Coverage for pygeodesy/osgr.py: 97%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''Ordnance Survey Grid References (OSGR) references on the UK U{National Grid 

5<https://www.OrdnanceSurvey.co.UK/documents/resources/guide-to-nationalgrid.pdf>}. 

6 

7Classes L{Osgr} and L{OSGRError} and functions L{parseOSGR} and L{toOsgr}. 

8 

9A pure Python implementation, transcoded from I{Chris Veness}' JavaScript originals U{OS National Grid 

10<https://www.Movable-Type.co.UK/scripts/latlong-os-gridref.html>} and U{Module osgridref 

11<https://www.Movable-Type.co.UK/scripts/geodesy/docs/module-osgridref.html>} and I{Charles Karney}'s 

12C++ class U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>}. 

13 

14OSGR provides geocoordinate references for UK mapping purposes, converted in 2015 to work with the C{WGS84} 

15or the original C{OSGB36} datum. In addition, this implementation includes both the OS recommended and the 

16Krüger-based method to convert between OSGR and geodetic coordinates (with keyword argument C{kTM} of 

17function L{toOsgr}, method L{Osgr.toLatLon} and method C{toOsgr} of any ellipsoidal C{LatLon} class). 

18 

19See U{Transverse Mercator: Redfearn series<https://WikiPedia.org/wiki/Transverse_Mercator:_Redfearn_series>}, 

20Karney's U{"Transverse Mercator with an accuracy of a few nanometers", 2011<https://ArXiv.org/pdf/1002.1417v3.pdf>} 

21(building on U{"Konforme Abbildung des Erdellipsoids in der Ebene", 1912<https://bib.GFZ-Potsdam.DE/pub/digi/krueger2.pdf>}, 

22U{"Die Mathematik der Gauß-Krueger-Abbildung", 2006<https://DE.WikiPedia.org/wiki/Gauß-Krüger-Koordinatensystem>}, 

23U{A Guide<https://www.OrdnanceSurvey.co.UK/documents/resources/guide-coordinate-systems-great-britain.pdf>} 

24and U{Ordnance Survey National Grid<https://WikiPedia.org/wiki/Ordnance_Survey_National_Grid>}. 

25''' 

26# make sure int/int division yields float quotient, see .basics 

27from __future__ import division as _; del _ # PYCHOK semicolon 

28 

29from pygeodesy.basics import halfs2, isbool, isfloat, map1, \ 

30 _splituple, _xsubclassof 

31from pygeodesy.constants import _1_0, _10_0, _N_2_0 # PYCHOK used! 

32from pygeodesy.datums import Datums, _ellipsoidal_datum, _WGS84 

33# from pygeodesy.dms import parseDMS2 # _MODS 

34from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB 

35from pygeodesy.errors import _parseX, _TypeError, _ValueError, \ 

36 _xkwds, _xkwds_get 

37from pygeodesy.fmath import Fdot, fpowers 

38from pygeodesy.fsums import _Fsumf_ 

39from pygeodesy.interns import MISSING, NN, _A_, _COLON_, _COMMA_, \ 

40 _COMMASPACE_, _DOT_, _ellipsoidal_, \ 

41 _latlon_, _not_, _SPACE_ 

42from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS 

43from pygeodesy.named import _NamedBase, nameof, _xnamed 

44from pygeodesy.namedTuples import EasNor2Tuple, LatLon2Tuple, \ 

45 LatLonDatum3Tuple 

46from pygeodesy.props import Property_RO, property_RO 

47from pygeodesy.streprs import _EN_WIDE, enstr2, _enstr2m3, Fmt, \ 

48 _resolution10, unstr, _xzipairs 

49from pygeodesy.units import Easting, Lam_, Lat, Lon, Northing, \ 

50 Phi_, Scalar, _10um, _100km 

51from pygeodesy.utily import degrees90, degrees180, sincostan3, truncate 

52 

53from math import cos, fabs, radians, sin, sqrt 

54 

55__all__ = _ALL_LAZY.osgr 

56__version__ = '23.12.03' 

57 

58_equivalent_ = 'equivalent' 

59_OSGR_ = 'OSGR' 

60_ord_A = ord(_A_) 

61_TRIPS = 33 # .toLatLon convergence 

62 

63 

64class _NG(object): 

65 '''Ordnance Survey National Grid parameters. 

