1

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

3

4 u'''I{Veness}' Universal Transverse Mercator (UTM) projection.

5

6 Classes L{Utm} and L{UTMError} and functions L{parseUTM5}, L{toUtm8} and

7 L{utmZoneBand5}.

8

9 Pure Python implementation of UTM / WGS-84 conversion functions using

10 an ellipsoidal earth model, transcoded from JavaScript originals by

11 I{(C) Chris Veness 2011-2024} published under the same MIT Licence**, see

12 U{UTM<https://www.Movable-Type.co.UK/scripts/latlong-utm-mgrs.html>} and

13 U{Module utm<https://www.Movable-Type.co.UK/scripts/geodesy/docs/module-utm.html>}.

14

15 The U{UTM<https://WikiPedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>}

16 system is a 2-dimensional Cartesian coordinate system providing another way

17 to identify locations on the surface of the earth. UTM is a set of 60

18 transverse Mercator projections, normally based on the WGS-84 ellipsoid.

19 Within each zone, coordinates are represented as B{C{easting}}s and B{C{northing}}s,

20 measured in metres.

21

22 This module includes some of I{Charles Karney}'s U{'Transverse Mercator with an

23 accuracy of a few nanometers'<https://ArXiv.org/pdf/1002.1417v3.pdf>}, 2011

24(building on Krüger's U{'Konforme Abbildung des Erdellipsoids in der Ebene'

25<https://bib.GFZ-Potsdam.DE/pub/digi/krueger2.pdf>}, 1912) and C++ class

26 U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/

27 classGeographicLib_1_1TransverseMercator.html>}.

28

29 Some other references are U{Universal Transverse Mercator coordinate system

30<https://WikiPedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>},

31 U{Transverse Mercator Projection<https://GeographicLib.SourceForge.io/tm.html>}

32 and Henrik Seidel U{'Die Mathematik der Gauß-Krueger-Abbildung'

33<https://DE.WikiPedia.org/wiki/Gauß-Krüger-Koordinatensystem>}, 2006.

34'''

35

36 from pygeodesy.basics import len2, map2, neg # splice

37 from pygeodesy.constants import EPS, EPS0, _K0_UTM, _0_0, _0_0001

38 from pygeodesy.datums import _ellipsoidal_datum, _WGS84, _under

39 from pygeodesy.dms import degDMS, parseDMS2

40 from pygeodesy.errors import MGRSError, RangeError, _ValueError, \

41 _xkwds_get, _xkwds_pop2

42 from pygeodesy.fmath import fdot_, fdot3, hypot, hypot1, _operator

43# from pygeodesy.internals import _under # from .datums

44 from pygeodesy.interns import MISSING, NN, _by_, _COMMASPACE_, _N_, \

45 _NS_, _outside_, _range_, _S_, _scale0_, \

46 _SPACE_, _UTM_, _V_, _X_, _zone_

47 from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS

48 from pygeodesy.namedTuples import EasNor2Tuple, UtmUps5Tuple, \

49 UtmUps8Tuple, UtmUpsLatLon5Tuple

50 from pygeodesy.props import deprecated_method, property_doc_, \

51 Property_RO

52 from pygeodesy.streprs import Fmt, unstr

53 from pygeodesy.units import Band, Int, Lat, Lon, Meter, Zone

54 from pygeodesy.utily import atan1, atan2, degrees90, degrees180, sincos2

55 from pygeodesy.utmupsBase import _hemi, _LLEB, _parseUTMUPS5, _to4lldn, \

56 _to3zBhp, _to3zll, _UPS_LATS, _UPS_ZONE, \

57 _UTM_LAT_MAX, _UTM_ZONE_MAX, \

58 _UTM_LAT_MIN, _UTM_ZONE_MIN, \

59 _UTM_ZONE_OFF_MAX, UtmUpsBase

60

61 from math import asinh, atanh, cos, cosh, degrees, fabs, radians, \

62 sin, sinh, tan, tanh # tan as _tan

63# import operator as _operator # from .fmath

64

65__all__ = _ALL_LAZY.utm

66__version__ = '24.11.26'

67

68_Bands = 'CDEFGHJKLMNPQRSTUVWXX' # UTM latitude bands C..X (no

69# I|O) 8° each, covering 80°S to 84°N and X repeated for 80-84°N

70_bandLat_ = 'bandLat'

71_FalseEasting = Meter( 500e3) # falsed offset (C{meter})

72_FalseNorthing = Meter(10000e3) # falsed offset (C{meter})

73_SvalbardXzone = {32: 9, 34: 21, 36: 33} # [zone] longitude

74

75

76 class UTMError(_ValueError):

77 '''Universal Transverse Mercator (UTM parse or other L{Utm} issue.

