Coverage for pygeodesy/webmercator.py: 99%
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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 near-spherical
10earth models.
12@see: 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<https://Web.Archive.org/web/20141009142830/
16http://earth-info.nga.mil/GandG/wgs84/web_mercator/(U)%20NGA_SIG_0011_1.0.0_WEBMERC.pdf>}.
17'''
18# make sure int/int division yields float quotient, see .basics
19from __future__ import division as _; del _ # PYCHOK semicolon
21from pygeodesy.basics import _splituple, _xinstanceof
22from pygeodesy.constants import PI_2, R_MA, _2_0
23from pygeodesy.datums import Datum, _spherical_datum
24from pygeodesy.dms import clipDegrees, parseDMS2
25from pygeodesy.errors import _parseX, _ValueError, _xattr, _xkwds, _xkwds_pop2
26from pygeodesy.interns import NN, _COMMASPACE_, _datum_, _earth_, _easting_, \
27 _northing_, _radius_, _SPACE_, _x_, _y_
28# from pygeodesy.lazily import _ALL_LAZY from .named
29from pygeodesy.named import _name2__, _NamedBase, _NamedTuple, _ALL_LAZY
30from pygeodesy.namedTuples import LatLon2Tuple, LatLonDatum3Tuple, PhiLam2Tuple
31from pygeodesy.props import deprecated_method, Property_RO
32from pygeodesy.streprs import Fmt, strs, _xzipairs
33from pygeodesy.units import Easting, _isRadius, Lat, Northing, Radius
34from pygeodesy.utily import degrees90, degrees180
36from math import atan, atanh, exp, radians, sin, tanh
38__all__ = _ALL_LAZY.webmercator
39__version__ = '24.11.06'
41# _FalseEasting = 0 # false Easting (C{meter})
42# _FalseNorthing = 0 # false Northing (C{meter})
43_LatLimit = Lat(limit=85.051129) # latitudinal limit (C{degrees})
44# _LonOrigin = 0 # longitude of natural origin (C{degrees})
47class EasNorRadius3Tuple(_NamedTuple):
48 '''3-Tuple C{(easting, northing, radius)}, all in C{meter}.
49 '''
50 _Names_ = (_easting_, _northing_, _radius_)
51 _Units_ = ( Easting, Northing, Radius)
54class WebMercatorError(_ValueError):
55 '''Web Mercator (WM) parser or L{Wm} issue.
56 '''
57 pass
60class Wm(_NamedBase):
61 '''Web Mercator (WM) coordinate.
62 '''
63 _datum = None # set further below
64 _earths = () # dito
65 _radius = R_MA # earth radius (C{meter})
66 _x = 0 # Easting (C{meter})
67 _y = 0 # Northing (C{meter})
69 def __init__(self, x, y, earth=R_MA, **name_radius):
70 '''New L{Wm} Web Mercator (WM) coordinate.
72 @arg x: Easting from central meridian (C{meter}).
73 @arg y: Northing from equator (C{meter}).
74 @kwarg earth: Earth radius (C{meter}), datum or ellipsoid (L{Datum},
75 L{a_f2Tuple}, L{Ellipsoid} or L{Ellipsoid2}).
76 @kwarg name_radius: Optional C{B{name}=NN} (C{str}) and DEPRECATED
77 keyword argument C{B{radius}=earth}, use B{C{earth}}.
79 @note: WM is strictly defined for spherical and WGS84 ellipsoidal
80 earth models only.
82 @raise WebMercatorError: Invalid B{C{x}}, B{C{y}} or B{C{radius}}.
83 '''
84 self._x = Easting( x=x, Error=WebMercatorError)
85 self._y = Northing(y=y, Error=WebMercatorError)
87 R, name = _xkwds_pop2(name_radius, radius=earth)
88 if name:
89 self.name = name
90 if R not in Wm._earths:
91 self._datum = _datum(R, _radius_ if _radius_ in name_radius else _earth_)
92 self._radius = self.datum.ellipsoid.a
94 @Property_RO
95 def datum(self):
96 '''Get the datum (C{Datum}).
97 '''
98 return self._datum
100 @Property_RO
101 def ellipsoid(self):
102 '''Get the ellipsoid (C{Ellipsoid}).
103 '''
104 return self.datum.ellipsoid
106 @Property_RO
107 def latlon(self):
108 '''Get the lat- and longitude (L{LatLon2Tuple}).
109 '''
110 return self.latlon2()
112 def latlon2(self, datum=None):
113 '''Convert this WM coordinate to a lat- and longitude.
115 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid},
116 L{Ellipsoid2} or L{a_f2Tuple}) or earth
117 radius (C{meter}), overriding this WM's
118 C{radius} and C{datum}.
120 @return: A L{LatLon2Tuple}C{(lat, lon)}.
122 @note: WM is strictly defined for spherical and WGS84
123 ellipsoidal earth models only.
125 @raise TypeError: Invalid or non-ellipsoidal B{C{datum}}.
