text: from collections import OrderedDict
  import types
  
  import numpy as np
  
  from matplotlib import cbook, rcParams
  from matplotlib.axes import Axes
  import matplotlib.axis as maxis
  import matplotlib.markers as mmarkers
  import matplotlib.patches as mpatches
  import matplotlib.path as mpath
  import matplotlib.ticker as mticker
  import matplotlib.transforms as mtransforms
  import matplotlib.spines as mspines
  
  
  class PolarTransform(mtransforms.Transform):
      """
      The base polar transform.  This handles projection *theta* and
      *r* into Cartesian coordinate space *x* and *y*, but does not
      perform the ultimate affine transformation into the correct
      position.
      """
      input_dims = 2
      output_dims = 2
      is_separable = False
  
      def __init__(self, axis=None, use_rmin=True,
                   _apply_theta_transforms=True):
          mtransforms.Transform.__init__(self)
          self._axis = axis
          self._use_rmin = use_rmin
          self._apply_theta_transforms = _apply_theta_transforms
  
      def __str__(self):
          return ("{}(\n"
                      "{},\n"
                  "    use_rmin={},\n"
                  "    _apply_theta_transforms={})"
                  .format(type(self).__name__,
                          mtransforms._indent_str(self._axis),
                          self._use_rmin,
                          self._apply_theta_transforms))
  
      def transform_non_affine(self, tr):
          # docstring inherited
          t, r = np.transpose(tr)
          # PolarAxes does not use the theta transforms here, but apply them for
          # backwards-compatibility if not being used by it.
          if self._apply_theta_transforms and self._axis is not None:
              t *= self._axis.get_theta_direction()
              t += self._axis.get_theta_offset()
          if self._use_rmin and self._axis is not None:
              r = (r - self._axis.get_rorigin()) * self._axis.get_rsign()
          r = np.where(r >= 0, r, np.nan)
          return np.column_stack([r * np.cos(t), r * np.sin(t)])
  
      def transform_path_non_affine(self, path):
          # docstring inherited
          vertices = path.vertices
          if len(vertices) == 2 and vertices[0, 0] == vertices[1, 0]:
              return mpath.Path(self.transform(vertices), path.codes)
          ipath = path.interpolated(path._interpolation_steps)
          return mpath.Path(self.transform(ipath.vertices), ipath.codes)
  
      def inverted(self):
          # docstring inherited
          return PolarAxes.InvertedPolarTransform(self._axis, self._use_rmin,
                                                  self._apply_theta_transforms)
  
  
  class PolarAffine(mtransforms.Affine2DBase):
      """
      The affine part of the polar projection.  Scales the output so
      that maximum radius rests on the edge of the axes circle.
      """
      def __init__(self, scale_transform, limits):
          """
          *limits* is the view limit of the data.  The only part of
          its bounds that is used is the y limits (for the radius limits).
          The theta range is handled by the non-affine transform.
          """
          mtransforms.Affine2DBase.__init__(self)
          self._scale_transform = scale_transform
          self._limits = limits
          self.set_children(scale_transform, limits)
          self._mtx = None
  
      def __str__(self):
          return ("{}(\n"
                      "{},\n"
                      "{})"
                  .format(type(self).__name__,
                          mtransforms._indent_str(self._scale_transform),
                          mtransforms._indent_str(self._limits)))
  
      def get_matrix(self):
          # docstring inherited
          if self._invalid:
              limits_scaled = self._limits.transformed(self._scale_transform)
              yscale = limits_scaled.ymax - limits_scaled.ymin
              affine = mtransforms.Affine2D() \
                  .scale(0.5 / yscale) \
                  .translate(0.5, 0.5)
              self._mtx = affine.get_matrix()
              self._inverted = None
              self._invalid = 0
          return self._mtx
  
  
  class InvertedPolarTransform(mtransforms.Transform):
      """
      The inverse of the polar transform, mapping Cartesian
      coordinate space *x* and *y* back to *theta* and *r*.
      """
      input_dims = 2
      output_dims = 2
      is_separable = False
  
      def __init__(self, axis=None, use_rmin=True,
                   _apply_theta_transforms=True):
          mtransforms.Transform.__init__(self)
          self._axis = axis
          self._use_rmin = use_rmin
          self._apply_theta_transforms = _apply_theta_transforms
  
      def __str__(self):
          return ("{}(\n"
                      "{},\n"
                  "    use_rmin={},\n"
                  "    _apply_theta_transforms={})"
                  .format(type(self).__name__,
                          mtransforms._indent_str(self._axis),
                          self._use_rmin,
                          self._apply_theta_transforms))
  
      def transform_non_affine(self, xy):
          # docstring inherited
          x = xy[:, 0:1]
          y = xy[:, 1:]
          r = np.hypot(x, y)
          theta = (np.arctan2(y, x) + 2 * np.pi) % (2 * np.pi)
  
          # PolarAxes does not use the theta transforms here, but apply them for
          # backwards-compatibility if not being used by it.
          if self._apply_theta_transforms and self._axis is not None:
              theta -= self._axis.get_theta_offset()
              theta *= self._axis.get_theta_direction()
              theta %= 2 * np.pi
  
          if self._use_rmin and self._axis is not None:
              r += self._axis.get_rorigin()
              r *= self._axis.get_rsign()
  
          return np.concatenate((theta, r), 1)
  
      def inverted(self):
          # docstring inherited
          return PolarAxes.PolarTransform(self._axis, self._use_rmin,
                                          self._apply_theta_transforms)
  
  
  class ThetaFormatter(mticker.Formatter):
      """
      Used to format the *theta* tick labels.  Converts the native
      unit of radians into degrees and adds a degree symbol.
      """
      def __call__(self, x, pos=None):
          vmin, vmax = self.axis.get_view_interval()
          d = np.rad2deg(abs(vmax - vmin))
          digits = max(-int(np.log10(d) - 1.5), 0)
  
          if rcParams['text.usetex'] and not rcParams['text.latex.unicode']:
              format_str = r"${value:0.{digits:d}f}^\circ$"
              return format_str.format(value=np.rad2deg(x), digits=digits)
          else:
              # we use unicode, rather than mathtext with \circ, so
              # that it will work correctly with any arbitrary font
              # (assuming it has a degree sign), whereas $5\circ$
              # will only work correctly with one of the supported
              # math fonts (Computer Modern and STIX)
              format_str = "{value:0.{digits:d}f}\N{DEGREE SIGN}"
              return format_str.format(value=np.rad2deg(x), digits=digits)
  
