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__ = '23.12.03'

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 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 = Fsum(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 * (Fsum( 5, 3 * ta2, -9 * ta2 * n2, n2) -

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

359

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

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

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

363 d2 / 42 * Fsum(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

468 def _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

482 def _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

494 def _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

509 def 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

583 def 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 * (Fsum(v_r, ta2) +

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

658 58 * n2 * ta2)))).fsum_(NG.eas0)

659

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

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

662 d2 / 30 * Fsum(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

682 if __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