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"""
Contains a class for managing paths (polylines).
"""
import math
from weakref import WeakValueDictionary
import numpy as np
from numpy import ma
from matplotlib._path import point_in_path, get_path_extents, \
point_in_path_collection, get_path_collection_extents, \
path_in_path, path_intersects_path, convert_path_to_polygons, \
cleanup_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`
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 also that 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 = 0x4f # 1 vertex
NUM_VERTICES = [1, 1, 1, 2,
3, 1, 1, 1,
1, 1, 1, 1,
1, 1, 1, 1]
code_type = np.uint8
def __init__(self, vertices, codes=None, _interpolation_steps=1):
"""
Create a new path with the given vertices and codes.
*vertices* is an Nx2 numpy float array, masked array or Python
sequence.
*codes* is an N-length numpy array or Python sequence of type
:attr:`matplotlib.path.Path.code_type`.
These two arrays must have the same length in the first
dimension.
If *codes* is None, *vertices* will be treated as a series of
line segments.
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`.
*interpolation_steps* is 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.
"""
if ma.isMaskedArray(vertices):
vertices = vertices.astype(np.float_).filled(np.nan)
else:
vertices = np.asarray(vertices, np.float_)
if codes is not None:
codes = np.asarray(codes, self.code_type)
assert codes.ndim == 1
assert len(codes) == len(vertices)
if len(codes):
assert codes[0] == self.MOVETO
assert vertices.ndim == 2
assert vertices.shape[1] == 2
self.should_simplify = (rcParams['path.simplify'] and
(len(vertices) >= 128 and
(codes is None or np.all(codes <= Path.LINETO))))
self.simplify_threshold = rcParams['path.simplify_threshold']
self.has_nonfinite = not np.isfinite(vertices).all()
self.codes = codes
self.vertices = vertices
self._interpolation_steps = _interpolation_steps
@classmethod
def make_compound_path_from_polys(cls, XY):
"""
(static method) 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
assert(two==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):
"""
(staticmethod) Make a compound path from a list of Path
objects. Only polygons (not curves) are supported.
"""
for p in args:
assert p.codes is None
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 = cls.LINETO * np.ones(total_length)
i = 0
for length in lengths:
codes[i] = cls.MOVETO
i += length
return cls(vertices, codes)
def __repr__(self):
return "Path(%s, %s)" % (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):
"""
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.
*transform*: if not None, the given affine transformation will
be applied to the path.
*remove_nans*: if True, will remove all NaNs from the path and
insert MOVETO commands to skip over them.
*clip*: if not None, must be a four-tuple (x1, y1, x2, y2)
defining a rectangle in which to clip the path.
*snap*: if None, auto-snap to pixels, to reduce
fuzziness of rectilinear lines. If True, force snapping, and
if False, don't snap.
*stroke_width*: the width of the stroke being drawn. Needed
as a hint for the snapping algorithm.
*simplify*: 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*: If True, curve segments will be returned as curve
segments. If False, all curves will be converted to line
segments.
"""
vertices = self.vertices
if not len(vertices):
return
codes = self.codes
NUM_VERTICES = self.NUM_VERTICES
MOVETO = self.MOVETO
LINETO = self.LINETO
CLOSEPOLY = self.CLOSEPOLY
STOP = self.STOP
vertices, codes = cleanup_path(self, transform, remove_nans, clip,
snap, stroke_width, simplify, curves)
len_vertices = len(vertices)
i = 0
while i < len_vertices:
code = codes[i]
if code == STOP:
return
else:
num_vertices = NUM_VERTICES[int(code) & 0xf]
curr_vertices = vertices[i:i+num_vertices].flatten()
yield curr_vertices, code
i += num_vertices
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):
"""
Returns *True* if the 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()
return point_in_path(point[0], point[1], self, transform)
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_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(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_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 convert_path_to_polygons(self, transform, width, height)
_unit_rectangle = None
@classmethod
def unit_rectangle(cls):
"""
(staticmethod) Returns a :class:`Path` 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()
@classmethod
def unit_regular_polygon(cls, numVertices):
"""
(staticmethod) Returns a :class:`Path` 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)
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):
"""
(staticmethod) Returns 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)
if numVertices <= 16:
cls._unit_regular_polygons[(numVertices, innerCircle)] = path
return path
@classmethod
def unit_regular_asterisk(cls, numVertices):
"""
(staticmethod) Returns 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):
"""
(staticmethod) Returns a :class:`Path` of the unit circle.
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>`_.
"""
if cls._unit_circle 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],
[-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]],
np.float_)
codes = cls.CURVE4 * np.ones(26)
codes[0] = cls.MOVETO
codes[-1] = cls.CLOSEPOLY
cls._unit_circle = cls(vertices, codes)
return cls._unit_circle
_unit_circle_righthalf = None
@classmethod
def unit_circle_righthalf(cls):
"""
(staticmethod) Returns 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]],
np.float_)
codes = cls.CURVE4 * np.ones(14)
codes[0] = cls.MOVETO
codes[-1] = cls.CLOSEPOLY
cls._unit_circle_righthalf = cls(vertices, codes)
return cls._unit_circle_righthalf
@classmethod
def arc(cls, theta1, theta2, n=None, is_wedge=False):
"""
(staticmethod) Returns 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)
if (theta2 - theta1 > np.pi) and (eta2 - eta1 < np.pi):
eta2 += 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.empty((length, 2), np.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), np.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)
@classmethod
def wedge(cls, theta1, theta2, n=None):
"""
(staticmethod) Returns 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
_get_path_collection_extents = get_path_collection_extents
def get_path_collection_extents(*args):
"""
Given a sequence of :class:`Path` objects, returns the bounding
box that encapsulates all of them.
"""
from transforms import Bbox
if len(args[1]) == 0:
raise ValueError("No paths provided")
return Bbox.from_extents(*_get_path_collection_extents(*args))