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, _xkwds_pop2 

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 _name2__, _NamedBase, nameof 

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, Lamd, Lat, Lon, Northing, \ 

50 Phid, 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__ = '24.11.06' 

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 Lamd(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 Phid(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, resolution=0, **name): 

198 '''New L{Osgr} coordinate. 

199 

200 @arg easting: Easting from the OS C{National Grid} origin (C{meter}). 

201 @arg northing: Northing from the OS C{National Grid} origin (C{meter}). 

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

203 @kwarg resolution: Optional resolution (C{meter}), C{0} for default. 

204 @kwarg name: Optional C{B{name}=NN} (C{str}). 

205 

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

207 or B{C{datum}} not an C{Datums.OSGB36} equivalent. 

208 ''' 

209 if datum: # PYCHOK no cover 

210 try: 

211 self._datum = _ellipsoidal_datum(datum) 

212 if self.datum != _NG.datum: 

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

214 except (TypeError, ValueError) as x: 

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

216 

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

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

219 

220 if name: 

221 self.name = name 

222 if resolution: 

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

224 

225 def __str__(self): 

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

227 

228 @Property_RO 

229 def datum(self): 

230 '''Get the datum (L{Datum}). 

231 ''' 

232 return self._datum 

233 

234 @Property_RO 

235 def easting(self): 

236 '''Get the easting (C{meter}). 

237 ''' 

238 return self._easting 

239 

240 @Property_RO 

241 def falsing0(self): 

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

243 ''' 

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

245 

246 @property_RO 

247 def iteration(self): 

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

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

250 ''' 

251 return self._iteration 

252 

253 @Property_RO 

254 def latlon0(self): 

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

256 ''' 

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

258 

259 @Property_RO 

260 def northing(self): 

261 '''Get the northing (C{meter}). 

262 ''' 

263 return self._northing 

264 

265 def parse(self, strOSGR, **name): 

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

267 

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

269 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name. 

270 

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

272 

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

274 ''' 

275 return parseOSGR(strOSGR, Osgr=self.classof, name=self._name__(name)) 

276 

277 @property_RO 

278 def resolution(self): 

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

280 ''' 

281 return self._resolution 

282 

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

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

285 point. 

286 

287 @kwarg LatLon: Optional ellipsoidal class to return the 

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

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

290 L{Ellipsoid}, L{Ellipsoid2}, L{Ellipsoid2} 

291 or L{a_f2Tuple}). 

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

293 module L{ktm}, otherwise use the Ordnance Survey 

294 formulation (C{bool}). 

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

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

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

298 

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

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

301 

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

303 the Ordnance Survey have deprecated the use of OSGB36 for 

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

305 this method returns WGS84 by default with OSGB36 as an 

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

307 

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

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

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

311 

312 @raise OSGRError: No convergence. 

313 

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

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

316 ''' 

317 NG = _NG 

318 if kTM: 

319 r = NG.reverse(self) 

320 

321 elif self._latlon is None: 

322 _F = _Fsumf_ 

323 e0 = self.easting - NG.eas0 

324 n0 = m = self.northing - NG.nor0 

325 

326 a0 = NG.a0 

327 _M = NG.Mabcd0 

328 a = NG.phi0 

329 _a = fabs 

330 _A = _F(a).fsum_ 

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

332 a = _A(m / a0) 

333 m = n0 - _M(a) # meridional arc 

334 if _a(m) < eps: 

335 break 

336 else: # PYCHOK no cover 

337 t = str(self) 

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

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

340 t = unstr(t, eps=eps, kTM=kTM) 

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

342 

343 sa, ca, ta = sincostan3(a) 

344 v, v_r, n2 = NG.nu_rho_eta3(sa) 

345 

346 ta2 = ta**2 

347 ta4 = ta2**2 

348 

349 ta *= v_r / 2 

350 d = e0 / v 

351 d2 = d**2 

352 

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

354 d2 / 12 * (_F( 5, 3 * ta2, -9 * ta2 * n2, n2) - 

355 d2 / 30 * _F(61, 90 * ta2, 45 * ta4)))).fsum_(a) 

356 

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

358 d2 / 6 * (_F(v_r, 2 * ta2) - 

359 d2 / 20 * (_F( 5, 28 * ta2, 24 * ta4) + 

360 d2 / 42 * _F(61, 662 * ta2, 1320 * ta4, 

361 720 * ta2 * ta4))))).fsum_(NG.lam0) 

362 

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

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

365 self._latlon = r 

366 else: 

367 r = self._latlon 

368 

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

370 

371 @Property_RO 

372 def scale0(self): 

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

374 ''' 

375 return _NG.k0 

376 

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

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

379 

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

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

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

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

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

385 3-C{tuple} of C{str}s. 