66 ''' 

67 @Property_RO 

68 def a0(self): # equatoradius, scaled 

69 return self.ellipsoid.a * self.k0 

70 

71 @Property_RO 

72 def b0(self): # polaradius, scaled 

73 return self.ellipsoid.b * self.k0 

74 

75 @Property_RO 

76 def datum(self): # datum, Airy130 ellipsoid 

77 return Datums.OSGB36 

78 

79 @Property_RO 

80 def eas0(self): # False origin easting (C{meter}) 

81 return Easting(4 * _100km) 

82 

83 @Property_RO 

84 def easX(self): # easting [0..extent] (C{meter}) 

85 return Easting(7 * _100km) 

86 

87 @Property_RO 

88 def ellipsoid(self): # ellipsoid, Airy130 

89 return self.datum.ellipsoid 

90 

91 def forward2(self, latlon): # convert C{latlon} to (easting, norting), as I{Karney}'s 

92 # U{Forward<https://GeographicLib.SourceForge.io/C++/doc/OSGB_8hpp_source.html>} 

93 t = self.kTM.forward(latlon.lat, latlon.lon, lon0=self.lon0) 

94 e = t.easting + self.eas0 

95 n = t.northing + self.nor0ffset 

96 return e, n 

97 

98 @Property_RO 

99 def k0(self): # central scale (C{float}), like I{Karney}'s CentralScale 

100 # <https://GeographicLib.SourceForge.io/C++/doc/OSGB_8hpp_source.html> 

101 _0_9998268 = (9998268 - 10000000) / 10000000 

102 return Scalar(_10_0**_0_9998268) # 0.9996012717... 

103 

104 @Property_RO 

105 def kTM(self): # the L{KTransverseMercator} instance, like I{Karney}'s OSGBTM 

106 # <https://GeographicLib.SourceForge.io/C++/doc/OSGB_8cpp_source.html> 

107 return _MODS.ktm.KTransverseMercator(self.datum, lon0=0, k0=self.k0) 

108 

109 @Property_RO 

110 def lam0(self): # True origin longitude C{radians} 

111 return Lam_(self.lon0) 

112 

113 @Property_RO 

114 def lat0(self): # True origin latitude, 49°N 

115 return Lat(49.0) 

116 

117 @Property_RO 

118 def lon0(self): # True origin longitude, 2°W 

119 return Lon(_N_2_0) 

120 

121 @Property_RO 

122 def Mabcd(self): # meridional coefficients (a, b, c, d) 

123 n, n2, n3 = fpowers(self.ellipsoid.n, 3) 

124 M = (_Fsumf_(4, 4 * n, 5 * n2, 5 * n3) / 4, 

125 _Fsumf_( 24 * n, 24 * n2, 21 * n3) / 8, 

126 _Fsumf_( 15 * n2, 15 * n3) / 8, 

127 (35 * n3 / 24)) 

128 return M 

129 

130 def Mabcd0(self, a): # meridional arc, scaled 

131 c = a + self.phi0 

132 s = a - self.phi0 

133 R = Fdot(self.Mabcd, s, -sin(s) * cos(c), 

134 sin(s * 2) * cos(c * 2), 

135 -sin(s * 3) * cos(c * 3)) 

136 return float(R * self.b0) 

137 

138 @Property_RO 

139 def nor0(self): # False origin northing (C{meter}) 

140 return Northing(-_100km) 

141 

142 @Property_RO 

143 def nor0ffset(self): # like I{Karney}'s computenorthoffset 

144 # <https://GeographicLib.SourceForge.io/C++/doc/OSGB_8cpp_source.html> 

145 return self.nor0 - self.kTM.forward(self.lat0, 0).northing 

146 

147 @Property_RO 

148 def norX(self): # northing [0..extent] (C{meter}) 

149 return Northing(13 * _100km) 

150 

151 def nu_rho_eta3(self, sa): # 3-tuple (nu, nu / rho, eta2) 

152 E = self.ellipsoid # rho, nu = E.roc2_(sa) # .k0? 

153 s = E.e2s2(sa) # == 1 - E.e2 * sa**2 

154 v = self.a0 / sqrt(s) # == nu, transverse roc 

155 # rho = .a0 * E.e21 / s**1.5 == v * E.e21 / s 

156 # r = v * E.e21 / s # == rho, meridional roc 

157 # nu / rho == v / (v * E.e21 / s) == s / E.e21 == ... 

158 s *= E._1_e21 # ... s * E._1_e21 == s * E.a2_b2 

159 return v, s, (s - _1_0) # η2 = nu / rho - 1 

160 

161 @Property_RO 

162 def phi0(self): # True origin latitude C{radians} 

163 return Phi_(self.lat0) 

164 

165 def reverse(self, osgr): # convert C{osgr} to (ellipsoidal} LatLon, as I{Karney}'s 

166 # U{Reverse<https://GeographicLib.SourceForge.io/C++/doc/OSGB_8hpp_source.html>} 

167 r = osgr._latlonTM 

168 if r is None: 

169 x = osgr.easting - self.eas0 

170 y = osgr.northing - self.nor0ffset 

171 t = self.kTM.reverse(x, y, lon0=self.lon0) 

172 r = _LLEB(t.lat, t.lon, datum=self.datum, name=osgr.name) 

173 osgr._latlonTM = r 

174 return r 

175 

176_NG = _NG() # PYCHOK singleton 

177 

178 

179class OSGRError(_ValueError): 

180 '''Error raised for a L{parseOSGR}, L{Osgr} or other OSGR issue. 