  
  class _AxisWrapper(object):
      def __init__(self, axis):
          self._axis = axis
  
      def get_view_interval(self):
          return np.rad2deg(self._axis.get_view_interval())
  
      def set_view_interval(self, vmin, vmax):
          self._axis.set_view_interval(*np.deg2rad((vmin, vmax)))
  
      def get_minpos(self):
          return np.rad2deg(self._axis.get_minpos())
  
      def get_data_interval(self):
          return np.rad2deg(self._axis.get_data_interval())
  
      def set_data_interval(self, vmin, vmax):
          self._axis.set_data_interval(*np.deg2rad((vmin, vmax)))
  
      def get_tick_space(self):
          return self._axis.get_tick_space()
  
  
  class ThetaLocator(mticker.Locator):
      """
      Used to locate theta ticks.
  
      This will work the same as the base locator except in the case that the
      view spans the entire circle. In such cases, the previously used default
      locations of every 45 degrees are returned.
      """
      def __init__(self, base):
          self.base = base
          self.axis = self.base.axis = _AxisWrapper(self.base.axis)
  
      def set_axis(self, axis):
          self.axis = _AxisWrapper(axis)
          self.base.set_axis(self.axis)
  
      def __call__(self):
          lim = self.axis.get_view_interval()
          if _is_full_circle_deg(lim[0], lim[1]):
              return np.arange(8) * 2 * np.pi / 8
          else:
              return np.deg2rad(self.base())
  
      def autoscale(self):
          return self.base.autoscale()
  
      def pan(self, numsteps):
          return self.base.pan(numsteps)
  
      def refresh(self):
          return self.base.refresh()
  
      def view_limits(self, vmin, vmax):
          vmin, vmax = np.rad2deg((vmin, vmax))
          return np.deg2rad(self.base.view_limits(vmin, vmax))
  
      def zoom(self, direction):
          return self.base.zoom(direction)
  
  
  class ThetaTick(maxis.XTick):
      """
      A theta-axis tick.
  
      This subclass of `XTick` provides angular ticks with some small
      modification to their re-positioning such that ticks are rotated based on
      tick location. This results in ticks that are correctly perpendicular to
      the arc spine.
  
      When 'auto' rotation is enabled, labels are also rotated to be parallel to
      the spine. The label padding is also applied here since it's not possible
      to use a generic axes transform to produce tick-specific padding.
      """
      def __init__(self, axes, *args, **kwargs):
          self._text1_translate = mtransforms.ScaledTranslation(
              0, 0,
              axes.figure.dpi_scale_trans)
          self._text2_translate = mtransforms.ScaledTranslation(
              0, 0,
              axes.figure.dpi_scale_trans)
          super().__init__(axes, *args, **kwargs)
  
      def _get_text1(self):
          t = super()._get_text1()
          t.set_rotation_mode('anchor')
          t.set_transform(t.get_transform() + self._text1_translate)
          return t
  
      def _get_text2(self):
          t = super()._get_text2()
          t.set_rotation_mode('anchor')
          t.set_transform(t.get_transform() + self._text2_translate)
          return t
  
      def _apply_params(self, **kw):
          super()._apply_params(**kw)
  
          # Ensure transform is correct; sometimes this gets reset.
          trans = self.label1.get_transform()
          if not trans.contains_branch(self._text1_translate):
              self.label1.set_transform(trans + self._text1_translate)
          trans = self.label2.get_transform()
          if not trans.contains_branch(self._text2_translate):
              self.label2.set_transform(trans + self._text2_translate)
  
      def _update_padding(self, pad, angle):
          padx = pad * np.cos(angle) / 72
          pady = pad * np.sin(angle) / 72
          self._text1_translate._t = (padx, pady)
          self._text1_translate.invalidate()
          self._text2_translate._t = (-padx, -pady)
          self._text2_translate.invalidate()
  
      def update_position(self, loc):
          super().update_position(loc)
          axes = self.axes
          angle = loc * axes.get_theta_direction() + axes.get_theta_offset()
          text_angle = np.rad2deg(angle) % 360 - 90
          angle -= np.pi / 2
  
          marker = self.tick1line.get_marker()
          if marker in (mmarkers.TICKUP, '|'):
              trans = mtransforms.Affine2D().scale(1, 1).rotate(angle)
          elif marker == mmarkers.TICKDOWN:
              trans = mtransforms.Affine2D().scale(1, -1).rotate(angle)
          else:
              # Don't modify custom tick line markers.
              trans = self.tick1line._marker._transform
          self.tick1line._marker._transform = trans
  
          marker = self.tick2line.get_marker()
          if marker in (mmarkers.TICKUP, '|'):
              trans = mtransforms.Affine2D().scale(1, 1).rotate(angle)
          elif marker == mmarkers.TICKDOWN:
              trans = mtransforms.Affine2D().scale(1, -1).rotate(angle)
          else:
              # Don't modify custom tick line markers.
              trans = self.tick2line._marker._transform
          self.tick2line._marker._transform = trans
  
          mode, user_angle = self._labelrotation
          if mode == 'default':
              text_angle = user_angle
          else:
              if text_angle > 90:
                  text_angle -= 180
              elif text_angle < -90:
                  text_angle += 180
              text_angle += user_angle
          self.label1.set_rotation(text_angle)
          self.label2.set_rotation(text_angle)
  
          # This extra padding helps preserve the look from previous releases but
          # is also needed because labels are anchored to their center.
          pad = self._pad + 7
          self._update_padding(pad,
                               self._loc * axes.get_theta_direction() +
                               axes.get_theta_offset())
  
  
  class ThetaAxis(maxis.XAxis):
      """
      A theta Axis.
  
