Coverage for pygeodesy/etm.py: 92%

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1 

2# -*- coding: utf-8 -*- 

3 

4u'''A pure Python version of I{Karney}'s C{Exact Transverse Mercator} (ETM) projection. 

5 

6Classes L{Etm}, L{ETMError} and L{ExactTransverseMercator}, transcoded from I{Karney}'s 

7C++ class U{TransverseMercatorExact<https://GeographicLib.SourceForge.io/C++/doc/ 

8classGeographicLib_1_1TransverseMercatorExact.html>}, abbreviated as C{TMExact} below. 

9 

10Class L{ExactTransverseMercator} provides C{Exact Transverse Mercator} projections while 

11instances of class L{Etm} represent ETM C{(easting, northing)} locations. See also 

12I{Karney}'s utility U{TransverseMercatorProj<https://GeographicLib.SourceForge.io/C++/doc/ 

13TransverseMercatorProj.1.html>} and use C{"python[3] -m pygeodesy.etm ..."} to compare 

14the results. 

15 

16Following is a copy of I{Karney}'s U{TransverseMercatorExact.hpp 

17<https://GeographicLib.SourceForge.io/C++/doc/TransverseMercatorExact_8hpp_source.html>} 

18file C{Header}. 

19 

20Copyright (C) U{Charles Karney<mailto:Karney@Alum.MIT.edu>} (2008-2023) and licensed 

21under the MIT/X11 License. For more information, see the U{GeographicLib<https:// 

22GeographicLib.SourceForge.io>} documentation. 

23 

24The method entails using the U{Thompson Transverse Mercator<https://WikiPedia.org/ 

25wiki/Transverse_Mercator_projection>} as an intermediate projection. The projections 

26from the intermediate coordinates to C{phi, lam} and C{x, y} are given by elliptic 

27functions. The inverse of these projections are found by Newton's method with a 

28suitable starting guess. 

29 

30The relevant section of L.P. Lee's paper U{Conformal Projections Based On Jacobian 

31Elliptic Functions<https://DOI.org/10.3138/X687-1574-4325-WM62>} in part V, pp 

3267-101. The C++ implementation and notation closely follow Lee, with the following 

33exceptions:: 

34 

35 Lee here Description 

36 

37 x/a xi Northing (unit Earth) 

38 

39 y/a eta Easting (unit Earth) 

40 

41 s/a sigma xi + i * eta 

42 

43 y x Easting 

44 

45 x y Northing 

46 

47 k e Eccentricity 

48 

49 k^2 mu Elliptic function parameter 

50 

51 k'^2 mv Elliptic function complementary parameter 

52 

53 m k Scale 

54 

55 zeta zeta Complex longitude = Mercator = chi in paper 

56 

57 s sigma Complex GK = zeta in paper 

58 

59Minor alterations have been made in some of Lee's expressions in an attempt to 

60control round-off. For example, C{atanh(sin(phi))} is replaced by C{asinh(tan(phi))} 

61which maintains accuracy near C{phi = pi/2}. Such changes are noted in the code. 

62''' 

63# make sure int/int division yields float quotient, see .basics 

64from __future__ import division as _; del _ # PYCHOK semicolon 

65 

66from pygeodesy.basics import map1, neg, neg_, _xinstanceof 

67from pygeodesy.constants import EPS, EPS02, PI_2, PI_4, _K0_UTM, \ 

68 _1_EPS, _0_0, _0_1, _0_5, _1_0, _2_0, \ 

69 _3_0, _4_0, _90_0, isnear0, isnear90 

70from pygeodesy.datums import _ellipsoidal_datum, _WGS84, _EWGS84 

71# from pygeodesy.ellipsoids import _EWGS84 # from .datums 

72from pygeodesy.elliptic import _ALL_LAZY, Elliptic 

73# from pygeodesy.errors import _incompatible # from .named 

74from pygeodesy.fmath import cbrt, hypot, hypot1, hypot2 

75from pygeodesy.fsums import Fsum, fsum1f_ 

76from pygeodesy.interns import NN, _COMMASPACE_, _DASH_, _near_, _SPACE_, \ 

77 _spherical_ 

78from pygeodesy.karney import _copyBit, _diff182, _fix90, _norm2, _norm180, \ 

79 _tand, _unsigned2 

80# from pygeodesy.lazily import _ALL_LAZY # from .elliptic 

81from pygeodesy.named import callername, _incompatible, _NamedBase 

82from pygeodesy.namedTuples import Forward4Tuple, Reverse4Tuple 

83from pygeodesy.props import deprecated_method, deprecated_property_RO, \ 

84 Property_RO, property_RO, _update_all, \ 

85 property_doc_ 

86from pygeodesy.streprs import Fmt, pairs, unstr 

87from pygeodesy.units import Degrees, Scalar_ 

88from pygeodesy.utily import atan1d, atan2d, _loneg, sincos2 

89from pygeodesy.utm import _cmlon, _LLEB, _parseUTM5, _toBand, _toXtm8, \ 

90 _to7zBlldfn, Utm, UTMError 

91 

92from math import asinh, atan2, degrees, radians, sinh, sqrt 

93 

94__all__ = _ALL_LAZY.etm 

95__version__ = '24.05.13' 

96 

97_OVERFLOW = _1_EPS**2 # about 2e+31 

98_TAYTOL = pow(EPS, 0.6) 

99_TAYTOL2 = _TAYTOL * _2_0 

100_TOL_10 = EPS * _0_1 

101_TRIPS = 21 # C++ 10 

102 

103 

104def _overflow(x): 

105 '''(INTERNAL) Like C{copysign0(OVERFLOW, B{x})}. 

106 ''' 

107 return _copyBit(_OVERFLOW, x) 

108 

109 

110class ETMError(UTMError): 

111 '''Exact Transverse Mercator (ETM) parse, projection or other 

112 L{Etm} issue or L{ExactTransverseMercator} conversion failure. 

113 ''' 

114 pass 

115 

116 

117class Etm(Utm): 

118 '''Exact Transverse Mercator (ETM) coordinate, a sub-class of L{Utm}, 

119 a Universal Transverse Mercator (UTM) coordinate using the 

120 L{ExactTransverseMercator} projection for highest accuracy. 

121 

122 @note: Conversion of (geodetic) lat- and longitudes to/from L{Etm} 

123 coordinates is 3-4 times slower than to/from L{Utm}. 

124 

125 @see: Karney's U{Detailed Description<https://GeographicLib.SourceForge.io/ 

126 C++/doc/classGeographicLib_1_1TransverseMercatorExact.html#details>}. 

127 ''' 

128 _Error = ETMError # see utm.UTMError 

129 _exactTM = None 

130 

131 __init__ = Utm.__init__ 

132 '''New L{Etm} Exact Transverse Mercator coordinate, raising L{ETMError}s. 

133 

134 @see: L{Utm.__init__} for more information. 

