Coverage for pygeodesy/webmercator.py: 98%
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« prev ^ index » next coverage.py v7.2.2, created at 2023-06-07 08:37 -0400
« prev ^ index » next coverage.py v7.2.2, created at 2023-06-07 08:37 -0400
2# -*- coding: utf-8 -*-
4u'''Web Mercator (WM) projection.
6Classes L{Wm} and L{WebMercatorError} and functions L{parseWM} and L{toWm}.
8Pure Python implementation of a U{Web Mercator<https://WikiPedia.org/wiki/Web_Mercator>}
9(aka I{Pseudo-Mercator}) class and conversion functions for spherical and
10near-spherical earth models.
12References U{Google Maps / Bing Maps Spherical Mercator Projection
13<https://AlastairA.WordPress.com/2011/01/23/the-google-maps-bing-maps-spherical-mercator-projection>},
14U{Geomatics Guidance Note 7, part 2<https://www.IOGP.org/wp-content/uploads/2019/09/373-07-02.pdf>}
15and U{Implementation Practice Web Mercator Map Projection
16<https://Earth-Info.NGA.mil/GandG/wgs84/web_mercator/%28U%29%20NGA_SIG_0011_1.0.0_WEBMERC.pdf>}.
17'''
19from pygeodesy.basics import isscalar, issubclassof
20from pygeodesy.constants import PI_2, R_M, R_MA, R_MB
21from pygeodesy.datums import _ellipsoidal_datum, _ALL_LAZY
22from pygeodesy.dms import clipDegrees, parseDMS2
23from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB
24from pygeodesy.errors import _parseX, _TypeError, _ValueError, _xkwds
25from pygeodesy.interns import NN, _COMMASPACE_, _datum_, _easting_, \
26 _northing_, _radius_, _SPACE_, _splituple
27from pygeodesy.interns import _x_, _y_ # PYCHOK used!
28# from pygeodesy.lazily import _ALL_LAZY from .datums
29from pygeodesy.named import _NamedBase, _NamedTuple
30from pygeodesy.namedTuples import LatLon2Tuple, PhiLam2Tuple
31from pygeodesy.props import deprecated_method, Property_RO
32from pygeodesy.streprs import Fmt, strs, _xzipairs
33from pygeodesy.units import Easting, Lam_, Lat, Lon, Northing, Phi_, \
34 Radius, Radius_
35from pygeodesy.utily import degrees90, degrees180
37from math import atan, atanh, exp, radians, sin, tanh
39__all__ = _ALL_LAZY.webmercator
40__version__ = '23.05.26'
42# _FalseEasting = 0 # false Easting (C{meter})
43# _FalseNorthing = 0 # false Northing (C{meter})
44_LatLimit = Lat(limit=85.051129) # latitudinal limit (C{degrees})
45# _LonOrigin = 0 # longitude of natural origin (C{degrees})
48class EasNorRadius3Tuple(_NamedTuple):
49 '''3-Tuple C{(easting, northing, radius)}, all in C{meter}.
50 '''
51 _Names_ = (_easting_, _northing_, _radius_)
52 _Units_ = ( Easting, Northing, Radius)
55class WebMercatorError(_ValueError):
56 '''Web Mercator (WM) parser or L{Wm} issue.
57 '''
58 pass
61class Wm(_NamedBase):
62 '''Web Mercator (WM) coordinate.
63 '''
64 _radius = R_MA # earth radius (C{meter})
65 _x = 0 # Easting (C{meter})
66 _y = 0 # Northing (C{meter})
68 def __init__(self, x, y, radius=R_MA, name=NN):
69 '''New L{Wm} Web Mercator (WM) coordinate.
71 @arg x: Easting from central meridian (C{meter}).
72 @arg y: Northing from equator (C{meter}).
73 @kwarg radius: Optional earth radius (C{meter}).
74 @kwarg name: Optional name (C{str}).
76 @raise WebMercatorError: Invalid B{C{x}}, B{C{y}} or B{C{radius}}.
78 @example:
80 >>> import pygeodesy
81 >>> w = pygeodesy.Wm(448251, 5411932)
82 '''
83 self._x = Easting( x=x, Error=WebMercatorError)
84 self._y = Northing(y=y, Error=WebMercatorError)
85 if radius != R_MA:
86 self._radius = Radius_(radius, Error=WebMercatorError)
88 if name:
89 self.name = name
91 @Property_RO
92 def latlon(self):
93 '''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).
94 '''
95 return self.latlon2()
97 def latlon2(self, datum=None):
98 '''Convert this WM coordinate to a lat- and longitude.
100 @kwarg datum: Optional, ellipsoidal datum (L{Datum},
101 L{Ellipsoid}, L{Ellipsoid2} or
102 L{a_f2Tuple}) or C{None}.
104 @return: A L{LatLon2Tuple}C{(lat, lon)}.
106 @raise TypeError: Invalid or non-ellipsoidal B{C{datum}}.
108 @see: Method C{toLatLon}.