      This overrides certain properties of an `XAxis` to provide special-casing
      for an angular axis.
      """
      __name__ = 'thetaaxis'
      axis_name = 'theta'
  
      def _get_tick(self, major):
          if major:
              tick_kw = self._major_tick_kw
          else:
              tick_kw = self._minor_tick_kw
          return ThetaTick(self.axes, 0, '', major=major, **tick_kw)
  
      def _wrap_locator_formatter(self):
          self.set_major_locator(ThetaLocator(self.get_major_locator()))
          self.set_major_formatter(ThetaFormatter())
          self.isDefault_majloc = True
          self.isDefault_majfmt = True
  
      def cla(self):
          super().cla()
          self.set_ticks_position('none')
          self._wrap_locator_formatter()
  
      def _set_scale(self, value, **kwargs):
          super()._set_scale(value, **kwargs)
          self._wrap_locator_formatter()
  
      def _copy_tick_props(self, src, dest):
          'Copy the props from src tick to dest tick'
          if src is None or dest is None:
              return
          super()._copy_tick_props(src, dest)
  
          # Ensure that tick transforms are independent so that padding works.
          trans = dest._get_text1_transform()[0]
          dest.label1.set_transform(trans + dest._text1_translate)
          trans = dest._get_text2_transform()[0]
          dest.label2.set_transform(trans + dest._text2_translate)
  
  
  class RadialLocator(mticker.Locator):
      """
      Used to locate radius ticks.
  
      Ensures that all ticks are strictly positive.  For all other
      tasks, it delegates to the base
      :class:`~matplotlib.ticker.Locator` (which may be different
      depending on the scale of the *r*-axis.
      """
      def __init__(self, base, axes=None):
          self.base = base
          self._axes = axes
  
      def __call__(self):
          show_all = True
          # Ensure previous behaviour with full circle non-annular views.
          if self._axes:
              if _is_full_circle_rad(*self._axes.viewLim.intervalx):
                  rorigin = self._axes.get_rorigin() * self._axes.get_rsign()
                  if self._axes.get_rmin() <= rorigin:
                      show_all = False
          if show_all:
              return self.base()
          else:
              return [tick for tick in self.base() if tick > rorigin]
  
      def autoscale(self):
          return self.base.autoscale()
  
      def pan(self, numsteps):
          return self.base.pan(numsteps)
  
      def zoom(self, direction):
          return self.base.zoom(direction)
  
      def refresh(self):
          return self.base.refresh()
  
      def view_limits(self, vmin, vmax):
          vmin, vmax = self.base.view_limits(vmin, vmax)
          if vmax > vmin:
              # this allows inverted r/y-lims
              vmin = min(0, vmin)
          return mtransforms.nonsingular(vmin, vmax)
  
  
  class _ThetaShift(mtransforms.ScaledTranslation):
      """
      Apply a padding shift based on axes theta limits.
  
      This is used to create padding for radial ticks.
  
      Parameters
      ----------
      axes : `~matplotlib.axes.Axes`
          The owning axes; used to determine limits.
      pad : float
          The padding to apply, in points.
      mode : {'min', 'max', 'rlabel'}
          Whether to shift away from the start (``'min'``) or the end (``'max'``)
          of the axes, or using the rlabel position (``'rlabel'``).
      """
      def __init__(self, axes, pad, mode):
          mtransforms.ScaledTranslation.__init__(self, pad, pad,
                                                 axes.figure.dpi_scale_trans)
          self.set_children(axes._realViewLim)
          self.axes = axes
          self.mode = mode
          self.pad = pad
  
      def __str__(self):
          return ("{}(\n"
                      "{},\n"
                      "{},\n"
                      "{})"
                  .format(type(self).__name__,
                          mtransforms._indent_str(self.axes),
                          mtransforms._indent_str(self.pad),
                          mtransforms._indent_str(repr(self.mode))))
  
      def get_matrix(self):
          if self._invalid:
              if self.mode == 'rlabel':
                  angle = (
                      np.deg2rad(self.axes.get_rlabel_position()) *
                      self.axes.get_theta_direction() +
                      self.axes.get_theta_offset()
                  )
              else:
                  if self.mode == 'min':
                      angle = self.axes._realViewLim.xmin
                  elif self.mode == 'max':
                      angle = self.axes._realViewLim.xmax
  
              if self.mode in ('rlabel', 'min'):
                  padx = np.cos(angle - np.pi / 2)
                  pady = np.sin(angle - np.pi / 2)
              else:
                  padx = np.cos(angle + np.pi / 2)
                  pady = np.sin(angle + np.pi / 2)
  
              self._t = (self.pad * padx / 72, self.pad * pady / 72)
          return mtransforms.ScaledTranslation.get_matrix(self)
  
  
  class RadialTick(maxis.YTick):
      """
      A radial-axis tick.
  
      This subclass of `YTick` provides radial ticks with some small modification
      to their re-positioning such that ticks are rotated based on axes limits.
      This results in ticks that are correctly perpendicular to the spine. Labels
      are also rotated to be perpendicular to the spine, when 'auto' rotation is
      enabled.
      """
      def _get_text1(self):
          t = super()._get_text1()
          t.set_rotation_mode('anchor')
          return t
  
      def _get_text2(self):
          t = super()._get_text2()
          t.set_rotation_mode('anchor')
          return t
  
      def _determine_anchor(self, mode, angle, start):
          # Note: angle is the (spine angle - 90) because it's used for the tick
          # & text setup, so all numbers below are -90 from (normed) spine angle.
          if mode == 'auto':
              if start:
                  if -90 <= angle <= 90:
                      return 'left', 'center'
                  else:
                      return 'right', 'center'
              else:
                  if -90 <= angle <= 90:
                      return 'right', 'center'
                  else:
                      return 'left', 'center'
          else:
              if start:
                  if angle < -68.5:
                      return 'center', 'top'
                  elif angle < -23.5:
                      return 'left', 'top'
                  elif angle < 22.5:
                      return 'left', 'center'
                  elif angle < 67.5:
                      return 'left', 'bottom'
                  elif angle < 112.5:
                      return 'center', 'bottom'
                  elif angle < 157.5:
                      return 'right', 'bottom'
                  elif angle < 202.5:
                      return 'right', 'center'
                  elif angle < 247.5:
                      return 'right', 'top'
                  else:
                      return 'center', 'top'
              else:
                  if angle < -68.5:
                      return 'center', 'bottom'
                  elif angle < -23.5:
                      return 'right', 'bottom'
                  elif angle < 22.5:
                      return 'right', 'center'
                  elif angle < 67.5:
                      return 'right', 'top'
                  elif angle < 112.5:
                      return 'center', 'top'
                  elif angle < 157.5:
                      return 'left', 'top'
                  elif angle < 202.5:
                      return 'left', 'center'
                  elif angle < 247.5:
                      return 'left', 'bottom'
                  else:
                      return 'center', 'bottom'
  