78 '''

79 pass

80

81

82 class _Kseries(object):

83 '''(INTERNAL) Alpha or Beta Krüger series.

84

85 Krüger series summations for B{C{eta}}, B{C{ksi}}, B{C{p}} and B{C{q}},

86 caching the C{cos}, C{cosh}, C{sin} and C{sinh} values for

87 the given B{C{eta}} and B{C{ksi}} angles (in C{radians}).

88 '''

89 def __init__(self, AB, x, y):

90 '''(INTERNAL) New Alpha or Beta Krüger series

91

92 @arg AB: Krüger Alpha or Beta series coefficients

93 (C{4-, 6- or 8-tuple}).

94 @arg x: Eta angle (C{radians}).

95 @arg y: Ksi angle (C{radians}).

96 '''

97 n, j2 = len2(range(2, len(AB) * 2 + 1, 2))

98 _m2, _x = map2, _operator.mul

99

100 self._ab = AB

101 self._pq = _m2(_x, j2, AB)

102# assert len(self._ab) == len(self._pq) == n

103

104 x2 = _m2(_x, j2, (x,) * n)

105 self._chx = _m2(cosh, x2)

106 self._shx = _m2(sinh, x2)

107# assert len(x2) == len(self._chx) == len(self._shx) == n

108

109 y2 = _m2(_x, j2, (y,) * n)

110 self._cy = _m2(cos, y2)

111 self._sy = _m2(sin, y2)

112 # self._sy, self._cy = splice(sincos2(*y2)) # PYCHOK false

113# assert len(y2) == len(self._cy) == len(self._sy) == n

114

115 def xs(self, x0):

116 '''(INTERNAL) Eta summation (C{float}).

117 '''

118 return fdot3(self._ab, self._cy, self._shx, start=x0)

119

120 def ys(self, y0):

121 '''(INTERNAL) Ksi summation (C{float}).

122 '''

123 return fdot3(self._ab, self._sy, self._chx, start=y0)

124

125 def ps(self, p0):

126 '''(INTERNAL) P summation (C{float}).

127 '''

128 return fdot3(self._pq, self._cy, self._chx, start=p0)

129

130 def qs(self, q0):

131 '''(INTERNAL) Q summation (C{float}).

132 '''

133 return fdot3(self._pq, self._sy, self._shx, start=q0)

134

135

136 class Utm(UtmUpsBase):

137 '''Universal Transverse Mercator (UTM) coordinate.

138 '''

139# _band = NN # latitudinal band letter ('C'|..|'X', no 'I'|'O')

140 _Bands = _Bands # latitudinal Band letters (C{tuple})

141 _Error = UTMError # or etm.ETMError

142# _scale = None # grid scale factor (C{scalar}) or C{None}

143 _scale0 = _K0_UTM # central scale factor (C{scalar})

144 _zone = 0 # longitudinal zone (C{int} 1..60)

145

146 def __init__(self, zone=31, hemisphere=_N_, easting=166022, # PYCHOK expected

147 northing=0, band=NN, datum=_WGS84, falsed=True,

148 gamma=None, scale=None, **name_convergence):

149 '''New L{Utm} UTM coordinate.

150

151 @kwarg zone: Longitudinal UTM zone (C{int}, 1..60) or zone with/-out

152 I{latitudinal} Band letter (C{str}, '1C'|..|'60X').

153 @kwarg hemisphere: Northern or southern hemisphere (C{str}, C{'N[orth]'}

154 or C{'S[outh]'}).

155 @kwarg easting: Easting, see B{C{falsed}} (C{meter}).

156 @kwarg northing: Northing, see B{C{falsed}} (C{meter}).

157 @kwarg band: Optional, I{latitudinal} band (C{str}, 'C'|..|'X', no 'I'|'O').

158 @kwarg datum: Optional, this coordinate's datum (L{Datum}, L{Ellipsoid},

159 L{Ellipsoid2} or L{a_f2Tuple}).

160 @kwarg falsed: If C{True}, both B{C{easting}} and B{C{northing}} are

161 falsed (C{bool}).

