Coverage for pygeodesy/utm.py: 97%

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1 

2# -*- coding: utf-8 -*- 

3 

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

5 

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

7L{utmZoneBand5}. 

8 

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

10an ellipsoidal earth model, transcoded from JavaScript originals by 

11I{(C) Chris Veness 2011-2016} published under the same MIT Licence**, see 

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

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

14 

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

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

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

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

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

20measured in metres. 

21 

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

23accuracy 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 

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

27classGeographicLib_1_1TransverseMercator.html>}. 

28 

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

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

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

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

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

34''' 

35 

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

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

38from pygeodesy.datums import _ellipsoidal_datum, _WGS84 

39from pygeodesy.dms import degDMS, parseDMS2 

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

41 _xkwds_get 

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

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

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

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

46from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS 

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

48from pygeodesy.namedTuples import EasNor2Tuple, UtmUps5Tuple, \ 

49 UtmUps8Tuple, UtmUpsLatLon5Tuple 

50from pygeodesy.props import deprecated_method, property_doc_, \ 

51 Property_RO 

52from pygeodesy.streprs import Fmt, unstr 

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

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

55from 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 

61from 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 

76class UTMError(_ValueError): 

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

78 ''' 

79 pass 

80 

81 

82class _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 

136def _cmlon(zone): 

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

138 ''' 

139 return (zone * 6) - 183 

140 

141 

142def _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 

154def _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 

168def _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 

201def _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 

232def _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 

250class 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 

578def _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 

596def 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 

620def 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 

697def _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 

718def 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.