135 ''' 

136 

137 @property_doc_(''' the ETM projection (L{ExactTransverseMercator}).''') 

138 def exactTM(self): 

139 '''Get the ETM projection (L{ExactTransverseMercator}). 

140 ''' 

141 if self._exactTM is None: 

142 self.exactTM = self.datum.exactTM # ExactTransverseMercator(datum=self.datum) 

143 return self._exactTM 

144 

145 @exactTM.setter # PYCHOK setter! 

146 def exactTM(self, exactTM): 

147 '''Set the ETM projection (L{ExactTransverseMercator}). 

148 

149 @raise ETMError: The B{C{exacTM}}'s datum incompatible 

150 with this ETM coordinate's C{datum}. 

151 ''' 

152 _xinstanceof(ExactTransverseMercator, exactTM=exactTM) 

153 

154 E = self.datum.ellipsoid 

155 if E != exactTM.ellipsoid: # may be None 

156 raise ETMError(repr(exactTM), txt=_incompatible(repr(E))) 

157 self._exactTM = exactTM 

158 self._scale0 = exactTM.k0 

159 

160 def parse(self, strETM, name=NN): 

161 '''Parse a string to a similar L{Etm} instance. 

162 

163 @arg strETM: The ETM coordinate (C{str}), 

164 see function L{parseETM5}. 

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

166 overriding this name. 

167 

168 @return: The instance (L{Etm}). 

169 

170 @raise ETMError: Invalid B{C{strETM}}. 

171 

172 @see: Function L{pygeodesy.parseUPS5}, L{pygeodesy.parseUTM5} 

173 and L{pygeodesy.parseUTMUPS5}. 

174 ''' 

175 return parseETM5(strETM, datum=self.datum, Etm=self.classof, 

176 name=name or self.name) 

177 

178 @deprecated_method 

179 def parseETM(self, strETM): # PYCHOK no cover 

180 '''DEPRECATED, use method L{Etm.parse}. 

181 ''' 

182 return self.parse(strETM) 

183 

184 def toLatLon(self, LatLon=None, unfalse=True, **unused): # PYCHOK expected 

185 '''Convert this ETM coordinate to an (ellipsoidal) geodetic point. 

186 

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

188 point (C{LatLon}) or C{None}. 

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

190 C{falsed} (C{bool}). 

191 

192 @return: This ETM coordinate as (B{C{LatLon}}) or a 

193 L{LatLonDatum5Tuple}C{(lat, lon, datum, gamma, 

194 scale)} if B{C{LatLon}} is C{None}. 

195 

196 @raise ETMError: This ETM coordinate's C{exacTM} and this C{datum} 

197 incompatible or no convergence transforming to 

198 lat- and longitude. 

199 

200 @raise TypeError: Invalid or non-ellipsoidal B{C{LatLon}}. 

201 ''' 

202 if not self._latlon or self._latlon._toLLEB_args != (unfalse, self.exactTM): 

203 self._toLLEB(unfalse=unfalse) 

204 return self._latlon5(LatLon) 

205 

206 def _toLLEB(self, unfalse=True, **unused): # PYCHOK signature 

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

208 ''' 

209 xTM, d = self.exactTM, self.datum 

210 # double check that this and exactTM's ellipsoid match 

211 if xTM._E != d.ellipsoid: # PYCHOK no cover 

212 t = repr(d.ellipsoid) 

213 raise ETMError(repr(xTM._E), txt=_incompatible(t)) 

214 

215 e, n = self.eastingnorthing2(falsed=not unfalse) 

216 lon0 = _cmlon(self.zone) if bool(unfalse) == self.falsed else None 

217 lat, lon, g, k = xTM.reverse(e, n, lon0=lon0) 

218 

219 ll = _LLEB(lat, lon, datum=d, name=self.name) # utm._LLEB 

220 ll._gamma = g 

221 ll._scale = k 

222 self._latlon5args(ll, _toBand, unfalse, xTM) 

223 

224 def toUtm(self): # PYCHOK signature 

225 '''Copy this ETM to a UTM coordinate. 

226 

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

228 ''' 

229 return self._xcopy2(Utm) 

230 

231 

232class ExactTransverseMercator(_NamedBase): 

233 '''Pure Python version of Karney's C++ class U{TransverseMercatorExact 

234 <https://GeographicLib.SourceForge.io/C++/doc/TransverseMercatorExact_8cpp_source.html>}, 

235 a numerically exact transverse Mercator projection, further referred to as C{TMExact}. 

236 ''' 

237 _datum = _WGS84 # Datum 

238 _E = _EWGS84 # Ellipsoid 

239 _extendp = False # use extended domain 

240# _iteration = None # ._sigmaInv2 and ._zetaInv2 

241 _k0 = _K0_UTM # central scale factor 

242 _lat0 = _0_0 # central parallel 

243 _lon0 = _0_0 # central meridian 

244 _mu = _EWGS84.e2 # 1st eccentricity squared 

245 _mv = _EWGS84.e21 # 1 - ._mu 

246 _raiser = False # throw Error 

247 _sigmaC = None # most recent _sigmaInv04 case C{int} 

248 _zetaC = None # most recent _zetaInv04 case C{int} 

249 

250 def __init__(self, datum=_WGS84, lon0=0, k0=_K0_UTM, extendp=False, name=NN, raiser=False): 

251 '''New L{ExactTransverseMercator} projection. 

252 

253 @kwarg datum: The I{non-spherical} datum or ellipsoid (L{Datum}, 

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

255 @kwarg lon0: Central meridian, default (C{degrees180}). 

256 @kwarg k0: Central scale factor (C{float}). 

257 @kwarg extendp: Use the I{extended} domain (C{bool}), I{standard} otherwise. 

258 @kwarg name: Optional name for the projection (C{str}). 

259 @kwarg raiser: If C{True}, throw an L{ETMError} for convergence failures (C{bool}). 

260 

261 @raise ETMError: Near-spherical B{C{datum}} or C{ellipsoid} or invalid B{C{lon0}} 

262 or B{C{k0}}. 

263 

264 @see: U{Constructor TransverseMercatorExact<https://GeographicLib.SourceForge.io/ 

265 C++/doc/classGeographicLib_1_1TransverseMercatorExact.html>} for more details, 

266 especially on B{X{extendp}}. 

267 

268 @note: For all 255.5K U{TMcoords.dat<https://Zenodo.org/record/32470>} tests (with 

269 C{0 <= lat <= 84} and C{0 <= lon}) the maximum error is C{5.2e-08 .forward} 

270 (or 52 nano-meter) easting and northing and C{3.8e-13 .reverse} (or 0.38 

271 pico-degrees) lat- and longitude (with Python 3.7.3+, 2.7.16+, PyPy6 3.5.3 

272 and PyPy6 2.7.13, all in 64-bit on macOS 10.13.6 High Sierra C{x86_64} and 

273 12.2 Monterey C{arm64} and C{"arm64_x86_64"}). 