127 @see: Method C{toLatLon} for other return types.
128 '''
129 d = self.datum if datum in (None, self.datum, self.radius) else _datum(datum)
130 E = d.ellipsoid
131 R = self.radius
132 x = self.x / R
133 y = atan(exp(self.y / R)) * _2_0 - PI_2
134 if E.es or E.a != R: # strictly, WGS84 only
135 # <https://Web.Archive.org/web/20141009142830/http://earth-info.nga.mil/
136 # GandG/wgs84/web_mercator/(U)%20NGA_SIG_0011_1.0.0_WEBMERC.pdf>
137 y = y / R # /= chokes PyChecker
138 y -= E.es_atanh(tanh(y))
139 y *= E.a
140 x *= E.a / R
142 return LatLon2Tuple(degrees90(y), degrees180(x), name=self.name)
144 def parse(self, strWM, **name):
145 '''Parse a string to a similar L{Wm} instance.
147 @arg strWM: The WM coordinate (C{str}), see function L{parseWM}.
148 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
150 @return: The similar instance (L{Wm}).
152 @raise WebMercatorError: Invalid B{C{strWM}}.
153 '''
154 return parseWM(strWM, radius=self.radius, Wm=self.classof,
155 name=self._name__(name))
157 @deprecated_method
158 def parseWM(self, strWM, name=NN): # PYCHOK no cover
159 '''DEPRECATED, use method L{Wm.parse}.'''
160 return self.parse(strWM, name=name)
162 @Property_RO
163 def philam(self):
164 '''Get the lat- and longitude ((L{PhiLam2Tuple}).
165 '''
166 return PhiLam2Tuple(*map(radians, self.latlon), name=self.name)
168 @Property_RO
169 def radius(self):
170 '''Get the earth radius (C{meter}).
171 '''
172 return self._radius
174 @deprecated_method
175 def to2ll(self, datum=None): # PYCHOK no cover
176 '''DEPRECATED, use method C{latlon2}.
178 @return: A L{LatLon2Tuple}C{(lat, lon)}.
179 '''
180 return self.latlon2(datum=datum)
182 def toLatLon(self, LatLon=None, datum=None, **LatLon_kwds):
183 '''Convert this WM coordinate to a geodetic point.
185 @kwarg LatLon: Ellipsoidal or sphperical C{LatLon} class to
186 return the geodetic point (C{LatLon}) or C{None}.
187 @kwarg datum: Optional, datum (C{Datum}) overriding this WM's.
188 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
189 arguments, ignored if C{B{LatLon} is None}.
191 @return: This WM coordinate as B{C{LatLon}} or if C{B{LatLon}
192 is None} a L{LatLonDatum3Tuple}.
194 @raise TypeError: If B{C{datum}} is invalid or if B{C{LatLon}}
195 and B{C{datum}} are incompatible.
196 '''
197 d = datum or self.datum
198 _xinstanceof(Datum, datum=d)
199 r = self.latlon2(datum=d)
200 r = LatLonDatum3Tuple(r.lat, r.lon, d, name=r.name) if LatLon is None else \
201 LatLon(r.lat, r.lon, **_xkwds(LatLon_kwds, datum=d, name=r.name))
202 return r
204 def toRepr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_, radius=False, **unused): # PYCHOK expected
205 '''Return a string representation of this WM coordinate.
207 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
208 @kwarg fmt: Enclosing backets format (C{str}).
209 @kwarg sep: Optional separator between name:value pairs (C{str}).
210 @kwarg radius: If C{True}, include the radius (C{bool}) or
211 C{scalar} to override this WM's radius.
213 @return: This WM as "[x:meter, y:meter]" (C{str}) or as "[x:meter,
214 y:meter], radius:meter]" if B{C{radius}} is C{True} or
215 C{scalar}.
217 @raise WebMercatorError: Invalid B{C{radius}}.
218 '''
219 t = self.toStr(prec=prec, sep=None, radius=radius)
220 n = (_x_, _y_, _radius_)[:len(t)]
221 return _xzipairs(n, t, sep=sep, fmt=fmt)
223 def toStr(self, prec=3, fmt=Fmt.F, sep=_SPACE_, radius=False, **unused): # PYCHOK expected
224 '''Return a string representation of this WM coordinate.
226 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
227 @kwarg fmt: Optional C{float} format (C{letter}).
228 @kwarg sep: Optional separator to join (C{str}) or C{None}
229 to return an unjoined C{tuple} of C{str}s.
230 @kwarg radius: If C{True}, include the radius (C{bool}) or
231 C{scalar} to override this WM's radius.
233 @return: This WM as "meter meter" (C{str}) or as "meter meter
234 radius" if B{C{radius}} is C{True} or C{scalar}.
236 @raise WebMercatorError: Invalid B{C{radius}}.
