1

2# -*- coding: utf-8 -*-

3

4 u'''Web Mercator (WM) projection.

5

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

7

8 Pure 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

10 near-spherical earth models.

11

12 References U{Google Maps / Bing Maps Spherical Mercator Projection

13<https://AlastairA.WordPress.com/2011/01/23/the-google-maps-bing-maps-spherical-mercator-projection>},

14 U{Geomatics Guidance Note 7, part 2<https://www.IOGP.org/wp-content/uploads/2019/09/373-07-02.pdf>}

15 and 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'''

18

19 from pygeodesy.basics import isscalar, issubclassof

20 from pygeodesy.constants import PI_2, R_M, R_MA, R_MB

21 from pygeodesy.datums import _ALL_LAZY, _ellipsoidal_datum

22 from pygeodesy.dms import clipDegrees, parseDMS2

23 from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB

24 from pygeodesy.errors import _IsnotError, _parseX, _TypeError, \

25 _ValueError, _xkwds

26 from pygeodesy.interns import NN, _COMMASPACE_, _easting_, \

27 _ellipsoidal_, _northing_, _radius_, \

28 _SPACE_, _splituple

29 from pygeodesy.interns import _x_, _y_ # PYCHOK used!

30# from pygeodesy.lazily import _ALL_LAZY from .datums

31 from pygeodesy.named import _NamedBase, _NamedTuple

32 from pygeodesy.namedTuples import LatLon2Tuple, PhiLam2Tuple

33 from pygeodesy.props import deprecated_method, Property_RO

34 from pygeodesy.streprs import Fmt, strs, _xzipairs

35 from pygeodesy.units import Easting, Lam_, Lat, Lon, Northing, Phi_, \

36 Radius, Radius_

37 from pygeodesy.utily import degrees90, degrees180

38

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

40

41__all__ = _ALL_LAZY.webmercator

42__version__ = '22.09.12'

43

44# _FalseEasting = 0 # false Easting (C{meter})

45# _FalseNorthing = 0 # false Northing (C{meter})

46_LatLimit = Lat(limit=85.051129) # latitudinal limit (C{degrees})

47# _LonOrigin = 0 # longitude of natural origin (C{degrees})

48

49

50 class EasNorRadius3Tuple(_NamedTuple):

51 '''3-Tuple C{(easting, northing, radius)}, all in C{meter}.

52 '''

53 _Names_ = (_easting_, _northing_, _radius_)

54 _Units_ = ( Easting, Northing, Radius)

55

56

57 class WebMercatorError(_ValueError):

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

59 '''

60 pass

61

62

63 class Wm(_NamedBase):

64 '''Web Mercator (WM) coordinate.

65 '''

66 _radius = R_MA # earth radius (C{meter})

67 _x = 0 # Easting (C{meter})

68 _y = 0 # Northing (C{meter})

69

70 def __init__(self, x, y, radius=R_MA, name=NN):

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

72

73 @arg x: Easting from central meridian (C{meter}).

74 @arg y: Northing from equator (C{meter}).

75 @kwarg radius: Optional earth radius (C{meter}).

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

77

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

79

80 @example:

81

82 >>> import pygeodesy

83 >>> w = pygeodesy.Wm(448251, 5411932)

84 '''

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

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

87 if radius != R_MA:

88 self._radius = Radius_(radius, Error=WebMercatorError)

89

90 if name:

91 self.name = name

92

93 @Property_RO

94 def latlon(self):

95 '''Get the lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}).

96 '''

97 return self.latlon2()

98

99 def latlon2(self, datum=None):

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

101

102 @kwarg datum: Optional, ellipsoidal datum (L{Datum},

103 L{Ellipsoid}, L{Ellipsoid2} or

104 L{a_f2Tuple}) or C{None}.

105

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

107

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

109

110 @see: Method C{toLatLon}.

111 '''

112 r = self.radius

113 x = self.x / r

114 y = 2 * atan(exp(self.y / r)) - PI_2

115 if datum is not None:

116 E = _ellipsoidal_datum(datum, name=self.name).ellipsoid

117 if not E.isEllipsoidal:

118 raise _IsnotError(_ellipsoidal_, datum=datum)

119 # <https://Earth-Info.NGA.mil/GandG/wgs84/web_mercator/

120 # %28U%29%20NGA_SIG_0011_1.0.0_WEBMERC.pdf>

121 y = y / r

122 if E.e:

123 y -= E.e * atanh(E.e * tanh(y)) # == E.es_atanh(tanh(y))

124 y *= E.a

125 x *= E.a / r

126

127 return LatLon2Tuple(Lat(degrees90( y)),

128 Lon(degrees180(x)), name=self.name)

129

130 def parse(self, strWM, name=NN):

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

132

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

134 function L{parseWM}.

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

136 overriding this name.

137

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

139

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

141 '''

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

143 name=name or self.name)

144

145 @deprecated_method

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

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

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

149

150 @Property_RO

151 def philam(self):

152 '''Get the lat- and longitude ((L{PhiLam2Tuple}C{(phi, lam)}).