274 ''' 

275 if extendp: 

276 self._extendp = True 

277 if name: 

278 self.name = name 

279 if raiser: 

280 self.raiser = True 

281 

282 TM = ExactTransverseMercator 

283 if datum not in (TM._datum, TM._E, None): 

284 self.datum = datum # invokes ._resets 

285 if lon0 or lon0 != TM._lon0: 

286 self.lon0 = lon0 

287 if k0 is not TM._k0: 

288 self.k0 = k0 

289 

290 @property_doc_(''' the datum (L{Datum}).''') 

291 def datum(self): 

292 '''Get the datum (L{Datum}) or C{None}. 

293 ''' 

294 return self._datum 

295 

296 @datum.setter # PYCHOK setter! 

297 def datum(self, datum): 

298 '''Set the datum and ellipsoid (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). 

299 

300 @raise ETMError: Near-spherical B{C{datum}} or C{ellipsoid}. 

301 ''' 

302 d = _ellipsoidal_datum(datum, name=self.name) # raiser=_datum_) 

303 self._resets(d) 

304 self._datum = d 

305 

306 @Property_RO 

307 def _e(self): 

308 '''(INTERNAL) Get and cache C{_e}. 

309 ''' 

310 return self._E.e 

311 

312 @Property_RO 

313 def _1_e_90(self): # PYCHOK no cover 

314 '''(INTERNAL) Get and cache C{(1 - _e) * 90}. 

315 ''' 

316 return (_1_0 - self._e) * _90_0 

317 

318 @property_RO 

319 def ellipsoid(self): 

320 '''Get the ellipsoid (L{Ellipsoid}). 

321 ''' 

322 return self._E 

323 

324 @Property_RO 

325 def _e_PI_2(self): 

326 '''(INTERNAL) Get and cache C{_e * PI / 2}. 

327 ''' 

328 return self._e * PI_2 

329 

330 @Property_RO 

331 def _e_PI_4_(self): 

332 '''(INTERNAL) Get and cache C{-_e * PI / 4}. 

333 ''' 

334 return -self._e * PI_4 

335 

336 @Property_RO 

337 def _1_e_PI_2(self): 

338 '''(INTERNAL) Get and cache C{(1 - _e) * PI / 2}. 

339 ''' 

340 return (_1_0 - self._e) * PI_2 

341 

342 @Property_RO 

343 def _1_2e_PI_2(self): 

344 '''(INTERNAL) Get and cache C{(1 - 2 * _e) * PI / 2}. 

345 ''' 

346 return (_1_0 - self._e * _2_0) * PI_2 

347 

348 @property_RO 

349 def equatoradius(self): 

350 '''Get the C{ellipsoid}'s equatorial radius, semi-axis (C{meter}). 

351 ''' 

352 return self._E.a 

353 

354 a = equatoradius 

355 

356 @Property_RO 

357 def _e_TAYTOL(self): 

358 '''(INTERNAL) Get and cache C{e * TAYTOL}. 

359 ''' 

360 return self._e * _TAYTOL 

361 

362 @Property_RO 

363 def _Eu(self): 

364 '''(INTERNAL) Get and cache C{Elliptic(_mu)}. 

365 ''' 

366 return Elliptic(self._mu) 

367 

368 @Property_RO 

369 def _Eu_cE(self): 

370 '''(INTERNAL) Get and cache C{_Eu.cE}. 

371 ''' 

372 return self._Eu.cE 

373 

374 def _Eu_2cE_(self, xi): 

375 '''(INTERNAL) Return C{_Eu.cE * 2 - B{xi}}. 

376 ''' 

377 return self._Eu_cE * _2_0 - xi 

378 

379 @Property_RO 

380 def _Eu_cE_4(self): 

381 '''(INTERNAL) Get and cache C{_Eu.cE / 4}. 

382 ''' 

383 return self._Eu_cE / _4_0 

384 

385 @Property_RO 

386 def _Eu_cK(self): 

387 '''(INTERNAL) Get and cache C{_Eu.cK}. 

388 ''' 

389 return self._Eu.cK 

390 

391 @Property_RO 

392 def _Eu_cK_cE(self): 

393 '''(INTERNAL) Get and cache C{_Eu.cK / _Eu.cE}. 

394 ''' 

395 return self._Eu_cK / self._Eu_cE 

396 

397 @Property_RO 

398 def _Eu_2cK_PI(self): 

399 '''(INTERNAL) Get and cache C{_Eu.cK * 2 / PI}. 

400 ''' 

401 return self._Eu_cK / PI_2 

402 

403 @Property_RO 

404 def _Ev(self): 

405 '''(INTERNAL) Get and cache C{Elliptic(_mv)}. 

406 ''' 

407 return Elliptic(self._mv) 

408 

409 @Property_RO 

410 def _Ev_cK(self): 

411 '''(INTERNAL) Get and cache C{_Ev.cK}. 

412 ''' 

413 return self._Ev.cK 

414 

415 @Property_RO 

416 def _Ev_cKE(self): 

417 '''(INTERNAL) Get and cache C{_Ev.cKE}. 

418 ''' 

419 return self._Ev.cKE 

420 

421 @Property_RO 

422 def _Ev_3cKE_4(self): 

423 '''(INTERNAL) Get and cache C{_Ev.cKE * 3 / 4}. 

424 ''' 

425 return self._Ev_cKE * 0.75 # _0_75 

426 

427 @Property_RO 

428 def _Ev_5cKE_4(self): 

429 '''(INTERNAL) Get and cache C{_Ev.cKE * 5 / 4}. 

430 ''' 

431 return self._Ev_cKE * 1.25 # _1_25 

432 

433 @Property_RO 

434 def extendp(self): 

435 '''Get the domain (C{bool}), I{extended} or I{standard}. 

436 ''' 

437 return self._extendp 

438 

439 @property_RO 

440 def flattening(self): 

441 '''Get the C{ellipsoid}'s flattening (C{scalar}). 

442 ''' 

443 return self._E.f 

444 

445 f = flattening 

446 

447 def forward(self, lat, lon, lon0=None, name=NN): # MCCABE 13 

448 '''Forward projection, from geographic to transverse Mercator. 

449 

450 @arg lat: Latitude of point (C{degrees}). 

451 @arg lon: Longitude of point (C{degrees}). 

452 @kwarg lon0: Central meridian (C{degrees180}), overriding 

453 the default if not C{None}. 

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

455 

456 @return: L{Forward4Tuple}C{(easting, northing, gamma, scale)}. 

457 

458 @see: C{void TMExact::Forward(real lon0, real lat, real lon, 

459 real &x, real &y, 

460 real &gamma, real &k)}. 