181 ''' 

182 pass 

183 

184 

185class Osgr(_NamedBase): 

186 '''Ordnance Survey Grid References (OSGR) coordinates on 

187 the U{National Grid<https://www.OrdnanceSurvey.co.UK/ 

188 documents/resources/guide-to-nationalgrid.pdf>}. 

189 ''' 

190 _datum = _NG.datum # default datum (L{Datums.OSGB36}) 

191 _easting = 0 # Easting (C{meter}) 

192 _latlon = None # cached B{C{_toLatlon}} 

193 _latlonTM = None # cached B{C{_toLatlon kTM}} 

194 _northing = 0 # Nothing (C{meter}) 

195 _resolution = 0 # from L{parseOSGR} (C{meter}) 

196 

197 def __init__(self, easting, northing, datum=None, name=NN, 

198 resolution=0): 

199 '''New L{Osgr} coordinate. 

200 

201 @arg easting: Easting from the OS C{National Grid} 

202 origin (C{meter}). 

203 @arg northing: Northing from the OS C{National Grid} 

204 origin (C{meter}). 

205 @kwarg datum: Override default datum (C{Datums.OSGB36}). 

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

207 @kwarg resolution: Optional resolution (C{meter}), 

208 C{0} for default. 

209 

210 @raise OSGRError: Invalid or negative B{C{easting}} or 

211 B{C{northing}} or B{C{datum}} not an 

212 C{Datums.OSGB36} equivalent. 

213 ''' 

214 if datum: # PYCHOK no cover 

215 try: 

216 self._datum = _ellipsoidal_datum(datum) 

217 if self.datum != _NG.datum: 

218 raise ValueError(_not_(_NG.datum.name, _equivalent_)) 

219 except (TypeError, ValueError) as x: 

220 raise OSGRError(datum=datum, cause=x) 

221 

222 self._easting = Easting( easting, Error=OSGRError, high=_NG.easX) 

223 self._northing = Northing(northing, Error=OSGRError, high=_NG.norX) 

224 

225 if name: 

226 self.name = name 

227 if resolution: 

228 self._resolution = _resolution10(resolution, Error=OSGRError) 

229 

230 def __str__(self): 

231 return self.toStr(GD=True, sep=_SPACE_) 

232 

233 @Property_RO 

234 def datum(self): 

235 '''Get the datum (L{Datum}). 

236 ''' 

237 return self._datum 

238 

239 @Property_RO 

240 def easting(self): 

241 '''Get the easting (C{meter}). 

242 ''' 

243 return self._easting 

244 

245 @Property_RO 

246 def falsing0(self): 

247 '''Get the C{OS National Grid} falsing (L{EasNor2Tuple}). 

248 ''' 

249 return EasNor2Tuple(_NG.eas0, _NG.nor0, name=_OSGR_) 

250 

251 @property_RO 

252 def iteration(self): 

253 '''Get the most recent C{Osgr.toLatLon} iteration number 

254 (C{int}) or C{None} if not available/applicable. 

255 ''' 

256 return self._iteration 

257 

258 @Property_RO 

259 def latlon0(self): 

260 '''Get the C{OS National Grid} origin (L{LatLon2Tuple}). 

261 ''' 

262 return LatLon2Tuple(_NG.lat, _NG.lon0, name=_OSGR_) 

263 

264 @Property_RO 

265 def northing(self): 

266 '''Get the northing (C{meter}). 

267 ''' 

268 return self._northing 

269 

270 def parse(self, strOSGR, name=NN): 

271 '''Parse an OSGR reference to a similar L{Osgr} instance. 

272 

273 @arg strOSGR: The OSGR reference (C{str}), see function L{parseOSGR}. 

274 @kwarg name: Optional instance name (C{str}), overriding this name. 

275 

276 @return: The similar instance (L{Osgr}) 

277 

278 @raise OSGRError: Invalid B{C{strOSGR}}. 

279 ''' 

280 return parseOSGR(strOSGR, Osgr=self.classof, name=name or self.name) 

281 

282 @property_RO 

283 def resolution(self): 

284 '''Get the OSGR resolution (C{meter}, power of 10) or C{0} if undefined. 