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

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

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

389 

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

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

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

393 

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

395 

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

397 and C{B{GD}=False}. 

398 

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

400 ''' 

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

402 

403 if GD: 

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

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

406 else: 

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

408 if fmt: 

409 t = fmt % (t,) 

410 return t 

411 

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

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

414 

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

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

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

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

419 3-C{tuple} of C{str}s. 

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

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

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

423 

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

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

426 C{"easting.d,northing.d"} 

427 

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

429 

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

431 < -4} and C{B{GD}=False}. 

432 

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

434 ''' 

435 def _i2c(i): 

436 if i > 7: 

437 i += 1 

438 return chr(_ord_A + i) 

439 

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

441 

442 if GD: 

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

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

445 E, N = int(E), int(N) 

446 if 0 > E or E > 6 or \ 

447 0 > N or N > 12: 

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

449 N = 19 - N 

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

451 _i2c((N * 5) % 25 + (E % 5)) 

452 t = enstr2(e, n, prec, EN) 

453 s = sep 

454 

455 elif prec <= -_EN_WIDE: 

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

457 else: 

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

459 wide=_EN_WIDE + 1) 

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

461 

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

463 

464 

465def _GD_prec2(GD, **prec_et_al): 

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

467 ''' 

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

469 prec = _xkwds_get(prec_et_al, prec=_EN_WIDE) 

470 GD = prec > 0 

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

472 elif isbool(GD): 

473 prec = _xkwds_get(prec_et_al, prec=0) 

474 else: 

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

476 return GD, prec 

477 

478 

479def _ll2datum(ll, datum, name): 

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

481 ''' 

482 if datum: 

483 try: 

484 if ll.datum != datum: 

485 ll = ll.toDatum(datum) 

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

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

488 return ll 

489 

490 

491def _ll2LatLon3(ll, LatLon, datum, LatLon_kwds): 

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

493 ''' 

494 n = nameof(ll) 

495 if LatLon is None: 

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

497 r = LatLonDatum3Tuple(r.lat, r.lon, r.datum, name=n) 

498 else: # must be ellipsoidal 

499 _xsubclassof(_LLEB, LatLon=LatLon) 

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

501 r = LatLon(r.lat, r.lon, datum=r.datum, **_xkwds(LatLon_kwds, name=n)) 

502 if r._iteration != ll._iteration: 

503 r._iteration = ll._iteration 

504 return r 

505 

506 

507def parseOSGR(strOSGR, Osgr=Osgr, **name_Osgr_kwds): 

508 '''Parse a string representing an OS Grid Reference, consisting of C{"[GD] 

509 easting northing"}. 

510 

511 Accepts standard OS Grid References like "SU 387 148", with or without 

512 whitespace separators, from 2- up to 22-digit references, or all-numeric, 

513 comma-separated references in meters, for example "438700,114800". 

514 

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

516 @kwarg Osgr: Optional class to return the OSGR coordinate (L{Osgr}) or C{None}. 

517 @kwarg name_Osgr_kwds: Optional C{B{name}=NN} (C{str}) and optionally, additional 

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

519 

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

521 L{EasNor2Tuple}C{(easting, northing)}. 

522 

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

524 ''' 

525 def _c2i(G): 

526 g = ord(G.upper()) - _ord_A 

527 if g > 7: 

528 g -= 1 

529 if g < 0 or g > 25: 

530 raise ValueError 

531 return g 

532 

533 def _OSGR(strOSGR, Osgr, kwds): 

534 s = _splituple(strOSGR.strip()) 

535 p = len(s) 

536 if not p: 

537 raise ValueError 

538 g = s[0] 

539 if p == 2 and isfloat(g, both=True): # "easting,northing" 

