00001 """ 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 from matplotlib.cbook import simple_linear_interpolation 00016 class Path(object): """ 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 Paths, as an optimization, do not store a codes array at all, but have a default one provided for them by :meth:`iter_segments`. """ # Path codes STOP = 0 # 1 vertex MOVETO = 1 # 1 vertex LINETO = 2 # 1 vertex CURVE3 = 3 # 2 vertices CURVE4 = 4 # 3 vertices CLOSEPOLY = 5 # 1 vertex NUM_VERTICES = [1, 1, 1, 2, 3, 1] code_type = np.uint8 00072 def __init__(self, vertices, codes=None): """ 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 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, the resulting path will be compressed, with MOVETO codes inserted in the correct places to jump over the masked regions. """ if ma.isMaskedArray(vertices): is_mask = True mask = ma.getmask(vertices) else: is_mask = False vertices = np.asarray(vertices, np.float_) mask = ma.nomask if codes is not None: codes = np.asarray(codes, self.code_type) assert codes.ndim == 1 assert len(codes) == len(vertices) # The path being passed in may have masked values. However, # the backends (and any affine transformations in matplotlib # itself), are not expected to deal with masked arrays, so we # must remove them from the array (using compressed), and add # MOVETO commands to the codes array accordingly. if is_mask: if mask is not ma.nomask: mask1d = np.logical_or.reduce(mask, axis=1) gmask1d = np.invert(mask1d) if codes is None: codes = np.empty((len(vertices)), self.code_type) codes.fill(self.LINETO) codes[0] = self.MOVETO vertices = vertices[gmask1d].filled() # ndarray codes[np.roll(mask1d, 1)] = self.MOVETO codes = codes[gmask1d] # np.compress is much slower else: vertices = np.asarray(vertices, np.float_) assert vertices.ndim == 2 assert vertices.shape[1] == 2 self.codes = codes self.vertices = vertices #@staticmethod 00129 def make_compound_path(*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 = Path.LINETO * np.ones(total_length) i = 0 for length in lengths: codes[i] = Path.MOVETO i += length return Path(vertices, codes) make_compound_path = staticmethod(make_compound_path) def __repr__(self): return "Path(%s, %s)" % (self.vertices, self.codes) def __len__(self): return len(self.vertices) 00158 def iter_segments(self): """ 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. """ vertices = self.vertices if not len(vertices): return codes = self.codes len_vertices = len(vertices) isnan = np.isnan any = np.any NUM_VERTICES = self.NUM_VERTICES MOVETO = self.MOVETO LINETO = self.LINETO CLOSEPOLY = self.CLOSEPOLY STOP = self.STOP if codes is None: next_code = MOVETO for v in vertices: if any(isnan(v)): next_code = MOVETO else: yield v, next_code next_code = LINETO else: i = 0 was_nan = False while i < len_vertices: code = codes[i] if code == CLOSEPOLY: yield [], code i += 1 elif code == STOP: return else: num_vertices = NUM_VERTICES[int(code)] curr_vertices = vertices[i:i+num_vertices].flatten() if any(isnan(curr_vertices)): was_nan = True elif was_nan: yield curr_vertices[-2:], MOVETO was_nan = False else: yield curr_vertices, code i += num_vertices 00210 def transformed(self, transform): """ Return a transformed copy of the path. See :class:`matplotlib.transforms.TransformedPath` for a path that will cache the transformed result and automatically update when the transform changes. """ return Path(transform.transform(self.vertices), self.codes) 00220 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) 00231 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) 00242 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 if transform is not None: transform = transform.frozen() return Bbox(get_path_extents(self, transform)) 00255 def intersects_path(self, other): """ Returns True if this path intersects another given path. """ return path_intersects_path(self, other) 00261 def intersects_bbox(self, bbox): """ Returns True if this path intersects a given :class:`~matplotlib.transforms.Bbox`. """ from transforms import BboxTransformTo rectangle = self.unit_rectangle().transformed( BboxTransformTo(bbox)) result = self.intersects_path(rectangle) return result 00272 def interpolated(self, steps): """ Returns a new path resampled to length N x steps. Does not currently handle interpolating curves. """ 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) 00286 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 00316 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 = \ Path([[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0], [0.0, 0.0]]) return cls._unit_rectangle unit_rectangle = classmethod(unit_rectangle) _unit_regular_polygons = WeakValueDictionary() #@classmethod 00329 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) path = Path(verts) cls._unit_regular_polygons[numVertices] = path return path unit_regular_polygon = classmethod(unit_regular_polygon) _unit_regular_stars = WeakValueDictionary() #@classmethod 00353 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() path = Path(verts) cls._unit_regular_polygons[(numVertices, innerCircle)] = path return path unit_regular_star = classmethod(unit_regular_star) #@classmethod 00378 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_regular_asterisk = classmethod(unit_regular_asterisk) _unit_circle = None #@classmethod 00389 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 = Path(vertices, codes) return cls._unit_circle unit_circle = classmethod(unit_circle) #@classmethod 00451 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.zeros((length, 2), np.float_) codes = Path.CURVE4 * np.ones((length, ), Path.code_type) vertices[1] = [xA[0], yA[0]] codes[0:2] = [Path.MOVETO, Path.LINETO] codes[-2:] = [Path.LINETO, Path.CLOSEPOLY] vertex_offset = 2 end = length - 2 else: length = n * 3 + 1 vertices = np.zeros((length, 2), np.float_) codes = Path.CURVE4 * np.ones((length, ), Path.code_type) vertices[0] = [xA[0], yA[0]] codes[0] = Path.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 Path(vertices, codes) arc = classmethod(arc) #@classmethod 00530 def wedge(cls, theta1, theta2, n=None): """ (staticmethod) Returns a wedge of the unit circle from angle theta1 to angle theta2 (in degrees). """ return cls.arc(theta1, theta2, n, True) wedge = classmethod(wedge) _get_path_collection_extents = get_path_collection_extents 00539 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))