1

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

3

4 u'''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

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

8

9 A 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

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

13

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

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

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

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

18

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

20 Karney'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>},

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

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

24 and 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

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

28

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

30 _splituple, _xsubclassof

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

32 from pygeodesy.datums import Datums, _ellipsoidal_datum, _WGS84

33# from pygeodesy.dms import parseDMS2 # _MODS

34 from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB

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

36 _xkwds, _xkwds_get

37 from pygeodesy.fmath import Fdot, fpowers, Fsum

38# from pygeodesy.fsums import Fsum # from .fmath

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

40 _COMMASPACE_, _DOT_, _ellipsoidal_, \

41 _latlon_, _not_, _SPACE_

42 from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS

43 from pygeodesy.named import _NamedBase, nameof, _xnamed

44 from pygeodesy.namedTuples import EasNor2Tuple, LatLon2Tuple, \

45 LatLonDatum3Tuple

46 from pygeodesy.props import Property_RO, property_RO

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

48 _resolution10, unstr, _xzipairs

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

50 Phi_, Scalar, _10um, _100km

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

52

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

54

55__all__ = _ALL_LAZY.osgr

56__version__ = '23.08.24'

57

58_equivalent_ = 'equivalent'

59_OSGR_ = 'OSGR'

60_ord_A = ord(_A_)

61_TRIPS = 33 # .toLatLon convergence

62

63

64 class _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 = (Fsum(4, 4 * n, 5 * n2, 5 * n3) / 4,

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

126 Fsum( 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

179 class OSGRError(_ValueError):

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

181 '''

182 pass

183

184

185 class 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 @example:

323

324 >>> from pygeodesy import Datums, ellipsoidalVincenty as eV, Osgr

325 >>> g = Osgr(651409.903, 313177.270)

326 >>> p = g.toLatLon(eV.LatLon) # 52°39′28.723″N, 001°42′57.787″E

327 >>> p = g.toLatLon(eV.LatLon, kTM=True) # 52°39′28.723″N, 001°42′57.787″E

328 >>> # to obtain (historical) OSGB36 lat-/longitude point

329 >>> p = g.toLatLon(eV.LatLon, datum=Datums.OSGB36) # 52°39′27.253″N, 001°43′04.518″E

330 '''

331 NG = _NG

332 if kTM:

333 r = NG.reverse(self)

334

335 elif self._latlon is None:

336 e0 = self.easting - NG.eas0

337 n0 = m = self.northing - NG.nor0

338

339 _M = NG.Mabcd0

340 a0 = NG.a0

341 a = NG.phi0

342 _A = Fsum(a).fsum_

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

344 a = _A(m / a0)

345 m = n0 - _M(a) # meridional arc

346 if fabs(m) < eps:

347 break

348 else: # PYCHOK no cover

349 t = str(self)

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

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

352 t = unstr(t, eps=eps, kTM=kTM)

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

354

355 sa, ca, ta = sincostan3(a)

356 v, v_r, n2 = NG.nu_rho_eta3(sa)

357

358 ta2 = ta**2

359 ta4 = ta2**2

360

361 ta *= v_r / 2

362 d = e0 / v

363 d2 = d**2

364

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

366 d2 / 12 * (Fsum( 5, 3 * ta2, -9 * ta2 * n2, n2) -

367 d2 / 30 * Fsum(61, 90 * ta2, 45 * ta4)))).fsum_(a)

368

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

370 d2 / 6 * (Fsum(v_r, 2 * ta2) -

371 d2 / 20 * (Fsum( 5, 28 * ta2, 24 * ta4) +

372 d2 / 42 * Fsum(61, 662 * ta2, 1320 * ta4,

373 720 * ta2 * ta4))))).fsum_(NG.lam0)

374

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

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

377 self._latlon = r

378 else:

379 r = self._latlon

380

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

382

383 @Property_RO

384 def scale0(self):

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

386 '''

387 return _NG.k0

388

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

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

391

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

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

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

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

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

397 3-C{tuple} of C{str}s.

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

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

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

401

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

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

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

405

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

407

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

409 and C{B{GD}=False}.

410

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

412 '''

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

414

415 if GD:

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

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

418 else:

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

420 if fmt:

421 t = fmt % (t,)

422 return t

423

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

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

426

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

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

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

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

431 3-C{tuple} of C{str}s.

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

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

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

435

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

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

438 C{"easting.d,northing.d"}

439

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

441

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

443 < -4} and C{B{GD}=False}.