285 ''' 

286 return self._resolution 

287 

288 def toLatLon(self, LatLon=None, datum=_WGS84, kTM=False, eps=_10um, **LatLon_kwds): 

289 '''Convert this L{Osgr} coordinate to an (ellipsoidal) geodetic 

290 point. 

291 

292 @kwarg LatLon: Optional ellipsoidal class to return the 

293 geodetic point (C{LatLon}) or C{None}. 

294 @kwarg datum: Optional datum to convert to (L{Datum}, 

295 L{Ellipsoid}, L{Ellipsoid2}, L{Ellipsoid2} 

296 or L{a_f2Tuple}). 

297 @kwarg kTM: If C{True} use I{Karney}'s Krüger method from 

298 module L{ktm}, otherwise use the Ordnance 

299 Survey formulation (C{bool}). 

300 @kwarg eps: Tolerance for OS convergence (C{meter}). 

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

302 arguments, ignored if C{B{LatLon} is None}. 

303 

304 @return: A B{C{LatLon}} instance or if B{C{LatLon}} is C{None} 

305 a L{LatLonDatum3Tuple}C{(lat, lon, datum)}. 

306 

307 @note: While OS grid references are based on the OSGB36 datum, 

308 the Ordnance Survey have deprecated the use of OSGB36 for 

309 lat-/longitude coordinates (in favour of WGS84). Hence, 

310 this method returns WGS84 by default with OSGB36 as an 

311 option, U{see<https://www.OrdnanceSurvey.co.UK/blog/2014/12/2>}. 

312 

313 @note: The formulation implemented here due to Thomas, Redfearn, 

314 etc. is as published by the Ordnance Survey, but is 

315 inferior to Krüger as used by e.g. Karney 2011. 

316 

317 @raise OSGRError: No convergence. 

318 

319 @raise TypeError: If B{C{LatLon}} is not ellipsoidal or B{C{datum}} 

320 is invalid or conversion to B{C{datum}} failed. 

321 ''' 

322 NG = _NG 

323 if kTM: 

324 r = NG.reverse(self) 

325 

326 elif self._latlon is None: 

327 e0 = self.easting - NG.eas0 

328 n0 = m = self.northing - NG.nor0 

329 

330 _M = NG.Mabcd0 

331 a0 = NG.a0 

332 a = NG.phi0 

333 _A = _Fsumf_(a).fsum_ 

334 for self._iteration in range(1, _TRIPS): 

335 a = _A(m / a0) 

336 m = n0 - _M(a) # meridional arc 

337 if fabs(m) < eps: 

338 break 

339 else: # PYCHOK no cover 

340 t = str(self) 

341 t = Fmt.PAREN(self.classname, repr(t)) 

342 t = _DOT_(t, self.toLatLon.__name__) 

343 t = unstr(t, eps=eps, kTM=kTM) 

344 raise OSGRError(Fmt.no_convergence(m), txt=t) 

345 

346 sa, ca, ta = sincostan3(a) 

347 v, v_r, n2 = NG.nu_rho_eta3(sa) 

348 

349 ta2 = ta**2 

350 ta4 = ta2**2 

351 

352 ta *= v_r / 2 

353 d = e0 / v 

354 d2 = d**2 

355 

356 a = (d2 * ta * (-1 + # Horner-like 

357 d2 / 12 * (_Fsumf_( 5, 3 * ta2, -9 * ta2 * n2, n2) - 

358 d2 / 30 * _Fsumf_(61, 90 * ta2, 45 * ta4)))).fsum_(a) 

359 

360 b = (d / ca * ( 1 - # Horner-like 

361 d2 / 6 * (_Fsumf_(v_r, 2 * ta2) - 

362 d2 / 20 * (_Fsumf_( 5, 28 * ta2, 24 * ta4) + 

363 d2 / 42 * _Fsumf_(61, 662 * ta2, 1320 * ta4, 

364 720 * ta2 * ta4))))).fsum_(NG.lam0) 

365 

366 r = _LLEB(degrees90(a), degrees180(b), datum=self.datum, name=self.name) 

367 r._iteration = self._iteration # only ellipsoidal LatLon 

368 self._latlon = r 

369 else: 

370 r = self._latlon 

371 

372 return _ll2LatLon3(r, LatLon, datum, LatLon_kwds) 

373 

374 @Property_RO 

375 def scale0(self): 

376 '''Get the C{OS National Grid} central scale (C{scalar}). 

377 ''' 

378 return _NG.k0 

379 

380 def toRepr(self, GD=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_, **prec): # PYCHOK expected 

381 '''Return a string representation of this L{Osgr} coordinate. 

