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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"

"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

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<h1>Source code for matplotlib.path</h1><div class="highlight"><pre>

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, rcParams

from .cbook import _to_unmasked_float_array, simple_linear_interpolation

<div class="viewcode-block" id="Path"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path">[docs]</a>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.

"""

# Path codes

STOP = 0 # 1 vertex

MOVETO = 1 # 1 vertex

LINETO = 2 # 1 vertex

CURVE3 = 3 # 2 vertices

CURVE4 = 4 # 3 vertices

CLOSEPOLY = 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}

code_type = np.uint8

def __init__(self, vertices, codes=None, _interpolation_steps=1,

closed=False, readonly=False):

"""

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.

readonly : bool, optional

Makes the path behave in an immutable way and sets the vertices

and codes as read-only arrays.

"""

vertices = _to_unmasked_float_array(vertices)

if vertices.ndim != 2 or vertices.shape[1] != 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[0] != 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[0] = 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()

if readonly:

self._vertices.flags.writeable = False

if self._codes is not None:

self._codes.flags.writeable = False

self._readonly = True

else:

self._readonly = False

@classmethod

def _fast_from_codes_and_verts(cls, verts, codes, internals=None):

"""

Creates a Path instance without the expense of calling the constructor

Parameters

----------

verts : numpy array

codes : numpy array

internals : dict or None

The attributes that the resulting path should have.

Allowed keys are ``readonly``, ``should_simplify``,

``simplify_threshold``, ``has_nonfinite`` and

``interpolation_steps``.

"""

internals = internals or {}

pth = cls.__new__(cls)

pth._vertices = _to_unmasked_float_array(verts)

pth._codes = codes

pth._readonly = internals.pop('readonly', False)

pth.should_simplify = internals.pop('should_simplify', True)

pth.simplify_threshold = (

internals.pop('simplify_threshold',

rcParams['path.simplify_threshold'])

)

pth._has_nonfinite = internals.pop('has_nonfinite', False)

pth._interpolation_steps = internals.pop('interpolation_steps', 1)

if internals:

raise ValueError('Unexpected internals provided to '

'_fast_from_codes_and_verts: '

'{0}'.format('\n *'.join(internals)))

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))

)

self._has_nonfinite = not np.isfinite(self._vertices).all()

@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):

if self._readonly:

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):

if self._readonly:

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

@property

def has_nonfinite(self):

"""

`True` if the vertices array has nonfinite values.

"""

return self._has_nonfinite

@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

def readonly(self):

"""

`True` if the `Path` is read-only.

"""

return self._readonly

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__

<div class="viewcode-block" id="Path.make_compound_path_from_polys"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.make_compound_path_from_polys">[docs]</a> @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.ones(nverts, int) * cls.LINETO

codes[0::stride] = cls.MOVETO

codes[numsides::stride] = cls.CLOSEPOLY

for i in range(numsides):

verts[i::stride] = XY[:, i]

return cls(verts, codes)</div>

<div class="viewcode-block" id="Path.make_compound_path"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.make_compound_path">[docs]</a> @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)</div>

def __repr__(self):

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

def __len__(self):

return len(self.vertices)

<div class="viewcode-block" id="Path.iter_segments"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.iter_segments">[docs]</a> 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

one of the :class:`Path` codes.

Additionally, this method can provide a number of standard

cleanups and conversions to the path.

Parameters

----------

transform : None or :class:`~matplotlib.transforms.Transform` instance

If not None, the given affine transformation will

be applied to the path.

remove_nans : {False, True}, optional

If True, will remove all NaNs from the path and

insert MOVETO commands to skip over them.

clip : None or sequence, 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 None, auto-snap to pixels, to reduce

fuzziness of rectilinear lines. If True, force snapping, and

if False, don't snap.

stroke_width : float, optional

The width of the stroke being drawn. Needed

as a hint for the snapping algorithm.

simplify : None or bool, optional

If True, perform simplification, to remove

vertices that do not affect the appearance of the path. If

False, perform no simplification. If None, use the

should_simplify member variable. See also the rcParams

path.simplify and path.simplify_threshold.

curves : {True, False}, 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)

vertices = cleaned.vertices

codes = cleaned.codes

len_vertices = vertices.shape[0]

# Cache these object lookups for performance in the loop.

NUM_VERTICES_FOR_CODE = self.NUM_VERTICES_FOR_CODE

STOP = self.STOP

i = 0

while i < len_vertices:

code = codes[i]

if code == STOP:

return

else:

num_vertices = NUM_VERTICES_FOR_CODE[code]

curr_vertices = vertices[i:i+num_vertices].flatten()

yield curr_vertices, code

i += num_vertices</div>

<div class="viewcode-block" id="Path.cleaned"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.cleaned">[docs]</a> def cleaned(self, transform=None, remove_nans=False, clip=None,

quantize=False, simplify=False, curves=False,

stroke_width=1.0, snap=False, sketch=None):

"""

Cleans up the path according to the parameters returning a new

Path instance.

.. seealso::

See :meth:`iter_segments` for details of the keyword arguments.

Returns

-------

Path instance with cleaned up vertices and codes.

"""

vertices, codes = _path.cleanup_path(self, transform,

remove_nans, clip,

snap, stroke_width,

simplify, curves, sketch)

internals = {'should_simplify': self.should_simplify and not simplify,

'has_nonfinite': self.has_nonfinite and not remove_nans,

'simplify_threshold': self.simplify_threshold,

'interpolation_steps': self._interpolation_steps}

return Path._fast_from_codes_and_verts(vertices, codes, internals)</div>

<div class="viewcode-block" id="Path.transformed"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.transformed">[docs]</a> def transformed(self, transform):

"""

Return a transformed copy of the path.

