Coverage for pygeodesy/webmercator.py: 99%

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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 

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 _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__ = '24.02.04' 

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=NN, **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 

75 ellipsoid (L{Datum}, L{a_f2Tuple}, 

76 L{Ellipsoid} or L{Ellipsoid2}). 

77 @kwarg name: Optional name (C{str}). 

78 @kwarg radius: DEPRECATED, use keyword argument B{C{earth}}. 

79 

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

81 ellipsoidal earth models only. 

82 

83 @raise WebMercatorError: Invalid B{C{x}}, B{C{y}} or B{C{radius}}. 

84 ''' 

85 self._x = Easting( x=x, Error=WebMercatorError) 

86 self._y = Northing(y=y, Error=WebMercatorError) 

87 

88 R = radius.get(_radius_, earth) 

89 if R not in Wm._earths: 

90 self._datum = _datum(R, _radius_ if radius else _earth_) 

91 self._radius = self.datum.ellipsoid.a 

92 

93 if name: 

94 self.name = name 

95 

96 @Property_RO 

97 def datum(self): 

98 '''Get the datum (C{Datum}). 

99 ''' 

100 return self._datum 

101 

102 @Property_RO 

103 def ellipsoid(self): 

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

105 ''' 

106 return self.datum.ellipsoid 

107 

108 @Property_RO 

109 def latlon(self): 

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

111 ''' 

112 return self.latlon2() 

113 

114 def latlon2(self, datum=None): 

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

116 

117 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, 

118 L{Ellipsoid2} or L{a_f2Tuple}) or earth 

119 radius (C{meter}), overriding this WM's 

120 C{radius} and C{datum}. 

121 

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

123 

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

125 ellipsoidal earth models only. 

126 

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

128 

129 @see: Method C{toLatLon} for other return types. 

130 ''' 

131 d = self.datum if datum in (None, self.datum, self.radius) else _datum(datum) 

132 E = d.ellipsoid 

133 R = self.radius 

134 x = self.x / R 

135 y = atan(exp(self.y / R)) * _2_0 - PI_2 

136 if E.es or E.a != R: # strictly, WGS84 only 

137 # <https://Web.Archive.org/web/20141009142830/http://earth-info.nga.mil/ 

138 # GandG/wgs84/web_mercator/(U)%20NGA_SIG_0011_1.0.0_WEBMERC.pdf> 

139 y = y / R # /= chokes PyChecker 

140 y -= E.es_atanh(tanh(y)) 

141 y *= E.a 

142 x *= E.a / R 

143 

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

145 

146 def parse(self, strWM, name=NN): 

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

148 

149 @arg strWM: The WM coordinate (C{str}), see 

150 function L{parseWM}. 

151 @kwarg name: Optional instance name (C{str}), 

152 overriding this name. 

153 

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

155 

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

157 ''' 

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

159 name=name or self.name) 

160 

161 @deprecated_method 

162 def parseWM(self, strWM, name=NN): # PYCHOK no cover 

163 '''DEPRECATED, use method L{Wm.parse}.''' 

164 return self.parse(strWM, name=name) 

165 

166 @Property_RO 

167 def philam(self): 

168 '''Get the lat- and longitude ((L{PhiLam2Tuple}). 

169 ''' 

170 return PhiLam2Tuple(*map(radians, self.latlon), name=self.name) 

171 

172 @Property_RO 

173 def radius(self): 

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

175 ''' 

176 return self._radius 

177 

178 @deprecated_method 

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

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

181 

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

183 ''' 

184 return self.latlon2(datum=datum) 

185 

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

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

188 

189 @kwarg LatLon: Ellipsoidal or sphperical C{LatLon} class to 

190 return the geodetic point (C{LatLon}) or C{None}. 

191 @kwarg datum: Optional, datum (C{Datum}) overriding this WM's. 

