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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 . import _path, rcParams
from .cbook import (_to_unmasked_float_array, simple_linear_interpolation,
maxdict)
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):
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)
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__
@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/api/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)
@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. 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
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 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)
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')
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)
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 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)
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, 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, 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 *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 = list(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)
_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_stars[(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 = 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[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 = 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 = 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).
*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
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).
*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*.
"""
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.
*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()))