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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. """
""" :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
#: A dictionary mapping Path codes to the number of vertices that the #: code expects. MOVETO: 1, LINETO: 1, CURVE3: 2, CURVE4: 3, CLOSEPOLY: 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. """ raise ValueError( "'vertices' must be a 2D list or array with shape Nx2")
raise ValueError("'codes' must be a 1D list or array with the " "same length of 'vertices'") raise ValueError("The first element of 'code' must be equal " "to 'MOVETO' ({})".format(self.MOVETO))
else:
""" 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.pop('simplify_threshold', rcParams['path.simplify_threshold']) ) raise ValueError('Unexpected internals provided to ' '_fast_from_codes_and_verts: ' '{0}'.format('\n *'.join(internals)))
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)) )
def vertices(self): """ The list of vertices in the `Path` as an Nx2 numpy array. """
def vertices(self, vertices): if self._readonly: raise AttributeError("Can't set vertices on a readonly Path") self._vertices = vertices self._update_values()
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. """
def codes(self, codes): if self._readonly: raise AttributeError("Can't set codes on a readonly Path") self._codes = codes self._update_values()
def simplify_threshold(self): """ The fraction of a pixel difference below which vertices will be simplified out. """
def simplify_threshold(self, threshold):
def has_nonfinite(self): """ `True` if the vertices array has nonfinite values. """ return self._has_nonfinite
def should_simplify(self): """ `True` if the vertices array should be simplified. """
def should_simplify(self, should_simplify):
def readonly(self): """ `True` if the `Path` is read-only. """ return self._readonly
""" Returns a shallow copy of the `Path`, which will share the vertices and codes with the source `Path`. """ import copy return copy.copy(self)
""" 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)
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)
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)
return len(self.vertices)
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
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)
""" 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. """ self._interpolation_steps)
""" 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. """ # `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. self = transform.transform_path(self) transform = None
""" 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. """ transform = transform.frozen()
""" 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)
""" 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. """ path = self.transformed(transform) transform = None
""" 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)
""" 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. """ bbox.x0, bbox.y0, bbox.x1, bbox.y1, filled)
""" Returns a new path resampled to length N x steps. Does not currently handle interpolating curves. """ return self
new_codes = Path.LINETO * np.ones(((len(codes) - 1) * steps + 1, )) new_codes[0::steps] = codes else:
""" 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)
def unit_rectangle(cls): """ Return a :class:`Path` instance of the unit rectangle from (0, 0) to (1, 1). """ 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)
def unit_regular_polygon(cls, numVertices): """ Return a :class:`Path` instance for a unit regular polygon with the given *numVertices* and radius of 1.0, centered at (0, 0). """ if numVertices <= 16: path = cls._unit_regular_polygons.get(numVertices) else: path = None if path is None: theta = ((2 * np.pi / numVertices) * np.arange(numVertices + 1) # This initial rotation is to make sure the polygon always # "points-up". + np.pi / 2) verts = np.column_stack((np.cos(theta), np.sin(theta))) codes = np.empty(numVertices + 1) codes[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
""" 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
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)
def unit_circle(cls): """ Return the readonly :class:`Path` of the unit circle.
For most cases, :func:`Path.circle` will be what you want.
""" readonly=True)
""" 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, -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)
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
""" 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>`_. """
# Ensure 2pi range is not flattened to 0 due to floating-point errors, # but don't try to expand existing 0 range.
# number of curve segments to make raise ValueError("n must be >= 1 or None")
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:
""" 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)
""" Given a hatch specifier, *hatchpattern*, generates a Path that can be used in a repeated hatching pattern. *density* is the number of lines per unit square. """ from matplotlib.hatch import get_path return (get_path(hatchpattern, density) if hatchpattern is not None else None)
""" 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)
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) """ raise ValueError("No paths provided") master_transform, paths, np.atleast_3d(transforms), offsets, offset_transform))
""" 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())) |