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__ = '24.05.13' 

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 _F = _Fsumf_ 

328 e0 = self.easting - NG.eas0 

329 n0 = m = self.northing - NG.nor0 

330 

331 a0 = NG.a0 

332 _M = NG.Mabcd0 

333 a = NG.phi0 

334 _a = fabs 

335 _A = _F(a).fsum_ 

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

337 a = _A(m / a0) 

338 m = n0 - _M(a) # meridional arc 

339 if _a(m) < eps: 

340 break 

341 else: # PYCHOK no cover 

342 t = str(self) 

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

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

345 t = unstr(t, eps=eps, kTM=kTM) 

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

347 

348 sa, ca, ta = sincostan3(a) 

349 v, v_r, n2 = NG.nu_rho_eta3(sa) 

350 

351 ta2 = ta**2 

352 ta4 = ta2**2 

353 

354 ta *= v_r / 2 

355 d = e0 / v 

356 d2 = d**2 

357 

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

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

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

361 

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

363 d2 / 6 * (_F(v_r, 2 * ta2) - 

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

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

366 720 * ta2 * ta4))))).fsum_(NG.lam0) 

367 

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

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

370 self._latlon = r 

371 else: 

372 r = self._latlon 

373 

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

375 

376 @Property_RO 

377 def scale0(self): 

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

379 ''' 

380 return _NG.k0 

381 

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

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

384 

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

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

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

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

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

390 3-C{tuple} of C{str}s. 

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

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

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

394 

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

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

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

398 

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

400 

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

402 and C{B{GD}=False}. 

403 

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

405 ''' 

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

407 

408 if GD: 

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

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

411 else: 

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

413 if fmt: 

414 t = fmt % (t,) 

415 return t 

416 

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

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

419 

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

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

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

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

424 3-C{tuple} of C{str}s. 

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

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

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

428 

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

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

431 C{"easting.d,northing.d"} 

432 

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

434 

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

436 < -4} and C{B{GD}=False}. 

437 

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

439 ''' 

440 def _i2c(i): 

441 if i > 7: 

442 i += 1 

443 return chr(_ord_A + i) 

444 

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

446 

447 if GD: 

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

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

450 E, N = int(E), int(N) 

451 if 0 > E or E > 6 or \ 

452 0 > N or N > 12: 

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

454 N = 19 - N 

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

456 _i2c((N * 5) % 25 + (E % 5)) 

457 t = enstr2(e, n, prec, EN) 

458 s = sep 

459 

460 elif prec <= -_EN_WIDE: 

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

462 else: 

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

464 wide=_EN_WIDE + 1) 

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

466 

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

468 

469 

470def _GD_prec2(GD, **prec_et_al): 

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

472 ''' 

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

474 prec = _xkwds_get(prec_et_al, prec=_EN_WIDE) 

475 GD = prec > 0 

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

477 elif isbool(GD): 

478 prec = _xkwds_get(prec_et_al, prec=0) 

479 else: 

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

481 return GD, prec 

482 

483 

484def _ll2datum(ll, datum, name): 

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

486 ''' 

487 if datum: 

488 try: 

489 if ll.datum != datum: 

490 ll = ll.toDatum(datum) 

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

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

493 return ll 

494 

495 

496def _ll2LatLon3(ll, LatLon, datum, LatLon_kwds): 

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

498 ''' 

499 if LatLon is None: 

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

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

502 else: # must be ellipsoidal 

503 _xsubclassof(_LLEB, LatLon=LatLon) 

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

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

506 if r._iteration != ll._iteration: 

507 r._iteration = ll._iteration 

508 return _xnamed(r, nameof(ll)) 

509 

510 

511def parseOSGR(strOSGR, Osgr=Osgr, name=NN, **Osgr_kwds): 

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

513 of C{"[GD] easting northing"}. 

514 

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

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

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

518 meters, for example "438700,114800". 

519 

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

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

522 (L{Osgr}) or C{None}. 

