Coverage for pygeodesy/webmercator.py: 99%

126 statements  

« prev     ^ index     » next       coverage.py v7.6.1, created at 2025-01-10 16:55 -0500

1 

2# -*- coding: utf-8 -*- 

3 

4u'''Web Mercator (WM) projection. 

5 

6Classes L{Wm} and L{WebMercatorError} and functions L{parseWM} and L{toWm}. 

7 

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. 

11 

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 

20 

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 

35 

36from math import atan, atanh, exp, radians, sin, tanh 

37 

38__all__ = _ALL_LAZY.webmercator 

39__version__ = '24.11.06' 

40 

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}) 

45 

46 

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) 

52 

53 

54class WebMercatorError(_ValueError): 

55 '''Web Mercator (WM) parser or L{Wm} issue. 

56 ''' 

57 pass 

58 

59 

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}) 

68 

69 def __init__(self, x, y, earth=R_MA, **name_radius): 

70 '''New L{Wm} Web Mercator (WM) coordinate. 

71 

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}}. 

78 

79 @note: WM is strictly defined for spherical and WGS84 ellipsoidal 

80 earth models only. 

81 

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) 

86 

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 

93 

94 @Property_RO 

95 def datum(self): 

96 '''Get the datum (C{Datum}). 

97 ''' 

98 return self._datum 

99 

100 @Property_RO 

101 def ellipsoid(self): 

102 '''Get the ellipsoid (C{Ellipsoid}). 

103 ''' 

104 return self.datum.ellipsoid 

105 

106 @Property_RO 

107 def latlon(self): 

108 '''Get the lat- and longitude (L{LatLon2Tuple}). 

109 ''' 

110 return self.latlon2() 

111 

112 def latlon2(self, datum=None): 

113 '''Convert this WM coordinate to a lat- and longitude. 

114 

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}. 

119 

120 @return: A L{LatLon2Tuple}C{(lat, lon)}. 

121 

122 @note: WM is strictly defined for spherical and WGS84 

123 ellipsoidal earth models only. 

124 

125 @raise TypeError: Invalid or non-ellipsoidal B{C{datum}}. 

126 

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 

141 

142 return LatLon2Tuple(degrees90(y), degrees180(x), name=self.name) 

143 

144 def parse(self, strWM, **name): 

145 '''Parse a string to a similar L{Wm} instance. 

146 

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. 

149 

150 @return: The similar instance (L{Wm}). 

151 

152 @raise WebMercatorError: Invalid B{C{strWM}}. 

153 ''' 

154 return parseWM(strWM, radius=self.radius, Wm=self.classof, 

155 name=self._name__(name)) 

156 

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) 

161 

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) 

167 

168 @Property_RO 

169 def radius(self): 

170 '''Get the earth radius (C{meter}). 

171 ''' 

172 return self._radius 

173 

174 @deprecated_method 

175 def to2ll(self, datum=None): # PYCHOK no cover 

176 '''DEPRECATED, use method C{latlon2}. 

177 

178 @return: A L{LatLon2Tuple}C{(lat, lon)}. 

179 ''' 

180 return self.latlon2(datum=datum) 

181 

182 def toLatLon(self, LatLon=None, datum=None, **LatLon_kwds): 

183 '''Convert this WM coordinate to a geodetic point. 

184 

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}. 

190 

191 @return: This WM coordinate as B{C{LatLon}} or if C{B{LatLon} 

192 is None} a L{LatLonDatum3Tuple}. 

193 

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 

203 

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. 

206 

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. 

212 

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}. 

216 

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) 

222 

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. 

225 

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. 

232 

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}. 

235 

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) 

247 

248 @Property_RO 

249 def x(self): 

250 '''Get the easting (C{meter}). 

251 ''' 

252 return self._x 

253 

254 @Property_RO 

255 def y(self): 

256 '''Get the northing (C{meter}). 

257 ''' 

258 return self._y 

259 

260Wm._datum = _spherical_datum(Wm._radius, name=Wm.__name__, raiser=_radius_) # PYCHOK defaults 

261Wm._earths = (Wm._radius, Wm._datum, Wm._datum.ellipsoid) 

262 

263 

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) 

273 

274 

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. 

278 

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}). 

285 

286 @return: The WM coordinate (B{C{Wm}}) or if C{B{Wm} is None}, an 

287 L{EasNorRadius3Tuple}C{(easting, northing, radius)}. 

288 

289 @raise WebMercatorError: Invalid B{C{strWM}}. 

290 ''' 

291 def _WM(strWM, radius, Wm, name): 

292 w = _splituple(strWM) 

293 

294 if len(w) == 2: 

295 w += (radius,) 

296 elif len(w) != 3: 

297 raise ValueError 

298 x, y, R = map(float, w) 

299 

300 return EasNorRadius3Tuple(x, y, R, **name) if Wm is None else \ 

301 Wm(x, y, earth=R, **name) 

302 

303 return _parseX(_WM, strWM, radius, Wm, name, 

304 strWM=strWM, Error=WebMercatorError) 

305 

306 

307def toWm(latlon, lon=None, earth=R_MA, Wm=Wm, **name_Wm_kwds_radius): 

308 '''Convert a lat-/longitude point to a WM coordinate. 

309 

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}}. 

321 

322 @return: The WM coordinate (B{C{Wm}}) or if C{B{Wm} is None}, an 

323 L{EasNorRadius3Tuple}C{(easting, northing, radius)}. 

324 

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 

352 

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.