import numpy as np
import matplotlib as mpl
from matplotlib import _api
from matplotlib.axes import Axes
import matplotlib.axis as maxis
from matplotlib.patches import Circle
from matplotlib.path import Path
import matplotlib.spines as mspines
from matplotlib.ticker import (
Formatter, NullLocator, FixedLocator, NullFormatter)
from matplotlib.transforms import Affine2D, BboxTransformTo, Transform
class GeoAxes(Axes):
"""An abstract base class for geographic projections."""
class ThetaFormatter(Formatter):
"""
Used to format the theta tick labels. Converts the native
unit of radians into degrees and adds a degree symbol.
"""
def __init__(self, round_to=1.0):
self._round_to = round_to
def __call__(self, x, pos=None):
degrees = round(np.rad2deg(x) / self._round_to) * self._round_to
return f"{degrees:0.0f}\N{DEGREE SIGN}"
RESOLUTION = 75
def _init_axis(self):
self.xaxis = maxis.XAxis(self, clear=False)
self.yaxis = maxis.YAxis(self, clear=False)
self.spines['geo'].register_axis(self.yaxis)
def clear(self):
# docstring inherited
super().clear()
self.set_longitude_grid(30)
self.set_latitude_grid(15)
self.set_longitude_grid_ends(75)
self.xaxis.set_minor_locator(NullLocator())
self.yaxis.set_minor_locator(NullLocator())
self.xaxis.set_ticks_position('none')
self.yaxis.set_ticks_position('none')
self.yaxis.set_tick_params(label1On=True)
# Why do we need to turn on yaxis tick labels, but
# xaxis tick labels are already on?
self.grid(mpl.rcParams['axes.grid'])
Axes.set_xlim(self, -np.pi, np.pi)
Axes.set_ylim(self, -np.pi / 2.0, np.pi / 2.0)
def _set_lim_and_transforms(self):
# A (possibly non-linear) projection on the (already scaled) data
self.transProjection = self._get_core_transform(self.RESOLUTION)
self.transAffine = self._get_affine_transform()
self.transAxes = BboxTransformTo(self.bbox)
# The complete data transformation stack -- from data all the
# way to display coordinates
self.transData = \
self.transProjection + \
self.transAffine + \
self.transAxes
# This is the transform for longitude ticks.
self._xaxis_pretransform = \
Affine2D() \
.scale(1, self._longitude_cap * 2) \
.translate(0, -self._longitude_cap)
self._xaxis_transform = \
self._xaxis_pretransform + \
self.transData
self._xaxis_text1_transform = \
Affine2D().scale(1, 0) + \
self.transData + \
Affine2D().translate(0, 4)
self._xaxis_text2_transform = \
Affine2D().scale(1, 0) + \
self.transData + \
Affine2D().translate(0, -4)
# This is the transform for latitude ticks.
yaxis_stretch = Affine2D().scale(np.pi * 2, 1).translate(-np.pi, 0)
yaxis_space = Affine2D().scale(1, 1.1)
self._yaxis_transform = \
yaxis_stretch + \
self.transData
yaxis_text_base = \
yaxis_stretch + \
self.transProjection + \
(yaxis_space +
self.transAffine +
self.transAxes)
self._yaxis_text1_transform = \
yaxis_text_base + \
Affine2D().translate(-8, 0)
self._yaxis_text2_transform = \
yaxis_text_base + \
Affine2D().translate(8, 0)
def _get_affine_transform(self):
transform = self._get_core_transform(1)
xscale, _ = transform.transform((np.pi, 0))
_, yscale = transform.transform((0, np.pi/2))
return Affine2D() \
.scale(0.5 / xscale, 0.5 / yscale) \
.translate(0.5, 0.5)
def get_xaxis_transform(self, which='grid'):
_api.check_in_list(['tick1', 'tick2', 'grid'], which=which)
return self._xaxis_transform
def get_xaxis_text1_transform(self, pad):
return self._xaxis_text1_transform, 'bottom', 'center'
def get_xaxis_text2_transform(self, pad):
return self._xaxis_text2_transform, 'top', 'center'
def get_yaxis_transform(self, which='grid'):
_api.check_in_list(['tick1', 'tick2', 'grid'], which=which)
return self._yaxis_transform
def get_yaxis_text1_transform(self, pad):
return self._yaxis_text1_transform, 'center', 'right'
def get_yaxis_text2_transform(self, pad):
return self._yaxis_text2_transform, 'center', 'left'
def _gen_axes_patch(self):
return Circle((0.5, 0.5), 0.5)
def _gen_axes_spines(self):
return {'geo': mspines.Spine.circular_spine(self, (0.5, 0.5), 0.5)}
def set_yscale(self, *args, **kwargs):
if args[0] != 'linear':
raise NotImplementedError
set_xscale = set_yscale
def set_xlim(self, *args, **kwargs):
"""Not supported. Please consider using Cartopy."""