461 

462 @raise ETMError: No convergence, thrown iff property 

463 C{B{raiser}=True}. 

464 ''' 

465 lat = _fix90(lat - self._lat0) 

466 lon, _ = _diff182((self.lon0 if lon0 is None else lon0), lon) 

467 if self.extendp: 

468 backside = _lat = _lon = False 

469 else: # enforce the parity 

470 lat, _lat = _unsigned2(lat) 

471 lon, _lon = _unsigned2(lon) 

472 backside = lon > 90 

473 if backside: # PYCHOK no cover 

474 lon = _loneg(lon) 

475 if lat == 0: 

476 _lat = True 

477 

478 # u, v = coordinates for the Thompson TM, Lee 54 

479 if lat == 90: # isnear90(lat) 

480 u = self._Eu_cK 

481 v = self._iteration = self._zetaC = 0 

482 elif lat == 0 and lon == self._1_e_90: # PYCHOK no cover 

483 u = self._iteration = self._zetaC = 0 

484 v = self._Ev_cK 

485 else: # tau = tan(phi), taup = sinh(psi) 

486 tau, lam = _tand(lat), radians(lon) 

487 u, v = self._zetaInv2(self._E.es_taupf(tau), lam) 

488 

489 sncndn6 = self._sncndn6(u, v) 

490 y, x, _ = self._sigma3(v, *sncndn6) 

491 g, k = (lon, self.k0) if isnear90(lat) else \ 

492 self._zetaScaled(sncndn6, ll=False) 

493 

494 if backside: 

495 y, g = self._Eu_2cE_(y), _loneg(g) 

496 y *= self._k0_a 

497 x *= self._k0_a 

498 if _lat: 

499 y, g = neg_(y, g) 

500 if _lon: 

501 x, g = neg_(x, g) 

502 return Forward4Tuple(x, y, g, k, iteration=self._iteration, 

503 name=name or self.name) 

504 

505 def _Inv03(self, psi, dlam, _3_mv_e): # (xi, deta, _3_mv) 

506 '''(INTERNAL) Partial C{_zetaInv04} or C{_sigmaInv04}, Case 2 

507 ''' 

508 # atan2(dlam-psi, psi+dlam) + 45d gives arg(zeta - zeta0) in 

509 # range [-135, 225). Subtracting 180 (multiplier is negative) 

510 # makes range [-315, 45). Multiplying by 1/3 (for cube root) 

511 # gives range [-105, 15). In particular the range [-90, 180] 

512 # in zeta space maps to [-90, 0] in w space as required. 

513 a = atan2(dlam - psi, psi + dlam) / _3_0 - PI_4 

514 s, c = sincos2(a) 

515 h = hypot(psi, dlam) 

516 r = cbrt(h * _3_mv_e) 

517 u = r * c 

518 v = r * s + self._Ev_cK 

519 # Error using this guess is about 0.068 * rad^(5/3) 

520 return u, v, h 

521 

522 @property_RO 

523 def iteration(self): 

524 '''Get the most recent C{ExactTransverseMercator.forward} 

525 or C{ExactTransverseMercator.reverse} iteration number 

526 (C{int}) or C{None} if not available/applicable. 

527 ''' 

528 return self._iteration 

529 

530 @property_doc_(''' the central scale factor (C{float}).''') 

531 def k0(self): 

532 '''Get the central scale factor (C{float}), aka I{C{scale0}}. 

533 ''' 

534 return self._k0 # aka scale0 

535 

536 @k0.setter # PYCHOK setter! 

537 def k0(self, k0): 

538 '''Set the central scale factor (C{float}), aka I{C{scale0}}. 

539 

540 @raise ETMError: Invalid B{C{k0}}. 

541 ''' 

542 k0 = Scalar_(k0=k0, Error=ETMError, low=_TOL_10, high=_1_0) 

543 if self._k0 != k0: 

544 ExactTransverseMercator._k0_a._update(self) # redo ._k0_a 

545 self._k0 = k0 

546 

547 @Property_RO 

548 def _k0_a(self): 

549 '''(INTERNAL) Get and cache C{k0 * equatoradius}. 

550 ''' 

551 return self.k0 * self.equatoradius 

552 

553 @property_doc_(''' the central meridian (C{degrees180}).''') 

554 def lon0(self): 

555 '''Get the central meridian (C{degrees180}). 

556 ''' 

557 return self._lon0 

558 

559 @lon0.setter # PYCHOK setter! 

560 def lon0(self, lon0): 

561 '''Set the central meridian (C{degrees180}). 

562 

563 @raise ETMError: Invalid B{C{lon0}}. 

564 ''' 

565 self._lon0 = _norm180(Degrees(lon0=lon0, Error=ETMError)) 

566 

567 @deprecated_property_RO 

568 def majoradius(self): # PYCHOK no cover 

569 '''DEPRECATED, use property C{equatoradius}.''' 

570 return self.equatoradius 

571 

572 @Property_RO 

573 def _1_mu_2(self): 

574 '''(INTERNAL) Get and cache C{_mu / 2 + 1}. 

575 ''' 

576 return self._mu * _0_5 + _1_0 

577 

578 @Property_RO 

579 def _3_mv(self): 

580 '''(INTERNAL) Get and cache C{3 / _mv}. 

581 ''' 

582 return _3_0 / self._mv 

583 

584 @Property_RO 

585 def _3_mv_e(self): 

586 '''(INTERNAL) Get and cache C{3 / (_mv * _e)}. 

587 ''' 

588 return _3_0 / (self._mv * self._e) 

589 

590 def _Newton2(self, taup, lam, u, v, C, *psi): # or (xi, eta, u, v) 

591 '''(INTERNAL) Invert C{_zetaInv2} or C{_sigmaInv2} using Newton's method. 

592 

593 @return: 2-Tuple C{(u, v)}. 

594 

595 @raise ETMError: No convergence. 

596 ''' 

597 sca1, tol2 = _1_0, _TOL_10 

598 if psi: # _zetaInv2 

599 sca1 = sca1 / hypot1(taup) # /= chokes PyChecker 

600 tol2 = tol2 / max(psi[0], _1_0)**2 

601 

602 _zeta3 = self._zeta3 

603 _zetaDwd2 = self._zetaDwd2 

604 else: # _sigmaInv2 

605 _zeta3 = self._sigma3 

606 _zetaDwd2 = self._sigmaDwd2 

607 

608 d2, r = tol2, self.raiser 

609 _U_2 = Fsum(u).fsum2f_ 

610 _V_2 = Fsum(v).fsum2f_ 

611 # min iterations 2, max 6 or 7, mean 3.9 or 4.0 

612 for i in range(1, _TRIPS): # GEOGRAPHICLIB_PANIC 

613 sncndn6 = self._sncndn6(u, v) 

614 du, dv = _zetaDwd2(*sncndn6) 

615 T, L, _ = _zeta3(v, *sncndn6) 

616 T = (taup - T) * sca1 

617 L -= lam 

618 u, dU = _U_2(T * du, L * dv) 

619 v, dV = _V_2(T * dv, -L * du) 

620 if d2 < tol2: 

621 r = False 

622 break 

623 d2 = hypot2(dU, dV) 

624 

625 self._iteration = i 

626 if r: # PYCHOK no cover 

627 n = callername(up=2, underOK=True) 

628 t = unstr(n, taup, lam, u, v, C=C) 

629 raise ETMError(Fmt.no_convergence(d2, tol2), txt=t) 

630 return u, v 

631 

632 @property_doc_(''' raise an L{ETMError} for convergence failures (C{bool}).''') 