162 @kwarg gamma: Optional meridian convergence, bearing off grid North,

163 clockwise from true North to save (C{degrees}) or C{None}.

164 @kwarg scale: Optional grid scale factor to save (C{scalar}) or C{None}.

165 @kwarg name_convergence: Optional C{B{name}=NN} (C{str}) and DEPRECATED

166 keyword argument C{B{convergence}=None}, use B{C{gamma}}.

167

168 @raise TypeError: Invalid or near-spherical B{C{datum}}.

169

170 @raise UTMError: Invalid B{C{zone}}, B{C{hemishere}}, B{C{easting}},

171 B{C{northing}}, B{C{band}}, B{C{convergence}} or

172 B{C{scale}}.

173 '''

174 if name_convergence:

175 gamma, name = _xkwds_pop2(name_convergence, convergence=gamma)

176 if name:

177 self.name = name

178

179 self._zone, B, _ = _to3zBlat(zone, band)

180

181 h = str(hemisphere)[:1].upper()

182 if h not in _NS_:

183 raise self._Error(hemisphere=hemisphere)

184 self._hemisphere = h

185

186 e, n = easting, northing # Easting(easting), ...

187# if not falsed:

188# e, n = _false2(e, n, h)

189# # check easting/northing (with 40km overlap

190# # between zones) - is this worthwhile?

191# @raise RangeError: If B{C{easting}} or B{C{northing}} outside

192# the valid UTM range.

193# if 120e3 > e or e > 880e3:

194# raise RangeError(easting=easting)

195# if 0 > n or n > _FalseNorthing:

196# raise RangeError(northing=northing)

197

198 UtmUpsBase.__init__(self, e, n, band=B, datum=datum, falsed=falsed,

199 gamma=gamma, scale=scale)

200

201 def __eq__(self, other):

202 return isinstance(other, Utm) and other.zone == self.zone \

203 and other.hemisphere == self.hemisphere \

204 and other.easting == self.easting \

205 and other.northing == self.northing \

206 and other.band == self.band \

207 and other.datum == self.datum

208

209 def __repr__(self):

210 return self.toRepr(B=True)

211

212 def __str__(self):

213 return self.toStr()

214

215 def _xcopy2(self, Xtm, **name):

216 '''(INTERNAL) Make copy as an B{C{Xtm}} instance.

217

218 @arg Xtm: Class to return the copy (C{Xtm=Etm}, C{Xtm=Utm} or

219 C{self.classof}).

220 '''

221 return Xtm(self.zone, self.hemisphere, self.easting, self.northing,

222 band=self.band, datum=self.datum, falsed=self.falsed,

223 gamma=self.gamma, scale=self.scale, name=self._name__(name))

224

225 @property_doc_(''' the I{latitudinal} band.''')

226 def band(self):

227 '''Get the I{latitudinal} band (C{'C'|..|'X'}).

228 '''

229 if not self._band:

230 self._toLLEB()

231 return self._band

232

233 @band.setter # PYCHOK setter!

234 def band(self, band):

235 '''Set or reset the I{latitudinal} band letter (C{'C'|..|'X'})

236 or C{None} or C{""} to reset.

237

238 @raise TypeError: Invalid B{C{band}}.

239

240 @raise ValueError: Invalid B{C{band}}.

241 '''

242 self._band1(band)

243

244 @Property_RO

245 def _etm(self):

246 '''(INTERNAL) Cache for method L{toEtm}.

247 '''

248 return self._xcopy2(_MODS.etm.Etm)

249

250 @Property_RO

251 def falsed2(self):

252 '''Get the easting and northing falsing (L{EasNor2Tuple}C{(easting, northing)}).

253 '''

254 e = n = 0

255 if self.falsed:

256 e = _FalseEasting # relative to central meridian

257 if self.hemisphere == _S_: # relative to equator

258 n = _FalseNorthing

259 return EasNor2Tuple(e, n)

260

261 def parse(self, strUTM, **name):

262 '''Parse a string to a similar L{Utm} instance.

263

264 @arg strUTM: The UTM coordinate (C{str}), see function L{parseUTM5}.

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

266

267 @return: The similar instance (L{Utm}).

268

269 @raise UTMError: Invalid B{C{strUTM}}.