raise TypeError("Changing axes limits of a geographic projection is "
"not supported. Please consider using Cartopy.")
set_ylim = set_xlim
def format_coord(self, lon, lat):
"""Return a format string formatting the coordinate."""
lon, lat = np.rad2deg([lon, lat])
ns = 'N' if lat >= 0.0 else 'S'
ew = 'E' if lon >= 0.0 else 'W'
return ('%f\N{DEGREE SIGN}%s, %f\N{DEGREE SIGN}%s'
% (abs(lat), ns, abs(lon), ew))
def set_longitude_grid(self, degrees):
"""
Set the number of degrees between each longitude grid.
"""
# Skip -180 and 180, which are the fixed limits.
grid = np.arange(-180 + degrees, 180, degrees)
self.xaxis.set_major_locator(FixedLocator(np.deg2rad(grid)))
self.xaxis.set_major_formatter(self.ThetaFormatter(degrees))
def set_latitude_grid(self, degrees):
"""
Set the number of degrees between each latitude grid.
"""
# Skip -90 and 90, which are the fixed limits.
grid = np.arange(-90 + degrees, 90, degrees)
self.yaxis.set_major_locator(FixedLocator(np.deg2rad(grid)))
self.yaxis.set_major_formatter(self.ThetaFormatter(degrees))
def set_longitude_grid_ends(self, degrees):
"""
Set the latitude(s) at which to stop drawing the longitude grids.
"""
self._longitude_cap = np.deg2rad(degrees)
self._xaxis_pretransform \
.clear() \
.scale(1.0, self._longitude_cap * 2.0) \
.translate(0.0, -self._longitude_cap)
def get_data_ratio(self):
"""Return the aspect ratio of the data itself."""
return 1.0
### Interactive panning
def can_zoom(self):
"""
Return whether this Axes supports the zoom box button functionality.
This Axes object does not support interactive zoom box.
"""
return False
def can_pan(self):
"""
Return whether this Axes supports the pan/zoom button functionality.
This Axes object does not support interactive pan/zoom.
"""
return False
def start_pan(self, x, y, button):
pass
def end_pan(self):
pass
def drag_pan(self, button, key, x, y):
pass
class _GeoTransform(Transform):
# Factoring out some common functionality.
input_dims = output_dims = 2
def __init__(self, resolution):
"""
Create a new geographical transform.
Resolution is the number of steps to interpolate between each input
line segment to approximate its path in curved space.
"""
super().__init__()
self._resolution = resolution
def __str__(self):
return f"{type(self).__name__}({self._resolution})"
def transform_path_non_affine(self, path):
# docstring inherited
ipath = path.interpolated(self._resolution)
return Path(self.transform(ipath.vertices), ipath.codes)
class AitoffAxes(GeoAxes):
name = 'aitoff'
class AitoffTransform(_GeoTransform):
"""The base Aitoff transform."""
