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 2011-2016} 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

39 from pygeodesy.dms import degDMS, parseDMS2

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

41 _xkwds_get

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

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

44 _NS_, _outside_, _range_, _S_, _scale0_, \

45 _SPACE_, _UTM_, _V_, _X_, _zone_, _under

46 from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS

47# from pygeodesy.named import _xnamed # from .utmupsBase

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, 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, _xnamed

60

61 from math import asinh, atanh, atan2, cos, cosh, degrees, fabs, \

62 radians, sin, sinh, tan, tanh

63# import operator as _operator # from .fmath

64

65__all__ = _ALL_LAZY.utm

66__version__ = '24.02.29'

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 def _cmlon(zone):

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

138 '''

139 return (zone * 6) - 183

140

141

142 def _false2(e, n, h):

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

144 '''

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

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

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

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

149 if h == _S_:

150 n += _FalseNorthing # make n relative to equator

151 return e, n

152

153

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

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

156 '''

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

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

159 elif _xkwds_get(strict_Error, strict=True):

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

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

162 E = _xkwds_get(strict_Error, Error=RangeError)

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

164 else:

165 return NN # None

166

167

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

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

170

171 @arg zone: Zone number or string.

172 @arg band: Band letter.

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

174

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

176 '''

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

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

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

180 raise Error(zone=zone)

181

182 b = None

183 if B:

184 if z == _UPS_ZONE: # polar

185 try:

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

187 except KeyError:

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

189 else: # UTM

190 b = _Bands.find(B)

191 if b < 0:

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

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

194 B = Band(B)

195 elif Error is not UTMError:

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

197

198 return Zone(z), B, b

199

200

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

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

203

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

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

206 @kwarg cmoff: Offset B{C{lon}} from zone's central meridian.

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

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

209

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

211 '''

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

213

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

215 if fabs(x) > _UTM_ZONE_OFF_MAX:

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

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

218

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

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

221 x = _SvalbardXzone.get(z, None)

222 if x: # Svalbard/Spitsbergen archipelago

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

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

225 z += 1 # SouthWestern Norway

226

227 if cmoff: # lon off central meridian

228 lon -= _cmlon(z) # z after Norway/Svalbard

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

230

231

232 def _to7zBlldfn(latlon, lon, datum, falsed, name, zone, strict, Error, **cmoff):

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

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

235 '''

236 f = falsed and _xkwds_get(cmoff, cmoff=True) # DEPRECATED

237 lat, lon, d, name = _to4lldn(latlon, lon, datum, name)

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

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

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

241 if r != z:

242 if not _UTM_ZONE_MIN <= r <= _UTM_ZONE_MAX:

243 raise Error(zone=zone)

244 if f: # re-offset from central meridian

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

246 z = r

247 return z, B, lat, lon, d, f, name

248

249

250 class Utm(UtmUpsBase):

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

252 '''

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

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

255 _Error = UTMError # or etm.ETMError

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

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

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

259

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

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

262 gamma=None, scale=None, name=NN, **convergence):

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

264

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

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

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

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

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

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

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

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

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

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

275 falsed (C{bool}).

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

277 clockwise from true North (C{degrees}) or C{None}.

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

279 @kwarg name: Optional name (C{str}).

280 @kwarg convergence: DEPRECATED, use keyword argument C{B{gamma}=None}.

281

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

283

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

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

286 B{C{scale}}.

287 '''

288 if name:

289 self.name = name

290

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

292

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

294 if h not in _NS_:

295 raise self._Error(hemisphere=hemisphere)

296

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

298# if not falsed:

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

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

301# # between zones) - is this worthwhile?

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

303# the valid UTM range.

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

305# raise RangeError(easting=easting)

306# if 0 > n or n > _FalseNorthing:

307# raise RangeError(northing=northing)

308

309 self._hemisphere = h

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

311 gamma=gamma, scale=scale, **convergence)

312

313 def __eq__(self, other):

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

315 and other.hemisphere == self.hemisphere \

316 and other.easting == self.easting \

317 and other.northing == self.northing \

318 and other.band == self.band \

319 and other.datum == self.datum

320

321 def __repr__(self):

322 return self.toRepr(B=True)

323

324 def __str__(self):

325 return self.toStr()

326

327 def _xcopy2(self, Xtm, name=NN):

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

329

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

331 C{self.classof}).

332 '''

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

334 band=self.band, datum=self.datum, falsed=self.falsed,

335 gamma=self.gamma, scale=self.scale, name=name or self.name)

336

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

338 def band(self):

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

340 '''

341 if not self._band:

342 self._toLLEB()

343 return self._band

344

345 @band.setter # PYCHOK setter!

