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. """ import copy from functools import lru_cache from weakref import WeakValueDictionary import numpy as np import matplotlib as mpl from . import _api, _path from .cbook import _to_unmasked_float_array, simple_linear_interpolation from .bezier import BezierSegment class Path: """ A series of possibly disconnected, possibly closed, line and curve segments. The underlying storage is made up of two parallel numpy arrays: - *vertices*: an (N, 2) float array of vertices - *codes*: an N-length `numpy.uint8` array of path codes, or None These two arrays always have the same length in the first dimension. For example, to represent a cubic curve, you must provide three vertices and three `CURVE4` codes. 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 Bézier curve from the current position, with the given control point, to the given end point. - `CURVE4` : 2 control points, 1 endpoint Draw a cubic Bézier 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. If *codes* is None, it is interpreted as a `MOVETO` followed by a series of `LINETO`. Users of Path objects should not access the vertices and codes arrays directly. Instead, they should use `iter_segments` or `cleaned` to get the vertex/code pairs. This helps, in particular, to consistently handle the case of *codes* being None. Some behavior of Path objects can be controlled by rcParams. See the rcParams whose keys start with '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. """ code_type = np.uint8 # Path codes STOP = code_type(0) # 1 vertex MOVETO = code_type(1) # 1 vertex LINETO = code_type(2) # 1 vertex CURVE3 = code_type(3) # 2 vertices CURVE4 = code_type(4) # 3 vertices CLOSEPOLY = code_type(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} 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 : (N, 2) array-like The path vertices, as an array, masked array or sequence of pairs. Masked values, if any, 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 : array-like or None, optional N-length array of 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. Note that the last vertex will then be ignored (as the corresponding code will be set to `CLOSEPOLY`). 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) _api.check_shape((None, 2), vertices=vertices) if codes is not None: codes = np.asarray(codes, self.code_type) if codes.ndim != 1 or len(codes) != len(vertices): raise ValueError("'codes' must be a 1D list or array with the " "same length of 'vertices'. " f"Your vertices have shape {vertices.shape} " f"but your codes have shape {codes.shape}") if len(codes) and codes[0] != self.MOVETO: raise ValueError("The first element of 'code' must be equal " f"to 'MOVETO' ({self.MOVETO}). " f"Your first code is {codes[0]}") elif closed and len(vertices): codes = np.empty(len(vertices), dtype=self.code_type) codes[0] = self.MOVETO codes[1:-1] = self.LINETO codes[-1] = self.CLOSEPOLY self._vertices = vertices self._codes = codes self._interpolation_steps = _interpolation_steps self._update_values() if readonly: self._vertices.flags.writeable = False if self._codes is not None: self._codes.flags.writeable = False self._readonly = True else: self._readonly = False @classmethod def _fast_from_codes_and_verts(cls, verts, codes, internals_from=None): """ Create a Path instance without the expense of calling the constructor. Parameters ---------- verts : array-like codes : array internals_from : Path or None If not None, another `Path` from which the attributes ``should_simplify``, ``simplify_threshold``, and ``interpolation_steps`` will be copied. Note that ``readonly`` is never copied, and always set to ``False`` by this constructor. """ pth = cls.__new__(cls) pth._vertices = _to_unmasked_float_array(verts) pth._codes = codes pth._readonly = False if internals_from is not None: pth._should_simplify = internals_from._should_simplify pth._simplify_threshold = internals_from._simplify_threshold pth._interpolation_steps = internals_from._interpolation_steps else: pth._should_simplify = True pth._simplify_threshold = mpl.rcParams['path.simplify_threshold'] pth._interpolation_steps = 1 return pth @classmethod def _create_closed(cls, vertices): """ Create a closed polygonal path going through *vertices*. Unlike ``Path(..., closed=True)``, *vertices* should **not** end with an entry for the CLOSEPATH; this entry is added by `._create_closed`. """ v = _to_unmasked_float_array(vertices) return cls(np.concatenate([v, v[:1]]), closed=True) def _update_values(self): self._simplify_threshold = mpl.rcParams['path.simplify_threshold'] self._should_simplify = ( self._simplify_threshold > 0 and mpl.rcParams['path.simplify'] and len(self._vertices) >= 128 and (self._codes is None or np.all(self._codes <= Path.LINETO)) ) @property def vertices(self): """The vertices of the `Path` as an (N, 2) 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 1D 