382 

383 @kwarg GD: If C{bool}, in- or exclude the 2-letter grid designation and get 

384 the new B{C{prec}} behavior, otherwise if C{None}, default to the 

385 DEPRECATED definition C{B{prec}=5} I{for backward compatibility}. 

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

387 @kwarg sep: Separator to join (C{str}) or C{None} to return an unjoined 2- or 

388 3-C{tuple} of C{str}s. 

389 @kwarg prec: Precison C{B{prec}=0}, the number of I{decimal} digits (C{int}) or 

390 if negative, the number of I{units to drop}, like MGRS U{PRECISION 

391 <https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html#PRECISION>}. 

392 

393 @return: This OSGR as (C{str}), C{"[G:GD, E:meter, N:meter]"} or if C{B{GD}=False} 

394 C{"[OSGR:easting,northing]"} or C{B{GD}=False} and C{B{prec} > 0} if 

395 C{"[OSGR:easting.d,northing.d]"}. 

396 

397 @note: OSGR easting and northing values are truncated, not rounded. 

398 

399 @raise OSGRError: If C{B{GD} not in (None, True, False)} or if C{B{prec} < -4} 

400 and C{B{GD}=False}. 

401 

402 @raise ValueError: Invalid B{C{prec}}. 

403 ''' 

404 GD, prec = _GD_prec2(GD, fmt=fmt, sep=sep, **prec) 

405 

406 if GD: 

407 t = self.toStr(GD=True, prec=prec, sep=None) 

408 t = _xzipairs('GEN', t, sep=sep, fmt=fmt) 

409 else: 

410 t = _COLON_(_OSGR_, self.toStr(GD=False, prec=prec)) 

411 if fmt: 

412 t = fmt % (t,) 

413 return t 

414 

415 def toStr(self, GD=None, sep=NN, **prec): # PYCHOK expected 

416 '''Return this L{Osgr} coordinate as a string. 

417 

418 @kwarg GD: If C{bool}, in- or exclude the 2-letter grid designation and get 

419 the new B{C{prec}} behavior, otherwise if C{None}, default to the 

420 DEPRECATED definition C{B{prec}=5} I{for backward compatibility}. 

421 @kwarg sep: Separator to join (C{str}) or C{None} to return an unjoined 2- or 

422 3-C{tuple} of C{str}s. 

423 @kwarg prec: Precison C{B{prec}=0}, the number of I{decimal} digits (C{int}) or 

424 if negative, the number of I{units to drop}, like MGRS U{PRECISION 

425 <https://GeographicLib.SourceForge.io/C++/doc/GeoConvert.1.html#PRECISION>}. 

426 

427 @return: This OSGR as (C{str}), C{"GD meter meter"} or if C{B{GD}=False} 

428 C{"easting,northing"} or if C{B{GD}=False} and C{B{prec} > 0} 

429 C{"easting.d,northing.d"} 

430 

431 @note: OSGR easting and northing values are truncated, not rounded. 

432 

433 @raise OSGRError: If C{B{GD} not in (None, True, False)} or if C{B{prec} 

434 < -4} and C{B{GD}=False}. 

435 

436 @raise ValueError: Invalid B{C{prec}}. 

437 ''' 

438 def _i2c(i): 

439 if i > 7: 

440 i += 1 

441 return chr(_ord_A + i) 

442 

443 GD, prec = _GD_prec2(GD, sep=sep, **prec) 

444 

445 if GD: 

446 E, e = divmod(self.easting, _100km) 

447 N, n = divmod(self.northing, _100km) 

448 E, N = int(E), int(N) 

449 if 0 > E or E > 6 or \ 

450 0 > N or N > 12: 

451 raise OSGRError(E=E, e=e, N=N, n=n, prec=prec, sep=sep) 

452 N = 19 - N 

453 EN = _i2c( N - (N % 5) + (E + 10) // 5) + \ 

454 _i2c((N * 5) % 25 + (E % 5)) 

455 t = enstr2(e, n, prec, EN) 

456 s = sep 

457 

458 elif prec <= -_EN_WIDE: 

459 raise OSGRError(GD=GD, prec=prec, sep=sep) 

460 else: 

461 t = enstr2(self.easting, self.northing, prec, dot=True, 

462 wide=_EN_WIDE + 1) 

463 s = sep if sep is None else (sep or _COMMA_) 

464 

465 return t if s is None else s.join(t) 

466 

467 

468def _GD_prec2(GD, **prec_et_al): 

469 '''(INTERNAL) Handle C{prec} backward compatibility. 

470 ''' 

471 if GD is None: # old C{prec} 5+ or neg 

472 prec = _xkwds_get(prec_et_al, prec=_EN_WIDE) 

473 GD = prec > 0 

474 prec = (prec - _EN_WIDE) if GD else -prec 

475 elif isbool(GD): 

476 prec = _xkwds_get(prec_et_al, prec=0) 

477 else: 

478 raise OSGRError(GD=GD, **prec_et_al) 

479 return GD, prec 

480 

481 

482def _ll2datum(ll, datum, name): 

483 '''(INTERNAL) Convert datum if needed. 

