511 lines
17 KiB
Python
511 lines
17 KiB
Python
import numpy as np
|
|
|
|
from matplotlib import cbook, rcParams
|
|
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)
|
|
self.yaxis = maxis.YAxis(self)
|
|
# Do not register xaxis or yaxis with spines -- as done in
|
|
# Axes._init_axis() -- until GeoAxes.xaxis.cla() works.
|
|
# self.spines['geo'].register_axis(self.yaxis)
|
|
self._update_transScale()
|
|
|
|
def cla(self):
|
|
Axes.cla(self)
|
|
|
|
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(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'):
|
|
cbook._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'):
|
|
cbook._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):
|
|
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])
|
|
if lat >= 0.0:
|
|
ns = 'N'
|
|
else:
|
|
ns = 'S'
|
|
if lon >= 0.0:
|
|
ew = 'E'
|
|
else:
|
|
ew = '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 *True* if this axes supports the zoom box button functionality.
|
|
|
|
This axes object does not support interactive zoom box.
|
|
"""
|
|
return False
|
|
|
|
def can_pan(self):
|
|
"""
|
|
Return *True* if 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.
|
|
"""
|
|
Transform.__init__(self)
|
|
self._resolution = resolution
|
|
|
|
def __str__(self):
|
|
return "{}({})".format(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."""
|
|
|
|
def transform_non_affine(self, ll):
|
|
# docstring inherited
|
|
longitude, latitude = ll.T
|
|
|
|
# Pre-compute some values
|
|
half_long = longitude / 2.0
|
|
cos_latitude = np.cos(latitude)
|
|
|
|
alpha = np.arccos(cos_latitude * np.cos(half_long))
|
|
# Avoid divide-by-zero errors using same method as NumPy.
|
|
alpha[alpha == 0.0] = 1e-20
|
|
# We want unnormalized sinc. numpy.sinc gives us normalized
|
|
sinc_alpha = np.sin(alpha) / alpha
|
|
|
|
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):
|
|
|
|
def transform_non_affine(self, xy):
|
|
# docstring inherited
|
|
# MGDTODO: Math is hard ;(
|
|
return xy
|
|
|
|
def inverted(self):
|
|
# docstring inherited
|
|
return AitoffAxes.AitoffTransform(self._resolution)
|
|
|
|
def __init__(self, *args, **kwargs):
|
|
self._longitude_cap = np.pi / 2.0
|
|
GeoAxes.__init__(self, *args, **kwargs)
|
|
self.set_aspect(0.5, adjustable='box', anchor='C')
|
|
self.cla()
|
|
|
|
def _get_core_transform(self, resolution):
|
|
return self.AitoffTransform(resolution)
|
|
|
|
|
|
class HammerAxes(GeoAxes):
|
|
name = 'hammer'
|
|
|
|
class HammerTransform(_GeoTransform):
|
|
"""The base Hammer transform."""
|
|
|
|
def transform_non_affine(self, ll):
|
|
# docstring inherited
|
|
longitude, latitude = ll.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):
|
|
|
|
def transform_non_affine(self, xy):
|
|
# docstring inherited
|
|
x, y = xy.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
|
|
GeoAxes.__init__(self, *args, **kwargs)
|
|
self.set_aspect(0.5, adjustable='box', anchor='C')
|
|
self.cla()
|
|
|
|
def _get_core_transform(self, resolution):
|
|
return self.HammerTransform(resolution)
|
|
|
|
|
|
class MollweideAxes(GeoAxes):
|
|
name = 'mollweide'
|
|
|
|
class MollweideTransform(_GeoTransform):
|
|
"""The base Mollweide transform."""
|
|
|
|
def transform_non_affine(self, ll):
|
|
# 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 = ll.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(ll.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):
|
|
|
|
def transform_non_affine(self, xy):
|
|
# docstring inherited
|
|
x, y = xy.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
|
|
GeoAxes.__init__(self, *args, **kwargs)
|
|
self.set_aspect(0.5, adjustable='box', anchor='C')
|
|
self.cla()
|
|
|
|
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
|
|
|
|
def transform_non_affine(self, ll):
|
|
# docstring inherited
|
|
longitude, latitude = ll.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
|
|
|
|
def transform_non_affine(self, xy):
|
|
# docstring inherited
|
|
x, y = xy.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
|
|
GeoAxes.__init__(self, *args, **kwargs)
|
|
self.set_aspect('equal', adjustable='box', anchor='C')
|
|
self.cla()
|
|
|
|
def cla(self):
|
|
GeoAxes.cla(self)
|
|
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)
|