192 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} 

193 keyword arguments, ignored if 

194 C{B{LatLon} is None}. 

195 

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

197 C{B{LatLon} is None} a L{LatLonDatum3Tuple}. 

198 

199 @raise TypeError: If B{C{LatLon}} and B{C{datum}} are 

200 incompatible or if B{C{datum}} is 

201 invalid. 

202 ''' 

203 d = datum or self.datum 

204 _xinstanceof(Datum, datum=d) 

205 r = self.latlon2(datum=d) 

206 r = LatLonDatum3Tuple(r.lat, r.lon, d, name=r.name) if LatLon is None else \ 

207 LatLon(r.lat, r.lon, **_xkwds(LatLon_kwds, datum=d, name=r.name)) 

208 return r 

209 

210 def toRepr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_, radius=False, **unused): # PYCHOK expected 

211 '''Return a string representation of this WM coordinate. 

212 

213 @kwarg prec: Number of (decimal) digits, unstripped (C{int}). 

214 @kwarg fmt: Enclosing backets format (C{str}). 

215 @kwarg sep: Optional separator between name:value pairs (C{str}). 

216 @kwarg radius: If C{True} include the radius (C{bool}) or 

217 C{scalar} to override this WM's radius. 

218 

219 @return: This WM as "[x:meter, y:meter]" (C{str}) or as "[x:meter, 

220 y:meter], radius:meter]" if B{C{radius}} is C{True} or 

221 C{scalar}. 

222 

223 @raise WebMercatorError: Invalid B{C{radius}}. 

224 ''' 

225 t = self.toStr(prec=prec, sep=None, radius=radius) 

226 n = (_x_, _y_, _radius_)[:len(t)] 

227 return _xzipairs(n, t, sep=sep, fmt=fmt) 

228 

229 def toStr(self, prec=3, fmt=Fmt.F, sep=_SPACE_, radius=False, **unused): # PYCHOK expected 

230 '''Return a string representation of this WM coordinate. 

231 

232 @kwarg prec: Number of (decimal) digits, unstripped (C{int}). 

233 @kwarg fmt: Optional C{float} format (C{letter}). 

234 @kwarg sep: Optional separator to join (C{str}) or C{None} 

235 to return an unjoined C{tuple} of C{str}s. 

236 @kwarg radius: If C{True} include the radius (C{bool}) or 

237 C{scalar} to override this WM's radius. 

238 

239 @return: This WM as "meter meter" (C{str}) or as "meter meter 

240 radius" if B{C{radius}} is C{True} or C{scalar}. 

241 

242 @raise WebMercatorError: Invalid B{C{radius}}. 

243 ''' 

244 fs = self.x, self.y 

245 if _isRadius(radius): 

246 fs += (radius,) 

247 elif radius: # is True: 

248 fs += (self.radius,) 

249 elif radius not in (None, False): 

250 raise WebMercatorError(radius=radius) 

251 t = strs(fs, prec=prec) 

252 return t if sep is None else sep.join(t) 

253 

254 @Property_RO 

255 def x(self): 

256 '''Get the easting (C{meter}). 

257 ''' 

258 return self._x 

259 

260 @Property_RO 

261 def y(self): 

262 '''Get the northing (C{meter}). 

263 ''' 

264 return self._y 

265 

266Wm._datum = _spherical_datum(Wm._radius, name=Wm.__name__, raiser=_radius_) # PYCHOK defaults 

267Wm._earths = (Wm._radius, Wm._datum, Wm._datum.ellipsoid) 

268 

269 

270def _datum(earth, name=_datum_): 

271 '''(INTERNAL) Make a datum from an C{earth} radius, datum or ellipsoid. 

272 ''' 

273 if earth in Wm._earths: 

274 return Wm._datum 

275 try: 

276 return _spherical_datum(earth, name=name) 

277 except Exception as x: 

278 raise WebMercatorError(name, earth, cause=x) 

279 

280 

281def parseWM(strWM, radius=R_MA, Wm=Wm, name=NN): 

282 '''Parse a string C{"e n [r]"} representing a WM coordinate, 

283 consisting of easting, northing and an optional radius. 