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

541 

542 else: 

543 if p == 1: # "GReastingnorthing" 

544 s = halfs2(g[2:]) 

545 g = g[:2] 

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

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

548 g = g[:2] # ... compatibility 

549 elif p != 3: 

550 raise ValueError 

551 else: # "GR easting northing" 

552 s = s[1:] 

553 

554 e, n = map(_c2i, g) 

555 n, m = divmod(n, 5) 

556 E = ((e - 2) % 5) * 5 + m 

557 N = 19 - (e // 5) * 5 - n 

558 if 0 > E or E > 6 or \ 

559 0 > N or N > 12: 

560 raise ValueError 

561 

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

563 e += E * _100km 

564 n += N * _100km 

565 

566 name, kwds = _name2__(**kwds) 

567 if Osgr is None: 

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

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

570 else: 

571 r = Osgr(e, n, name=name, **_xkwds(kwds, resolution=m)) 

572 return r 

573 

574 return _parseX(_OSGR, strOSGR, Osgr, name_Osgr_kwds, 

575 strOSGR=strOSGR, Error=OSGRError) 

576 

577 

578def toOsgr(latlon, lon=None, kTM=False, datum=_WGS84, Osgr=Osgr, # MCCABE 14 

579 **prec_name_Osgr_kwds): 

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

581 

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

583 C{LatLon} point. 

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

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

586 module L{ktm}, otherwise use the Ordnance Survey 

587 formulation (C{bool}). 

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

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

590 L{a_f2Tuple}). 

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

592 (L{Osgr}) or C{None}. 

593 @kwarg prec_name_Osgr_kwds: Optional C{B{name}=NN} (C{str}), 

594 optional L{truncate} precision C{B{prec}=ndigits} 

595 and additional B{C{Osgr}} keyword arguments, 

596 ignored if C{B{Osgr} is None}. 

597 

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

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

600 

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

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

603 

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

605 

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

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

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

609 ''' 

610 if lon is not None: 

611 try: 

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

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

614 except Exception as x: 

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

616 elif not isinstance(latlon, _LLEB): 

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

618 

619 NG = _NG 

620 # convert latlon to OSGB36 first 

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

622 

623 if kTM: 

624 e, n = NG.forward2(ll) 

625 

626 else: 

627 try: 

628 a, b = ll.philam 

629 except AttributeError: 

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

631 

632 sa, ca, ta = sincostan3(a) 

633 v, v_r, n2 = NG.nu_rho_eta3(sa) 

634 

635 m0 = NG.Mabcd0(a) 

636 b -= NG.lam0 

637 t = b * sa * v / 2 

638 d = b * ca 

639 d2 = d**2 

640 

641 ta2 = -(ta**2) 

642 ta4 = ta2**2 

643 

644 e = (d * v * ( 1 + # Horner-like 

645 d2 / 6 * (_Fsumf_(v_r, ta2) + 

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

647 58 * n2 * ta2)))).fsum_(NG.eas0) 

648 

649 n = (d * t * ( 1 + # Horner-like 

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

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

652 

653 t, kwds = _name2__(prec_name_Osgr_kwds, _or_nameof=latlon) 

654 if kwds: 

655 p, kwds = _xkwds_pop2(kwds, prec=MISSING) 

656 if p is not MISSING: 

657 e = truncate(e, p) 

658 n = truncate(n, p) 

659 

660 if Osgr is None: 

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

662 r = EasNor2Tuple(e, n, name=t) 

663 else: 

664 r = Osgr(e, n, name=t, **kwds) # datum=NG.datum 

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

666 if kTM: 

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

668 else: 

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

670 return r 

671 

672 

673if __name__ == '__main__': 

674 

675 from pygeodesy import printf 

676 from random import random, seed 

677 from time import localtime 

678 

679 seed(localtime().tm_yday) 

680 

681 def _rnd(X, n): 

682 X -= 2 

683 d = set() 

684 while len(d) < n: 

685 r = 1 + int(random() * X) 

686 if r not in d: 

687 d.add(r) 

688 yield r 

689 

690 D = _NG.datum 

691 i = t = 0 

692 t1 = t2 = 0, 0, 0, 0 

693 for e in _rnd(_NG.easX, 256): 