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 `vertices` and `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 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): """ Return a shallow copy of the `Path`, which will share the vertices and codes with the source `Path`. """ return copy.copy(self) def __deepcopy__(self, memo=None): """ Return a deepcopy of the `Path`. The `Path` will not be readonly, even if the source `Path` is. """ # Deepcopying arrays (vertices, codes) strips the writeable=False flag. p = copy.deepcopy(super(), memo) p._readonly = False return p 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. .. plot:: gallery/misc/histogram_path.py Parameters ---------- XY : (numpolys, numsides, 2) array """ # 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.full(nverts, cls.LINETO, dtype=cls.code_type) 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): r""" Concatenate a list of `Path`\s into a single `Path`, removing all `STOP`\s. """ if not args: return Path(np.empty([0, 2], dtype=np.float32)) vertices = np.concatenate([path.vertices for path in args]) codes = np.empty(len(vertices), dtype=cls.code_type) i = 0 for path in args: size = len(path.vertices) if path.codes is None: if size: codes[i] = cls.MOVETO codes[i+1:i+size] = cls.LINETO else: codes[i:i+size] = path.codes i += size not_stop_mask = codes != cls.STOP # Remove STOPs, as internal STOPs are a bug. return cls(vertices[not_stop_mask], codes[not_stop_mask]) def __repr__(self): return f"Path({self.vertices!r}, {self.codes!r})" 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): """ Iterate over all curve segments in the path. Each iteration returns a pair ``(vertices, code)``, where ``vertices`` is a sequence of 1-3 coordinate pairs, and ``code`` is a `Path` code. Additionally, this method can provide a number of standard cleanups and conversions to the path. Parameters ---------- transform : None or :class:`~matplotlib.transforms.Transform` If not None, the given affine transformation will be applied to the path. remove_nans : bool, optional Whether to remove all NaNs from the path and skip over them using MOVETO commands. clip : None or (float, float, float, float), 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 True, snap all nodes to pixels; if False, don't snap them. If None, snap if the path contains only segments parallel to the x or y axes, and no more than 1024 of them. stroke_width : float, optional The width of the stroke being drawn (used for path snapping). simplify : None or bool, optional Whether to simplify the path by removing vertices that do not affect its appearance. If None, use the :attr:`should_simplify` attribute. See also :rc:`path.simplify` and :rc:`path.simplify_threshold`. curves : bool, 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) # Cache these object lookups for performance in the loop. NUM_VERTICES_FOR_CODE = self.NUM_VERTICES_FOR_CODE STOP = self.STOP vertices = iter(cleaned.vertices) codes = iter(cleaned.codes) for curr_vertices, code in zip(vertices, codes): if code == STOP: break extra_vertices = NUM_VERTICES_FOR_CODE[code] - 1 if extra_vertices: for i in range(extra_vertices): next(codes) curr_vertices = np.append(curr_vertices, next(vertices)) yield curr_vertices, code def iter_bezier(self, **kwargs): """ Iterate over each Bézier curve (lines included) in a `Path`. Parameters ---------- **kwargs Forwarded to `.iter_segments`. Yields ------ B : `~matplotlib.bezier.BezierSegment` The Bézier curves that make up the current path. Note in particular that freestanding points are Bézier curves of order 0, and lines are Bézier curves of order 1 (with two control points). code : `~matplotlib.path.Path.code_type` The code describing what kind of curve is being returned. `MOVETO`, `LINETO`, `CURVE3`, and `CURVE4` correspond to Bézier curves with 1, 2, 3, and 4 control points (respectively). `CLOSEPOLY` is a `LINETO` with the control points correctly chosen based on the start/end points of the current stroke. """ first_vert = None prev_vert = None for verts, code in self.iter_segments(**kwargs): if first_vert is None: if code != Path.MOVETO: raise ValueError("Malformed path, must start with MOVETO.") if code == Path.MOVETO: # a point is like "CURVE1" first_vert = verts yield BezierSegment(np.array([first_vert])), code elif code == Path.LINETO: # "CURVE2" yield BezierSegment(np.array([prev_vert, verts])), code elif code == Path.CURVE3: yield BezierSegment(np.array([prev_vert, verts[:2], verts[2:]])), code elif code == Path.CURVE4: yield BezierSegment(np.array([prev_vert, verts[:2], verts[2:4], verts[4:]])), code elif code == Path.CLOSEPOLY: yield BezierSegment(np.array([prev_vert, first_vert])), code elif code == Path.STOP: return else: raise ValueError(f"Invalid Path.code_type: {code}") prev_vert = verts[-2:] def _iter_connected_components(self): """Return subpaths split at MOVETOs.""" if self.codes is None: yield self else: idxs = np.append((self.codes == Path.MOVETO).nonzero()[0], len(self.codes)) for sl in map(slice, idxs, idxs[1:]): yield Path._fast_from_codes_and_verts( self.vertices[sl], self.codes[sl], self) def cleaned(self, transform=None, remove_nans=False, clip=None, *, simplify=False, curves=False, stroke_width=1.0, snap=False, sketch=None): """ Return a new `Path` with vertices and codes cleaned according to the parameters. See Also -------- Path.iter_segments : for details of the keyword arguments. """ vertices, codes = _path.cleanup_path( self, transform, remove_nans, clip, snap, stroke_width, simplify, curves, sketch) pth = Path._fast_from_codes_and_verts(vertices, codes, self) if not simplify: pth._should_simplify = False return pth def transformed(self, transform): """ Return a transformed copy of the path. See Also -------- 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): """ Return whether the area enclosed by the path contains the given point. The path is always treated as closed; i.e. if the last code is not `CLOSEPOLY` an implicit segment connecting the last vertex to the first vertex is assumed. Parameters ---------- point : (float, float) The point (x, y) to check. transform : `~matplotlib.transforms.Transform`, optional If not ``None``, *point* will be compared to ``self`` transformed by *transform*; i.e. for a correct check, *transform* should transform the path into the coordinate system of *point*. radius : float, default: 0 Additional margin on the path in coordinates of *point*. The path is extended tangentially by *radius/2*; i.e. if you would draw the path with a linewidth of *radius*, all points on the line would still be considered to be contained in the area. Conversely, negative values shrink the area: Points on the imaginary line will be considered outside the area. Returns ------- bool Notes ----- The current algorithm has some limitations: - The result is undefined for points exactly at the boundary (i.e. at the path shifted by *radius/2*). - The result is undefined if there is no enclosed area, i.e. all vertices are on a straight line. - If bounding lines start to cross each other due to *radius* shift, the result is not guaranteed to be correct. """ 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): """ Return whether the area enclosed by the path contains the given points. The path is always treated as closed; i.e. if the last code is not `CLOSEPOLY` an implicit segment connecting the last vertex to the first vertex is assumed. Parameters ---------- points : (N, 2) array The points to check. Columns contain x and y values. transform : `~matplotlib.transforms.Transform`, optional If not ``None``, *points* will be compared to ``self`` transformed by *transform*; i.e. for a correct check, *transform* should transform the path into the coordinate system of *points*. radius : float, default: 0 Additional margin on the path in coordinates of *points*. The path is extended tangentially by *radius/2*; i.e. if you would draw the path with a linewidth of *radius*, all points on the line would still be considered to be contained in the area. Conversely, negative values shrink the area: Points on the imaginary line will be considered outside the area. Returns ------- length-N bool array Notes ----- The current algorithm has some limitations: - The result is undefined for points exactly at the boundary (i.e. at the path shifted by *radius/2*). - The result is undefined if there is no enclosed area, i.e. all vertices are on a straight line. - If bounding lines start to cross each other due to *radius* shift, the result is not guaranteed to be correct. """ 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): """ Return whether this (closed) path completely contains the given path. If *transform* is not ``None``, the path will be transformed before checking for containment. """ if transform is not None: transform = transform.frozen() return _path.path_in_path(self, None, path, transform) def get_extents(self, transform=None, **kwargs): """ Get Bbox of the path. Parameters ---------- transform : `~matplotlib.transforms.Transform`, optional Transform to apply to path before computing extents, if any. **kwargs Forwarded to `.iter_bezier`. Returns ------- matplotlib.transforms.Bbox The extents of the path Bbox([[xmin, ymin], [xmax, ymax]]) """ from .transforms import Bbox if transform is not None: self = transform.transform_path(self) if self.codes is None: xys = self.vertices elif len(np.intersect1d(self.codes, [Path.CURVE3, Path.CURVE4])) == 0: # Optimization for the straight line case. # Instead of iterating through each curve, consider # each line segment's end-points # (recall that STOP and CLOSEPOLY vertices are ignored) xys = self.vertices[np.isin(self.codes, [Path.MOVETO, Path.LINETO])] else: xys = [] for curve, code in self.iter_bezier(**kwargs): # places where the derivative is zero can be extrema _, dzeros = curve.axis_aligned_extrema() # as can the ends of the curve xys.append(curve([0, *dzeros, 1])) xys = np.concatenate(xys) if len(xys): return Bbox([xys.min(axis=0), xys.max(axis=0)]) else: return Bbox.null() def intersects_path(self, other, filled=True): """ Return whether if this path intersects another given path. If *filled* is True, then this also returns True if one path completely encloses the other (i.e., the paths are treated as filled). """ return _path.path_intersects_path(self, other, filled) def intersects_bbox(self, bbox, filled=True): """ Return whether this path intersects a given `~.transforms.Bbox`. If *filled* is True, then this also returns True if the path completely encloses the `.Bbox` (i.e., the path is treated as filled). 