB
yB_dot = xB

if is_wedge:
length = n * 3 + 4
vertices = np.zeros((length, 2), float)
codes = np.full(length, cls.CURVE4, dtype=cls.code_type)
vertices = [xA, yA]
codes[0:2] = [cls.MOVETO, cls.LINETO]
codes[-2:] = [cls.LINETO, cls.CLOSEPOLY]
vertex_offset = 2
end = length - 2
else:
length = n * 3 + 1
vertices = np.empty((length, 2), float)
codes = np.full(length, cls.CURVE4, dtype=cls.code_type)
vertices = [xA, yA]
codes = cls.MOVETO
vertex_offset = 1
end = length

vertices[vertex_offset:end:3, 0] = xA + alpha * xA_dot
vertices[vertex_offset:end:3, 1] = yA + alpha * yA_dot
vertices[vertex_offset+1:end:3, 0] = xB - alpha * xB_dot
vertices[vertex_offset+1:end:3, 1] = yB - alpha * yB_dot
vertices[vertex_offset+2:end:3, 0] = xB
vertices[vertex_offset+2:end:3, 1] = yB

[docs]    @classmethod
def wedge(cls, theta1, theta2, n=None):
"""
Return the unit circle wedge from angles *theta1* to *theta2* (in
degrees).

*theta2* is unwrapped to produce the shortest wedge within 360 degrees.
That is, if *theta2* > *theta1* + 360, the wedge will be from *theta1*
to *theta2* - 360 and not a full circle plus some extra overlap.

If *n* is provided, it is the number of spline segments to make.
If *n* is not provided, the number of spline segments is
determined based on the delta between *theta1* and *theta2*.

See Path.arc for the reference on the approximation used.
"""
return cls.arc(theta1, theta2, n, True)

[docs]    @staticmethod
@lru_cache(8)
def hatch(hatchpattern, density=6):
"""
Given a hatch specifier, *hatchpattern*, generates a Path that
can be used in a repeated hatching pattern.  *density* is the
number of lines per unit square.
"""
from matplotlib.hatch import get_path
return (get_path(hatchpattern, density)
if hatchpattern is not None else None)

[docs]    def clip_to_bbox(self, bbox, inside=True):
"""
Clip the path to the given bounding box.

The path must be made up of one or more closed polygons.  This
algorithm will not behave correctly for unclosed paths.

If *inside* is True, clip to the inside of the box, otherwise
to the outside of the box.
"""
# Use make_compound_path_from_polys
verts = _path.clip_path_to_rect(self, bbox, inside)
paths = [Path(poly) for poly in verts]
return self.make_compound_path(*paths)

[docs]def get_path_collection_extents(
master_transform, paths, transforms, offsets, offset_transform):
r"""
Given a sequence of Path\s, ~.Transform\s objects, and offsets, as
found in a ~.PathCollection, returns the bounding box that encapsulates
all of them.

Parameters
----------
master_transform : ~.Transform
Global transformation applied to all paths.
paths : list of Path
transform : list of ~.Affine2D
offsets : (N, 2) array-like
offset_transform : ~.Affine2D
Transform applied to the offsets before offsetting the path.

Notes
-----
The way that *paths*, *transforms* and *offsets* are combined
follows the same method as for collections:  Each is iterated over
independently, so if you have 3 paths, 2 transforms and 1 offset,
their combinations are as follows:

(A, A, A), (B, B, A), (C, A, A)
"""
from .transforms import Bbox
if len(paths) == 0:
raise ValueError("No paths provided")
return Bbox.from_extents(*_path.get_path_collection_extents(
master_transform, paths, np.atleast_3d(transforms),
offsets, offset_transform))

[docs]@cbook.deprecated("3.1", alternative="get_paths_collection_extents")
def get_paths_extents(paths, transforms=[]):
"""
Given a sequence of :class:Path objects and optional
:class:~matplotlib.transforms.Transform objects, returns the
bounding box that encapsulates all of them.

*paths* is a sequence of :class:Path instances.

*transforms* is an optional sequence of
:class:~matplotlib.transforms.Affine2D instances to apply to
each path.
"""
from .transforms import Bbox, Affine2D
if len(paths) == 0:
raise ValueError("No paths provided")
return Bbox.from_extents(*_path.get_path_collection_extents(
Affine2D(), paths, transforms, [], Affine2D()))