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from collections import OrderedDict 

import types 

 

import numpy as np 

 

from matplotlib.axes import Axes 

import matplotlib.axis as maxis 

from matplotlib import cbook 

from matplotlib import docstring 

import matplotlib.markers as mmarkers 

import matplotlib.patches as mpatches 

import matplotlib.path as mpath 

from matplotlib import rcParams 

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): 

xy = np.empty(tr.shape, float) 

 

t = tr[:, 0:1] 

r = tr[:, 1:2] 

x = xy[:, 0:1] 

y = xy[:, 1:2] 

 

# 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() 

mask = r < 0 

x[:] = np.where(mask, np.nan, r * np.cos(t)) 

y[:] = np.where(mask, np.nan, r * np.sin(t)) 

 

return xy 

transform_non_affine.__doc__ = \ 

mtransforms.Transform.transform_non_affine.__doc__ 

 

def transform_path_non_affine(self, path): 

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) 

transform_path_non_affine.__doc__ = \ 

mtransforms.Transform.transform_path_non_affine.__doc__ 

 

def inverted(self): 

return PolarAxes.InvertedPolarTransform(self._axis, self._use_rmin, 

self._apply_theta_transforms) 

inverted.__doc__ = mtransforms.Transform.inverted.__doc__ 

 

 

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): 

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 

get_matrix.__doc__ = mtransforms.Affine2DBase.get_matrix.__doc__ 

 

 

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): 

x = xy[:, 0:1] 

y = xy[:, 1:] 

r = np.sqrt(x*x + y*y) 

with np.errstate(invalid='ignore'): 

# At x=y=r=0 this will raise an 

# invalid value warning when doing 0/0 

# Divide by zero warnings are only raised when 

# the numerator is different from 0. That 

# should not happen here. 

theta = np.arccos(x / r) 

theta = np.where(y < 0, 2 * np.pi - theta, theta) 

 

# 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() 

 

return np.concatenate((theta, r), 1) 

transform_non_affine.__doc__ = \ 

mtransforms.Transform.transform_non_affine.__doc__ 

 

def inverted(self): 

return PolarAxes.PolarTransform(self._axis, self._use_rmin, 

self._apply_theta_transforms) 

inverted.__doc__ = mtransforms.Transform.inverted.__doc__ 

 

 

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 

 

if self.tick1On: 

marker = self.tick1line.get_marker() 

if marker in (mmarkers.TICKUP, '|'): 

trans = mtransforms.Affine2D().scale(1.0, 1.0).rotate(angle) 

elif marker == mmarkers.TICKDOWN: 

trans = mtransforms.Affine2D().scale(1.0, -1.0).rotate(angle) 

else: 

# Don't modify custom tick line markers. 

trans = self.tick1line._marker._transform 

self.tick1line._marker._transform = trans 

if self.tick2On: 

marker = self.tick2line.get_marker() 

if marker in (mmarkers.TICKUP, '|'): 

trans = mtransforms.Affine2D().scale(1.0, 1.0).rotate(angle) 

elif marker == mmarkers.TICKDOWN: 

trans = mtransforms.Affine2D().scale(1.0, -1.0).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 

if self.label1On: 

self.label1.set_rotation(text_angle) 

if self.label2On: 

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() 

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) 

return mtransforms.nonsingular(min(0, 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. 

start : str, {'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 

if angle > 90: 

text_angle = angle - 180 

elif angle < -90: 

text_angle = angle + 180 

else: 

text_angle = angle 

else: 

angle = (thetamin * direction + offset) % 360 - 90 

if direction > 0: 

tick_angle = np.deg2rad(angle) 

else: 

tick_angle = np.deg2rad(angle + 180) 

if angle > 90: 

text_angle = angle - 180 

elif angle < -90: 

text_angle = angle + 180 

else: 

text_angle = angle 

mode, user_angle = self._labelrotation 

if mode == 'auto': 

text_angle += user_angle 

else: 

text_angle = user_angle 

if self.label1On: 

if full: 

ha = self.label1.get_ha() 

va = self.label1.get_va() 

else: 

ha, va = self._determine_anchor(mode, angle, direction > 0) 

self.label1.set_ha(ha) 

self.label1.set_va(va) 

self.label1.set_rotation(text_angle) 

if self.tick1On: 

marker = self.tick1line.get_marker() 

if marker == mmarkers.TICKLEFT: 

trans = (mtransforms.Affine2D() 