270

271 @see: Functions L{pygeodesy.parseUPS5} and L{pygeodesy.parseUTMUPS5}.

272 '''

273 return parseUTM5(strUTM, datum=self.datum, Utm=self.classof,

274 name=self._name__(name))

275

276 @deprecated_method

277 def parseUTM(self, strUTM): # PYCHOK no cover

278 '''DEPRECATED, use method L{Utm.parse}.'''

279 return self.parse(strUTM)

280

281 @Property_RO

282 def pole(self):

283 '''Get the top center of (stereographic) projection, C{""} always.

284 '''

285 return NN # N/A for UTM

286

287 def toEtm(self):

288 '''Copy this UTM to an ETM coordinate.

289

290 @return: The ETM coordinate (L{Etm}).

291 '''

292 return self._etm

293

294 def toLatLon(self, LatLon=None, eps=EPS, unfalse=True, **LatLon_kwds):

295 '''Convert this UTM coordinate to an (ellipsoidal) geodetic point.

296

297 @kwarg LatLon: Optional, ellipsoidal class to return the geodetic

298 point (C{LatLon}) or C{None}.

299 @kwarg eps: Optional convergence limit, L{EPS} or above (C{float}).

300 @kwarg unfalse: Unfalse B{C{easting}} and B{C{northing}}

301 if falsed (C{bool}).

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

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

304

305 @return: This UTM as (B{C{LatLon}}) or if B{C{LatLon}} is

306 C{None}, as L{LatLonDatum5Tuple}C{(lat, lon, datum,

307 gamma, scale)}.

308

309 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon}} is not ellipsoidal.

310

311 @raise UTMError: Invalid meridional radius or H-value.

312

313 '''

314 if eps < EPS:

315 eps = EPS # less doesn't converge

316

317 if self._latlon and self._latlon._toLLEB_args == (unfalse, eps):

318 return self._latlon5(LatLon)

319 else:

320 self._toLLEB(unfalse=unfalse, eps=eps)

321 return self._latlon5(LatLon, **LatLon_kwds)

322

323 def _toLLEB(self, unfalse=True, eps=EPS): # PYCHOK signature

324 '''(INTERNAL) Compute (ellipsoidal) lat- and longitude.

325 '''

326 x, y = self.eastingnorthing2(falsed=not unfalse)

327

328 E = self.datum.ellipsoid

329 # from Karney 2011 Eq 15-22, 36

330 A0 = self.scale0 * E.A

331 if A0 < EPS0:

332 raise self._Error(meridional=A0)

333 x = x / A0 # /= chokes PyChecker

334 y = y / A0

335 K = _Kseries(E.BetaKs, x, y) # Krüger series

336 x = neg(K.xs(-x)) # η' eta

337 y = neg(K.ys(-y)) # ξ' ksi

338

339 sy, cy = sincos2(y)

340 shx = sinh(x)

341 H = hypot(shx, cy)

342 if H < EPS0:

343 raise self._Error(H=H)

344

345 T = sy / H # τʹ == τ0

346 p = _0_0 # previous d

347 e = _0_0001 * eps

348 for T, i, d in E._es_tauf3(T, T): # 4-5 trips

349 # d may toggle on +/-1.12e-16 or +/-4.47e-16,

350 # see the references at C{Ellipsoid.es_tauf}

351 if fabs(d) < eps or fabs(d + p) < e:

352 break

353 p = d

354 else:

355 t = unstr(self.toLatLon, eps=eps, unfalse=unfalse)

356 raise self._Error(Fmt.no_convergence(d, eps), txt=t)

357

358 a = atan1(T) # phi, lat

359 b = atan2(shx, cy)

360 if unfalse and self.falsed:

361 b += radians(_cmlon(self.zone))

362 ll = _LLEB(degrees90(a), degrees180(b), datum=self.datum, name=self.name)

363

364 # gamma and scale: Karney 2011 Eq 26, 27 and 28

365 p = neg(K.ps(-1))

366 q = K.qs(0)

367 g = degrees(atan1(tan(y) * tanh(x)) + atan2(q, p))

368 k = hypot(p, q) * E.a / A0

369 if k:

370 k = E.e2s(sin(a)) * hypot1(T) * H / k # INF?

371 ll._iteration = i

372 self._latlon5args(ll, g, k, _toBand, unfalse, eps)

373

374 def toRepr(self, prec=0, fmt=Fmt.SQUARE, sep=_COMMASPACE_, B=False, cs=False, **unused): # PYCHOK expected

375 '''Return a string representation of this UTM coordinate.