633 def raiser(self): 

634 '''Get the error setting (C{bool}). 

635 ''' 

636 return self._raiser 

637 

638 @raiser.setter # PYCHOK setter! 

639 def raiser(self, raiser): 

640 '''Set the error setting (C{bool}), if C{True} throw an L{ETMError} 

641 for convergence failures. 

642 ''' 

643 self._raiser = bool(raiser) 

644 

645 def reset(self, lat0, lon0): 

646 '''Set the central parallel and meridian. 

647 

648 @arg lat0: Latitude of the central parallel (C{degrees90}). 

649 @arg lon0: Longitude of the central parallel (C{degrees180}). 

650 

651 @return: 2-Tuple C{(lat0, lon0)} of the previous central 

652 parallel and meridian. 

653 

654 @raise ETMError: Invalid B{C{lat0}} or B{C{lon0}}. 

655 ''' 

656 t = self._lat0, self.lon0 

657 self._lat0 = _fix90(Degrees(lat0=lat0, Error=ETMError)) 

658 self. lon0 = lon0 

659 return t 

660 

661 def _resets(self, datum): 

662 '''(INTERNAL) Set the ellipsoid and elliptic moduli. 

663 

664 @arg datum: Ellipsoidal datum (C{Datum}). 

665 

666 @raise ETMError: Near-spherical B{C{datum}} or C{ellipsoid}. 

667 ''' 

668 E = datum.ellipsoid 

669 mu = E.e2 # .eccentricity1st2 

670 mv = E.e21 # _1_0 - mu 

671 if isnear0(E.e) or isnear0(mu, eps0=EPS02) \ 

672 or isnear0(mv, eps0=EPS02): # or sqrt(mu) != E.e 

673 raise ETMError(ellipsoid=E, txt=_near_(_spherical_)) 

674 

675 if self._datum or self._E: 

676 _i = ExactTransverseMercator.iteration._uname 

677 _update_all(self, _i, '_sigmaC', '_zetaC') # _under 

678 

679 self._E = E 

680 self._mu = mu 

681 self._mv = mv 

682 

683 def reverse(self, x, y, lon0=None, name=NN): 

684 '''Reverse projection, from Transverse Mercator to geographic. 

685 

686 @arg x: Easting of point (C{meters}). 

687 @arg y: Northing of point (C{meters}). 

688 @kwarg lon0: Central meridian (C{degrees180}), overriding 

689 the default if not C{None}. 

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

691 

692 @return: L{Reverse4Tuple}C{(lat, lon, gamma, scale)}. 

693 

694 @see: C{void TMExact::Reverse(real lon0, real x, real y, 

695 real &lat, real &lon, 

696 real &gamma, real &k)} 

697 

698 @raise ETMError: No convergence, thrown iff property 

699 C{B{raiser}=True}. 

700 ''' 

701 # undoes the steps in .forward. 

702 xi = y / self._k0_a 

703 eta = x / self._k0_a 

704 if self.extendp: 

705 backside = _lat = _lon = False 

706 else: # enforce the parity 

707 eta, _lon = _unsigned2(eta) 

708 xi, _lat = _unsigned2(xi) 

709 backside = xi > self._Eu_cE 

710 if backside: # PYCHOK no cover 

711 xi = self._Eu_2cE_(xi) 

712 

713 # u, v = coordinates for the Thompson TM, Lee 54 

714 if xi or eta != self._Ev_cKE: 

715 u, v = self._sigmaInv2(xi, eta) 

716 else: # PYCHOK no cover 

717 u = self._iteration = self._sigmaC = 0 

718 v = self._Ev_cK 

719 

720 if v or u != self._Eu_cK: 

721 g, k, lat, lon = self._zetaScaled(self._sncndn6(u, v)) 

722 else: # PYCHOK no cover 

723 g, k, lat, lon = _0_0, self.k0, _90_0, _0_0 

724 

725 if backside: # PYCHOK no cover 

726 lon, g = _loneg(lon), _loneg(g) 

727 if _lat: 

728 lat, g = neg_(lat, g) 

729 if _lon: 

730 lon, g = neg_(lon, g) 

731 lat += self._lat0 

732 lon += self._lon0 if lon0 is None else _norm180(lon0) 

733 return Reverse4Tuple(lat, _norm180(lon), g, k, # _norm180(lat) 

734 iteration=self._iteration, 

735 name=name or self.name) 

736 

737 def _scaled2(self, tau, d2, snu, cnu, dnu, snv, cnv, dnv): 

738 '''(INTERNAL) C{scaled}. 

739 

740 @note: Argument B{C{d2}} is C{_mu * cnu**2 + _mv * cnv**2} 

741 from C{._zeta3}. 

742 

743 @return: 2-Tuple C{(convergence, scale)}. 

744 

745 @see: C{void TMExact::Scale(real tau, real /*lam*/, 

746 real snu, real cnu, real dnu, 

747 real snv, real cnv, real dnv, 

748 real &gamma, real &k)}. 

749 ''' 

750 mu, mv = self._mu, self._mv 

751 cnudnv = cnu * dnv 

752 # Lee 55.12 -- negated for our sign convention. g gives 

753 # the bearing (clockwise from true north) of grid north 

754 g = atan2d(mv * cnv * snv * snu, cnudnv * dnu) 

755 # Lee 55.13 with nu given by Lee 9.1 -- in sqrt change 

756 # the numerator from (1 - snu^2 * dnv^2) to (_mv * snv^2 

757 # + cnu^2 * dnv^2) to maintain accuracy near phi = 90 

758 # and change the denomintor from (dnu^2 + dnv^2 - 1) to 

759 # (_mu * cnu^2 + _mv * cnv^2) to maintain accuracy near 

760 # phi = 0, lam = 90 * (1 - e). Similarly rewrite sqrt in 

761 # 9.1 as _mv + _mu * c^2 instead of 1 - _mu * sin(phi)^2 

762 if d2 > 0: 

763 # originally: sec2 = 1 + tau**2 # sec(phi)^2 

764 # d2 = (mu * cnu**2 + mv * cnv**2) 

765 # q2 = (mv * snv**2 + cnudnv**2) / d2 

766 # k = sqrt(mv + mu / sec2) * sqrt(sec2) * sqrt(q2) 

767 # = sqrt(mv * sec2 + mu) * sqrt(q2) 

768 # = sqrt(mv + mv * tau**2 + mu) * sqrt(q2) 

769 k, q2 = _0_0, (mv * snv**2 + cnudnv**2) 

770 if q2 > 0: 

771 k2 = fsum1f_(mu, mv, mv * tau**2) 

772 if k2 > 0: 

773 k = sqrt(k2) * sqrt(q2 / d2) * self.k0 

774 else: 

775 k = _OVERFLOW 

776 return g, k 

777 

778 def _sigma3(self, v, snu, cnu, dnu, snv, cnv, dnv): 

779 '''(INTERNAL) C{sigma}. 