.scale(1.0, 1.0) 

.rotate(tick_angle)) 

elif marker == '_': 

trans = (mtransforms.Affine2D() 

.scale(1.0, 1.0) 

.rotate(tick_angle + np.pi / 2)) 

elif marker == mmarkers.TICKRIGHT: 

trans = (mtransforms.Affine2D() 

.scale(-1.0, 1.0) 

.rotate(tick_angle)) 

else: 

# Don't modify custom tick line markers. 

trans = self.tick1line._marker._transform 

self.tick1line._marker._transform = trans 

 

if full: 

self.label2On = False 

self.tick2On = False 

else: 

angle = (thetamax * direction + offset) % 360 - 90 

if direction > 0: 

tick_angle = np.deg2rad(angle) 

else: 

tick_angle = np.deg2rad(angle + 180) 

if angle > 90: 

text_angle = angle - 180 

elif angle < -90: 

text_angle = angle + 180 

else: 

text_angle = angle 

mode, user_angle = self._labelrotation 

if mode == 'auto': 

text_angle += user_angle 

else: 

text_angle = user_angle 

if self.label2On: 

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) 

if self.tick2On: 

marker = self.tick2line.get_marker() 

if marker == mmarkers.TICKLEFT: 

trans = (mtransforms.Affine2D() 

.scale(1.0, 1.0) 

.rotate(tick_angle)) 

elif marker == '_': 

trans = (mtransforms.Affine2D() 

.scale(1.0, 1.0) 

.rotate(tick_angle + np.pi / 2)) 

elif marker == mmarkers.TICKRIGHT: 

trans = (mtransforms.Affine2D() 

.scale(-1.0, 1.0) 

.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): 

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] 

if h < w: 

deltah = (w - h) / 2.0 

deltaw = 0.0 

elif w < h: 

deltah = 0.0 

deltaw = (h - w) / 2.0 

else: 

deltah = 0.0 

deltaw = 0.0 

self._points += np.array([[-deltaw, -deltah], [deltaw, deltah]]) 

 

self._invalid = 0 

 

return self._points 

get_points.__doc__ = mtransforms.Bbox.get_points.__doc__ 

 

 

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): 

""" 

Create a new Polar Axes for a polar plot. 

""" 

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() 

__init__.__doc__ = Axes.__init__.__doc__ 

 

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'): 

if which not in ['tick1', 'tick2', 'grid']: 

raise ValueError( 

"'which' must be one of 'tick1', 'tick2', or 'grid'") 

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: 

raise ValueError( 

"'which' must be one of 'tick1', 'tick2', or 'grid'") 

 

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() 

 

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): 

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',): 

mtx[0, 0] = -1 

elif direction in ('counterclockwise', 'anticlockwise'): 

mtx[0, 0] = 1 

elif direction in (1, -1): 

mtx[0, 0] = direction 

else: 

raise ValueError( 

"direction must be 1, -1, clockwise or counterclockwise") 

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): 

self.viewLim.y1 = rmax 

 

def get_rmax(self): 

return self.viewLim.ymax 

 

def set_rmin(self, rmin): 

self.viewLim.y0 = rmin 

 

def get_rmin(self): 

return self.viewLim.ymin 

 

def set_rorigin(self, rorigin): 

self._originViewLim.locked_y0 = rorigin 

 

def get_rorigin(self): 

return self._originViewLim.y0 

 

def set_rlim(self, *args, **kwargs): 

if 'rmin' in kwargs: 

kwargs['ymin'] = kwargs.pop('rmin') 

if 'rmax' in kwargs: 

kwargs['ymax'] = kwargs.pop('rmax') 

return self.set_ylim(*args, **kwargs) 

 

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 

 

 

# These are a couple of aborted attempts to project a polar plot using 

# cubic bezier curves. 

 

# def transform_path(self, path): 

# twopi = 2.0 * np.pi 

# halfpi = 0.5 * np.pi 

 

# vertices = path.vertices 

# t0 = vertices[0:-1, 0] 

# t1 = vertices[1: , 0] 

# td = np.where(t1 > t0, t1 - t0, twopi - (t0 - t1)) 

# maxtd = td.max() 

# interpolate = np.ceil(maxtd / halfpi) 

# if interpolate > 1.0: 

# vertices = self.interpolate(vertices, interpolate) 

 

