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 

74# from pygeodesy.fsums import Fsum # from .fmath 

75from pygeodesy.fmath import cbrt, hypot, hypot1, hypot2, Fsum 

76from pygeodesy.interns import _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__ = '24.06.11' 

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 

104class ETMError(UTMError): 

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

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

107 ''' 

108 pass 

109 

110 

111class Etm(Utm): 

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

113 a Universal Transverse Mercator (UTM) coordinate using the 

114 L{ExactTransverseMercator} projection for highest accuracy. 

115 

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

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

118 

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

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

121 ''' 

122 _Error = ETMError # see utm.UTMError 

123 _exactTM = None 

124 

125 __init__ = Utm.__init__ 

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

127 

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

129 ''' 

130 

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

132 def exactTM(self): 

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

134 ''' 

135 if self._exactTM is None: 

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

137 return self._exactTM 

138 

139 @exactTM.setter # PYCHOK setter! 

140 def exactTM(self, exactTM): 

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

142 

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

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

145 ''' 

146 _xinstanceof(ExactTransverseMercator, exactTM=exactTM) 

147 

148 E = self.datum.ellipsoid 

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

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

151 self._exactTM = exactTM 

152 self._scale0 = exactTM.k0 

153 

154 def parse(self, strETM, **name): 

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

156 

157 @arg strETM: The ETM coordinate (C{str}), see function L{parseETM5}. 

158 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name. 

159 

160 @return: The instance (L{Etm}). 

161 

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

163 

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

165 L{pygeodesy.parseUTMUPS5}. 

166 ''' 

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

168 name=self._name__(name)) 

169 

170 @deprecated_method 

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

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

173 ''' 

174 return self.parse(strETM) 

175 

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

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

178 

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

180 (C{LatLon}) or C{None}. 

181 @kwarg unfalse: Unfalse B{C{easting}} and B{C{northing}} if C{falsed} (C{bool}). 

182 

183 @return: This ETM coordinate as (B{C{LatLon}}) or if C{B{LatLon} is None}, 

184 a L{LatLonDatum5Tuple}C{(lat, lon, datum, gamma, scale)}. 

185 

186 @raise ETMError: This ETM coordinate's C{exacTM} and this C{datum} are not 

187 compatible or no convergence transforming to lat-/longitude. 

188 

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

190 ''' 

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

192 self._toLLEB(unfalse=unfalse) 

193 return self._latlon5(LatLon) 

194 

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

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

197 ''' 

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

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

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

201 t = repr(d.ellipsoid) 

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

203 

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

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

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

207 

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

209 self._latlon5args(ll, g, k, _toBand, unfalse, xTM) 

210 

211 def toUtm(self): # PYCHOK signature 

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

213 

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

215 ''' 

216 return self._xcopy2(Utm) 

217 

218 

219class ExactTransverseMercator(_NamedBase): 

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

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

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

223 ''' 

224 _datum = _WGS84 # Datum 

225 _E = _EWGS84 # Ellipsoid 

226 _extendp = False # use extended domain 

227# _iteration = None # ._sigmaInv2 and ._zetaInv2 

228 _k0 = _K0_UTM # central scale factor 

229 _lat0 = _0_0 # central parallel 

230 _lon0 = _0_0 # central meridian 

231 _mu = _EWGS84.e2 # 1st eccentricity squared 

232 _mv = _EWGS84.e21 # 1 - ._mu 

233 _raiser = False # throw Error 

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

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

236 

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

238 '''New L{ExactTransverseMercator} projection. 

239 

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

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

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

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

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

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

246 @kwarg name: Optional C{B{name}=NN} for the projection (C{str}). 

247 

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

249 or B{C{k0}}. 

250 

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

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

253 especially on B{X{extendp}}. 

254 

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

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

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

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

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

260 12.2 Monterey C{arm64} and C{"arm64_x86_64"}). 

261 ''' 

262 if extendp: 

263 self._extendp = True 

264 if name: 

265 self.name = name 

266 if raiser: 

267 self.raiser = True 

268 

269 TM = ExactTransverseMercator 

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

271 self.datum = datum # invokes ._resets 

272 if lon0 or lon0 != TM._lon0: 

273 self.lon0 = lon0 

274 if k0 is not TM._k0: 

275 self.k0 = k0 

276 

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

278 def datum(self): 

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

280 ''' 

281 return self._datum 

282 

283 @datum.setter # PYCHOK setter! 