780 

781 @return: 3-Tuple C{(xi, eta, d2)}. 

782 

783 @see: C{void TMExact::sigma(real /*u*/, real snu, real cnu, real dnu, 

784 real v, real snv, real cnv, real dnv, 

785 real &xi, real &eta)}. 

786 

787 @raise ETMError: No convergence. 

788 ''' 

789 mu = self._mu * cnu 

790 mv = self._mv * cnv 

791 # Lee 55.4 writing 

792 # dnu^2 + dnv^2 - 1 = _mu * cnu^2 + _mv * cnv^2 

793 d2 = cnu * mu + cnv * mv 

794 mu *= snu * dnu 

795 mv *= snv * dnv 

796 if d2 > 0: # /= chokes PyChecker 

797 mu = mu / d2 

798 mv = mv / d2 

799 else: 

800 mu, mv = map1(_overflow, mu, mv) 

801 xi = self._Eu.fE(snu, cnu, dnu) - mu 

802 v -= self._Ev.fE(snv, cnv, dnv) - mv 

803 return xi, v, d2 

804 

805 def _sigmaDwd2(self, snu, cnu, dnu, snv, cnv, dnv): 

806 '''(INTERNAL) C{sigmaDwd}. 

807 

808 @return: 2-Tuple C{(du, dv)}. 

809 

810 @see: C{void TMExact::dwdsigma(real /*u*/, real snu, real cnu, real dnu, 

811 real /*v*/, real snv, real cnv, real dnv, 

812 real &du, real &dv)}. 

813 ''' 

814 snuv = snu * snv 

815 # Reciprocal of 55.9: dw / ds = dn(w)^2/_mv, 

816 # expanding complex dn(w) using A+S 16.21.4 

817 d = self._mv * (cnv**2 + self._mu * snuv**2)**2 

818 r = cnv * dnu * dnv 

819 i = cnu * snuv * self._mu 

820 du = (r**2 - i**2) / d 

821 dv = neg(r * i * _2_0 / d) 

822 return du, dv 

823 

824 def _sigmaInv2(self, xi, eta): 

825 '''(INTERNAL) Invert C{sigma} using Newton's method. 

826 

827 @return: 2-Tuple C{(u, v)}. 

828 

829 @see: C{void TMExact::sigmainv(real xi, real eta, 

830 real &u, real &v)}. 

831 

832 @raise ETMError: No convergence. 

833 ''' 

834 u, v, t, self._sigmaC = self._sigmaInv04(xi, eta) 

835 if not t: 

836 u, v = self._Newton2(xi, eta, u, v, self._sigmaC) 

837 return u, v 

838 

839 def _sigmaInv04(self, xi, eta): 

840 '''(INTERNAL) Starting point for C{sigmaInv}. 

841 

842 @return: 4-Tuple C{(u, v, trip, Case)}. 

843 

844 @see: C{bool TMExact::sigmainv0(real xi, real eta, 

845 real &u, real &v)}. 

846 ''' 

847 t = False 

848 d = eta - self._Ev_cKE 

849 if eta > self._Ev_5cKE_4 or (xi < d and xi < -self._Eu_cE_4): 

850 # sigma as a simple pole at 

851 # w = w0 = Eu.K() + i * Ev.K() 

852 # and sigma is approximated by 

853 # sigma = (Eu.E() + i * Ev.KE()) + 1 / (w - w0) 

854 u, v = _norm2(xi - self._Eu_cE, -d) 

855 u += self._Eu_cK 

856 v += self._Ev_cK 

857 C = 1 

858 

859 elif (eta > self._Ev_3cKE_4 and xi < self._Eu_cE_4) or d > 0: 

860 # At w = w0 = i * Ev.K(), we have 

861 # sigma = sigma0 = i * Ev.KE() 

862 # sigma' = sigma'' = 0 

863 # including the next term in the Taylor series gives: 

864 # sigma = sigma0 - _mv / 3 * (w - w0)^3 

865 # When inverting this, we map arg(w - w0) = [-pi/2, -pi/6] 

866 # to arg(sigma - sigma0) = [-pi/2, pi/2] mapping arg = 

867 # [-pi/2, -pi/6] to [-pi/2, pi/2] 

868 u, v, h = self._Inv03(xi, d, self._3_mv) 

869 t = h < _TAYTOL2 

870 C = 2 

871 

872 else: # use w = sigma * Eu.K/Eu.E (correct in limit _e -> 0) 

873 u = v = self._Eu_cK_cE 

874 u *= xi 

875 v *= eta 

876 C = 3 

877 

878 return u, v, t, C 

879 

880 def _sncndn6(self, u, v): 

881 '''(INTERNAL) Get 6-tuple C{(snu, cnu, dnu, snv, cnv, dnv)}. 

882 ''' 

883 # snu, cnu, dnu = self._Eu.sncndn(u) 

884 # snv, cnv, dnv = self._Ev.sncndn(v) 

885 return self._Eu.sncndn(u) + self._Ev.sncndn(v) 

886 

887 def toStr(self, joined=_COMMASPACE_, **kwds): # PYCHOK signature 

888 '''Return a C{str} representation. 

889 

890 @kwarg joined: Separator to join the attribute strings 

891 (C{str} or C{None} or C{NN} for non-joined). 

892 @kwarg kwds: Optional, overriding keyword arguments. 

893 ''' 

894 d = dict(datum=self.datum.name, lon0=self.lon0, 

895 k0=self.k0, extendp=self.extendp) 

896 if self.name: 

897 d.update(name=self.name) 

898 t = pairs(d, **kwds) 

899 return joined.join(t) if joined else t 

900 

901 def _zeta3(self, unused, snu, cnu, dnu, snv, cnv, dnv): # _sigma3 signature 

902 '''(INTERNAL) C{zeta}. 

903 

904 @return: 3-Tuple C{(taup, lambda, d2)}. 