376

377 Note that UTM coordinates are rounded, not truncated (unlike

378 MGRS grid references).

379

380 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).

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

382 @kwarg sep: Optional separator between name:value pairs (C{str}).

383 @kwarg B: Optionally, include latitudinal band (C{bool}).

384 @kwarg cs: Optionally, include meridian convergence and grid

385 scale factor (C{bool} or non-zero C{int} to specify

386 the precison like B{C{prec}}).

387

388 @return: This UTM as a string C{"[Z:09[band], H:N|S, E:meter,

389 N:meter]"} plus C{", C:degrees, S:float"} if C{B{cs}

390 is True} (C{str}).

391 '''

392 return self._toRepr(fmt, B, cs, prec, sep)

393

394 def toStr(self, prec=0, sep=_SPACE_, B=False, cs=False): # PYCHOK expected

395 '''Return a string representation of this UTM coordinate.

396

397 To distinguish from MGRS grid zone designators, a space is

398 left between the zone and the hemisphere.

399

400 Note that UTM coordinates are rounded, not truncated (unlike

401 MGRS grid references).

402

403 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).

404 @kwarg sep: Optional separator to join (C{str}) or C{None}

405 to return an unjoined C{tuple} of C{str}s.

406 @kwarg B: Optionally, include latitudinal band (C{bool}).

407 @kwarg cs: Optionally, include meridian convergence and grid

408 scale factor (C{bool} or non-zero C{int} to specify

409 the precison like B{C{prec}}).

410

411 @return: This UTM as a string with C{zone[band], hemisphere,

412 easting, northing, [convergence, scale]} in

413 C{"00 N|S meter meter"} plus C{" degrees float"} if

414 C{B{cs} is True} (C{str}).

415 '''

416 return self._toStr(self.hemisphere, B, cs, prec, sep)

417

418 def toUps(self, pole=NN, eps=EPS, falsed=True, **unused):

419 '''Convert this UTM coordinate to a UPS coordinate.

420

421 @kwarg pole: Optional top/center of the UPS projection,

422 (C{str}, 'N[orth]'|'S[outh]').

423 @kwarg eps: Optional convergence limit, L{EPS} or above

424 (C{float}), see method L{Utm.toLatLon}.

425 @kwarg falsed: If C{True}, false both easting and northing

426 (C{bool}).

427

428 @return: The UPS coordinate (L{Ups}).

429 '''

430 u = self._ups

431 if u is None or u.pole != (pole or u.pole) or bool(falsed) != u.falsed:

432 ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True)

433 ups = _MODS.ups

434 self._ups = u = ups.toUps8(ll, Ups=ups.Ups, falsed=falsed,

435 name=self.name, pole=pole)

436 return u

437

438 def toUtm(self, zone, eps=EPS, falsed=True, **unused):

439 '''Convert this UTM coordinate to a different zone.

440

441 @arg zone: New UTM zone (C{int}).

442 @kwarg eps: Optional convergence limit, L{EPS} or above

443 (C{float}), see method L{Utm.toLatLon}.

444 @kwarg falsed: If C{True}, fFalse both easting and northing

445 (C{bool}).

446

447 @return: The UTM coordinate (L{Utm}).

448 '''

449 if zone == self.zone and falsed == self.falsed:

450 return self.copy()

451 elif zone:

452 u = self._utm

453 if u is None or u.zone != zone or bool(falsed) != u.falsed:

454 ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True)

455 self._utm = u = toUtm8(ll, Utm=self.classof, falsed=falsed,

456 name=self.name, zone=zone)

457 return u

458 raise self._Error(zone=zone)

459

460 @Property_RO

461 def zone(self):

462 '''Get the (longitudinal) zone (C{int}, 1..60).

463 '''

464 return self._zone

465

466

467 def _cmlon(zone):

468 '''(INTERNAL) Central meridian longitude (C{degrees180}).

469 '''

470 return (zone * 6) - 183

471

472

473 def _false2(e, n, h):

474 '''(INTERNAL) False easting and northing.