      def update_position(self, loc):
          super().update_position(loc)
          axes = self.axes
          thetamin = axes.get_thetamin()
          thetamax = axes.get_thetamax()
          direction = axes.get_theta_direction()
          offset_rad = axes.get_theta_offset()
          offset = np.rad2deg(offset_rad)
          full = _is_full_circle_deg(thetamin, thetamax)
  
          if full:
              angle = (axes.get_rlabel_position() * direction +
                       offset) % 360 - 90
              tick_angle = 0
          else:
              angle = (thetamin * direction + offset) % 360 - 90
              if direction > 0:
                  tick_angle = np.deg2rad(angle)
              else:
                  tick_angle = np.deg2rad(angle + 180)
          text_angle = (angle + 90) % 180 - 90  # between -90 and +90.
          mode, user_angle = self._labelrotation
          if mode == 'auto':
              text_angle += user_angle
          else:
              text_angle = user_angle
  
          if full:
              ha = self.label1.get_horizontalalignment()
              va = self.label1.get_verticalalignment()
          else:
              ha, va = self._determine_anchor(mode, angle, direction > 0)
          self.label1.set_horizontalalignment(ha)
          self.label1.set_verticalalignment(va)
          self.label1.set_rotation(text_angle)
  
          marker = self.tick1line.get_marker()
          if marker == mmarkers.TICKLEFT:
              trans = mtransforms.Affine2D().rotate(tick_angle)
          elif marker == '_':
              trans = mtransforms.Affine2D().rotate(tick_angle + np.pi / 2)
          elif marker == mmarkers.TICKRIGHT:
              trans = mtransforms.Affine2D().scale(-1, 1).rotate(tick_angle)
          else:
              # Don't modify custom tick line markers.
              trans = self.tick1line._marker._transform
          self.tick1line._marker._transform = trans
  
          if full:
              self.label2.set_visible(False)
              self.tick2line.set_visible(False)
          angle = (thetamax * direction + offset) % 360 - 90
          if direction > 0:
              tick_angle = np.deg2rad(angle)
          else:
              tick_angle = np.deg2rad(angle + 180)
          text_angle = (angle + 90) % 180 - 90  # between -90 and +90.
          mode, user_angle = self._labelrotation
          if mode == 'auto':
              text_angle += user_angle
          else:
              text_angle = user_angle
  
          ha, va = self._determine_anchor(mode, angle, direction < 0)
          self.label2.set_ha(ha)
          self.label2.set_va(va)
          self.label2.set_rotation(text_angle)
  
          marker = self.tick2line.get_marker()
          if marker == mmarkers.TICKLEFT:
              trans = mtransforms.Affine2D().rotate(tick_angle)
          elif marker == '_':
              trans = mtransforms.Affine2D().rotate(tick_angle + np.pi / 2)
          elif marker == mmarkers.TICKRIGHT:
              trans = mtransforms.Affine2D().scale(-1, 1).rotate(tick_angle)
          else:
              # Don't modify custom tick line markers.
              trans = self.tick2line._marker._transform
          self.tick2line._marker._transform = trans
  
  
  class RadialAxis(maxis.YAxis):
      """
      A radial Axis.
  
      This overrides certain properties of a `YAxis` to provide special-casing
      for a radial axis.
      """
      __name__ = 'radialaxis'
      axis_name = 'radius'
  
      def __init__(self, *args, **kwargs):
          super().__init__(*args, **kwargs)
          self.sticky_edges.y.append(0)
  
      def _get_tick(self, major):
          if major:
              tick_kw = self._major_tick_kw
          else:
              tick_kw = self._minor_tick_kw
          return RadialTick(self.axes, 0, '', major=major, **tick_kw)
  
      def _wrap_locator_formatter(self):
          self.set_major_locator(RadialLocator(self.get_major_locator(),
                                               self.axes))
          self.isDefault_majloc = True
  
      def cla(self):
          super().cla()
          self.set_ticks_position('none')
          self._wrap_locator_formatter()
  
      def _set_scale(self, value, **kwargs):
          super()._set_scale(value, **kwargs)
          self._wrap_locator_formatter()
  
  
  def _is_full_circle_deg(thetamin, thetamax):
      """
      Determine if a wedge (in degrees) spans the full circle.
  
      The condition is derived from :class:`~matplotlib.patches.Wedge`.
      """
      return abs(abs(thetamax - thetamin) - 360.0) < 1e-12
  
  
  def _is_full_circle_rad(thetamin, thetamax):
      """
      Determine if a wedge (in radians) spans the full circle.
  
      The condition is derived from :class:`~matplotlib.patches.Wedge`.
      """
      return abs(abs(thetamax - thetamin) - 2 * np.pi) < 1.74e-14
  
  
  class _WedgeBbox(mtransforms.Bbox):
      """
      Transform (theta,r) wedge Bbox into axes bounding box.
  
      Parameters
      ----------
      center : (float, float)
          Center of the wedge
      viewLim : `~matplotlib.transforms.Bbox`
          Bbox determining the boundaries of the wedge
      originLim : `~matplotlib.transforms.Bbox`
          Bbox determining the origin for the wedge, if different from *viewLim*
      """
      def __init__(self, center, viewLim, originLim, **kwargs):
          mtransforms.Bbox.__init__(self,
                                    np.array([[0.0, 0.0], [1.0, 1.0]], np.float),
                                    **kwargs)
          self._center = center
          self._viewLim = viewLim
          self._originLim = originLim
          self.set_children(viewLim, originLim)
  
      def __str__(self):
          return ("{}(\n"
                      "{},\n"
                      "{},\n"
                      "{})"
                  .format(type(self).__name__,
                          mtransforms._indent_str(self._center),
                          mtransforms._indent_str(self._viewLim),
                          mtransforms._indent_str(self._originLim)))
  
      def get_points(self):
          # docstring inherited
          if self._invalid:
              points = self._viewLim.get_points().copy()
              # Scale angular limits to work with Wedge.
              points[:, 0] *= 180 / np.pi
              if points[0, 0] > points[1, 0]:
                  points[:, 0] = points[::-1, 0]
  