109 '''
110 r = self.radius
111 x = self.x / r
112 y = 2 * atan(exp(self.y / r)) - PI_2
113 if datum is not None:
114 E = _ellipsoidal_datum(datum, name=self.name, raiser=_datum_).ellipsoid
115 # <https://Earth-Info.NGA.mil/GandG/wgs84/web_mercator/
116 # %28U%29%20NGA_SIG_0011_1.0.0_WEBMERC.pdf>
117 y = y / r
118 if E.e:
119 y -= E.e * atanh(E.e * tanh(y)) # == E.es_atanh(tanh(y))
120 y *= E.a
121 x *= E.a / r
123 return LatLon2Tuple(Lat(degrees90( y)),
124 Lon(degrees180(x)), name=self.name)
126 def parse(self, strWM, name=NN):
127 '''Parse a string to a similar L{Wm} instance.
129 @arg strWM: The WM coordinate (C{str}), see
130 function L{parseWM}.
131 @kwarg name: Optional instance name (C{str}),
132 overriding this name.
134 @return: The similar instance (L{Wm}).
136 @raise WebMercatorError: Invalid B{C{strWM}}.
137 '''
138 return parseWM(strWM, radius=self.radius, Wm=self.classof,
139 name=name or self.name)
141 @deprecated_method
142 def parseWM(self, strWM, name=NN): # PYCHOK no cover
143 '''DEPRECATED, use method L{Wm.parse}.'''
144 return self.parse(strWM, name=name)
146 @Property_RO
147 def philam(self):
148 '''Get the lat- and longitude ((L{PhiLam2Tuple}C{(phi, lam)}).
149 '''
150 r = self.latlon
151 return PhiLam2Tuple(Phi_(r.lat), Lam_(r.lon), name=r.name)
153 @Property_RO
154 def radius(self):
155 '''Get the earth radius (C{meter}).
156 '''
157 return self._radius
159 @deprecated_method
160 def to2ll(self, datum=None): # PYCHOK no cover
161 '''DEPRECATED, use method C{latlon2}.
163 @return: A L{LatLon2Tuple}C{(lat, lon)}.
164 '''
165 return self.latlon2(datum=datum)
167 def toLatLon(self, LatLon, datum=None, **LatLon_kwds):
168 '''Convert this WM coordinate to a geodetic point.
170 @arg LatLon: Ellipsoidal class to return the geodetic
171 point (C{LatLon}).
172 @kwarg datum: Optional datum for ellipsoidal or C{None}
173 for spherical B{C{LatLon}} (C{Datum}).
174 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}
175 keyword arguments.
177 @return: Point of this WM coordinate (B{C{LatLon}}).
179 @raise TypeError: If B{C{LatLon}} and B{C{datum}} are
180 incompatible or if B{C{datum}} is
181 invalid or not ellipsoidal.
183 @example:
185 >>> w = Wm(448251.795, 5411932.678)
186 >>> from pygeodesy import sphericalTrigonometry as sT
187 >>> ll = w.toLatLon(sT.LatLon) # 43°39′11.58″N, 004°01′36.17″E
188 '''
189 e = issubclassof(LatLon, _LLEB)
190 if e and datum:
191 kwds = _xkwds(LatLon_kwds, datum=datum)
192 elif not (e or datum): # and LatLon
193 kwds = LatLon_kwds
194 datum = None
195 else:
196 raise _TypeError(LatLon=LatLon, datum=datum)
198 r = self.latlon2(datum=datum)
199 return LatLon(r.lat, r.lon, **_xkwds(kwds, name=r.name))
201 def toRepr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_, radius=False, **unused): # PYCHOK expected
202 '''Return a string representation of this WM coordinate.
204 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
205 @kwarg fmt: Enclosing backets format (C{str}).
206 @kwarg sep: Optional separator between name:value pairs (C{str}).
207 @kwarg radius: If C{True} include the radius (C{bool}) or
208 C{scalar} to override this WM's radius.
210 @return: This WM as "[x:meter, y:meter]" (C{str}) plus
211 ", radius:meter]" if B{C{radius}} is C{True} or
212 C{scalar}.
214 @raise WebMercatorError: Invalid B{C{radius}}.
215 '''
216 t = self.toStr(prec=prec, sep=None, radius=radius)
217 n = (_x_, _y_, _radius_)[:len(t)]
218 return _xzipairs(n, t, sep=sep, fmt=fmt)
220 def toStr(self, prec=3, fmt=Fmt.F, sep=_SPACE_, radius=False, **unused): # PYCHOK expected
221 '''Return a string representation of this WM coordinate.
223 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
224 @kwarg fmt: The C{float} format (C{str}).
225 @kwarg sep: Optional separator to join (C{str}) or C{None}
226 to return an unjoined C{tuple} of C{str}s.
227 @kwarg radius: If C{True} include the radius (C{bool}) or
228 C{scalar} to override this WM's radius.
230 @return: This WM as "meter meter" (C{str}) or as "meter meter
231 radius" if B{C{radius}} is C{True} or C{scalar}.
233 @raise WebMercatorError: Invalid B{C{radius}}.
