matplotlib/lib/matplotlib/path.py at master · feisuo/matplotlib · GitHub

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"""

A module for dealing with the polylines used throughout matplotlib.

The primary class for polyline handling in matplotlib is :class:`Path`.

Almost all vector drawing makes use of Paths somewhere in the drawing

pipeline.

Whilst a :class:`Path` instance itself cannot be drawn, there exists

:class:`~matplotlib.artist.Artist` subclasses which can be used for

convenient Path visualisation - the two most frequently used of these are

:class:`~matplotlib.patches.PathPatch` and

:class:`~matplotlib.collections.PathCollection`.

"""

from __future__ import (absolute_import, division, print_function,

unicode_literals)

import six

import math

from weakref import WeakValueDictionary

import numpy as np

from matplotlib import _path

from matplotlib.cbook import simple_linear_interpolation, maxdict

from matplotlib import rcParams

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`.

.. 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.

"""

if isinstance(vertices, np.ma.MaskedArray):

vertices = vertices.astype(float).filled(np.nan)

else:

vertices = np.asarray(vertices, float)

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

msg = "'vertices' must be a 2D list or array with shape Nx2"

raise ValueError(msg)

if codes is not None:

codes = np.asarray(codes, self.code_type)

if (codes.ndim != 1) or len(codes) != len(vertices):

msg = ("'codes' must be a 1D list or array with the same"

" length of 'vertices'")

raise ValueError(msg)

if len(codes) and codes[0] != self.MOVETO:

msg = ("The first element of 'code' must be equal to 'MOVETO':"

" {0}")

raise ValueError(msg.format(self.MOVETO))

elif closed:

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)

if isinstance(verts, np.ma.MaskedArray):

verts = verts.astype(float).filled(np.nan)

else:

verts = np.asarray(verts, float)

pth._vertices = 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(six.iterkeys(

internals

))))

return pth

def _update_values(self):

self._should_simplify = (

rcParams['path.simplify'] and

(len(self._vertices) >= 128 and

(self._codes is None or np.all(self._codes <= Path.LINETO)))

)

self._simplify_threshold = rcParams['path.simplify_threshold']

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):

"""

Returns a deepcopy of the `Path`. The `Path` will not be

readonly, even if the source `Path` is.

"""

return self.__class__(

self.vertices.copy(), self.codes.copy(),

_interpolation_steps=self._interpolation_steps)

deepcopy = __deepcopy__

@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:: mpl_examples/api/histogram_path_demo.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)

@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)

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.

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

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)

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)

def contains_point(self, point, transform=None, radius=0.0):

"""

Returns *True* if the 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()

result = _path.point_in_path(point[0], point[1], radius, self,

transform)

return result

def contains_points(self, points, transform=None, radius=0.0):

"""

Returns a bool array which is *True* if the 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

def contains_path(self, path, transform=None):

"""

Returns *True* if this 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)

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))

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)

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 one path completely encloses the other,

:meth:`intersects_path` will return True.

"""

from .transforms import BboxTransformTo

rectangle = self.unit_rectangle().transformed(

BboxTransformTo(bbox))

result = self.intersects_path(rectangle, filled)

return result

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)

def to_polygons(self, transform=None, width=0, height=0):

"""

Convert this path to a list of polygons. Each polygon 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, such as GDK.

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 len(self.vertices) == 0:

return []

if transform is not None:

transform = transform.frozen()

if self.codes is None and (width == 0 or height == 0):

if transform is None:

return [self.vertices]

else:

return [transform.transform(self.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)

_unit_rectangle = None

@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

_unit_regular_polygons = WeakValueDictionary()

@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).reshape((numVertices + 1, 1)))

# This initial rotation is to make sure the polygon always

# "points-up"

theta += np.pi / 2.0

verts = np.concatenate((np.cos(theta), np.sin(theta)), 1)

codes = np.empty((numVertices + 1,))

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

_unit_regular_stars = WeakValueDictionary()

@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[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, innerCircle)] = path

return path

@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

@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

@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 = np.sqrt((MAGIC*MAGIC) / 2.0)

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[0] = cls.MOVETO

codes[-1] = cls.CLOSEPOLY

return Path(vertices * radius + center, codes, readonly=readonly)

_unit_circle_righthalf = None

@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

SQRTHALF = np.sqrt(0.5)

MAGIC45 = np.sqrt((MAGIC*MAGIC) / 2.0)

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 = cls.CURVE4 * np.ones(14)

codes[0] = cls.MOVETO

codes[-1] = cls.CLOSEPOLY

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

return cls._unit_circle_righthalf

@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).

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>`_.

"""

# degrees to radians

theta1 *= np.pi / 180.0

theta2 *= np.pi / 180.0

twopi = np.pi * 2.0

halfpi = np.pi * 0.5

eta1 = np.arctan2(np.sin(theta1), np.cos(theta1))

eta2 = np.arctan2(np.sin(theta2), np.cos(theta2))

eta2 -= twopi * np.floor((eta2 - eta1) / twopi)

# 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 = cls.CURVE4 * np.ones((length, ), cls.code_type)

vertices[1] = [xA[0], yA[0]]

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 = cls.CURVE4 * np.ones((length, ), cls.code_type)

vertices[0] = [xA[0], yA[0]]

codes[0] = 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

return cls(vertices, codes, readonly=True)

@classmethod

def wedge(cls, theta1, theta2, n=None):

"""

Return a wedge of the unit circle from angle

*theta1* to angle *theta2* (in degrees).

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*.

"""

return cls.arc(theta1, theta2, n, True)

_hatch_dict = maxdict(8)

@classmethod

def hatch(cls, 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

if hatchpattern is None:

return None

hatch_path = cls._hatch_dict.get((hatchpattern, density))

if hatch_path is not None:

return hatch_path

hatch_path = get_path(hatchpattern, density)

cls._hatch_dict[(hatchpattern, density)] = hatch_path

return hatch_path

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)

def get_path_collection_extents(

master_transform, paths, transforms, offsets, offset_transform):

"""

Given a sequence of :class:`Path` objects,

:class:`~matplotlib.transforms.Transform` objects and offsets, as

found in a :class:`~matplotlib.collections.PathCollection`,

returns the bounding box that encapsulates all of them.

*master_transform* is a global transformation to apply to all paths

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

*transforms* is a sequence of

:class:`~matplotlib.transforms.Affine2D` instances.

*offsets* is a sequence of (x, y) offsets (or an Nx2 array)

*offset_transform* is a :class:`~matplotlib.transforms.Affine2D`

to apply to the offsets before applying the offset to the path.

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))

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.

View remainder of file in raw view

matplotlib/lib/matplotlib/path.py at master · feisuo/matplotlib · GitHub

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