@_api.rename_parameter("3.8", "ll", "values")
def transform_non_affine(self, values):
# docstring inherited
longitude, latitude = values.T
# Pre-compute some values
half_long = longitude / 2.0
cos_latitude = np.cos(latitude)
alpha = np.arccos(cos_latitude * np.cos(half_long))
sinc_alpha = np.sinc(alpha / np.pi) # np.sinc is sin(pi*x)/(pi*x).
x = (cos_latitude * np.sin(half_long)) / sinc_alpha
y = np.sin(latitude) / sinc_alpha
return np.column_stack([x, y])
def inverted(self):
# docstring inherited
return AitoffAxes.InvertedAitoffTransform(self._resolution)
class InvertedAitoffTransform(_GeoTransform):
@_api.rename_parameter("3.8", "xy", "values")
def transform_non_affine(self, values):
# docstring inherited
# MGDTODO: Math is hard ;(
return np.full_like(values, np.nan)
def inverted(self):
# docstring inherited
return AitoffAxes.AitoffTransform(self._resolution)
def __init__(self, *args, **kwargs):
self._longitude_cap = np.pi / 2.0
super().__init__(*args, **kwargs)
self.set_aspect(0.5, adjustable='box', anchor='C')
self.clear()
def _get_core_transform(self, resolution):
return self.AitoffTransform(resolution)
class HammerAxes(GeoAxes):
name = 'hammer'
class HammerTransform(_GeoTransform):
"""The base Hammer transform."""
@_api.rename_parameter("3.8", "ll", "values")
def transform_non_affine(self, values):
# docstring inherited
longitude, latitude = values.T
half_long = longitude / 2.0
cos_latitude = np.cos(latitude)
sqrt2 = np.sqrt(2.0)
alpha = np.sqrt(1.0 + cos_latitude * np.cos(half_long))
x = (2.0 * sqrt2) * (cos_latitude * np.sin(half_long)) / alpha
y = (sqrt2 * np.sin(latitude)) / alpha
return np.column_stack([x, y])
def inverted(self):
# docstring inherited
return HammerAxes.InvertedHammerTransform(self._resolution)
class InvertedHammerTransform(_GeoTransform):
@_api.rename_parameter("3.8", "xy", "values")
def transform_non_affine(self, values):
# docstring inherited
x, y = values.T
z = np.sqrt(1 - (x / 4) ** 2 - (y / 2) ** 2)
longitude = 2 * np.arctan((z * x) / (2 * (2 * z ** 2 - 1)))
latitude = np.arcsin(y*z)
return np.column_stack([longitude, latitude])
def inverted(self):
# docstring inherited
return HammerAxes.HammerTransform(self._resolution)
def __init__(self, *args, **kwargs):
self._longitude_cap = np.pi / 2.0
super().__init__(*args, **kwargs)
self.set_aspect(0.5, adjustable='box', anchor='C')
self.clear()
def _get_core_transform(self, resolution):
return self.HammerTransform(resolution)
class MollweideAxes(GeoAxes):
name = 'mollweide'
class MollweideTransform(_GeoTransform):
"""The base Mollweide transform."""
@_api.rename_parameter("3.8", "ll", "values")
def transform_non_affine(self, values):
# docstring inherited
def d(theta):
delta = (-(theta + np.sin(theta) - pi_sin_l)
/ (1 + np.cos(theta)))
return delta, np.abs(delta) > 0.001
longitude, latitude = values.T
clat = np.pi/2 - np.abs(latitude)
ihigh = clat < 0.087 # within 5 degrees of the poles
ilow = ~ihigh
aux = np.empty(latitude.shape, dtype=float)
if ilow.any(): # Newton-Raphson iteration
pi_sin_l = np.pi * np.sin(latitude[ilow])
theta = 2.0 * latitude[ilow]
delta, large_delta = d(theta)
while np.any(large_delta):
theta[large_delta] += delta[large_delta]
delta, large_delta = d(theta)
aux[ilow] = theta / 2
if ihigh.any(): # Taylor series-based approx. solution
e = clat[ihigh]
d = 0.5 * (3 * np.pi * e**2) ** (1.0/3)
aux[ihigh] = (np.pi/2 - d) * np.sign(latitude[ihigh])
xy = np.empty(values.shape, dtype=float)
xy[:, 0] = (2.0 * np.sqrt(2.0) / np.pi) * longitude * np.cos(aux)
xy[:, 1] = np.sqrt(2.0) * np.sin(aux)
return xy
def inverted(self):
# docstring inherited
return MollweideAxes.InvertedMollweideTransform(self._resolution)
class InvertedMollweideTransform(_GeoTransform):
@_api.rename_parameter("3.8", "xy", "values")
def transform_non_affine(self, values):
# docstring inherited
x, y = values.T
# from Equations (7, 8) of
# https://mathworld.wolfram.com/MollweideProjection.html
theta = np.arcsin(y / np.sqrt(2))
longitude = (np.pi / (2 * np.sqrt(2))) * x / np.cos(theta)
latitude = np.arcsin((2 * theta + np.sin(2 * theta)) / np.pi)
return np.column_stack([longitude, latitude])
def inverted(self):
# docstring inherited
return MollweideAxes.MollweideTransform(self._resolution)
def __init__(self, *args, **kwargs):
self._longitude_cap = np.pi / 2.0
super().__init__(*args, **kwargs)
self.set_aspect(0.5, adjustable='box', anchor='C')
self.clear()
def _get_core_transform(self, resolution):
return self.MollweideTransform(resolution)
class LambertAxes(GeoAxes):
name = 'lambert'
class LambertTransform(_GeoTransform):
"""The base Lambert transform."""