237 '''
238 fs = self.x, self.y
239 if _isRadius(radius):
240 fs += (radius,)
241 elif radius: # is True:
242 fs += (self.radius,)
243 elif radius not in (None, False):
244 raise WebMercatorError(radius=radius)
245 t = strs(fs, prec=prec)
246 return t if sep is None else sep.join(t)
248 @Property_RO
249 def x(self):
250 '''Get the easting (C{meter}).
251 '''
252 return self._x
254 @Property_RO
255 def y(self):
256 '''Get the northing (C{meter}).
257 '''
258 return self._y
260Wm._datum = _spherical_datum(Wm._radius, name=Wm.__name__, raiser=_radius_) # PYCHOK defaults
261Wm._earths = (Wm._radius, Wm._datum, Wm._datum.ellipsoid)
264def _datum(earth, name=_datum_):
265 '''(INTERNAL) Make a datum from an C{earth} radius, datum or ellipsoid.
266 '''
267 if earth in Wm._earths:
268 return Wm._datum
269 try:
270 return _spherical_datum(earth, name=name)
271 except Exception as x:
272 raise WebMercatorError(name, earth, cause=x)
275def parseWM(strWM, radius=R_MA, Wm=Wm, **name):
276 '''Parse a string C{"e n [r]"} representing a WM coordinate,
277 consisting of easting, northing and an optional radius.
279 @arg strWM: A WM coordinate (C{str}).
280 @kwarg radius: Optional earth radius (C{meter}), needed in
281 case B{C{strWM}} doesn't include C{r}.
282 @kwarg Wm: Optional class to return the WM coordinate (L{Wm})
283 or C{None}.
284 @kwarg name: Optional C{B{name}=NN} (C{str}).
286 @return: The WM coordinate (B{C{Wm}}) or if C{B{Wm} is None}, an
287 L{EasNorRadius3Tuple}C{(easting, northing, radius)}.
289 @raise WebMercatorError: Invalid B{C{strWM}}.
290 '''
291 def _WM(strWM, radius, Wm, name):
292 w = _splituple(strWM)
294 if len(w) == 2:
295 w += (radius,)
296 elif len(w) != 3:
297 raise ValueError
298 x, y, R = map(float, w)
300 return EasNorRadius3Tuple(x, y, R, **name) if Wm is None else \
301 Wm(x, y, earth=R, **name)
303 return _parseX(_WM, strWM, radius, Wm, name,
304 strWM=strWM, Error=WebMercatorError)
307def toWm(latlon, lon=None, earth=R_MA, Wm=Wm, **name_Wm_kwds_radius):
308 '''Convert a lat-/longitude point to a WM coordinate.
310 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal or spherical)
311 geodetic C{LatLon} point.
312 @kwarg lon: Optional longitude (C{degrees} or C{None}).
313 @kwarg earth: Earth radius (C{meter}), datum or ellipsoid (L{Datum},
314 L{a_f2Tuple}, L{Ellipsoid} or L{Ellipsoid2}), overridden
315 by B{C{latlon}}'s datum if present.
316 @kwarg Wm: Optional class to return the WM coordinate (L{Wm}) or C{None}.
317 @kwarg name_Wm_kwds_radius: Optional C{B{name}=NN} (C{str}), optionally,
318 additional B{C{Wm}} keyword arguments, ignored if C{B{Wm} is
319 None} and DEPRECATED keyword argument C{B{radius}=earth}, use
320 B{C{earth}}.
322 @return: The WM coordinate (B{C{Wm}}) or if C{B{Wm} is None}, an
323 L{EasNorRadius3Tuple}C{(easting, northing, radius)}.
325 @raise ValueError: If B{C{earth}} is invalid, if B{C{lon}} value is missing,
326 if B{C{latlon}} is not scalar, or if B{C{latlon}} is beyond
327 the valid WM range and L{rangerrrors<pygeodesy.rangerrors>}
328 is C{True}.
329 '''
330 name, kwds = _name2__(name_Wm_kwds_radius)
331 R, kwds = _xkwds_pop2(kwds, radius=earth)
332 d = _datum(R, _radius_ if _radius_ in name_Wm_kwds_radius else _earth_)
333 try:
334 y, x = latlon.lat, latlon.lon
335 y = clipDegrees(y, _LatLimit)
336 d = _xattr(latlon, datum=d)
337 n = latlon._name__(name)
338 except AttributeError:
339 y, x = parseDMS2(latlon, lon, clipLat=_LatLimit)
340 n = name
341 E = d.ellipsoid
342 R = E.a
343 s = sin(radians(y))
344 y = atanh(s) # == log(tand((90 + lat) / 2)) == log(tanPI_2_2(radians(lat)))
345 if E.es:
346 y -= E.es_atanh(s) # strictly, WGS84 only
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(kwds, earth=d, name=n))
351 return r
353# **) MIT License
354#
355# Copyright (C) 2016-2025 -- 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,
369# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
370# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
371# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
372# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
373# OTHER DEALINGS IN THE SOFTWARE.