484 ''' 

485 if datum: 

486 try: 

487 if ll.datum != datum: 

488 ll = ll.toDatum(datum) 

489 except (AttributeError, TypeError, ValueError) as x: 

490 raise _TypeError(cause=x, datum=datum.name, **{name: ll}) 

491 return ll 

492 

493 

494def _ll2LatLon3(ll, LatLon, datum, LatLon_kwds): 

495 '''(INTERNAL) Convert C{ll} to C{LatLon} 

496 ''' 

497 if LatLon is None: 

498 r = _ll2datum(ll, datum, LatLonDatum3Tuple.__name__) 

499 r = LatLonDatum3Tuple(r.lat, r.lon, r.datum) 

500 else: # must be ellipsoidal 

501 _xsubclassof(_LLEB, LatLon=LatLon) 

502 r = _ll2datum(ll, datum, LatLon.__name__) 

503 r = LatLon(r.lat, r.lon, datum=r.datum, **LatLon_kwds) 

504 if r._iteration != ll._iteration: 

505 r._iteration = ll._iteration 

506 return _xnamed(r, nameof(ll)) 

507 

508 

509def parseOSGR(strOSGR, Osgr=Osgr, name=NN, **Osgr_kwds): 

510 '''Parse a string representing an OS Grid Reference, consisting 

511 of C{"[GD] easting northing"}. 

512 

513 Accepts standard OS Grid References like "SU 387 148", with 

514 or without whitespace separators, from 2- up to 22-digit 

515 references, or all-numeric, comma-separated references in 

516 meters, for example "438700,114800". 

517 

518 @arg strOSGR: An OSGR coordinate (C{str}). 

519 @kwarg Osgr: Optional class to return the OSGR coordinate 

520 (L{Osgr}) or C{None}. 

521 @kwarg name: Optional B{C{Osgr}} name (C{str}). 

522 @kwarg Osgr_kwds: Optional, additional B{C{Osgr}} keyword 

523 arguments, ignored if C{B{Osgr} is None}. 

524 

525 @return: An (B{C{Osgr}}) instance or if B{C{Osgr}} is 

526 C{None} an L{EasNor2Tuple}C{(easting, northing)}. 

527 

528 @raise OSGRError: Invalid B{C{strOSGR}}. 

529 ''' 

530 def _c2i(G): 

531 g = ord(G.upper()) - _ord_A 

532 if g > 7: 

533 g -= 1 

534 if g < 0 or g > 25: 

535 raise ValueError 

536 return g 

537 

538 def _OSGR(strOSGR, Osgr, name): 

539 s = _splituple(strOSGR.strip()) 

540 p = len(s) 

541 if not p: 

542 raise ValueError 

543 g = s[0] 

544 if p == 2 and isfloat(g): # "easting,northing" 

545 e, n, m = _enstr2m3(*s, wide=_EN_WIDE + 1) 

546 

547 else: 

548 if p == 1: # "GReastingnorthing" 

549 s = halfs2(g[2:]) 

550 g = g[:2] 

551 elif p == 2: # "GReasting northing" 

552 s = g[2:], s[1] # for backward ... 

553 g = g[:2] # ... compatibility 

554 elif p != 3: 

555 raise ValueError 

556 else: # "GR easting northing" 

557 s = s[1:] 

558 

559 e, n = map(_c2i, g) 

560 n, m = divmod(n, 5) 

561 E = ((e - 2) % 5) * 5 + m 

562 N = 19 - (e // 5) * 5 - n 

563 if 0 > E or E > 6 or \ 

564 0 > N or N > 12: 

565 raise ValueError 

566 

567 e, n, m = _enstr2m3(*s, wide=_EN_WIDE) 

568 e += E * _100km 

569 n += N * _100km 

570 

571 if Osgr is None: 

572 _ = _MODS.osgr.Osgr(e, n, resolution=m) # validate 

573 r = EasNor2Tuple(e, n, name=name) 

574 else: 

575 r = Osgr(e, n, name=name, 

576 **_xkwds(Osgr_kwds, resolution=m)) 

577 return r 

578 

579 return _parseX(_OSGR, strOSGR, Osgr, name, 

580 strOSGR=strOSGR, Error=OSGRError) 

581 

582 

583def toOsgr(latlon, lon=None, kTM=False, datum=_WGS84, Osgr=Osgr, name=NN, # MCCABE 14 

584 **prec_Osgr_kwds): 

585 '''Convert a lat-/longitude point to an OSGR coordinate. 