284 def datum(self, datum): 

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

286 

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

288 ''' 

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

290 self._resets(d) 

291 self._datum = d 

292 

293 @Property_RO 

294 def _e(self): 

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

296 ''' 

297 return self._E.e 

298 

299 @Property_RO 

300 def _1_e_90(self): # PYCHOK no cover 

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

302 ''' 

303 return (_1_0 - self._e) * _90_0 

304 

305 @property_RO 

306 def ellipsoid(self): 

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

308 ''' 

309 return self._E 

310 

311 @Property_RO 

312 def _e_PI_2(self): 

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

314 ''' 

315 return self._e * PI_2 

316 

317 @Property_RO 

318 def _e_PI_4_(self): 

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

320 ''' 

321 return -self._e * PI_4 

322 

323 @Property_RO 

324 def _1_e_PI_2(self): 

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

326 ''' 

327 return (_1_0 - self._e) * PI_2 

328 

329 @Property_RO 

330 def _1_2e_PI_2(self): 

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

332 ''' 

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

334 

335 @property_RO 

336 def equatoradius(self): 

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

338 ''' 

339 return self._E.a 

340 

341 a = equatoradius 

342 

343 @Property_RO 

344 def _e_TAYTOL(self): 

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

346 ''' 

347 return self._e * _TAYTOL 

348 

349 @Property_RO 

350 def _Eu(self): 

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

352 ''' 

353 return Elliptic(self._mu) 

354 

355 @Property_RO 

356 def _Eu_cE(self): 

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

358 ''' 

359 return self._Eu.cE 

360 

361 def _Eu_2cE_(self, xi): 

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

363 ''' 

364 return self._Eu_cE * _2_0 - xi 

365 

366 @Property_RO 

367 def _Eu_cE_4(self): 

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

369 ''' 

370 return self._Eu_cE / _4_0 

371 

372 @Property_RO 

373 def _Eu_cK(self): 

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

375 ''' 

376 return self._Eu.cK 

377 

378 @Property_RO 

379 def _Eu_cK_cE(self): 

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

381 ''' 

382 return self._Eu_cK / self._Eu_cE 

383 

384 @Property_RO 

385 def _Eu_2cK_PI(self): 

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

387 ''' 

388 return self._Eu_cK / PI_2 

389 

390 @Property_RO 

391 def _Ev(self): 

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

393 ''' 

394 return Elliptic(self._mv) 

395 

396 @Property_RO 

397 def _Ev_cK(self): 

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

399 ''' 

400 return self._Ev.cK 

401 

402 @Property_RO 

403 def _Ev_cKE(self): 

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

405 ''' 

406 return self._Ev.cKE 

407 

408 @Property_RO 

409 def _Ev_3cKE_4(self): 

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

411 ''' 

412 return self._Ev_cKE * 0.75 # _0_75 

413 

414 @Property_RO 

415 def _Ev_5cKE_4(self): 

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

417 ''' 

418 return self._Ev_cKE * 1.25 # _1_25 

419 

420 @Property_RO 

421 def extendp(self): 

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

423 ''' 

424 return self._extendp 

425 

426 @property_RO 

427 def flattening(self): 

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

429 ''' 

430 return self._E.f 

431 

432 f = flattening 

433 

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

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

436 

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

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

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

440 the default if not C{None}. 

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

442 

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

444 

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

446 real &x, real &y, 

447 real &gamma, real &k)}. 

448 

449 @raise ETMError: No convergence, thrown iff property 

450 C{B{raiser}=True}. 

451 ''' 

452 lat = _fix90(lat - self._lat0) 

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

454 if self.extendp: 

455 backside = _lat = _lon = False 

456 else: # enforce the parity 

457 lat, _lat = _unsigned2(lat) 

458 lon, _lon = _unsigned2(lon) 

459 backside = lon > 90 

460 if backside: # PYCHOK no cover 

461 lon = _loneg(lon) 

462 if lat == 0: 

463 _lat = True 

464 

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

466 if lat == 90: # isnear90(lat) 

467 u = self._Eu_cK 

468 v = self._iteration = self._zetaC = 0 

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

470 u = self._iteration = self._zetaC = 0 

471 v = self._Ev_cK 

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

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

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

475 

476 sncndn6 = self._sncndn6(u, v) 

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

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

479 self._zetaScaled(sncndn6, ll=False) 

480 

481 if backside: 

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

483 y *= self._k0_a 

484 x *= self._k0_a 

485 if _lat: 

486 y, g = neg_(y, g) 

487 if _lon: 

488 x, g = neg_(x, g) 

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

490 name=self._name__(name)) 

491 

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

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

494 ''' 

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

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

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

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

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

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

501 s, c = sincos2(a) 

502 h = hypot(psi, dlam) 

503 r = cbrt(h * _3_mv_e) 

504 u = r * c 

505 v = r * s + self._Ev_cK 

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

507 return u, v, h 

508 

509 @property_RO 

510 def iteration(self): 

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

512 or C{ExactTransverseMercator.reverse} iteration number 

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

514 ''' 

515 return self._iteration 

516 

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

518 def k0(self): 

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

520 ''' 

521 return self._k0 # aka scale0 

522 

523 @k0.setter # PYCHOK setter! 