346 def band(self, band):

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

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

349

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

351

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

353 '''

354 self._band1(band)

355

356 @Property_RO

357 def _etm(self):

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

359 '''

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

361

362 @Property_RO

363 def falsed2(self):

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

365 '''

366 e = n = 0

367 if self.falsed:

368 e = _FalseEasting # relative to central meridian

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

370 n = _FalseNorthing

371 return EasNor2Tuple(e, n)

372

373 def parse(self, strUTM, name=NN):

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

375

376 @arg strUTM: The UTM coordinate (C{str}),

377 see function L{parseUTM5}.

378 @kwarg name: Optional instance name (C{str}),

379 overriding this name.

380

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

382

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

384

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

386 '''

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

388 name=name or self.name)

389

390 @deprecated_method

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

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

393 return self.parse(strUTM)

394

395 @Property_RO

396 def pole(self):

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

398 '''

399 return NN # N/A for UTM

400

401 def toEtm(self):

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

403

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

405 '''

406 return self._etm

407

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

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

410

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

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

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

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

415 if falsed (C{bool}).

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

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

418

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

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

421 gamma, scale)}.

422

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

424

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

426

427 '''

428 if eps < EPS:

429 eps = EPS # less doesn't converge

430

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

432 return self._latlon5(LatLon)

433 else:

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

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

436

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

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

439 '''

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

441

442 E = self.datum.ellipsoid

443 # from Karney 2011 Eq 15-22, 36

444 A0 = self.scale0 * E.A

445 if A0 < EPS0:

446 raise self._Error(meridional=A0)

447 x = x / A0 # /= chokes PyChecker

448 y = y / A0

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

450 x = neg(K.xs(-x)) # η' eta

451 y = neg(K.ys(-y)) # ξ' ksi

452

453 sy, cy = sincos2(y)

454 shx = sinh(x)

455 H = hypot(shx, cy)

456 if H < EPS0:

457 raise self._Error(H=H)

458

459 T = sy / H # τʹ == τ0

460 p = _0_0 # previous d

461 e = _0_0001 * eps

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

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

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

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

466 break

467 p = d

468 else:

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

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

471

472 a = atan1(T) # phi, lat

473 b = atan2(shx, cy)

474 if unfalse and self.falsed:

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

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

477

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

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

480 q = K.qs(0)

481 s = hypot(p, q) * E.a / A0

482 ll._gamma = degrees(atan1(tan(y) * tanh(x)) + atan2(q, p))

483 ll._scale = (E.e2s(sin(a)) * hypot1(T) * H / s) if s else s # INF?

484 ll._iteration = i

485 self._latlon5args(ll, _toBand, unfalse, eps)

486

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

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

489

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

491 MGRS grid references).

492

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

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

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

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

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

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

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

500

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

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

503 C{True} (C{str}).

504 '''

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

506

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

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

509

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

511 left between the zone and the hemisphere.

512

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

514 MGRS grid references).

515

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

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

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

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

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

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

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

523

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

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

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

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

528 '''

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

530

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

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

533

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

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

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

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

538 @kwarg falsed: False both easting and northing (C{bool}).

539

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

541 '''

542 u = self._ups

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

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

545 ups = _MODS.ups

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

547 name=self.name, pole=pole)

548 return u

549

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

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

552

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

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

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

556 @kwarg falsed: False both easting and northing (C{bool}).

557

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

559 '''

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

561 return self.copy()

562 elif zone:

563 u = self._utm

564 if u is None or u.zone != zone or falsed != u.falsed:

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

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

567 name=self.name, zone=zone)

568 return u

569 raise self._Error(zone=zone)

570

571 @Property_RO

572 def zone(self):

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

574 '''

575 return self._zone

576

577

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

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

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

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

582 '''

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

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

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

586

587 if Xtm is None:

588 r = UtmUps5Tuple(z, h, e, n, B, Error=Error, name=name)

589 else:

590 r = Xtm(z, h, e, n, band=B, datum=datum, falsed=falsed)

591 if name:

592 r = _xnamed(r, name, force=True)

593 return r

594

595

596 def parseUTM5(strUTM, datum=_WGS84, Utm=Utm, falsed=True, name=NN):

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

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

599

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

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

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

603 @kwarg Utm: Optional class to return the UTM coordinate

604 (L{Utm}) or C{None}.