475 '''

476 # Karney, "Test data for the transverse Mercator projection (2009)"

477 # <https://GeographicLib.SourceForge.io/C++/doc/transversemercator.html>

478 # and <https://Zenodo.org/record/32470#.W4LEJS2ZON8>

479 e += _FalseEasting # make e relative to central meridian

480 if h == _S_:

481 n += _FalseNorthing # make n relative to equator

482 return e, n

483

484

485 def _parseUTM5(strUTM, datum, Xtm, falsed, Error=UTMError, **name): # imported by .etm

486 '''(INTERNAL) Parse a string representing a UTM coordinate,

487 consisting of C{"zone[band] hemisphere easting northing"},

488 see L{pygeodesy.parseETM5} and L{parseUTM5}.

489 '''

490 z, h, e, n, B = _parseUTMUPS5(strUTM, None, Error=Error)

491 if _UTM_ZONE_MIN > z or z > _UTM_ZONE_MAX or (B and B not in _Bands):

492 raise Error(strUTM=strUTM, zone=z, band=B)

493

494 return UtmUps5Tuple(z, h, e, n, B, Error=Error, **name) if Xtm is None else \

495 Xtm(z, h, e, n, band=B, datum=datum, falsed=bool(falsed), **name)

496

497

498 def parseUTM5(strUTM, datum=_WGS84, Utm=Utm, falsed=True, **name):

499 '''Parse a string representing a UTM coordinate, consisting

500 of C{"zone[band] hemisphere easting northing"}.

501

502 @arg strUTM: A UTM coordinate (C{str}).

503 @kwarg datum: Optional datum to use (L{Datum}, L{Ellipsoid},

504 L{Ellipsoid2} or L{a_f2Tuple}).

505 @kwarg Utm: Optional class to return the UTM coordinate (L{Utm})

506 or C{None}.

507 @kwarg falsed: Use C{B{falsed}=False} if both easting and northing

508 are I{not falsed} (C{bool}).

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

510

511 @return: The UTM coordinate (B{C{Utm}}) or if C{B{Utm} is None}, a

512 L{UtmUps5Tuple}C{(zone, hemipole, easting, northing, band)}.

513 The C{hemipole} is the C{'N'|'S'} hemisphere.

514

515 @raise UTMError: Invalid B{C{strUTM}}.

516

517 @raise TypeError: Invalid B{C{datum}}.

518 '''

519 return _parseUTM5(strUTM, datum, Utm, falsed, **name)

520

521

522 def toUtm8(latlon, lon=None, datum=None, Utm=Utm, falsed=True,

523 strict=True, zone=None, **name_cmoff):

524 '''Convert a lat-/longitude point to a UTM coordinate.

525

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

527 geodetic C{LatLon} point.

528 @kwarg lon: Longitude (C{degrees}), required if B{C{latlon}} is

529 C{degrees}, ignored otherwise.

530 @kwarg datum: Optional datum for this UTM coordinate, overriding

531 B{C{latlon}}'s datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}

532 or L{a_f2Tuple}).

533 @kwarg Utm: Optional class to return the UTM coordinate (L{Utm}) or C{None}.

534 @kwarg falsed: If C{True}, false both easting and northing (C{bool}).

535 @kwarg strict: If C{True}, restrict B{C{lat}} to UTM ranges (C{bool}).

536 @kwarg zone: Optional UTM zone to enforce (C{int} or C{str}).

537 @kwarg name_cmoff: Optional C{B{name}=NN} (C{str}) and DEPRECATED keyword

538 argument C{B{cmoff}=True} to offset the longitude from the zone's

539 central meridian (C{bool}), use C{B{falsed}} instead.

540

541 @return: The UTM coordinate (B{C{Utm}}) or if C{B{Utm} is None} or C{B{falsed}

542 is False}, a L{UtmUps8Tuple}C{(zone, hemipole, easting, northing, band,

543 datum, gamma, scale)} where C{hemipole} is the C{'N'|'S'} hemisphere.

544

545 @raise RangeError: If B{C{lat}} outside the valid UTM bands or if B{C{lat}}

546 or B{C{lon}} outside the valid range and L{rangerrors

547 <pygeodesy.rangerrors>} is C{True}.

548

549 @raise TypeError: Invalid B{C{datum}} or B{C{latlon}} not ellipsoidal.

550

551 @raise UTMError: Invalid B{C{zone}}.

552

553 @raise ValueError: If B{C{lon}} is missing or B{C{latlon}} is invalid.