              # Scale radial limits based on origin radius.
              points[:, 1] -= self._originLim.y0
  
              # Scale radial limits to match axes limits.
              rscale = 0.5 / points[1, 1]
              points[:, 1] *= rscale
              width = min(points[1, 1] - points[0, 1], 0.5)
  
              # Generate bounding box for wedge.
              wedge = mpatches.Wedge(self._center, points[1, 1],
                                     points[0, 0], points[1, 0],
                                     width=width)
              self.update_from_path(wedge.get_path())
  
              # Ensure equal aspect ratio.
              w, h = self._points[1] - self._points[0]
              deltah = max(w - h, 0) / 2
              deltaw = max(h - w, 0) / 2
              self._points += np.array([[-deltaw, -deltah], [deltaw, deltah]])
  
              self._invalid = 0
  
          return self._points
  
  
  class PolarAxes(Axes):
      """
      A polar graph projection, where the input dimensions are *theta*, *r*.
  
      Theta starts pointing east and goes anti-clockwise.
      """
      name = 'polar'
  
      def __init__(self, *args,
                   theta_offset=0, theta_direction=1, rlabel_position=22.5,
                   **kwargs):
          # docstring inherited
          self._default_theta_offset = theta_offset
          self._default_theta_direction = theta_direction
          self._default_rlabel_position = np.deg2rad(rlabel_position)
          super().__init__(*args, **kwargs)
          self.use_sticky_edges = True
          self.set_aspect('equal', adjustable='box', anchor='C')
          self.cla()
  
      def cla(self):
          Axes.cla(self)
  
          self.title.set_y(1.05)
  
          start = self.spines.get('start', None)
          if start:
              start.set_visible(False)
          end = self.spines.get('end', None)
          if end:
              end.set_visible(False)
          self.set_xlim(0.0, 2 * np.pi)
  
          self.grid(rcParams['polaraxes.grid'])
          inner = self.spines.get('inner', None)
          if inner:
              inner.set_visible(False)
  
          self.set_rorigin(None)
          self.set_theta_offset(self._default_theta_offset)
          self.set_theta_direction(self._default_theta_direction)
  
      def _init_axis(self):
          "move this out of __init__ because non-separable axes don't use it"
          self.xaxis = ThetaAxis(self)
          self.yaxis = RadialAxis(self)
          # Calling polar_axes.xaxis.cla() or polar_axes.xaxis.cla()
          # results in weird artifacts. Therefore we disable this for
          # now.
          # self.spines['polar'].register_axis(self.yaxis)
          self._update_transScale()
  
      def _set_lim_and_transforms(self):
          # A view limit where the minimum radius can be locked if the user
          # specifies an alternate origin.
          self._originViewLim = mtransforms.LockableBbox(self.viewLim)
  
          # Handle angular offset and direction.
          self._direction = mtransforms.Affine2D() \
              .scale(self._default_theta_direction, 1.0)
          self._theta_offset = mtransforms.Affine2D() \
              .translate(self._default_theta_offset, 0.0)
          self.transShift = mtransforms.composite_transform_factory(
              self._direction,
              self._theta_offset)
          # A view limit shifted to the correct location after accounting for
          # orientation and offset.
          self._realViewLim = mtransforms.TransformedBbox(self.viewLim,
                                                          self.transShift)
  
          # Transforms the x and y axis separately by a scale factor
          # It is assumed that this part will have non-linear components
          self.transScale = mtransforms.TransformWrapper(
              mtransforms.IdentityTransform())
  
          # Scale view limit into a bbox around the selected wedge. This may be
          # smaller than the usual unit axes rectangle if not plotting the full
          # circle.
          self.axesLim = _WedgeBbox((0.5, 0.5),
                                    self._realViewLim, self._originViewLim)
  
          # Scale the wedge to fill the axes.
          self.transWedge = mtransforms.BboxTransformFrom(self.axesLim)
  
          # Scale the axes to fill the figure.
          self.transAxes = mtransforms.BboxTransformTo(self.bbox)
  
          # A (possibly non-linear) projection on the (already scaled)
          # data.  This one is aware of rmin
          self.transProjection = self.PolarTransform(
              self,
              _apply_theta_transforms=False)
          # Add dependency on rorigin.
          self.transProjection.set_children(self._originViewLim)
  
          # An affine transformation on the data, generally to limit the
          # range of the axes
          self.transProjectionAffine = self.PolarAffine(self.transScale,
                                                        self._originViewLim)
  
          # The complete data transformation stack -- from data all the
          # way to display coordinates
          self.transData = (
              self.transScale + self.transShift + self.transProjection +
              (self.transProjectionAffine + self.transWedge + self.transAxes))
  
          # This is the transform for theta-axis ticks.  It is
          # equivalent to transData, except it always puts r == 0.0 and r == 1.0
          # at the edge of the axis circles.
          self._xaxis_transform = (
              mtransforms.blended_transform_factory(
                  mtransforms.IdentityTransform(),
                  mtransforms.BboxTransformTo(self.viewLim)) +
              self.transData)
          # The theta labels are flipped along the radius, so that text 1 is on
          # the outside by default. This should work the same as before.
          flipr_transform = mtransforms.Affine2D() \
              .translate(0.0, -0.5) \
              .scale(1.0, -1.0) \
              .translate(0.0, 0.5)
          self._xaxis_text_transform = flipr_transform + self._xaxis_transform
  