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

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

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

526 

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

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

529 

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

531 ''' 

532 def _c2i(G): 

533 g = ord(G.upper()) - _ord_A 

534 if g > 7: 

535 g -= 1 

536 if g < 0 or g > 25: 

537 raise ValueError 

538 return g 

539 

540 def _OSGR(strOSGR, Osgr, name): 

541 s = _splituple(strOSGR.strip()) 

542 p = len(s) 

543 if not p: 

544 raise ValueError 

545 g = s[0] 

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

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

548 

549 else: 

550 if p == 1: # "GReastingnorthing" 

551 s = halfs2(g[2:]) 

552 g = g[:2] 

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

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

555 g = g[:2] # ... compatibility 

556 elif p != 3: 

557 raise ValueError 

558 else: # "GR easting northing" 

559 s = s[1:] 

560 

561 e, n = map(_c2i, g) 

562 n, m = divmod(n, 5) 

563 E = ((e - 2) % 5) * 5 + m 

564 N = 19 - (e // 5) * 5 - n 

565 if 0 > E or E > 6 or \ 

566 0 > N or N > 12: 

567 raise ValueError 

568 

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

570 e += E * _100km 

571 n += N * _100km 

572 

573 if Osgr is None: 

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

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

576 else: 

577 r = Osgr(e, n, name=name, 

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

579 return r 

580 

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

582 strOSGR=strOSGR, Error=OSGRError) 

583 

584 

585def toOsgr(latlon, lon=None, kTM=False, datum=_WGS84, Osgr=Osgr, name=NN, # MCCABE 14 

586 **prec_Osgr_kwds): 

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

588 

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

590 C{LatLon} point. 

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

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

593 module L{ktm}, otherwise use the Ordnance 

594 Survey formulation (C{bool}). 

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

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

597 L{a_f2Tuple}). 

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

599 (L{Osgr}) or C{None}. 

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

601 @kwarg prec_Osgr_kwds: Optional L{truncate} precision 

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

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

604 if C{B{Osgr} is None}. 

605 

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

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

608 

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

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

611 

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

613 

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

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

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

617 ''' 

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

619 return prec, kwds 

620 

621 if lon is not None: 

622 try: 

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

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

625 except Exception as x: 

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

627 elif not isinstance(latlon, _LLEB): 

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

629 elif not name: # use latlon.name 

630 name = nameof(latlon) 

631 

632 NG = _NG 

633 # convert latlon to OSGB36 first 

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

635 

636 if kTM: 

637 e, n = NG.forward2(ll) 

638 

639 else: 

640 try: 

641 a, b = ll.philam 

642 except AttributeError: 

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

644 

645 sa, ca, ta = sincostan3(a) 

646 v, v_r, n2 = NG.nu_rho_eta3(sa) 

647 

648 m0 = NG.Mabcd0(a) 

649 b -= NG.lam0 

650 t = b * sa * v / 2 

651 d = b * ca 

652 d2 = d**2 

653 

654 ta2 = -(ta**2) 

655 ta4 = ta2**2 

656 

657 e = (d * v * ( 1 + # Horner-like 

658 d2 / 6 * (_Fsumf_(v_r, ta2) + 

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

660 58 * n2 * ta2)))).fsum_(NG.eas0) 

661 

662 n = (d * t * ( 1 + # Horner-like 

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

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

665 

666 p, kwds = _prec_kwds2(**prec_Osgr_kwds) 

667 if p is not MISSING: 

668 e = truncate(e, p) 

669 n = truncate(n, p) 

670 

671 if Osgr is None: 

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

673 r = EasNor2Tuple(e, n) 

674 else: 

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

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

677 if kTM: 

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

679 else: 

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

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

682 

683 

684if __name__ == '__main__': 

685 

686 from pygeodesy import printf 

687 from random import random, seed 

688 from time import localtime 

689 

690 seed(localtime().tm_yday) 

691 

692 def _rnd(X, n): 

693 X -= 2 

694 d = set() 

695 while len(d) < n: 

696 r = 1 + int(random() * X) 

697 if r not in d: 

698 d.add(r) 

699 yield r 

700 

701 D = _NG.datum 

702 i = t = 0 

703 t1 = t2 = 0, 0, 0, 0 

704 for e in _rnd(_NG.easX, 256): 

705 for n in _rnd(_NG.norX, 512): 