905 

906 @see: C{void TMExact::zeta(real /*u*/, real snu, real cnu, real dnu, 

907 real /*v*/, real snv, real cnv, real dnv, 

908 real &taup, real &lam)} 

909 ''' 

910 e, cnu2, mv = self._e, cnu**2, self._mv 

911 # Overflow value like atan(overflow) = pi/2 

912 t1 = t2 = _overflow(snu) 

913 # Lee 54.17 but write 

914 # atanh(snu * dnv) = asinh(snu * dnv / sqrt(cnu^2 + _mv * snu^2 * snv^2)) 

915 # atanh(_e * snu / dnv) = asinh(_e * snu / sqrt(_mu * cnu^2 + _mv * cnv^2)) 

916 d1 = cnu2 + mv * (snu * snv)**2 

917 if d1 > EPS02: # _EPSmin 

918 t1 = snu * dnv / sqrt(d1) 

919 else: 

920 d1 = 0 

921 d2 = self._mu * cnu2 + mv * cnv**2 

922 if d2 > EPS02: # _EPSmin 

923 t2 = sinh(e * asinh(e * snu / sqrt(d2))) 

924 else: 

925 d2 = 0 

926 # psi = asinh(t1) - asinh(t2) 

927 # taup = sinh(psi) 

928 taup = t1 * hypot1(t2) - t2 * hypot1(t1) 

929 lam = (atan2(dnu * snv, cnu * cnv) - 

930 atan2(cnu * snv * e, dnu * cnv) * e) if d1 and d2 else _0_0 

931 return taup, lam, d2 

932 

933 def _zetaDwd2(self, snu, cnu, dnu, snv, cnv, dnv): 

934 '''(INTERNAL) C{zetaDwd}. 

935 

936 @return: 2-Tuple C{(du, dv)}. 

937 

938 @see: C{void TMExact::dwdzeta(real /*u*/, real snu, real cnu, real dnu, 

939 real /*v*/, real snv, real cnv, real dnv, 

940 real &du, real &dv)}. 

941 ''' 

942 cnu2 = cnu**2 * self._mu 

943 cnv2 = cnv**2 

944 dnuv = dnu * dnv 

945 dnuv2 = dnuv**2 

946 snuv = snu * snv 

947 snuv2 = snuv**2 * self._mu 

948 # Lee 54.21 but write (see A+S 16.21.4) 

949 # (1 - dnu^2 * snv^2) = (cnv^2 + _mu * snu^2 * snv^2) 

950 d = self._mv * (cnv2 + snuv2)**2 # max(d, EPS02)? 

951 du = cnu * dnuv * (cnv2 - snuv2) / d 

952 dv = cnv * snuv * (cnu2 + dnuv2) / d 

953 return du, neg(dv) 

954 

955 def _zetaInv2(self, taup, lam): 

956 '''(INTERNAL) Invert C{zeta} using Newton's method. 

957 

958 @return: 2-Tuple C{(u, v)}. 

959 

960 @see: C{void TMExact::zetainv(real taup, real lam, 

961 real &u, real &v)}. 

962 

963 @raise ETMError: No convergence. 

964 ''' 

965 psi = asinh(taup) 

966 u, v, t, self._zetaC = self._zetaInv04(psi, lam) 

967 if not t: 

968 u, v = self._Newton2(taup, lam, u, v, self._zetaC, psi) 

969 return u, v 

970 

971 def _zetaInv04(self, psi, lam): 

972 '''(INTERNAL) Starting point for C{zetaInv}. 

973 

974 @return: 4-Tuple C{(u, v, trip, Case)}. 

975 

976 @see: C{bool TMExact::zetainv0(real psi, real lam, # radians 

977 real &u, real &v)}. 

978 ''' 

979 if lam > self._1_2e_PI_2: 

980 d = lam - self._1_e_PI_2 

981 if psi < d and psi < self._e_PI_4_: # PYCHOK no cover 

982 # N.B. this branch is normally *not* taken because psi < 0 

983 # is converted psi > 0 by .forward. There's a log singularity 

984 # at w = w0 = Eu.K() + i * Ev.K(), corresponding to the south 

985 # pole, where we have, approximately 

986 # psi = _e + i * pi/2 - _e * atanh(cos(i * (w - w0)/(1 + _mu/2))) 

987 # Inverting this gives: 

988 e = self._e # eccentricity 

989 s, c = sincos2((PI_2 - lam) / e) 

990 h, r = sinh(_1_0 - psi / e), self._1_mu_2 

991 u = self._Eu_cK - r * asinh(s / hypot(c, h)) 

992 v = self._Ev_cK - r * atan2(c, h) 

993 return u, v, False, 1 

994 

995 elif psi < self._e_PI_2: 

996 # At w = w0 = i * Ev.K(), we have 

997 # zeta = zeta0 = i * (1 - _e) * pi/2 

998 # zeta' = zeta'' = 0 

999 # including the next term in the Taylor series gives: 

1000 # zeta = zeta0 - (_mv * _e) / 3 * (w - w0)^3 

1001 # When inverting this, we map arg(w - w0) = [-90, 0] 

1002 # to arg(zeta - zeta0) = [-90, 180] 

1003 u, v, h = self._Inv03(psi, d, self._3_mv_e) 

1004 return u, v, (h < self._e_TAYTOL), 2 

1005 

1006 # Use spherical TM, Lee 12.6 -- writing C{atanh(sin(lam) / 

1007 # cosh(psi)) = asinh(sin(lam) / hypot(cos(lam), sinh(psi)))}. 

1008 # This takes care of the log singularity at C{zeta = Eu.K()}, 

1009 # corresponding to the north pole. 

1010 s, c = sincos2(lam) 

1011 h, r = sinh(psi), self._Eu_2cK_PI 

1012 # But scale to put 90, 0 on the right place 

1013 u = r * atan2(h, c) 

1014 v = r * asinh(s / hypot(h, c)) 

1015 return u, v, False, 3 

1016 

1017 def _zetaScaled(self, sncndn6, ll=True): 

1018 '''(INTERNAL) Recompute (T, L) from (u, v) to improve accuracy of Scale. 

1019 

1020 @arg sncndn6: 6-Tuple C{(snu, cnu, dnu, snv, cnv, dnv)}. 

1021 

1022 @return: 2-Tuple C{(g, k)} if not C{B{ll}} else 

1023 4-tuple C{(g, k, lat, lon)}. 

1024 ''' 

1025 t, lam, d2 = self._zeta3(None, *sncndn6) 

1026 tau = self._E.es_tauf(t) 

1027 g_k = self._scaled2(tau, d2, *sncndn6) 

1028 if ll: 

1029 g_k += atan1d(tau), degrees(lam) 

1030 return g_k # or (g, k, lat, lon) 

1031 

1032 

1033def parseETM5(strUTM, datum=_WGS84, Etm=Etm, falsed=True, name=NN): 

1034 '''Parse a string representing a UTM coordinate, consisting 

1035 of C{"zone[band] hemisphere easting northing"}. 

1036 

1037 @arg strUTM: A UTM coordinate (C{str}). 

1038 @kwarg datum: Optional datum to use (L{Datum}, L{Ellipsoid}, 

1039 L{Ellipsoid2} or L{a_f2Tuple}). 

1040 @kwarg Etm: Optional class to return the UTM coordinate 

1041 (L{Etm}) or C{None}. 

1042 @kwarg falsed: Both easting and northing are C{falsed} (C{bool}). 

1043 @kwarg name: Optional B{C{Etm}} name (C{str}). 