          # This is the transform for r-axis ticks.  It scales the theta
          # axis so the gridlines from 0.0 to 1.0, now go from thetamin to
          # thetamax.
          self._yaxis_transform = (
              mtransforms.blended_transform_factory(
                  mtransforms.BboxTransformTo(self.viewLim),
                  mtransforms.IdentityTransform()) +
              self.transData)
          # The r-axis labels are put at an angle and padded in the r-direction
          self._r_label_position = mtransforms.Affine2D() \
              .translate(self._default_rlabel_position, 0.0)
          self._yaxis_text_transform = mtransforms.TransformWrapper(
              self._r_label_position + self.transData)
  
      def get_xaxis_transform(self, which='grid'):
          cbook._check_in_list(['tick1', 'tick2', 'grid'], which=which)
          return self._xaxis_transform
  
      def get_xaxis_text1_transform(self, pad):
          return self._xaxis_text_transform, 'center', 'center'
  
      def get_xaxis_text2_transform(self, pad):
          return self._xaxis_text_transform, 'center', 'center'
  
      def get_yaxis_transform(self, which='grid'):
          if which in ('tick1', 'tick2'):
              return self._yaxis_text_transform
          elif which == 'grid':
              return self._yaxis_transform
          else:
              cbook._check_in_list(['tick1', 'tick2', 'grid'], which=which)
  
      def get_yaxis_text1_transform(self, pad):
          thetamin, thetamax = self._realViewLim.intervalx
          if _is_full_circle_rad(thetamin, thetamax):
              return self._yaxis_text_transform, 'bottom', 'left'
          elif self.get_theta_direction() > 0:
              halign = 'left'
              pad_shift = _ThetaShift(self, pad, 'min')
          else:
              halign = 'right'
              pad_shift = _ThetaShift(self, pad, 'max')
          return self._yaxis_text_transform + pad_shift, 'center', halign
  
      def get_yaxis_text2_transform(self, pad):
          if self.get_theta_direction() > 0:
              halign = 'right'
              pad_shift = _ThetaShift(self, pad, 'max')
          else:
              halign = 'left'
              pad_shift = _ThetaShift(self, pad, 'min')
          return self._yaxis_text_transform + pad_shift, 'center', halign
  
      def draw(self, *args, **kwargs):
          thetamin, thetamax = np.rad2deg(self._realViewLim.intervalx)
          if thetamin > thetamax:
              thetamin, thetamax = thetamax, thetamin
          rmin, rmax = ((self._realViewLim.intervaly - self.get_rorigin()) *
                          self.get_rsign())
          if isinstance(self.patch, mpatches.Wedge):
              # Backwards-compatibility: Any subclassed Axes might override the
              # patch to not be the Wedge that PolarAxes uses.
              center = self.transWedge.transform_point((0.5, 0.5))
              self.patch.set_center(center)
              self.patch.set_theta1(thetamin)
              self.patch.set_theta2(thetamax)
  
              edge, _ = self.transWedge.transform_point((1, 0))
              radius = edge - center[0]
              width = min(radius * (rmax - rmin) / rmax, radius)
              self.patch.set_radius(radius)
              self.patch.set_width(width)
  
              inner_width = radius - width
              inner = self.spines.get('inner', None)
              if inner:
                  inner.set_visible(inner_width != 0.0)
  
          visible = not _is_full_circle_deg(thetamin, thetamax)
          # For backwards compatibility, any subclassed Axes might override the
          # spines to not include start/end that PolarAxes uses.
          start = self.spines.get('start', None)
          end = self.spines.get('end', None)
          if start:
              start.set_visible(visible)
          if end:
              end.set_visible(visible)
          if visible:
              yaxis_text_transform = self._yaxis_transform
          else:
              yaxis_text_transform = self._r_label_position + self.transData
          if self._yaxis_text_transform != yaxis_text_transform:
              self._yaxis_text_transform.set(yaxis_text_transform)
              self.yaxis.reset_ticks()
              self.yaxis.set_clip_path(self.patch)
  
          Axes.draw(self, *args, **kwargs)
  
      def _gen_axes_patch(self):
          return mpatches.Wedge((0.5, 0.5), 0.5, 0.0, 360.0)
  
      def _gen_axes_spines(self):
          spines = OrderedDict([
              ('polar', mspines.Spine.arc_spine(self, 'top',
                                                (0.5, 0.5), 0.5, 0.0, 360.0)),
              ('start', mspines.Spine.linear_spine(self, 'left')),
              ('end', mspines.Spine.linear_spine(self, 'right')),
              ('inner', mspines.Spine.arc_spine(self, 'bottom',
                                                (0.5, 0.5), 0.0, 0.0, 360.0))
          ])
          spines['polar'].set_transform(self.transWedge + self.transAxes)
          spines['inner'].set_transform(self.transWedge + self.transAxes)
          spines['start'].set_transform(self._yaxis_transform)
          spines['end'].set_transform(self._yaxis_transform)
          return spines
  
      def set_thetamax(self, thetamax):
          self.viewLim.x1 = np.deg2rad(thetamax)
  
      def get_thetamax(self):
          return np.rad2deg(self.viewLim.xmax)
  
      def set_thetamin(self, thetamin):
          self.viewLim.x0 = np.deg2rad(thetamin)
  
      def get_thetamin(self):
          return np.rad2deg(self.viewLim.xmin)
  
      def set_thetalim(self, *args, **kwargs):
          """
          Set the minimum and maximum theta values.
  
          Parameters
          ----------
          thetamin : float
              Minimum value in degrees.
          thetamax : float
              Maximum value in degrees.
          """
          if 'thetamin' in kwargs:
              kwargs['xmin'] = np.deg2rad(kwargs.pop('thetamin'))
          if 'thetamax' in kwargs:
              kwargs['xmax'] = np.deg2rad(kwargs.pop('thetamax'))
          return tuple(np.rad2deg(self.set_xlim(*args, **kwargs)))
  
      def set_theta_offset(self, offset):
          """
          Set the offset for the location of 0 in radians.
          """
          mtx = self._theta_offset.get_matrix()
          mtx[0, 2] = offset
          self._theta_offset.invalidate()
  
      def get_theta_offset(self):
          """
          Get the offset for the location of 0 in radians.
          """
          return self._theta_offset.get_matrix()[0, 2]
  
      def set_theta_zero_location(self, loc, offset=0.0):
          """
          Sets the location of theta's zero.  (Calls set_theta_offset
          with the correct value in radians under the hood.)
  
          loc : str
              May be one of "N", "NW", "W", "SW", "S", "SE", "E", or "NE".
  
