518 lines
17 KiB
Python
518 lines
17 KiB
Python
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import numpy as np
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from matplotlib import cbook, rcParams
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from matplotlib.axes import Axes
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import matplotlib.axis as maxis
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from matplotlib.patches import Circle
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from matplotlib.path import Path
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import matplotlib.spines as mspines
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from matplotlib.ticker import (
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Formatter, NullLocator, FixedLocator, NullFormatter)
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from matplotlib.transforms import Affine2D, BboxTransformTo, Transform
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class GeoAxes(Axes):
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"""An abstract base class for geographic projections."""
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class ThetaFormatter(Formatter):
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"""
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Used to format the theta tick labels. Converts the native
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unit of radians into degrees and adds a degree symbol.
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"""
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def __init__(self, round_to=1.0):
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self._round_to = round_to
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def __call__(self, x, pos=None):
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degrees = round(np.rad2deg(x) / self._round_to) * self._round_to
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if rcParams['text.usetex'] and not rcParams['text.latex.unicode']:
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return r"$%0.0f^\circ$" % degrees
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else:
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return "%0.0f\N{DEGREE SIGN}" % degrees
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RESOLUTION = 75
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def _init_axis(self):
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self.xaxis = maxis.XAxis(self)
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self.yaxis = maxis.YAxis(self)
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# Do not register xaxis or yaxis with spines -- as done in
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# Axes._init_axis() -- until GeoAxes.xaxis.cla() works.
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# self.spines['geo'].register_axis(self.yaxis)
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self._update_transScale()
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def cla(self):
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Axes.cla(self)
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self.set_longitude_grid(30)
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self.set_latitude_grid(15)
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self.set_longitude_grid_ends(75)
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self.xaxis.set_minor_locator(NullLocator())
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self.yaxis.set_minor_locator(NullLocator())
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self.xaxis.set_ticks_position('none')
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self.yaxis.set_ticks_position('none')
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self.yaxis.set_tick_params(label1On=True)
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# Why do we need to turn on yaxis tick labels, but
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# xaxis tick labels are already on?
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self.grid(rcParams['axes.grid'])
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Axes.set_xlim(self, -np.pi, np.pi)
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Axes.set_ylim(self, -np.pi / 2.0, np.pi / 2.0)
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def _set_lim_and_transforms(self):
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# A (possibly non-linear) projection on the (already scaled) data
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self.transProjection = self._get_core_transform(self.RESOLUTION)
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self.transAffine = self._get_affine_transform()
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self.transAxes = BboxTransformTo(self.bbox)
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# The complete data transformation stack -- from data all the
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# way to display coordinates
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self.transData = \
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self.transProjection + \
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self.transAffine + \
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self.transAxes
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# This is the transform for longitude ticks.
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self._xaxis_pretransform = \
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Affine2D() \
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.scale(1, self._longitude_cap * 2) \
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.translate(0, -self._longitude_cap)
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self._xaxis_transform = \
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self._xaxis_pretransform + \
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self.transData
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self._xaxis_text1_transform = \
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Affine2D().scale(1, 0) + \
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self.transData + \
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Affine2D().translate(0, 4)
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self._xaxis_text2_transform = \
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Affine2D().scale(1, 0) + \
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self.transData + \
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Affine2D().translate(0, -4)
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# This is the transform for latitude ticks.
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yaxis_stretch = Affine2D().scale(np.pi * 2, 1).translate(-np.pi, 0)
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yaxis_space = Affine2D().scale(1, 1.1)
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self._yaxis_transform = \
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yaxis_stretch + \
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self.transData
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yaxis_text_base = \
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yaxis_stretch + \
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self.transProjection + \
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(yaxis_space +
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self.transAffine +
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self.transAxes)
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self._yaxis_text1_transform = \
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yaxis_text_base + \
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Affine2D().translate(-8, 0)
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self._yaxis_text2_transform = \
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yaxis_text_base + \
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Affine2D().translate(8, 0)
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def _get_affine_transform(self):
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transform = self._get_core_transform(1)
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xscale, _ = transform.transform((np.pi, 0))
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_, yscale = transform.transform((0, np.pi/2))
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return Affine2D() \
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.scale(0.5 / xscale, 0.5 / yscale) \
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.translate(0.5, 0.5)
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def get_xaxis_transform(self, which='grid'):
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cbook._check_in_list(['tick1', 'tick2', 'grid'], which=which)
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return self._xaxis_transform
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def get_xaxis_text1_transform(self, pad):
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return self._xaxis_text1_transform, 'bottom', 'center'
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def get_xaxis_text2_transform(self, pad):
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return self._xaxis_text2_transform, 'top', 'center'
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def get_yaxis_transform(self, which='grid'):
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cbook._check_in_list(['tick1', 'tick2', 'grid'], which=which)
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return self._yaxis_transform
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def get_yaxis_text1_transform(self, pad):
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return self._yaxis_text1_transform, 'center', 'right'
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def get_yaxis_text2_transform(self, pad):
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return self._yaxis_text2_transform, 'center', 'left'
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def _gen_axes_patch(self):
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return Circle((0.5, 0.5), 0.5)
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def _gen_axes_spines(self):
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return {'geo': mspines.Spine.circular_spine(self, (0.5, 0.5), 0.5)}
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def set_yscale(self, *args, **kwargs):
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if args[0] != 'linear':
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raise NotImplementedError
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set_xscale = set_yscale
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def set_xlim(self, *args, **kwargs):
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raise TypeError("It is not possible to change axes limits "
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"for geographic projections. Please consider "
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"using Basemap or Cartopy.")