694 for n in _rnd(_NG.norX, 512): 

695 p = False 

696 t += 1 

697 

698 g = Osgr(e, n) 

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

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

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

702 if d > t1[2]: 

703 t1 = e, n, d, t 

704 p = True 

705 

706 ll = _LLEB((v.lat + k.lat) / 2, 

707 (v.lon + k.lon) / 2, datum=D) 

708 v = ll.toOsgr(kTM=False) 

709 k = ll.toOsgr(kTM=True) 

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

711 fabs(v.northing - k.northing)) 

712 if d > t2[2]: 

713 t2 = ll.lat, ll.lon, d, t 

714 p = True 

715 

716 if p: 

717 i += 1 

718 printf('%5d: %s %s', i, 

719 'll(%.2f, %.2f) %.3e %d' % t2, 

720 'en(%d, %d) %.3e %d' % t1) 

721 printf('%d total %s', t, D.name) 

722 

723# **) MIT License 

724# 

725# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

726# 

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

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

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

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

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

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

733# 

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

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

736# 

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

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

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

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

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

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

743# OTHER DEALINGS IN THE SOFTWARE. 

744 

745# % python3 -m pygeodesy.osgr 

746# 1: ll(53.42, -0.59) 4.672e-07 1 en(493496, 392519) 2.796e-11 1 

747# 2: ll(60.86, -0.28) 2.760e-05 2 en(493496, 1220986) 2.509e-10 2 

748# 3: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1281644) 2.774e-10 13 

749# 4: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192797) 3.038e-10 20 

750# 5: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192249) 3.073e-10 120 

751# 6: ll(61.55, -0.24) 3.120e-05 160 en(493496, 1192249) 3.073e-10 120 

752# 7: ll(61.55, -0.24) 3.122e-05 435 en(493496, 1192249) 3.073e-10 120 

753# 8: ll(61.57, -0.24) 3.130e-05 473 en(493496, 1192249) 3.073e-10 120 

754# 9: ll(58.66, -8.56) 8.084e-04 513 en(19711, 993800) 3.020e-06 513 

755# 10: ll(52.83, -7.65) 8.156e-04 518 en(19711, 993800) 3.020e-06 513 

756# 11: ll(51.55, -7.49) 8.755e-04 519 en(19711, 993800) 3.020e-06 513 

757# 12: ll(60.20, -8.87) 9.439e-04 521 en(19711, 1165686) 4.318e-06 521 

758# 13: ll(60.45, -8.92) 9.668e-04 532 en(19711, 1194002) 4.588e-06 532 

759# 14: ll(61.17, -9.08) 1.371e-03 535 en(19711, 1274463) 5.465e-06 535 

760# 15: ll(61.31, -9.11) 1.463e-03 642 en(19711, 1290590) 5.663e-06 642 

761# 16: ll(61.35, -9.12) 1.488e-03 807 en(19711, 1294976) 5.718e-06 807 

762# 17: ll(61.38, -9.13) 1.510e-03 929 en(19711, 1298667) 5.765e-06 929 

763# 18: ll(61.11, -9.24) 1.584e-03 11270 en(10307, 1268759) 6.404e-06 11270 

764# 19: ll(61.20, -9.26) 1.650e-03 11319 en(10307, 1278686) 6.545e-06 11319 

765# 20: ll(61.23, -9.27) 1.676e-03 11383 en(10307, 1282514) 6.600e-06 11383 

766# 21: ll(61.36, -9.30) 1.776e-03 11437 en(10307, 1297037) 6.816e-06 11437 

767# 22: ll(61.38, -9.30) 1.789e-03 11472 en(10307, 1298889) 6.844e-06 11472 

768# 23: ll(61.25, -9.39) 1.885e-03 91137 en(4367, 1285831) 7.392e-06 91137 

769# 24: ll(61.32, -9.40) 1.944e-03 91207 en(4367, 1293568) 7.519e-06 91207 

770# 25: ll(61.34, -9.41) 1.963e-03 91376 en(4367, 1296061) 7.561e-06 91376 

771# 26: ll(61.37, -9.41) 1.986e-03 91595 en(4367, 1298908) 7.608e-06 91595 

772# 131072 total OSGB36