.. seealso::

:class:`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)</div>

<div class="viewcode-block" id="Path.contains_point"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.contains_point">[docs]</a> 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.

*radius* allows the path to be made slightly larger or smaller.

"""

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[0], point[1], radius, self, transform)</div>

<div class="viewcode-block" id="Path.contains_points"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.contains_points">[docs]</a> 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.

*radius* allows the path to be made slightly larger or smaller.

"""

if transform is not None:

transform = transform.frozen()

result = _path.points_in_path(points, radius, self, transform)

return result.astype('bool')</div>

<div class="viewcode-block" id="Path.contains_path"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.contains_path">[docs]</a> 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)</div>

<div class="viewcode-block" id="Path.get_extents"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.get_extents">[docs]</a> 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))</div>

<div class="viewcode-block" id="Path.intersects_path"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.intersects_path">[docs]</a> 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)</div>

<div class="viewcode-block" id="Path.intersects_bbox"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.intersects_bbox">[docs]</a> 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)</div>

<div class="viewcode-block" id="Path.interpolated"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.interpolated">[docs]</a> 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 = Path.LINETO * np.ones(((len(codes) - 1) * steps + 1, ))

new_codes[0::steps] = codes

else:

new_codes = None

return Path(vertices, new_codes)</div>

<div class="viewcode-block" id="Path.to_polygons"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.to_polygons">[docs]</a> 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[0] != vertices[-1]):

vertices = [*vertices, vertices[0]]

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)</div>

_unit_rectangle = None

<div class="viewcode-block" id="Path.unit_rectangle"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.unit_rectangle">[docs]</a> @classmethod

def unit_rectangle(cls):

"""

Return a :class:`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],

readonly=True)

return cls._unit_rectangle</div>

_unit_regular_polygons = WeakValueDictionary()

<div class="viewcode-block" id="Path.unit_regular_polygon"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.unit_regular_polygon">[docs]</a> @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[0] = cls.MOVETO

codes[1:-1] = cls.LINETO

codes[-1] = cls.CLOSEPOLY

path = cls(verts, codes, readonly=True)

if numVertices <= 16:

cls._unit_regular_polygons[numVertices] = path

return path</div>

_unit_regular_stars = WeakValueDictionary()

<div class="viewcode-block" id="Path.unit_regular_star"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.unit_regular_star">[docs]</a> @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[1:-1] = cls.LINETO

codes[-1] = cls.CLOSEPOLY

if numVertices <= 16:

cls._unit_regular_stars[(numVertices, innerCircle)] = path

return path</div>

<div class="viewcode-block" id="Path.unit_regular_asterisk"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.unit_regular_asterisk">[docs]</a> @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)</div>

_unit_circle = None

<div class="viewcode-block" id="Path.unit_circle"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.unit_circle">[docs]</a> @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:

cls._unit_circle = cls.circle(center=(0, 0), radius=1,

readonly=True)

return cls._unit_circle</div>

<div class="viewcode-block" id="Path.circle"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.circle">[docs]</a> @classmethod

def circle(cls, center=(0., 0.), radius=1., readonly=False):

"""

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)``.

radius : float

The radius of the circle. Default is 1.

readonly : bool

Whether the created path should have the "readonly" argument

set when creating the Path instance.

Notes

-----

The circle is approximated using cubic Bezier curves. This

uses 8 splines around the circle using the approach presented

here:

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[-1] = cls.CLOSEPOLY

return Path(vertices * radius + center, codes, readonly=readonly)</div>

_unit_circle_righthalf = None

<div class="viewcode-block" id="Path.unit_circle_righthalf"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.unit_circle_righthalf">[docs]</a> @classmethod

def unit_circle_righthalf(cls):

"""

Return a :class:`Path` of the right half

of a unit circle. The circle is approximated using cubic Bezier

curves. This uses 4 splines around the circle using the approach

presented here:

Lancaster, Don. `Approximating a Circle or an Ellipse Using Four

Bezier Cubic Splines <http://www.tinaja.com/glib/ellipse4.pdf>`_.

"""

if cls._unit_circle_righthalf is None:

MAGIC = 0.2652031

MAGIC45 = SQRTHALF * MAGIC

vertices = np.array(

[[0.0, -1.0],

[MAGIC, -1.0],

[SQRTHALF, -SQRTHALF],

[1.0, -MAGIC],

[1.0, 0.0],

[1.0, MAGIC],

[SQRTHALF, SQRTHALF],

[MAGIC, 1.0],

[0.0, 1.0],

[0.0, -1.0]],

float)

codes = cls.CURVE4 * np.ones(14)

codes[-1] = cls.CLOSEPOLY

cls._unit_circle_righthalf = cls(vertices, codes, readonly=True)

return cls._unit_circle_righthalf</div>

<div class="viewcode-block" id="Path.arc"><a class="viewcode-back" href="../../api/path_api.html#matplotlib.path.Path.arc">[docs]</a> @classmethod

def arc(cls, theta1, theta2, n=None, is_wedge=False):

"""

Return an arc on the unit circle from angle

*theta1* to angle *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

eta1, eta2 = np.deg2rad([eta1, eta2])

# 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

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