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set_ylim = set_xlim
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def format_coord(self, lon, lat):
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'return a format string formatting the coordinate'
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lon, lat = np.rad2deg([lon, lat])
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if lat >= 0.0:
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ns = 'N'
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else:
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ns = 'S'
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if lon >= 0.0:
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ew = 'E'
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else:
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ew = 'W'
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return ('%f\N{DEGREE SIGN}%s, %f\N{DEGREE SIGN}%s'
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% (abs(lat), ns, abs(lon), ew))
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def set_longitude_grid(self, degrees):
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"""
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Set the number of degrees between each longitude grid.
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"""
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# Skip -180 and 180, which are the fixed limits.
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grid = np.arange(-180 + degrees, 180, degrees)
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self.xaxis.set_major_locator(FixedLocator(np.deg2rad(grid)))
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self.xaxis.set_major_formatter(self.ThetaFormatter(degrees))
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def set_latitude_grid(self, degrees):
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"""
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Set the number of degrees between each latitude grid.
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"""
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# Skip -90 and 90, which are the fixed limits.
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grid = np.arange(-90 + degrees, 90, degrees)
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self.yaxis.set_major_locator(FixedLocator(np.deg2rad(grid)))
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self.yaxis.set_major_formatter(self.ThetaFormatter(degrees))
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def set_longitude_grid_ends(self, degrees):
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"""
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Set the latitude(s) at which to stop drawing the longitude grids.
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"""
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self._longitude_cap = np.deg2rad(degrees)
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self._xaxis_pretransform \
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.clear() \
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.scale(1.0, self._longitude_cap * 2.0) \
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.translate(0.0, -self._longitude_cap)
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def get_data_ratio(self):
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'''
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Return the aspect ratio of the data itself.
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'''
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return 1.0
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### Interactive panning
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def can_zoom(self):
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"""
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Return *True* if this axes supports the zoom box button functionality.
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This axes object does not support interactive zoom box.
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"""
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return False
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def can_pan(self):
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"""
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Return *True* if this axes supports the pan/zoom button functionality.
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This axes object does not support interactive pan/zoom.
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"""
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return False
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def start_pan(self, x, y, button):
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pass
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def end_pan(self):
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pass
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def drag_pan(self, button, key, x, y):
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pass
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class _GeoTransform(Transform):
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# Factoring out some common functionality.
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input_dims = 2
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output_dims = 2
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is_separable = False
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def __init__(self, resolution):
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"""
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Create a new geographical transform.
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Resolution is the number of steps to interpolate between each input
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line segment to approximate its path in curved space.
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"""
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Transform.__init__(self)
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self._resolution = resolution
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def __str__(self):
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return "{}({})".format(type(self).__name__, self._resolution)
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def transform_path_non_affine(self, path):
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# docstring inherited
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ipath = path.interpolated(self._resolution)
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return Path(self.transform(ipath.vertices), ipath.codes)
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class AitoffAxes(GeoAxes):
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name = 'aitoff'
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class AitoffTransform(_GeoTransform):
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"""The base Aitoff transform."""
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def transform_non_affine(self, ll):
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# docstring inherited
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longitude, latitude = ll.T
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# Pre-compute some values
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half_long = longitude / 2.0
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cos_latitude = np.cos(latitude)
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alpha = np.arccos(cos_latitude * np.cos(half_long))
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# Avoid divide-by-zero errors using same method as NumPy.