284 

285 @arg strWM: A WM coordinate (C{str}). 

286 @kwarg radius: Optional earth radius (C{meter}), needed in 

287 case B{C{strWM}} doesn't include C{r}. 

288 @kwarg Wm: Optional class to return the WM coordinate (L{Wm}) 

289 or C{None}. 

290 @kwarg name: Optional name (C{str}). 

291 

292 @return: The WM coordinate (B{C{Wm}}) or an 

293 L{EasNorRadius3Tuple}C{(easting, northing, radius)} 

294 if B{C{Wm}} is C{None}. 

295 

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

297 ''' 

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

299 w = _splituple(strWM) 

300 

301 if len(w) == 2: 

302 w += (radius,) 

303 elif len(w) != 3: 

304 raise ValueError 

305 x, y, R = map(float, w) 

306 

307 return EasNorRadius3Tuple(x, y, R, name=name) if Wm is None else \ 

308 Wm(x, y, earth=R, name=name) 

309 

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

311 strWM=strWM, Error=WebMercatorError) 

312 

313 

314def toWm(latlon, lon=None, earth=R_MA, Wm=Wm, name=NN, **Wm_kwds): 

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

316 

317 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal or 

318 spherical) geodetic C{LatLon} point. 

319 @kwarg lon: Optional longitude (C{degrees} or C{None}). 

320 @kwarg earth: Earth radius (C{meter}), datum or ellipsoid 

321 (L{Datum}, L{a_f2Tuple}, L{Ellipsoid} or 

322 L{Ellipsoid2}), overridden by B{C{latlon}}'s 

323 datum if present. 

324 @kwarg Wm: Optional class to return the WM coordinate (L{Wm}) 

325 or C{None}. 

326 @kwarg name: Optional name (C{str}). 

327 @kwarg Wm_kwds: Optional, additional B{C{Wm}} keyword arguments, 

328 ignored if C{B{Wm} is None}. 

329 

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

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

332 

333 @raise ValueError: If B{C{lon}} value is missing, if B{C{latlon}} is not 

334 scalar, if B{C{latlon}} is beyond the valid WM range 

335 and L{pygeodesy.rangerrors} is set to C{True} or if 

336 B{C{earth}} is invalid. 

337 ''' 

338 if _radius_ in Wm_kwds: # remove DEPRECATED, radius 

339 d = _datum(Wm_kwds.pop(_radius_), _radius_) 

340 else: 

341 d = _datum(earth, _earth_) 

342 try: 

343 y, x = latlon.lat, latlon.lon 

344 y = clipDegrees(y, _LatLimit) 

345 d = _xattr(latlon, datum=d) 

346 n = name or _xattr(latlon, name=NN) 

347 except AttributeError: 

348 y, x = parseDMS2(latlon, lon, clipLat=_LatLimit) 

349 n = name 

350 

351 E = d.ellipsoid 

352 R = E.a 

353 s = sin(radians(y)) 

354 y = atanh(s) # == log(tand((90 + lat) / 2)) == log(tanPI_2_2(radians(lat))) 

355 if E.es: 

356 y -= E.es_atanh(s) # strictly, WGS84 only 

357 y *= R 

358 x = R * radians(x) 

359 r = EasNorRadius3Tuple(x, y, R, name=n) if Wm is None else \ 

360 Wm(x, y, **_xkwds(Wm_kwds, earth=d, name=n)) 

361 return r 

362 

363# **) MIT License 

364# 

365# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

366# 

367# Permission is hereby granted, free of charge, to any person obtaining a 

368# copy of this software and associated documentation files (the "Software"), 

369# to deal in the Software without restriction, including without limitation 

370# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

371# and/or sell copies of the Software, and to permit persons to whom the 

372# Software is furnished to do so, subject to the following conditions: 

373# 

374# The above copyright notice and this permission notice shall be included 

375# in all copies or substantial portions of the Software. 

376# 

377# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

378# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

379# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

380# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

381# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

382# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

383# OTHER DEALINGS IN THE SOFTWARE.