          offset : float, optional
              An offset in degrees to apply from the specified `loc`. **Note:**
              this offset is *always* applied counter-clockwise regardless of
              the direction setting.
          """
          mapping = {
              'N': np.pi * 0.5,
              'NW': np.pi * 0.75,
              'W': np.pi,
              'SW': np.pi * 1.25,
              'S': np.pi * 1.5,
              'SE': np.pi * 1.75,
              'E': 0,
              'NE': np.pi * 0.25}
          return self.set_theta_offset(mapping[loc] + np.deg2rad(offset))
  
      def set_theta_direction(self, direction):
          """
          Set the direction in which theta increases.
  
          clockwise, -1:
             Theta increases in the clockwise direction
  
          counterclockwise, anticlockwise, 1:
             Theta increases in the counterclockwise direction
          """
          mtx = self._direction.get_matrix()
          if direction in ('clockwise', -1):
              mtx[0, 0] = -1
          elif direction in ('counterclockwise', 'anticlockwise', 1):
              mtx[0, 0] = 1
          else:
              cbook._check_in_list(
                  [-1, 1, 'clockwise', 'counterclockwise', 'anticlockwise'],
                  direction=direction)
          self._direction.invalidate()
  
      def get_theta_direction(self):
          """
          Get the direction in which theta increases.
  
          -1:
             Theta increases in the clockwise direction
  
          1:
             Theta increases in the counterclockwise direction
          """
          return self._direction.get_matrix()[0, 0]
  
      def set_rmax(self, rmax):
          """
          Set the outer radial limit.
  
          Parameters
          ----------
          rmax : float
          """
          self.viewLim.y1 = rmax
  
      def get_rmax(self):
          """
          Returns
          -------
          float
              Outer radial limit.
          """
          return self.viewLim.ymax
  
      def set_rmin(self, rmin):
          """
          Set the inner radial limit.
  
          Parameters
          ----------
          rmin : float
          """
          self.viewLim.y0 = rmin
  
      def get_rmin(self):
          """
          Returns
          -------
          float
              The inner radial limit.
          """
          return self.viewLim.ymin
  
      def set_rorigin(self, rorigin):
          """
          Update the radial origin.
  
          Parameters
          ----------
          rorigin : float
          """
          self._originViewLim.locked_y0 = rorigin
  
      def get_rorigin(self):
          """
          Returns
          -------
          float
          """
          return self._originViewLim.y0
  
      def get_rsign(self):
          return np.sign(self._originViewLim.y1 - self._originViewLim.y0)
  
      def set_rlim(self, bottom=None, top=None, emit=True, auto=False, **kwargs):
          """
          See `~.polar.PolarAxes.set_ylim`.
          """
          if 'rmin' in kwargs:
              if bottom is None:
                  bottom = kwargs.pop('rmin')
              else:
                  raise ValueError('Cannot supply both positional "bottom"'
                                   'argument and kwarg "rmin"')
          if 'rmax' in kwargs:
              if top is None:
                  top = kwargs.pop('rmax')
              else:
                  raise ValueError('Cannot supply both positional "top"'
                                   'argument and kwarg "rmax"')
          return self.set_ylim(bottom=bottom, top=top, emit=emit, auto=auto,
                               **kwargs)
  
      def set_ylim(self, bottom=None, top=None, emit=True, auto=False,
                   *, ymin=None, ymax=None):
          """
          Set the data limits for the radial axis.
  
          Parameters
          ----------
          bottom : scalar, optional
              The bottom limit (default: None, which leaves the bottom
              limit unchanged).
              The bottom and top ylims may be passed as the tuple
              (*bottom*, *top*) as the first positional argument (or as
              the *bottom* keyword argument).
  
          top : scalar, optional
              The top limit (default: None, which leaves the top limit
              unchanged).
  
          emit : bool, optional
              Whether to notify observers of limit change (default: True).
  
          auto : bool or None, optional
              Whether to turn on autoscaling of the y-axis. True turns on,
              False turns off (default action), None leaves unchanged.
  
          ymin, ymax : scalar, optional
              These arguments are deprecated and will be removed in a future
              version.  They are equivalent to *bottom* and *top* respectively,
              and it is an error to pass both *ymin* and *bottom* or
              *ymax* and *top*.
  
          Returns
          -------
          bottom, top : (float, float)
              The new y-axis limits in data coordinates.
          """
          if ymin is not None:
              if bottom is not None:
                  raise ValueError('Cannot supply both positional "bottom" '
                                   'argument and kwarg "ymin"')
              else:
                  bottom = ymin
          if ymax is not None:
              if top is not None:
                  raise ValueError('Cannot supply both positional "top" '
                                   'argument and kwarg "ymax"')
              else:
                  top = ymax
          if top is None and np.iterable(bottom):
              bottom, top = bottom[0], bottom[1]
          return super().set_ylim(bottom=bottom, top=top, emit=emit, auto=auto)
  
      def get_rlabel_position(self):
          """
          Returns
          -------
          float
              The theta position of the radius labels in degrees.
          """
          return np.rad2deg(self._r_label_position.get_matrix()[0, 2])
  
      def set_rlabel_position(self, value):
          """Updates the theta position of the radius labels.
  
          Parameters
          ----------
          value : number
              The angular position of the radius labels in degrees.
          """
          self._r_label_position.clear().translate(np.deg2rad(value), 0.0)
  
      def set_yscale(self, *args, **kwargs):
          Axes.set_yscale(self, *args, **kwargs)
          self.yaxis.set_major_locator(
              self.RadialLocator(self.yaxis.get_major_locator(), self))
  
      def set_rscale(self, *args, **kwargs):
          return Axes.set_yscale(self, *args, **kwargs)
  
      def set_rticks(self, *args, **kwargs):
          return Axes.set_yticks(self, *args, **kwargs)
  
      def set_thetagrids(self, angles, labels=None, fmt=None, **kwargs):
          """
          Set the theta gridlines in a polar plot.
  
          Parameters
          ----------
          angles : tuple with floats, degrees
              The angles of the theta gridlines.
  
          labels : tuple with strings or None
              The labels to use at each theta gridline. The
              `.projections.polar.ThetaFormatter` will be used if None.
  
          fmt : str or None
              Format string used in `matplotlib.ticker.FormatStrFormatter`.
              For example '%f'. Note that the angle that is used is in
              radians.
  
          Returns
          -------
          lines, labels : list of `.lines.Line2D`, list of `.text.Text`
              *lines* are the theta gridlines and *labels* are the tick labels.
  