1044 

1045 @return: The UTM coordinate (B{C{Etm}}) or if B{C{Etm}} is 

1046 C{None}, a L{UtmUps5Tuple}C{(zone, hemipole, easting, 

1047 northing, band)}. The C{hemipole} is the hemisphere 

1048 C{'N'|'S'}. 

1049 

1050 @raise ETMError: Invalid B{C{strUTM}}. 

1051 

1052 @raise TypeError: Invalid or near-spherical B{C{datum}}. 

1053 ''' 

1054 r = _parseUTM5(strUTM, datum, Etm, falsed, Error=ETMError, name=name) 

1055 return r 

1056 

1057 

1058def toEtm8(latlon, lon=None, datum=None, Etm=Etm, falsed=True, 

1059 name=NN, strict=True, 

1060 zone=None, **cmoff): 

1061 '''Convert a geodetic lat-/longitude to an ETM coordinate. 

1062 

1063 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal) 

1064 geodetic C{LatLon} instance. 

1065 @kwarg lon: Optional longitude (C{degrees}) or C{None}. 

1066 @kwarg datum: Optional datum for the ETM coordinate, 

1067 overriding B{C{latlon}}'s datum (L{Datum}, 

1068 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). 

1069 @kwarg Etm: Optional class to return the ETM coordinate 

1070 (L{Etm}) or C{None}. 

1071 @kwarg falsed: False both easting and northing (C{bool}). 

1072 @kwarg name: Optional B{C{Utm}} name (C{str}). 

1073 @kwarg strict: Restrict B{C{lat}} to UTM ranges (C{bool}). 

1074 @kwarg zone: Optional UTM zone to enforce (C{int} or C{str}). 

1075 @kwarg cmoff: DEPRECATED, use B{C{falsed}}. Offset longitude 

1076 from the zone's central meridian (C{bool}). 

1077 

1078 @return: The ETM coordinate as an B{C{Etm}} instance or a 

1079 L{UtmUps8Tuple}C{(zone, hemipole, easting, northing, 

1080 band, datum, gamma, scale)} if B{C{Etm}} is C{None} 

1081 or not B{C{falsed}}. The C{hemipole} is the C{'N'|'S'} 

1082 hemisphere. 

1083 

1084 @raise ETMError: No convergence transforming to ETM easting 

1085 and northing. 

1086 

1087 @raise ETMError: Invalid B{C{zone}} or near-spherical or 

1088 incompatible B{C{datum}} or C{ellipsoid}. 

1089 

1090 @raise RangeError: If B{C{lat}} outside the valid UTM bands or 

1091 if B{C{lat}} or B{C{lon}} outside the valid 

1092 range and L{pygeodesy.rangerrors} set to C{True}. 

1093 

1094 @raise TypeError: Invalid or near-spherical B{C{datum}} or 

1095 B{C{latlon}} not ellipsoidal. 

1096 

1097 @raise ValueError: The B{C{lon}} value is missing or B{C{latlon}} 

1098 is invalid. 

1099 ''' 

1100 z, B, lat, lon, d, f, name = _to7zBlldfn(latlon, lon, datum, 

1101 falsed, name, zone, 

1102 strict, ETMError, **cmoff) 

1103 lon0 = _cmlon(z) if f else None 

1104 x, y, g, k = d.exactTM.forward(lat, lon, lon0=lon0) 

1105 

1106 return _toXtm8(Etm, z, lat, x, y, B, d, g, k, f, 

1107 name, latlon, d.exactTM, Error=ETMError) 

1108 

1109 

1110if __name__ == '__main__': # MCCABE 13 

1111 

1112 from pygeodesy.internals import _usage 

1113 from pygeodesy import fstr, KTransverseMercator, printf 

1114 from sys import argv, exit as _exit 

1115 

1116 # mimick some of I{Karney}'s utility C{TransverseMercatorProj} 

1117 _f = _r = _s = _t = False 

1118 _as = argv[1:] 

1119 while _as and _as[0].startswith(_DASH_): 

1120 _a = _as.pop(0) 

1121 if len(_a) < 2: 

1122 _exit('%s: option %r invalid' % (_usage(*argv), _a)) 

1123 elif '-forward'.startswith(_a): 

1124 _f, _r = True, False 

1125 elif '-reverse'.startswith(_a): 

1126 _f, _r = False, True 

1127 elif '-series'.startswith(_a): 

1128 _s, _t = True, False 

1129 elif _a == '-t': 

1130 _s, _t = False, True 

1131 elif '-help'.startswith(_a): 

1132 _exit(_usage(argv[0], '[-s | -t]', 

1133 '[-f[orward] <lat> <lon>', 

1134 '| -r[everse] <easting> <northing>', 

1135 '| <lat> <lon>]', 

1136 '| -h[elp]')) 

1137 else: 

1138 _exit('%s: option %r not supported' % (_usage(*argv), _a)) 

1139 if len(_as) > 1: 

1140 f2 = map1(float, *_as[:2]) 

1141 else: 

1142 _exit('%s ...: incomplete' % (_usage(*argv),)) 

1143 

1144 if _s: # -series 

1145 tm = KTransverseMercator() 

1146 else: 

1147 tm = ExactTransverseMercator(extendp=_t) 

1148 

1149 if _f: 

1150 t = tm.forward(*f2) 

1151 elif _r: 

1152 t = tm.reverse(*f2) 

1153 else: 

1154 t = tm.forward(*f2) 

1155 printf('%s: %s', tm.classname, fstr(t, sep=_SPACE_)) 

1156 t = tm.reverse(t.easting, t.northing) 

1157 printf('%s: %s', tm.classname, fstr(t, sep=_SPACE_)) 

1158 

1159 

1160# % python3 -m pygeodesy.etm 33.33 44.44 

1161# ExactTransverseMercator: 4276926.114804 4727193.767015 28.375537 1.233325 

1162# ExactTransverseMercator: 33.33 44.44 28.375537 1.233325 

1163 

1164# % python3 -m pygeodesy.etm -s 33.33 44.44 

1165# KTransverseMercator: 4276926.114804 4727193.767015 28.375537 1.233325 

1166# KTransverseMercator: 33.33 44.44 28.375537 1.233325 

1167 

1168# % echo 33.33 44.44 | .../bin/TransverseMercatorProj 

1169# 4276926.114804 4727193.767015 28.375536563148 1.233325101778 

1170 

1171# **) MIT License 

1172# 

1173# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1174# 

1175# Permission is hereby granted, free of charge, to any person obtaining a 

1176# copy of this software and associated documentation files (the "Software"), 

1177# to deal in the Software without restriction, including without limitation 

1178# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1179# and/or sell copies of the Software, and to permit persons to whom the 

1180# Software is furnished to do so, subject to the following conditions: 

1181# 

1182# The above copyright notice and this permission notice shall be included 

1183# in all copies or substantial portions of the Software. 

1184# 

1185# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1186# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1187# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1188# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1189# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1190# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1191# OTHER DEALINGS IN THE SOFTWARE.