444

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

446

447 @example:

448

449 >>> r = Osgr(651409, 313177)

450 >>> str(r) # 'TG 5140 1317'

451 >>> r.toStr() # 'TG5140913177'

452 >>> r.toStr(GD=False) # '651409,313177'

453 '''

454 def _i2c(i):

455 if i > 7:

456 i += 1

457 return chr(_ord_A + i)

458

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

460

461 if GD:

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

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

464 E, N = int(E), int(N)

465 if 0 > E or E > 6 or \

466 0 > N or N > 12:

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

468 N = 19 - N

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

470 _i2c((N * 5) % 25 + (E % 5))

471 t = enstr2(e, n, prec, EN)

472 s = sep

473

474 elif prec <= -_EN_WIDE:

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

476 else:

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

478 wide=_EN_WIDE + 1)

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

480

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

482

483

484 def _GD_prec2(GD, **prec_et_al):

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

486 '''

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

488 prec = _xkwds_get(prec_et_al, prec=_EN_WIDE)

489 GD = prec > 0

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

491 elif isbool(GD):

492 prec = _xkwds_get(prec_et_al, prec=0)

493 else:

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

495 return GD, prec

496

497

498 def _ll2datum(ll, datum, name):

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

500 '''

501 if datum:

502 try:

503 if ll.datum != datum:

504 ll = ll.toDatum(datum)

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

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

507 return ll

508

509

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

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

512 '''

513 if LatLon is None:

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

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

516 else: # must be ellipsoidal

517 _xsubclassof(_LLEB, LatLon=LatLon)

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

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

520 if r._iteration != ll._iteration:

521 r._iteration = ll._iteration

522 return _xnamed(r, nameof(ll))

523

524

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

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

527 of C{"[GD] easting northing"}.

528

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

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

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

532 meters, for example "438700,114800".

533

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

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

536 (L{Osgr}) or C{None}.

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

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

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

540

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

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

543

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

545

546 @example:

547

548 >>> r = parseOSGR('TG5140913177')

549 >>> str(r) # 'TG 51409 13177'

550 >>> r = parseOSGR('TG 51409 13177')

551 >>> r.toStr() # 'TG5140913177'

552 >>> r = parseOSGR('651409,313177')

553 >>> r.toStr(sep=' ') # 'TG 51409 13177'

554 >>> r.toStr(GD=False) # '651409,313177'

555 '''

556 def _c2i(G):

557 g = ord(G.upper()) - _ord_A

558 if g > 7:

559 g -= 1

560 if g < 0 or g > 25:

561 raise ValueError

562 return g

563

564 def _OSGR(strOSGR, Osgr, name):

565 s = _splituple(strOSGR.strip())

566 p = len(s)

567 if not p:

568 raise ValueError

569 g = s[0]

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

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

572

573 else:

574 if p == 1: # "GReastingnorthing"

575 s = halfs2(g[2:])

576 g = g[:2]

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

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

579 g = g[:2] # ... compatibility

580 elif p != 3:

581 raise ValueError

582 else: # "GR easting northing"

583 s = s[1:]

584

585 e, n = map(_c2i, g)

586 n, m = divmod(n, 5)

587 E = ((e - 2) % 5) * 5 + m

588 N = 19 - (e // 5) * 5 - n

589 if 0 > E or E > 6 or \

590 0 > N or N > 12:

591 raise ValueError

592

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

594 e += E * _100km

595 n += N * _100km

596

597 if Osgr is None:

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

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

600 else:

601 r = Osgr(e, n, name=name,

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

603 return r

604

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

606 strOSGR=strOSGR, Error=OSGRError)

607

608

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

610 **prec_Osgr_kwds):

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

612

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

614 C{LatLon} point.

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

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

617 module L{ktm}, otherwise use the Ordnance

618 Survey formulation (C{bool}).

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

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

621 L{a_f2Tuple}).

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

623 (L{Osgr}) or C{None}.

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

625 @kwarg prec_Osgr_kwds: Optional L{truncate} precision

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

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

628 if C{B{Osgr} is None}.

629

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

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

632

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

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

635

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

637

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

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

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

641

642 @example:

643

644 >>> p = LatLon(52.65798, 1.71605)

645 >>> r = toOsgr(p) # [G:TG, E:51409, N:13177]

646 >>> # for conversion of (historical) OSGB36 lat-/longitude:

647 >>> r = toOsgr(52.65757, 1.71791, datum=Datums.OSGB36)

648 >>> # alternatively and using Krüger

649 >>> r = p.toOsgr(kTM=True) # [G:TG, E:51409, N:13177]

650 '''

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

652 return prec, kwds

653

654 if lon is not None:

655 try:

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

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

658 except Exception as x:

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

660 elif not isinstance(latlon, _LLEB):

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

662 elif not name: # use latlon.name

663 name = nameof(latlon)

664

665 NG = _NG

666 # convert latlon to OSGB36 first

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

668

669 if kTM:

670 e, n = NG.forward2(ll)

671

672 else:

673 try:

674 a, b = ll.philam

675 except AttributeError:

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

677

678 sa, ca, ta = sincostan3(a)

679 v, v_r, n2 = NG.nu_rho_eta3(sa)

680

681 m0 = NG.Mabcd0(a)

682 b -= NG.lam0

683 t = b * sa * v / 2

684 d = b * ca

685 d2 = d**2

686

687 ta2 = -(ta**2)

688 ta4 = ta2**2

689

690 e = (d * v * (1 + # Horner-like

691 d2 / 6 * (Fsum(v_r, ta2) +

692 d2 / 20 * Fsum(5, 18 * ta2, ta4, 14 * n2,

693 58 * n2 * ta2)))).fsum_(NG.eas0)