235 @example:
237 >>> w = Wm(448251, 5411932.0001)
238 >>> w.toStr(4) # 448251.0 5411932.0001
239 >>> w.toStr(sep=', ') # 448251, 5411932
240 '''
241 fs = self.x, self.y
242 if isscalar(radius):
243 fs += (radius,)
244 elif radius: # is True:
245 fs += (self.radius,)
246 elif radius not in (None, False):
247 raise WebMercatorError(radius=radius)
248 t = strs(fs, prec=prec)
249 return t if sep is None else sep.join(t)
251 @Property_RO
252 def x(self):
253 '''Get the easting (C{meter}).
254 '''
255 return self._x
257 @Property_RO
258 def y(self):
259 '''Get the northing (C{meter}).
260 '''
261 return self._y
264def parseWM(strWM, radius=R_MA, Wm=Wm, name=NN):
265 '''Parse a string C{"e n [r]"} representing a WM coordinate,
266 consisting of easting, northing and an optional radius.
268 @arg strWM: A WM coordinate (C{str}).
269 @kwarg radius: Optional earth radius (C{meter}).
270 @kwarg Wm: Optional class to return the WM coordinate (L{Wm})
271 or C{None}.
272 @kwarg name: Optional name (C{str}).
274 @return: The WM coordinate (B{C{Wm}}) or an
275 L{EasNorRadius3Tuple}C{(easting, northing, radius)}
276 if B{C{Wm}} is C{None}.
278 @raise WebMercatorError: Invalid B{C{strWM}}.
280 @example:
282 >>> u = parseWM('448251 5411932')
283 >>> u.toRepr() # [E:448251, N:5411932]
284 '''
285 def _WM(strWM, radius, Wm, name):
286 w = _splituple(strWM)
288 if len(w) == 2:
289 w += (radius,)
290 elif len(w) != 3:
291 raise ValueError
292 x, y, r = map(float, w)
294 return EasNorRadius3Tuple(x, y, r, name=name) if Wm is None else \
295 Wm(x, y, radius=r, name=name)
297 return _parseX(_WM, strWM, radius, Wm, name,
298 strWM=strWM, Error=WebMercatorError)
301def toWm(latlon, lon=None, radius=R_MA, Wm=Wm, name=NN, **Wm_kwds):
302 '''Convert a lat-/longitude point to a WM coordinate.
304 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal or
305 spherical) geodetic C{LatLon} point.
306 @kwarg lon: Optional longitude (C{degrees} or C{None}).
307 @kwarg radius: Optional earth radius (C{meter}), overridden
308 by the B{C{latlon}}'s equatorial radius.
309 @kwarg Wm: Optional class to return the WM coordinate (L{Wm})
310 or C{None}.
311 @kwarg name: Optional name (C{str}).
312 @kwarg Wm_kwds: Optional, additional B{C{Wm}} keyword arguments,
313 ignored if C{B{Wm} is None}.
315 @return: The WM coordinate (B{C{Wm}}) or if B{C{Wm}} is C{None}
316 an L{EasNorRadius3Tuple}C{(easting, northing, radius)}.
318 @raise ValueError: If B{C{lon}} value is missing, if B{C{latlon}} is not
319 scalar, if B{C{latlon}} is beyond the valid WM range
320 and L{pygeodesy.rangerrors} is set to C{True} or if
321 B{C{radius}} is invalid.
323 @example:
325 >>> p = LatLon(48.8582, 2.2945) # 448251.8 5411932.7
326 >>> w = toWm(p) # 448252 5411933
327 >>> p = LatLon(13.4125, 103.8667) # 377302.4 1483034.8
328 >>> w = toWm(p) # 377302 1483035
329 '''
330 e, r, n = 0, radius, name
331 if r not in (R_MA, R_MB, R_M):
332 r = Radius(radius)
333 try:
334 y, x = latlon.lat, latlon.lon
335 if isinstance(latlon, _LLEB):
336 E = latlon.datum.ellipsoid
337 e, r = E.e, E.a
338 y = clipDegrees(y, _LatLimit)
339 n = name or latlon.name
340 except AttributeError:
341 y, x = parseDMS2(latlon, lon, clipLat=_LatLimit)
343 s = sin(radians(y))
344 y = atanh(s) # == log(tan((90 + lat) / 2)) == log(tanPI_2_2(radians(lat)))
345 if e:
346 y -= e * atanh(e * s)
347 y *= r
348 x = r * radians(x)
349 r = EasNorRadius3Tuple(x, y, r, name=n) if Wm is None else \
350 Wm(x, y, **_xkwds(Wm_kwds, radius=r, name=n))
351 return r
353# **) MIT License
354#
355# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
356#
357# Permission is hereby granted, free of charge, to any person obtaining a
358# copy of this software and associated documentation files (the "Software"),
359# to deal in the Software without restriction, including without limitation
360# the rights to use, copy, modify, merge, publish, distribute, sublicense,
361# and/or sell copies of the Software, and to permit persons to whom the
362# Software is furnished to do so, subject to the following conditions:
363#
364# The above copyright notice and this permission notice shall be included
365# in all copies or substantial portions of the Software.
366#
367# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
368# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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370# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
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