          Other Parameters
          ----------------
          **kwargs
              *kwargs* are optional `~.Text` properties for the labels.
  
          See Also
          --------
          .PolarAxes.set_rgrids
          .Axis.get_gridlines
          .Axis.get_ticklabels
          """
  
          # Make sure we take into account unitized data
          angles = self.convert_yunits(angles)
          angles = np.deg2rad(angles)
          self.set_xticks(angles)
          if labels is not None:
              self.set_xticklabels(labels)
          elif fmt is not None:
              self.xaxis.set_major_formatter(mticker.FormatStrFormatter(fmt))
          for t in self.xaxis.get_ticklabels():
              t.update(kwargs)
          return self.xaxis.get_ticklines(), self.xaxis.get_ticklabels()
  
      def set_rgrids(self, radii, labels=None, angle=None, fmt=None,
                     **kwargs):
          """
          Set the radial gridlines on a polar plot.
  
          Parameters
          ----------
          radii : tuple with floats
              The radii for the radial gridlines
  
          labels : tuple with strings or None
              The labels to use at each radial gridline. The
              `matplotlib.ticker.ScalarFormatter` will be used if None.
  
          angle : float
              The angular position of the radius labels in degrees.
  
          fmt : str or None
              Format string used in `matplotlib.ticker.FormatStrFormatter`.
              For example '%f'.
  
          Returns
          -------
          lines, labels : list of `.lines.Line2D`, list of `.text.Text`
              *lines* are the radial gridlines and *labels* are the tick labels.
  
          Other Parameters
          ----------------
          **kwargs
              *kwargs* are optional `~.Text` properties for the labels.
  
          See Also
          --------
          .PolarAxes.set_thetagrids
          .Axis.get_gridlines
          .Axis.get_ticklabels
          """
          # Make sure we take into account unitized data
          radii = self.convert_xunits(radii)
          radii = np.asarray(radii)
  
          self.set_yticks(radii)
          if labels is not None:
              self.set_yticklabels(labels)
          elif fmt is not None:
              self.yaxis.set_major_formatter(mticker.FormatStrFormatter(fmt))
          if angle is None:
              angle = self.get_rlabel_position()
          self.set_rlabel_position(angle)
          for t in self.yaxis.get_ticklabels():
              t.update(kwargs)
          return self.yaxis.get_gridlines(), self.yaxis.get_ticklabels()
  
      def set_xscale(self, scale, *args, **kwargs):
          if scale != 'linear':
              raise NotImplementedError(
                  "You can not set the xscale on a polar plot.")
  
      def format_coord(self, theta, r):
          """
          Return a format string formatting the coordinate using Unicode
          characters.
          """
          if theta < 0:
              theta += 2 * np.pi
          theta /= np.pi
          return ('\N{GREEK SMALL LETTER THETA}=%0.3f\N{GREEK SMALL LETTER PI} '
                  '(%0.3f\N{DEGREE SIGN}), r=%0.3f') % (theta, theta * 180.0, r)
  
      def get_data_ratio(self):
          '''
          Return the aspect ratio of the data itself.  For a polar plot,
          this should always be 1.0
          '''
          return 1.0
  
      # # # Interactive panning
  
      def can_zoom(self):
          """
          Return *True* if this axes supports the zoom box button functionality.
  
          Polar axes do not support zoom boxes.
          """
          return False
  
      def can_pan(self):
          """
          Return *True* if this axes supports the pan/zoom button functionality.
  
          For polar axes, this is slightly misleading. Both panning and
          zooming are performed by the same button. Panning is performed
          in azimuth while zooming is done along the radial.
          """
          return True
  
      def start_pan(self, x, y, button):
          angle = np.deg2rad(self.get_rlabel_position())
          mode = ''
          if button == 1:
              epsilon = np.pi / 45.0
              t, r = self.transData.inverted().transform_point((x, y))
              if angle - epsilon <= t <= angle + epsilon:
                  mode = 'drag_r_labels'
          elif button == 3:
              mode = 'zoom'
  
          self._pan_start = types.SimpleNamespace(
              rmax=self.get_rmax(),
              trans=self.transData.frozen(),
              trans_inverse=self.transData.inverted().frozen(),
              r_label_angle=self.get_rlabel_position(),
              x=x,
              y=y,
              mode=mode)
  
      def end_pan(self):
          del self._pan_start
  
      def drag_pan(self, button, key, x, y):
          p = self._pan_start
  
          if p.mode == 'drag_r_labels':
              startt, startr = p.trans_inverse.transform_point((p.x, p.y))
              t, r = p.trans_inverse.transform_point((x, y))
  
              # Deal with theta
              dt0 = t - startt
              dt1 = startt - t
              if abs(dt1) < abs(dt0):
                  dt = abs(dt1) * np.sign(dt0) * -1.0
              else:
                  dt = dt0 * -1.0
              dt = (dt / np.pi) * 180.0
              self.set_rlabel_position(p.r_label_angle - dt)
  
              trans, vert1, horiz1 = self.get_yaxis_text1_transform(0.0)
              trans, vert2, horiz2 = self.get_yaxis_text2_transform(0.0)
              for t in self.yaxis.majorTicks + self.yaxis.minorTicks:
                  t.label1.set_va(vert1)
                  t.label1.set_ha(horiz1)
                  t.label2.set_va(vert2)
                  t.label2.set_ha(horiz2)
  
          elif p.mode == 'zoom':
              startt, startr = p.trans_inverse.transform_point((p.x, p.y))
              t, r = p.trans_inverse.transform_point((x, y))
  
              # Deal with r
              scale = r / startr
              self.set_rmax(p.rmax / scale)
  
  
  # to keep things all self contained, we can put aliases to the Polar classes
  # defined above. This isn't strictly necessary, but it makes some of the
  # code more readable (and provides a backwards compatible Polar API)
  PolarAxes.PolarTransform = PolarTransform
  PolarAxes.PolarAffine = PolarAffine
  PolarAxes.InvertedPolarTransform = InvertedPolarTransform
  PolarAxes.ThetaFormatter = ThetaFormatter
  PolarAxes.RadialLocator = RadialLocator
  PolarAxes.ThetaLocator = ThetaLocator
  