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alpha[alpha == 0.0] = 1e-20
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# We want unnormalized sinc. numpy.sinc gives us normalized
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sinc_alpha = np.sin(alpha) / alpha
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x = (cos_latitude * np.sin(half_long)) / sinc_alpha
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y = np.sin(latitude) / sinc_alpha
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return np.column_stack([x, y])
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def inverted(self):
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# docstring inherited
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return AitoffAxes.InvertedAitoffTransform(self._resolution)
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class InvertedAitoffTransform(_GeoTransform):
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def transform_non_affine(self, xy):
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# docstring inherited
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# MGDTODO: Math is hard ;(
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return xy
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def inverted(self):
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# docstring inherited
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return AitoffAxes.AitoffTransform(self._resolution)
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def __init__(self, *args, **kwargs):
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self._longitude_cap = np.pi / 2.0
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GeoAxes.__init__(self, *args, **kwargs)
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self.set_aspect(0.5, adjustable='box', anchor='C')
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self.cla()
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def _get_core_transform(self, resolution):
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return self.AitoffTransform(resolution)
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class HammerAxes(GeoAxes):
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name = 'hammer'
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class HammerTransform(_GeoTransform):
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"""The base Hammer transform."""
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def transform_non_affine(self, ll):
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# docstring inherited
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longitude, latitude = ll.T
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half_long = longitude / 2.0
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cos_latitude = np.cos(latitude)
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sqrt2 = np.sqrt(2.0)
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alpha = np.sqrt(1.0 + cos_latitude * np.cos(half_long))
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x = (2.0 * sqrt2) * (cos_latitude * np.sin(half_long)) / alpha
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y = (sqrt2 * np.sin(latitude)) / alpha
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return np.column_stack([x, y])
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def inverted(self):
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# docstring inherited
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return HammerAxes.InvertedHammerTransform(self._resolution)
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class InvertedHammerTransform(_GeoTransform):
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def transform_non_affine(self, xy):
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# docstring inherited
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x, y = xy.T
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z = np.sqrt(1 - (x / 4) ** 2 - (y / 2) ** 2)
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longitude = 2 * np.arctan((z * x) / (2 * (2 * z ** 2 - 1)))
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latitude = np.arcsin(y*z)
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return np.column_stack([longitude, latitude])
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def inverted(self):
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# docstring inherited
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return HammerAxes.HammerTransform(self._resolution)
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def __init__(self, *args, **kwargs):
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self._longitude_cap = np.pi / 2.0
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GeoAxes.__init__(self, *args, **kwargs)
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self.set_aspect(0.5, adjustable='box', anchor='C')
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self.cla()
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def _get_core_transform(self, resolution):
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return self.HammerTransform(resolution)
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class MollweideAxes(GeoAxes):
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name = 'mollweide'
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class MollweideTransform(_GeoTransform):
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"""The base Mollweide transform."""
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def transform_non_affine(self, ll):
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# docstring inherited
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def d(theta):
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delta = (-(theta + np.sin(theta) - pi_sin_l)
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/ (1 + np.cos(theta)))
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return delta, np.abs(delta) > 0.001
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longitude, latitude = ll.T
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clat = np.pi/2 - np.abs(latitude)
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ihigh = clat < 0.087 # within 5 degrees of the poles
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ilow = ~ihigh
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aux = np.empty(latitude.shape, dtype=float)
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||
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if ilow.any(): # Newton-Raphson iteration
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pi_sin_l = np.pi * np.sin(latitude[ilow])
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theta = 2.0 * latitude[ilow]
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delta, large_delta = d(theta)
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while np.any(large_delta):
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theta[large_delta] += delta[large_delta]
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delta, large_delta = d(theta)
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aux[ilow] = theta / 2
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|
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||
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if ihigh.any(): # Taylor series-based approx. solution
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e = clat[ihigh]
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|
d = 0.5 * (3 * np.pi * e**2) ** (1.0/3)
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|
aux[ihigh] = (np.pi/2 - d) * np.sign(latitude[ihigh])
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||
|
|
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||
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|
xy = np.empty(ll.shape, dtype=float)
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||
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|
xy[:, 0] = (2.0 * np.sqrt(2.0) / np.pi) * longitude * np.cos(aux)
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xy[:, 1] = np.sqrt(2.0) * np.sin(aux)
|
||
|
|
|
||
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|
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
|
||
|
|
# http://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)
|