706 p = False 

707 t += 1 

708 

709 g = Osgr(e, n) 

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

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

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

713 if d > t1[2]: 

714 t1 = e, n, d, t 

715 p = True 

716 

717 ll = _LLEB((v.lat + k.lat) / 2, 

718 (v.lon + k.lon) / 2, datum=D) 

719 v = ll.toOsgr(kTM=False) 

720 k = ll.toOsgr(kTM=True) 

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

722 fabs(v.northing - k.northing)) 

723 if d > t2[2]: 

724 t2 = ll.lat, ll.lon, d, t 

725 p = True 

726 

727 if p: 

728 i += 1 

729 printf('%5d: %s %s', i, 

730 'll(%.2f, %.2f) %.3e %d' % t2, 

731 'en(%d, %d) %.3e %d' % t1) 

732 printf('%d total %s', t, D.name) 

733 

734# **) MIT License 

735# 

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

737# 

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

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

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

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

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

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

744# 

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

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

747# 

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

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

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

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

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

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

754# OTHER DEALINGS IN THE SOFTWARE. 

755 

756# % python3 -m pygeodesy.osgr 

757# 1: ll(53.42, -0.59) 4.672e-07 1 en(493496, 392519) 2.796e-11 1 

758# 2: ll(60.86, -0.28) 2.760e-05 2 en(493496, 1220986) 2.509e-10 2 

759# 3: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1281644) 2.774e-10 13 

760# 4: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192797) 3.038e-10 20 

761# 5: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192249) 3.073e-10 120 

762# 6: ll(61.55, -0.24) 3.120e-05 160 en(493496, 1192249) 3.073e-10 120 

763# 7: ll(61.55, -0.24) 3.122e-05 435 en(493496, 1192249) 3.073e-10 120 

764# 8: ll(61.57, -0.24) 3.130e-05 473 en(493496, 1192249) 3.073e-10 120 

765# 9: ll(58.66, -8.56) 8.084e-04 513 en(19711, 993800) 3.020e-06 513 

766# 10: ll(52.83, -7.65) 8.156e-04 518 en(19711, 993800) 3.020e-06 513 

767# 11: ll(51.55, -7.49) 8.755e-04 519 en(19711, 993800) 3.020e-06 513 

768# 12: ll(60.20, -8.87) 9.439e-04 521 en(19711, 1165686) 4.318e-06 521 

769# 13: ll(60.45, -8.92) 9.668e-04 532 en(19711, 1194002) 4.588e-06 532 

770# 14: ll(61.17, -9.08) 1.371e-03 535 en(19711, 1274463) 5.465e-06 535 

771# 15: ll(61.31, -9.11) 1.463e-03 642 en(19711, 1290590) 5.663e-06 642 

772# 16: ll(61.35, -9.12) 1.488e-03 807 en(19711, 1294976) 5.718e-06 807 

773# 17: ll(61.38, -9.13) 1.510e-03 929 en(19711, 1298667) 5.765e-06 929 

774# 18: ll(61.11, -9.24) 1.584e-03 11270 en(10307, 1268759) 6.404e-06 11270 

775# 19: ll(61.20, -9.26) 1.650e-03 11319 en(10307, 1278686) 6.545e-06 11319 

776# 20: ll(61.23, -9.27) 1.676e-03 11383 en(10307, 1282514) 6.600e-06 11383 

777# 21: ll(61.36, -9.30) 1.776e-03 11437 en(10307, 1297037) 6.816e-06 11437 

778# 22: ll(61.38, -9.30) 1.789e-03 11472 en(10307, 1298889) 6.844e-06 11472 

779# 23: ll(61.25, -9.39) 1.885e-03 91137 en(4367, 1285831) 7.392e-06 91137 

780# 24: ll(61.32, -9.40) 1.944e-03 91207 en(4367, 1293568) 7.519e-06 91207 

781# 25: ll(61.34, -9.41) 1.963e-03 91376 en(4367, 1296061) 7.561e-06 91376 

782# 26: ll(61.37, -9.41) 1.986e-03 91595 en(4367, 1298908) 7.608e-06 91595 

783# 131072 total OSGB36