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/ projections / polar.py
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