524 def k0(self, k0): 

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

526 

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

528 ''' 

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

530 if self._k0 != k0: 

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

532 self._k0 = k0 

533 

534 @Property_RO 

535 def _k0_a(self): 

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

537 ''' 

538 return self.k0 * self.equatoradius 

539 

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

541 def lon0(self): 

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

543 ''' 

544 return self._lon0 

545 

546 @lon0.setter # PYCHOK setter! 

547 def lon0(self, lon0): 

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

549 

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

551 ''' 

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

553 

554 @deprecated_property_RO 

555 def majoradius(self): # PYCHOK no cover 

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

557 return self.equatoradius 

558 

559 @Property_RO 

560 def _1_mu_2(self): 

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

562 ''' 

563 return self._mu * _0_5 + _1_0 

564 

565 @Property_RO 

566 def _3_mv(self): 

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

568 ''' 

569 return _3_0 / self._mv 

570 

571 @Property_RO 

572 def _3_mv_e(self): 

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

574 ''' 

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

576 

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

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

579 

580 @return: 2-Tuple C{(u, v)}. 

581 

582 @raise ETMError: No convergence. 

583 ''' 

584 sca1, tol2 = _1_0, _TOL_10 

585 if psi: # _zetaInv2 

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

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

588 

589 _zeta3 = self._zeta3 

590 _zetaDwd2 = self._zetaDwd2 

591 else: # _sigmaInv2 

592 _zeta3 = self._sigma3 

593 _zetaDwd2 = self._sigmaDwd2 

594 

595 d2, r = tol2, self.raiser 

596 _U_2 = Fsum(u).fsum2f_ 

597 _V_2 = Fsum(v).fsum2f_ 

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

599 _hy2 = hypot2 

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

601 sncndn6 = self._sncndn6(u, v) 

602 du, dv = _zetaDwd2(*sncndn6) 

603 T, L, _ = _zeta3(v, *sncndn6) 

604 T = (taup - T) * sca1 

605 L -= lam 

606 u, dU = _U_2(T * du, L * dv) 

607 v, dV = _V_2(T * dv, -L * du) 

608 if d2 < tol2: 

609 r = False 

610 break 

611 d2 = _hy2(dU, dV) 

612 

613 self._iteration = i 

614 if r: # PYCHOK no cover 

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

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

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

618 return u, v 

619 

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

621 def raiser(self): 

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

623 ''' 

624 return self._raiser 

625 

626 @raiser.setter # PYCHOK setter! 

627 def raiser(self, raiser): 

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

629 for convergence failures. 

630 ''' 

631 self._raiser = bool(raiser) 

632 

633 def reset(self, lat0, lon0): 

634 '''Set the central parallel and meridian. 

635 

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

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

638 

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

640 parallel and meridian. 

641 

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

643 ''' 

644 t = self._lat0, self.lon0 

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

646 self. lon0 = lon0 

647 return t 

648 

649 def _resets(self, datum): 

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

651 

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

653 

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

655 ''' 

656 E = datum.ellipsoid 

657 mu = E.e2 # .eccentricity1st2 

658 mv = E.e21 # _1_0 - mu 

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

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

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

662 

663 if self._datum or self._E: 

664 _i = ExactTransverseMercator.iteration._uname 

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

666 

667 self._E = E 

668 self._mu = mu 

669 self._mv = mv 

670 

671 def reverse(self, x, y, lon0=None, **name): 

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

673 

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

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

676 @kwarg lon0: Optional central meridian (C{degrees180}), 

677 overriding the default (C{iff not None}). 

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

679 

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

681 

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

683 real &lat, real &lon, 

684 real &gamma, real &k)} 

685 

686 @raise ETMError: No convergence, thrown iff property 

687 C{B{raiser}=True}. 

688 ''' 

689 # undoes the steps in .forward. 