153 '''

154 r = self.latlon

155 return PhiLam2Tuple(Phi_(r.lat), Lam_(r.lon), name=r.name)

156

157 @Property_RO

158 def radius(self):

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

160 '''

161 return self._radius

162

163 @deprecated_method

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

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

166

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

168 '''

169 return self.latlon2(datum=datum)

170

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

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

173

174 @arg LatLon: Ellipsoidal class to return the geodetic

175 point (C{LatLon}).

176 @kwarg datum: Optional datum for ellipsoidal or C{None}

177 for spherical B{C{LatLon}} (C{Datum}).

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

179 keyword arguments.

180

181 @return: Point of this WM coordinate (B{C{LatLon}}).

182

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

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

185 invalid or not ellipsoidal.

186

187 @example:

188

189 >>> w = Wm(448251.795, 5411932.678)

190 >>> from pygeodesy import sphericalTrigonometry as sT

191 >>> ll = w.toLatLon(sT.LatLon) # 43°39′11.58″N, 004°01′36.17″E

192 '''

193 e = issubclassof(LatLon, _LLEB)

194 if e and datum:

195 kwds = _xkwds(LatLon_kwds, datum=datum)

196 elif not (e or datum): # and LatLon

197 kwds = LatLon_kwds

198 datum = None

199 else:

200 raise _TypeError(LatLon=LatLon, datum=datum)

201

202 r = self.latlon2(datum=datum)

203 return LatLon(r.lat, r.lon, **_xkwds(kwds, name=r.name))

204

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

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

207

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

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

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

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

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

213

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

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

216 C{scalar}.

217

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

219 '''

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

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

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

223

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

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

226

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

228 @kwarg fmt: The C{float} format (C{str}).

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

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

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

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

233

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

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

236

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

238

239 @example:

240

241 >>> w = Wm(448251, 5411932.0001)

242 >>> w.toStr(4) # 448251.0 5411932.0001

243 >>> w.toStr(sep=', ') # 448251, 5411932

244 '''

245 fs = self.x, self.y

246 if isscalar(radius):

247 fs += (radius,)

248 elif radius: # is True:

249 fs += (self.radius,)

250 elif radius not in (None, False):

251 raise WebMercatorError(radius=radius)

252 t = strs(fs, prec=prec)

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

254

255 @Property_RO

256 def x(self):

257 '''Get the easting (C{meter}).

258 '''

259 return self._x

260

261 @Property_RO

262 def y(self):

263 '''Get the northing (C{meter}).

264 '''

265 return self._y

266

267

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

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

270 consisting of easting, northing and an optional radius.

271

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

273 @kwarg radius: Optional earth radius (C{meter}).

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

275 or C{None}.

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

277

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

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

280 if B{C{Wm}} is C{None}.

281

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

283

284 @example:

285

286 >>> u = parseWM('448251 5411932')

287 >>> u.toRepr() # [E:448251, N:5411932]

288 '''

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

290 w = _splituple(strWM)

291

292 if len(w) == 2:

293 w += (radius,)

294 elif len(w) != 3:

295 raise ValueError

296 x, y, r = map(float, w)

297

298 return EasNorRadius3Tuple(x, y, r, name=name) if Wm is None else \

299 Wm(x, y, radius=r, name=name)

300

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

302 strWM=strWM, Error=WebMercatorError)

303

304

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

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

307

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

309 spherical) geodetic C{LatLon} point.

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

311 @kwarg radius: Optional earth radius (C{meter}), overridden

312 by the B{C{latlon}}'s equatorial radius.

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

314 or C{None}.

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

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

317 ignored if C{B{Wm} is None}.

318

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

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

321

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

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

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

325 B{C{radius}} is invalid.

326

327 @example:

328

329 >>> p = LatLon(48.8582, 2.2945) # 448251.8 5411932.7

330 >>> w = toWm(p) # 448252 5411933

331 >>> p = LatLon(13.4125, 103.8667) # 377302.4 1483034.8

332 >>> w = toWm(p) # 377302 1483035

333 '''

334 e, r, n = 0, radius, name

335 if r not in (R_MA, R_MB, R_M):

336 r = Radius(radius)

337 try:

338 y, x = latlon.lat, latlon.lon

339 if isinstance(latlon, _LLEB):

340 E = latlon.datum.ellipsoid

341 e, r = E.e, E.a

342 y = clipDegrees(y, _LatLimit)

343 n = name or latlon.name

344 except AttributeError:

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

346

347 s = sin(radians(y))

348 y = atanh(s) # == log(tan((90 + lat) / 2)) == log(tanPI_2_2(radians(lat)))

349 if e:

350 y -= e * atanh(e * s)

351 y *= r

352 x = r * radians(x)

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

354 Wm(x, y, **_xkwds(Wm_kwds, radius=r, name=n))

355 return r

356

357# **) MIT License

358#

359# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

360#

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

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

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

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

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

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

367#

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

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

370#

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

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

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

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

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

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

377# OTHER DEALINGS IN THE SOFTWARE.