content: """
  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
  
  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 = 5 # 1 vertex
  
      NUM_VERTICES = [1, 1, 1, 2, 3, 1]
  
      code_type = np.uint8
  
      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
          :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`.
          """
          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)
  
          assert vertices.ndim == 2
          assert vertices.shape[1] == 2
  
          self.should_simplify = (len(vertices) >= 128 and
                                  (codes is None or np.all(codes <= Path.LINETO)))
          self.has_nonfinite = not np.isfinite(vertices).all()
          self.codes = codes
          self.vertices = vertices
  
      #@staticmethod
      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)
  
      def iter_segments(self, simplify=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.
  
          If *simplify* is provided, it must be a tuple (*width*,
          *height*) defining the size of the figure, in native units
          (e.g. pixels or points).  Simplification implies both removing
          adjacent line segments that are very close to parallel, and
          removing line segments outside of the figure.  The path will
          be simplified *only* if :attr:`should_simplify` is True, which
          is determined in the constructor by this criteria:
  
             - No curves
             - More than 128 vertices
          """
          vertices = self.vertices
          if not len(vertices):
              return
  
          codes        = self.codes
          len_vertices = len(vertices)
          isfinite     = np.isfinite
  
          NUM_VERTICES = self.NUM_VERTICES
          MOVETO       = self.MOVETO
          LINETO       = self.LINETO
          CLOSEPOLY    = self.CLOSEPOLY
          STOP         = self.STOP
  
          if simplify is not None and self.should_simplify:
              polygons = self.to_polygons(None, *simplify)
              for vertices in polygons:
                  yield vertices[0], MOVETO
                  for v in vertices[1:]:
                      yield v, LINETO
          elif codes is None:
              if self.has_nonfinite:
                  next_code = MOVETO
                  for v in vertices:
                      if np.isfinite(v).all():
                          yield v, next_code
                          next_code = LINETO
                      else:
                          next_code = MOVETO
              else:
                  yield vertices[0], MOVETO
                  for v in vertices[1:]:
                      yield v, 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 not isfinite(curr_vertices).all():
                          was_nan = True
                      elif was_nan:
                          yield curr_vertices[-2:], MOVETO
                          was_nan = False
                      else:
                          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)
  
      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
          if transform is not None:
              transform = transform.frozen()
          return Bbox(get_path_extents(self, 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.
          """
          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 = \
                  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
      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
      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
      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
      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
      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
      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)
      wedge = classmethod(wedge)
  
  _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))
  