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): """ Return a new path resampled to length N x *steps*. Codes other than `LINETO` are not handled correctly. """ if steps == 1: return self vertices = simple_linear_interpolation(self.vertices, steps) codes = self.codes if codes is not None: new_codes = np.full((len(codes) - 1) * steps + 1, Path.LINETO, dtype=self.code_type) 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 (N, 2) 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 Bézier 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. The resulting polygons will be simplified if the :attr:`Path.should_simplify` attribute of the path is `True`. 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) _unit_rectangle = None @classmethod def unit_rectangle(cls): """ Return a `Path` instance of the unit rectangle from (0, 0) to (1, 1). """ if cls._unit_rectangle is None: cls._unit_rectangle = cls([[0, 0], [1, 0], [1, 1], [0, 1], [0, 0]], closed=True, 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* such that the circumscribing circle has radius 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))) path = cls(verts, closed=True, 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 = (r * np.vstack((np.cos(theta), np.sin(theta)))).T path = cls(verts, closed=True, 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 : (float, float), default: (0, 0) The center of the circle. radius : float, default: 1 The radius of the circle. readonly : bool Whether the created path should have the "readonly" argument set when creating the Path instance. Notes ----- The circle is approximated using 8 cubic Bézier curves, as described in Lancaster, Don. `Approximating a Circle or an Ellipse Using Four Bezier Cubic Splines `_. """ 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 `Path` of the right half of a unit circle. See `Path.circle` for the reference on the approximation used. """ 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 = np.full(14, cls.CURVE4, dtype=cls.code_type) 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 a `Path` for the unit circle arc from angles *theta1* to *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 `_. """ 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 = np.full(length, cls.CURVE4, dtype=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 = np.full(length, cls.CURVE4, dtype=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 `Path` for the unit circle wedge from angles *theta1* to *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*. See `Path.arc` for the reference on the approximation used. """ return cls.arc(theta1, theta2, n, True) @staticmethod @lru_cache(8) def hatch(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 return (get_path(hatchpattern, density) if hatchpattern is not None else None) 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. """ 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): r""" Get bounding box of a `.PathCollection`\s internal objects. That is, given a sequence of `Path`\s, `.Transform`\s objects, and offsets, as found in a `.PathCollection`, return the bounding box that encapsulates all of them. Parameters ---------- master_transform : `~matplotlib.transforms.Transform` Global transformation applied to all paths. paths : list of `Path` transforms : list of `~matplotlib.transforms.Affine2DBase` If non-empty, this overrides *master_transform*. offsets : (N, 2) array-like offset_transform : `~matplotlib.transforms.Affine2DBase` Transform applied to the offsets before offsetting the path. Notes ----- 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 (A, B, C), 2 transforms (α, β) and 1 offset (O), their combinations are as follows: - (A, α, O) - (B, β, O) - (C, α, O) """ from .transforms import Bbox if len(paths) == 0: raise ValueError("No paths provided") if len(offsets) == 0: _api.warn_deprecated( "3.8", message="Calling get_path_collection_extents() with an" " empty offsets list is deprecated since %(since)s. Support will" " be removed %(removal)s.") extents, minpos = _path.get_path_collection_extents( master_transform, paths, np.atleast_3d(transforms), offsets, offset_transform) return Bbox.from_extents(*extents, minpos=minpos)