694

695 n = (d * t * (1 + # Horner-like

696 d2 / 12 * (Fsum( 5, ta2, 9 * n2) +

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

698

699 p, kwds = _prec_kwds2(**prec_Osgr_kwds)

700 if p is not MISSING:

701 e = truncate(e, p)

702 n = truncate(n, p)

703

704 if Osgr is None:

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

706 r = EasNor2Tuple(e, n)

707 else:

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

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

710 if kTM:

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

712 else:

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

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

715

716

717 if __name__ == '__main__':

718

719 from pygeodesy.lazily import printf

720 from random import random, seed

721 from time import localtime

722

723 seed(localtime().tm_yday)

724

725 def _rnd(X, n):

726 X -= 2

727 d = set()

728 while len(d) < n:

729 r = 1 + int(random() * X)

730 if r not in d:

731 d.add(r)

732 yield r

733

734 D = _NG.datum

735 i = t = 0

736 t1 = t2 = 0, 0, 0, 0

737 for e in _rnd(_NG.easX, 256):

738 for n in _rnd(_NG.norX, 512):

739 p = False

740 t += 1

741

742 g = Osgr(e, n)

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

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

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

746 if d > t1[2]:

747 t1 = e, n, d, t

748 p = True

749

750 ll = _LLEB((v.lat + k.lat) / 2,

751 (v.lon + k.lon) / 2, datum=D)

752 v = ll.toOsgr(kTM=False)

753 k = ll.toOsgr(kTM=True)

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

755 fabs(v.northing - k.northing))

756 if d > t2[2]:

757 t2 = ll.lat, ll.lon, d, t

758 p = True

759

760 if p:

761 i += 1

762 printf('%5d: %s %s', i,

763 'll(%.2f, %.2f) %.3e %d' % t2,

764 'en(%d, %d) %.3e %d' % t1)

765 printf('%d total %s', t, D.name)

766

767# **) MIT License

768#

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

770#

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

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

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

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

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

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

777#

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

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

780#

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

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

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

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

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

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

787# OTHER DEALINGS IN THE SOFTWARE.

788

789# % python3 -m pygeodesy.osgr

790# 1: ll(53.42, -0.59) 4.672e-07 1 en(493496, 392519) 2.796e-11 1

791# 2: ll(60.86, -0.28) 2.760e-05 2 en(493496, 1220986) 2.509e-10 2

792# 3: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1281644) 2.774e-10 13

793# 4: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192797) 3.038e-10 20

794# 5: ll(61.41, -0.25) 3.045e-05 13 en(493496, 1192249) 3.073e-10 120

795# 6: ll(61.55, -0.24) 3.120e-05 160 en(493496, 1192249) 3.073e-10 120

796# 7: ll(61.55, -0.24) 3.122e-05 435 en(493496, 1192249) 3.073e-10 120

797# 8: ll(61.57, -0.24) 3.130e-05 473 en(493496, 1192249) 3.073e-10 120

798# 9: ll(58.66, -8.56) 8.084e-04 513 en(19711, 993800) 3.020e-06 513

799# 10: ll(52.83, -7.65) 8.156e-04 518 en(19711, 993800) 3.020e-06 513

800# 11: ll(51.55, -7.49) 8.755e-04 519 en(19711, 993800) 3.020e-06 513

801# 12: ll(60.20, -8.87) 9.439e-04 521 en(19711, 1165686) 4.318e-06 521

802# 13: ll(60.45, -8.92) 9.668e-04 532 en(19711, 1194002) 4.588e-06 532

803# 14: ll(61.17, -9.08) 1.371e-03 535 en(19711, 1274463) 5.465e-06 535

804# 15: ll(61.31, -9.11) 1.463e-03 642 en(19711, 1290590) 5.663e-06 642

805# 16: ll(61.35, -9.12) 1.488e-03 807 en(19711, 1294976) 5.718e-06 807

806# 17: ll(61.38, -9.13) 1.510e-03 929 en(19711, 1298667) 5.765e-06 929

807# 18: ll(61.11, -9.24) 1.584e-03 11270 en(10307, 1268759) 6.404e-06 11270

808# 19: ll(61.20, -9.26) 1.650e-03 11319 en(10307, 1278686) 6.545e-06 11319

809# 20: ll(61.23, -9.27) 1.676e-03 11383 en(10307, 1282514) 6.600e-06 11383

810# 21: ll(61.36, -9.30) 1.776e-03 11437 en(10307, 1297037) 6.816e-06 11437

811# 22: ll(61.38, -9.30) 1.789e-03 11472 en(10307, 1298889) 6.844e-06 11472

812# 23: ll(61.25, -9.39) 1.885e-03 91137 en(4367, 1285831) 7.392e-06 91137

813# 24: ll(61.32, -9.40) 1.944e-03 91207 en(4367, 1293568) 7.519e-06 91207

814# 25: ll(61.34, -9.41) 1.963e-03 91376 en(4367, 1296061) 7.561e-06 91376

815# 26: ll(61.37, -9.41) 1.986e-03 91595 en(4367, 1298908) 7.608e-06 91595

816# 131072 total OSGB36