605 @kwarg falsed: Both easting and northing are falsed (C{bool}).

606 @kwarg name: Optional B{C{Utm}} name (C{str}).

607

608 @return: The UTM coordinate (B{C{Utm}}) or if B{C{Utm}}

609 is C{None}, a L{UtmUps5Tuple}C{(zone, hemipole,

610 easting, northing, band)}. The C{hemipole} is

611 the C{'N'|'S'} hemisphere.

612

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

614

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

616 '''

617 return _parseUTM5(strUTM, datum, Utm, falsed, name=name)

618

619

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

621 name=NN, strict=True,

622 zone=None, **cmoff):

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

624

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

626 geodetic C{LatLon} point.

627 @kwarg lon: Optional longitude (C{degrees}) or C{None}.

628 @kwarg datum: Optional datum for this UTM coordinate,

629 overriding B{C{latlon}}'s datum (L{Datum},

630 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).

631 @kwarg Utm: Optional class to return the UTM coordinate

632 (L{Utm}) or C{None}.

633 @kwarg falsed: False both easting and northing (C{bool}).

634 @kwarg name: Optional B{C{Utm}} name (C{str}).

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

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

637 @kwarg cmoff: DEPRECATED, use B{C{falsed}}. Offset longitude

638 from the zone's central meridian (C{bool}).

639

640 @return: The UTM coordinate (B{C{Utm}}) or if B{C{Utm}} is

641 C{None} or not B{C{falsed}}, a L{UtmUps8Tuple}C{(zone,

642 hemipole, easting, northing, band, datum, gamma,

643 scale)}. The C{hemipole} is the C{'N'|'S'} hemisphere.

644

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

646 B{C{lat}} or B{C{lon}} outside the valid range

647 and L{pygeodesy.rangerrors} set to C{True}.

648

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

650

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

652

653 @raise ValueError: If B{C{lon}} value is missing or if

654 B{C{latlon}} is invalid.

655

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

657 giving results accurate to 5 nm (or better) for distances

658 up to 3,900 Km from the central meridian.

659 '''

660 z, B, lat, lon, d, f, name = _to7zBlldfn(latlon, lon, datum,

661 falsed, name, zone,

662 strict, UTMError, **cmoff)

663 d = _ellipsoidal_datum(d, name=name)

664 E = d.ellipsoid

665

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

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

668 sb, cb = sincos2(b)

669

670 T = tan(a)

671 T12 = hypot1(T)

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

673

674 T_ = T * hypot1(S) - S * T12

675 H = hypot(T_, cb)

676

677 y = atan2(T_, cb) # ξ' ksi

678 x = asinh(sb / H) # η' eta

679

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

681

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

683 y = K.ys(y) * A0 # ξ

684 x = K.xs(x) * A0 # η

685

686 # convergence: Karney 2011 Eq 23, 24

687 p_ = K.ps(1)

688 q_ = K.qs(0)

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

690 # scale: Karney 2011 Eq 25

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

692

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

694 B, d, g, k, f, name, latlon, EPS)

695

696

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

698 name, latlon, eps, Error=UTMError):

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

700 '''

701 h = _hemi(lat)

702 if f:

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

704 if Xtm is None: # DEPRECATED

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

706 else:

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

708 gamma=g, scale=k), name)

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

710 r._latlon5args(latlon, _toBand, f, eps) # XXX weakref(latlon)?

711 latlon._gamma = g

712 latlon._scale = k

713 elif not r._band:

714 r._band = _toBand(lat)

715 return r

716

717

718 def utmZoneBand5(lat, lon, cmoff=False, name=NN):

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

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

721

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

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

724 @kwarg cmoff: Offset longitude from the zone's central

725 meridian (C{bool}).

726 @kwarg name: Optional name (C{str}).

727

728 @return: A L{UtmUpsLatLon5Tuple}C{(zone, band, hemipole,

729 lat, lon)} where C{hemipole} is the C{'N'|'S'}

730 UTM hemisphere.

731

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

733 B{C{lat}} or B{C{lon}} outside the valid range

734 and L{pygeodesy.rangerrors} set to C{True}.

735

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

737 '''

738 lat, lon = parseDMS2(lat, lon)

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

740 return UtmUpsLatLon5Tuple(z, B, _hemi(lat), lat, lon, name=name)

741

742# **) MIT License

743#

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

745#

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

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

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

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

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

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

752#

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

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

755#

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

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

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

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

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

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

762# OTHER DEALINGS IN THE SOFTWARE.