def __init__(self, center_longitude, center_latitude, resolution):
"""
Create a new Lambert transform. Resolution is the number of steps
to interpolate between each input line segment to approximate its
path in curved Lambert space.
"""
_GeoTransform.__init__(self, resolution)
self._center_longitude = center_longitude
self._center_latitude = center_latitude
@_api.rename_parameter("3.8", "ll", "values")
def transform_non_affine(self, values):
# docstring inherited
longitude, latitude = values.T
clong = self._center_longitude
clat = self._center_latitude
cos_lat = np.cos(latitude)
sin_lat = np.sin(latitude)
diff_long = longitude - clong
cos_diff_long = np.cos(diff_long)
inner_k = np.maximum( # Prevent divide-by-zero problems
1 + np.sin(clat)*sin_lat + np.cos(clat)*cos_lat*cos_diff_long,
1e-15)
k = np.sqrt(2 / inner_k)
x = k * cos_lat*np.sin(diff_long)
y = k * (np.cos(clat)*sin_lat - np.sin(clat)*cos_lat*cos_diff_long)
return np.column_stack([x, y])
def inverted(self):
# docstring inherited
return LambertAxes.InvertedLambertTransform(
self._center_longitude,
self._center_latitude,
self._resolution)
class InvertedLambertTransform(_GeoTransform):
def __init__(self, center_longitude, center_latitude, resolution):
_GeoTransform.__init__(self, resolution)
self._center_longitude = center_longitude
self._center_latitude = center_latitude
@_api.rename_parameter("3.8", "xy", "values")
def transform_non_affine(self, values):
# docstring inherited
x, y = values.T
clong = self._center_longitude
clat = self._center_latitude
p = np.maximum(np.hypot(x, y), 1e-9)
c = 2 * np.arcsin(0.5 * p)
sin_c = np.sin(c)
cos_c = np.cos(c)
latitude = np.arcsin(cos_c*np.sin(clat) +
((y*sin_c*np.cos(clat)) / p))
longitude = clong + np.arctan(
(x*sin_c) / (p*np.cos(clat)*cos_c - y*np.sin(clat)*sin_c))
return np.column_stack([longitude, latitude])
def inverted(self):
# docstring inherited
return LambertAxes.LambertTransform(
self._center_longitude,
self._center_latitude,
self._resolution)
def __init__(self, *args, center_longitude=0, center_latitude=0, **kwargs):
self._longitude_cap = np.pi / 2
self._center_longitude = center_longitude
self._center_latitude = center_latitude
super().__init__(*args, **kwargs)
self.set_aspect('equal', adjustable='box', anchor='C')
self.clear()
def clear(self):
# docstring inherited
super().clear()
self.yaxis.set_major_formatter(NullFormatter())
def _get_core_transform(self, resolution):
return self.LambertTransform(
self._center_longitude,
self._center_latitude,
resolution)
def _get_affine_transform(self):
return Affine2D() \
.scale(0.25) \
.translate(0.5, 0.5)