586 

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

588 C{LatLon} point. 

589 @kwarg lon: Optional longitude in degrees (scalar or C{None}). 

590 @kwarg kTM: If C{True} use I{Karney}'s Krüger method from 

591 module L{ktm}, otherwise use the Ordnance 

592 Survey formulation (C{bool}). 

593 @kwarg datum: Optional datum to convert B{C{lat, lon}} from 

594 (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

595 L{a_f2Tuple}). 

596 @kwarg Osgr: Optional class to return the OSGR coordinate 

597 (L{Osgr}) or C{None}. 

598 @kwarg name: Optional B{C{Osgr}} name (C{str}). 

599 @kwarg prec_Osgr_kwds: Optional L{truncate} precision 

600 C{B{prec}=ndigits} and/or additional 

601 B{C{Osgr}} keyword arguments, ignored 

602 if C{B{Osgr} is None}. 

603 

604 @return: An (B{C{Osgr}}) instance or if B{C{Osgr}} is C{None} 

605 an L{EasNor2Tuple}C{(easting, northing)}. 

606 

607 @note: If L{isint}C{(B{prec})} both easting and northing are 

608 L{truncate}d to the given number of digits. 

609 

610 @raise OSGRError: Invalid B{C{latlon}} or B{C{lon}}. 

611 

612 @raise TypeError: Non-ellipsoidal B{C{latlon}} or invalid 

613 B{C{datum}}, B{C{Osgr}}, B{C{Osgr_kwds}} 

614 or conversion to C{Datums.OSGB36} failed. 

615 ''' 

616 def _prec_kwds2(prec=MISSING, **kwds): 

617 return prec, kwds 

618 

619 if lon is not None: 

620 try: 

621 lat, lon = _MODS.dms.parseDMS2(latlon, lon) 

622 latlon = _LLEB(lat, lon, datum=datum) 

623 except Exception as x: 

624 raise OSGRError(latlon=latlon, lon=lon, datum=datum, cause=x) 

625 elif not isinstance(latlon, _LLEB): 

626 raise _TypeError(latlon=latlon, txt=_not_(_ellipsoidal_)) 

627 elif not name: # use latlon.name 

628 name = nameof(latlon) 

629 

630 NG = _NG 

631 # convert latlon to OSGB36 first 

632 ll = _ll2datum(latlon, NG.datum, _latlon_) 

633 

634 if kTM: 

635 e, n = NG.forward2(ll) 

636 

637 else: 

638 try: 

639 a, b = ll.philam 

640 except AttributeError: 

641 a, b = map1(radians, ll.lat, ll.lon) 

642 

643 sa, ca, ta = sincostan3(a) 

644 v, v_r, n2 = NG.nu_rho_eta3(sa) 

645 

646 m0 = NG.Mabcd0(a) 

647 b -= NG.lam0 

648 t = b * sa * v / 2 

649 d = b * ca 

650 d2 = d**2 

651 

652 ta2 = -(ta**2) 

653 ta4 = ta2**2 

654 

655 e = (d * v * ( 1 + # Horner-like 

656 d2 / 6 * (_Fsumf_(v_r, ta2) + 

657 d2 / 20 * _Fsumf_(5, 18 * ta2, ta4, 14 * n2, 

658 58 * n2 * ta2)))).fsum_(NG.eas0) 

659 

660 n = (d * t * ( 1 + # Horner-like 

661 d2 / 12 * (_Fsumf_( 5, ta2, 9 * n2) + 

662 d2 / 30 * _Fsumf_(61, ta4, 58 * ta2)))).fsum_(m0, NG.nor0) 

663 

664 p, kwds = _prec_kwds2(**prec_Osgr_kwds) 

665 if p is not MISSING: 

666 e = truncate(e, p) 

667 n = truncate(n, p) 

668 

669 if Osgr is None: 

670 _ = _MODS.osgr.Osgr(e, n) # validate 

671 r = EasNor2Tuple(e, n) 

672 else: 

673 r = Osgr(e, n, **kwds) # datum=NG.datum 

674 if lon is None and isinstance(latlon, _LLEB): 

675 if kTM: 

676 r._latlonTM = latlon # XXX weakref(latlon)? 

677 else: 

678 r._latlon = latlon # XXX weakref(latlon)? 