554

555 @note: Implements Karney’s method, using 8-th order Krüger series, giving

556 results accurate to 5 nm (or better) for distances up to 3,900 Km

557 from the central meridian.

558 '''

559 z, B, lat, lon, d, f, n = _to7zBlldfn(latlon, lon, datum,

560 falsed, zone, strict,

561 UTMError, **name_cmoff)

562 d = _ellipsoidal_datum(d, name=n)

563 E = d.ellipsoid

564

565 a, b = radians(lat), radians(lon)

566 # easting, northing: Karney 2011 Eq 7-14, 29, 35

567 sb, cb = sincos2(b)

568

569 T = tan(a)

570 T12 = hypot1(T)

571 S = sinh(E.e * atanh(E.e * T / T12))

572

573 T_ = fdot_(T, hypot1(S), -S, T12)

574 H = hypot(T_, cb)

575

576 y = atan2(T_, cb) # ξ' ksi

577 x = asinh(sb / H) # η' eta

578

579 A0 = E.A * getattr(Utm, _under(_scale0_), _K0_UTM) # Utm is class or None

580

581 K = _Kseries(E.AlphaKs, x, y) # Krüger series

582 y = K.ys(y) * A0 # ξ

583 x = K.xs(x) * A0 # η

584

585 # convergence: Karney 2011 Eq 23, 24

586 p_ = K.ps(1)

587 q_ = K.qs(0)

588 g = degrees(atan2(T_ * tan(b), hypot1(T_)) + atan2(q_, p_))

589 # scale: Karney 2011 Eq 25

590 k = E.e2s(sin(a)) * T12 / H * (A0 / E.a * hypot(p_, q_))

591

592 return _toXtm8(Utm, z, lat, x, y,

593 B, d, g, k, f, n, latlon, EPS)

594

595

596 def _toBand(lat, *unused, **strict_Error): # see ups._toBand

597 '''(INTERNAL) Get the I{latitudinal} Band (row) letter.

598 '''

599 if _UTM_LAT_MIN <= lat < _UTM_LAT_MAX: # [-80, 84) like Veness

600 return _Bands[int(lat - _UTM_LAT_MIN) >> 3]

601 elif _xkwds_get(strict_Error, strict=True):

602 r = _range_(_UTM_LAT_MIN, _UTM_LAT_MAX, ropen=True)

603 t = _SPACE_(_outside_, _UTM_, _range_, r)

604 E = _xkwds_get(strict_Error, Error=RangeError)

605 raise E(lat=degDMS(lat), txt=t)

606 else:

607 return NN # None

608

609

610 def _toXtm8(Xtm, z, lat, x, y, B, d, g, k, f, # PYCHOK 13+ args

611 n, latlon, eps_other, Error=UTMError):

612 '''(INTERNAL) Helper for methods L{toEtm8} and L{toUtm8}.

613 '''

614 h = _hemi(lat)

615 if f:

616 x, y = _false2(x, y, h)

617 if Xtm is None: # DEPRECATED

618 r = UtmUps8Tuple(z, h, x, y, B, d, g, k, Error=Error, name=n)

619 else:

620 r = Xtm(z, h, x, y, band=B, datum=d, falsed=f,

621 gamma=g, scale=k, name=n)

622 if isinstance(latlon, _LLEB) and d is latlon.datum: # see ups.toUtm8

623 r._latlon5args(latlon, g, k, _toBand, f, eps_other) # XXX weakref(latlon)?

624 elif not r._band:

625 r._band = _toBand(lat)

626 return r

627

628

629 def _to3zBlat(zone, band, Error=UTMError): # in .mgrs

630 '''(INTERNAL) Check and return zone, Band and band latitude.

631

632 @arg zone: Zone number or string.

633 @arg band: Band letter.

634 @arg Error: Exception to raise (L{UTMError}).

635

636 @return: 3-Tuple (zone, Band, latitude).

637 '''

638 z, B, _ = _to3zBhp(zone, band, Error=Error)

639 if not (_UTM_ZONE_MIN <= z <= _UTM_ZONE_MAX or

640 (_UPS_ZONE == z and Error is MGRSError)):

641 raise Error(zone=zone)

642

643 b = None

644 if B:

645 if z == _UPS_ZONE: # polar

646 try:

647 b = Lat(_UPS_LATS[B], name=_bandLat_)

648 except KeyError:

649 raise Error(band=band or B, zone=z)

650 else: # UTM

651 b = _Bands.find(B)

652 if b < 0:

653 raise Error(band=band or B, zone=z)

654 b = Int((b << 3) - 80, name=_bandLat_)

655 B = Band(B)

656 elif Error is not UTMError:

657 raise Error(band=band, txt=MISSING)

658

659 return Zone(z), B, b

660

661

662 def _to4zBll(lat, lon, cmoff=True, strict=True, Error=RangeError):

663 '''(INTERNAL) Return zone, Band and lat- and (central) longitude in degrees.