# vertices = self.transform(vertices) 

 

# result = np.zeros((len(vertices) * 3 - 2, 2), float) 

# codes = mpath.Path.CURVE4 * np.ones((len(vertices) * 3 - 2, ), 

# mpath.Path.code_type) 

# result[0] = vertices[0] 

# codes[0] = mpath.Path.MOVETO 

 

# kappa = 4.0 * ((np.sqrt(2.0) - 1.0) / 3.0) 

# kappa = 0.5 

 

# p0 = vertices[0:-1] 

# p1 = vertices[1: ] 

 

# x0 = p0[:, 0:1] 

# y0 = p0[:, 1: ] 

# b0 = ((y0 - x0) - y0) / ((x0 + y0) - x0) 

# a0 = y0 - b0*x0 

 

# x1 = p1[:, 0:1] 

# y1 = p1[:, 1: ] 

# b1 = ((y1 - x1) - y1) / ((x1 + y1) - x1) 

# a1 = y1 - b1*x1 

 

# x = -(a0-a1) / (b0-b1) 

# y = a0 + b0*x 

 

# xk = (x - x0) * kappa + x0 

# yk = (y - y0) * kappa + y0 

 

# result[1::3, 0:1] = xk 

# result[1::3, 1: ] = yk 

 

# xk = (x - x1) * kappa + x1 

# yk = (y - y1) * kappa + y1 

 

# result[2::3, 0:1] = xk 

# result[2::3, 1: ] = yk 

 

# result[3::3] = p1 

 

# print(vertices[-2:]) 

# print(result[-2:]) 

 

# return mpath.Path(result, codes) 

 

# twopi = 2.0 * np.pi 

# halfpi = 0.5 * np.pi 

 

# vertices = path.vertices 

# t0 = vertices[0:-1, 0] 

# t1 = vertices[1: , 0] 

# td = np.where(t1 > t0, t1 - t0, twopi - (t0 - t1)) 

# maxtd = td.max() 

# interpolate = np.ceil(maxtd / halfpi) 

 

# print("interpolate", interpolate) 

# if interpolate > 1.0: 

# vertices = self.interpolate(vertices, interpolate) 

 

# result = np.zeros((len(vertices) * 3 - 2, 2), float) 

# codes = mpath.Path.CURVE4 * np.ones((len(vertices) * 3 - 2, ), 

# mpath.Path.code_type) 

# result[0] = vertices[0] 

# codes[0] = mpath.Path.MOVETO 

 

# kappa = 4.0 * ((np.sqrt(2.0) - 1.0) / 3.0) 

# tkappa = np.arctan(kappa) 

# hyp_kappa = np.sqrt(kappa*kappa + 1.0) 

 

# t0 = vertices[0:-1, 0] 

# t1 = vertices[1: , 0] 

# r0 = vertices[0:-1, 1] 

# r1 = vertices[1: , 1] 

 

# td = np.where(t1 > t0, t1 - t0, twopi - (t0 - t1)) 

# td_scaled = td / (np.pi * 0.5) 

# rd = r1 - r0 

# r0kappa = r0 * kappa * td_scaled 

# r1kappa = r1 * kappa * td_scaled 

# ravg_kappa = ((r1 + r0) / 2.0) * kappa * td_scaled 

 

# result[1::3, 0] = t0 + (tkappa * td_scaled) 

# result[1::3, 1] = r0*hyp_kappa 

# # result[1::3, 1] = r0 / np.cos(tkappa * td_scaled) 

# # np.sqrt(r0*r0 + ravg_kappa*ravg_kappa) 

 

# result[2::3, 0] = t1 - (tkappa * td_scaled) 

# result[2::3, 1] = r1*hyp_kappa 

# # result[2::3, 1] = r1 / np.cos(tkappa * td_scaled) 

# # np.sqrt(r1*r1 + ravg_kappa*ravg_kappa) 

 

# result[3::3, 0] = t1 

# result[3::3, 1] = r1 

 

# print(vertices[:6], result[:6], t0[:6], t1[:6], td[:6], 

# td_scaled[:6], tkappa) 

# result = self.transform(result) 

# return mpath.Path(result, codes) 

# transform_path_non_affine = transform_path