679 return _xnamed(r, name or nameof(latlon)) 

680 

681 

682if __name__ == '__main__': 

683 

684 from pygeodesy.lazily import printf 

685 from random import random, seed 

686 from time import localtime 

687 

688 seed(localtime().tm_yday) 

689 

690 def _rnd(X, n): 

691 X -= 2 

692 d = set() 

693 while len(d) < n: 

694 r = 1 + int(random() * X) 

695 if r not in d: 

696 d.add(r) 

697 yield r 

698 

699 D = _NG.datum 

700 i = t = 0 

701 t1 = t2 = 0, 0, 0, 0 

702 for e in _rnd(_NG.easX, 256): 

703 for n in _rnd(_NG.norX, 512): 

704 p = False 

705 t += 1 

706 

707 g = Osgr(e, n) 

708 v = g.toLatLon(kTM=False, datum=D) 

709 k = g.toLatLon(kTM=True, datum=D) 

710 d = max(fabs(v.lat - k.lat), fabs(v.lon - k.lon)) 

711 if d > t1[2]: 

712 t1 = e, n, d, t 

713 p = True 

714 

715 ll = _LLEB((v.lat + k.lat) / 2, 

716 (v.lon + k.lon) / 2, datum=D) 

717 v = ll.toOsgr(kTM=False) 

718 k = ll.toOsgr(kTM=True) 

719 d = max(fabs(v.easting - k.easting), 

720 fabs(v.northing - k.northing)) 

721 if d > t2[2]: 

722 t2 = ll.lat, ll.lon, d, t 

723 p = True 

724 

725 if p: 

726 i += 1 

727 printf('%5d: %s %s', i, 

728 'll(%.2f, %.2f) %.3e %d' % t2, 

729 'en(%d, %d) %.3e %d' % t1) 

730 printf('%d total %s', t, D.name) 

731 

732# **) MIT License 

733# 

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

735# 

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

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

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

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

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

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

742# 

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

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

745# 

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

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

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

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

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

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

752# OTHER DEALINGS IN THE SOFTWARE. 

753 

754# % python3 -m pygeodesy.osgr 

755# 1: ll(53.42, -0.59) 4.672e-07 1 en(493496, 392519) 2.796e-11 1 

756# 2: ll(60.86, -0.28) 2.760e-05 2 en(493496, 1220986) 2.509e-10 2 

757# 3: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1281644) 2.774e-10 13 

758# 4: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192797) 3.038e-10 20 

759# 5: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192249) 3.073e-10 120 

760# 6: ll(61.55, -0.24) 3.120e-05 160 en(493496, 1192249) 3.073e-10 120 

761# 7: ll(61.55, -0.24) 3.122e-05 435 en(493496, 1192249) 3.073e-10 120 

762# 8: ll(61.57, -0.24) 3.130e-05 473 en(493496, 1192249) 3.073e-10 120 

763# 9: ll(58.66, -8.56) 8.084e-04 513 en(19711, 993800) 3.020e-06 513 

764# 10: ll(52.83, -7.65) 8.156e-04 518 en(19711, 993800) 3.020e-06 513 

765# 11: ll(51.55, -7.49) 8.755e-04 519 en(19711, 993800) 3.020e-06 513 

766# 12: ll(60.20, -8.87) 9.439e-04 521 en(19711, 1165686) 4.318e-06 521 

767# 13: ll(60.45, -8.92) 9.668e-04 532 en(19711, 1194002) 4.588e-06 532 

768# 14: ll(61.17, -9.08) 1.371e-03 535 en(19711, 1274463) 5.465e-06 535 

769# 15: ll(61.31, -9.11) 1.463e-03 642 en(19711, 1290590) 5.663e-06 642 

770# 16: ll(61.35, -9.12) 1.488e-03 807 en(19711, 1294976) 5.718e-06 807 

771# 17: ll(61.38, -9.13) 1.510e-03 929 en(19711, 1298667) 5.765e-06 929 

772# 18: ll(61.11, -9.24) 1.584e-03 11270 en(10307, 1268759) 6.404e-06 11270 

773# 19: ll(61.20, -9.26) 1.650e-03 11319 en(10307, 1278686) 6.545e-06 11319 

774# 20: ll(61.23, -9.27) 1.676e-03 11383 en(10307, 1282514) 6.600e-06 11383 

775# 21: ll(61.36, -9.30) 1.776e-03 11437 en(10307, 1297037) 6.816e-06 11437 

776# 22: ll(61.38, -9.30) 1.789e-03 11472 en(10307, 1298889) 6.844e-06 11472 

777# 23: ll(61.25, -9.39) 1.885e-03 91137 en(4367, 1285831) 7.392e-06 91137 

778# 24: ll(61.32, -9.40) 1.944e-03 91207 en(4367, 1293568) 7.519e-06 91207 

779# 25: ll(61.34, -9.41) 1.963e-03 91376 en(4367, 1296061) 7.561e-06 91376 

780# 26: ll(61.37, -9.41) 1.986e-03 91595 en(4367, 1298908) 7.608e-06 91595 

781# 131072 total OSGB36