664

665 @arg lat: Latitude (C{degrees}).

666 @arg lon: Longitude (C{degrees}).

667 @kwarg cmoff: If C{True}, offset B{C{lon}} from the zone's central meridian.

668 @kwarg strict: Restrict B{C{lat}} to the UTM ranges (C{bool}).

669 @kwarg Error: Error for out of UTM range B{C{lat}}s.

670

671 @return: 4-Tuple (zone, Band, lat, lon).

672 '''

673 z, lat, lon = _to3zll(lat, lon) # in .utmupsBase

674

675 x = lon - _cmlon(z) # z before Norway/Svalbard

676 if fabs(x) > _UTM_ZONE_OFF_MAX:

677 t = _SPACE_(_outside_, _UTM_, _zone_, str(z), _by_, degDMS(x, prec=6))

678 raise Error(lon=degDMS(lon), txt=t)

679

680 B = _toBand(lat, strict=strict, Error=Error)

681 if B == _X_: # and 0 <= lon < 42: z = int(lon + 183) // 6 + 1

682 x = _SvalbardXzone.get(z, None)

683 if x: # Svalbard/Spitsbergen archipelago

684 z += 1 if lon >= x else -1

685 elif B == _V_ and z == 31 and lon >= 3:

686 z += 1 # SouthWestern Norway

687

688 if cmoff: # lon off central meridian

689 lon -= _cmlon(z) # z I{after} Norway/Svalbard

690 return Zone(z), (Band(B) if B else None), Lat(lat), Lon(lon)

691

692

693 def _to7zBlldfn(latlon, lon, datum, falsed, zone, strict, Error, **name_cmoff):

694 '''(INTERNAL) Determine 7-tuple (zone, band, lat, lon, datum,

695 falsed, name) for methods L{toEtm8} and L{toUtm8}.

696 '''

697 f, name = _xkwds_pop2(name_cmoff, cmoff=falsed) # DEPRECATED

698 lat, lon, d, n = _to4lldn(latlon, lon, datum, name)

699 z, B, lat, lon = _to4zBll(lat, lon, cmoff=f, strict=strict)

700 if zone: # re-zone for ETM/UTM

701 r, _, _ = _to3zBhp(zone, B)

702 if r != z:

703 if not _UTM_ZONE_MIN <= r <= _UTM_ZONE_MAX:

704 raise Error(zone=zone)

705 if f: # re-offset from central meridian

706 lon += _cmlon(z) - _cmlon(r)

707 z = r

708 return z, B, lat, lon, d, f, n

709

710

711 def utmZoneBand5(lat, lon, cmoff=False, **name):

712 '''Return the UTM zone number, Band letter, hemisphere and

713 (clipped) lat- and longitude for a given location.

714

715 @arg lat: Latitude in degrees (C{scalar} or C{str}).

716 @arg lon: Longitude in degrees (C{scalar} or C{str}).

717 @kwarg cmoff: If C{True}, offset longitude from the zone's central

718 meridian (C{bool}).

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

720

721 @return: A L{UtmUpsLatLon5Tuple}C{(zone, band, hemipole, lat, lon)}

722 where C{hemipole} is the C{'N'|'S'} UTM hemisphere.

723

724 @raise RangeError: If B{C{lat}} outside the valid UTM bands or if

725 B{C{lat}} or B{C{lon}} outside the valid range and

726 L{rangerrors<pygeodesy.rangerrors>} is C{True}.

727

728 @raise ValueError: Invalid B{C{lat}} or B{C{lon}}.

729 '''

730 lat, lon = parseDMS2(lat, lon)

731 z, B, lat, lon = _to4zBll(lat, lon, cmoff=cmoff)

732 return UtmUpsLatLon5Tuple(z, B, _hemi(lat), lat, lon, **name)

733

734# **) MIT License

735#

736# Copyright (C) 2016-2025 -- 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.