690 xi = y / self._k0_a 

691 eta = x / self._k0_a 

692 if self.extendp: 

693 backside = _lat = _lon = False 

694 else: # enforce the parity 

695 eta, _lon = _unsigned2(eta) 

696 xi, _lat = _unsigned2(xi) 

697 backside = xi > self._Eu_cE 

698 if backside: # PYCHOK no cover 

699 xi = self._Eu_2cE_(xi) 

700 

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

702 if xi or eta != self._Ev_cKE: 

703 u, v = self._sigmaInv2(xi, eta) 

704 else: # PYCHOK no cover 

705 u = self._iteration = self._sigmaC = 0 

706 v = self._Ev_cK 

707 

708 if v or u != self._Eu_cK: 

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

710 else: # PYCHOK no cover 

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

712 

713 if backside: # PYCHOK no cover 

714 lon, g = _loneg(lon), _loneg(g) 

715 if _lat: 

716 lat, g = neg_(lat, g) 

717 if _lon: 

718 lon, g = neg_(lon, g) 

719 lat += self._lat0 

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

721 return Reverse4Tuple(lat, _norm180(lon), g, k, # _fix90(lat) 

722 iteration=self._iteration, 

723 name=self._name__(name)) 

724 

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

726 '''(INTERNAL) C{scaled}. 

727 

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

729 from C{._zeta3}. 

730 

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

732 

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

734 real snu, real cnu, real dnu, 

735 real snv, real cnv, real dnv, 

736 real &gamma, real &k)}. 

737 ''' 

738 mu, mv = self._mu, self._mv 

739 cnudnv = cnu * dnv 

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

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

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

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

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

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

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

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

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

749 # 9.1 as _mv + _mu * c^2 instead of 1 - _mu * sin(phi)^2 

750 if d2 > 0: 

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

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

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

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

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

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

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

758 if q2 > 0: 

759 k2 = (tau**2 + _1_0) * mv + mu 

760 if k2 > 0: 

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

762 else: 

763 k = _OVERFLOW 

764 return g, k 

765 

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

767 '''(INTERNAL) C{sigma}. 

768 

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

770 

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

772 real v, real snv, real cnv, real dnv, 

773 real &xi, real &eta)}. 

774 

775 @raise ETMError: No convergence. 

776 ''' 

777 mu = self._mu * cnu 

778 mv = self._mv * cnv 

779 # Lee 55.4 writing 

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

781 d2 = cnu * mu + cnv * mv 

782 mu *= snu * dnu 

783 mv *= snv * dnv 

784 if d2 > 0: # /= chokes PyChecker 

785 mu = mu / d2 

786 mv = mv / d2 

787 else: 

788 mu, mv = map1(_overflow, mu, mv) 

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

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

791 return xi, v, d2 

792 

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

794 '''(INTERNAL) C{sigmaDwd}. 

795 

796 @return: 2-Tuple C{(du, dv)}. 

797 

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

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

800 real &du, real &dv)}. 

801 ''' 

802 mu = self._mu 

803 snuv = snu * snv 

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

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

806 d = (cnv**2 + snuv**2 * mu)**2 * self._mv 

807 r = cnv * dnu * dnv 

808 i = cnu * snuv * mu 

809 du = (r**2 - i**2) / d # (r + i) * (r - i) / d 

810 dv = neg(r * i * _2_0 / d) 

811 return du, dv 

812 

813 def _sigmaInv2(self, xi, eta): 

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

815 

816 @return: 2-Tuple C{(u, v)}. 

817 

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

819 real &u, real &v)}. 

820 

821 @raise ETMError: No convergence. 

822 ''' 

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

824 if not t: 

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

826 return u, v 

827 

828 def _sigmaInv04(self, xi, eta): 

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

830 

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

832 

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

834 real &u, real &v)}. 

835 ''' 

836 t = False 

837 d = eta - self._Ev_cKE 

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

839 # sigma as a simple pole at 

840 # w = w0 = Eu.K() + i * Ev.K() 

841 # and sigma is approximated by 

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

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

844 u += self._Eu_cK 

845 v += self._Ev_cK 

846 C = 1 

847 

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

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

850 # sigma = sigma0 = i * Ev.KE() 

851 # sigma' = sigma'' = 0 

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

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

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

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

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

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

858 t = h < _TAYTOL2 

859 C = 2 

860 

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

862 u = v = self._Eu_cK_cE 

863 u *= xi 

864 v *= eta 

865 C = 3 

866 

867 return u, v, t, C 

868 

869 def _sncndn6(self, u, v): 

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

871 ''' 

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

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

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

875 

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

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

878 

879 @kwarg joined: Separator to join the attribute strings 

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

881 @kwarg kwds: Optional, overriding keyword arguments. 

882 ''' 

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

884 k0=self.k0, extendp=self.extendp) 

885 if self.name: 

886 d.update(name=self.name) 

887 t = pairs(d, **kwds) 

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

889 

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

891 '''(INTERNAL) C{zeta}. 

892 

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

894 

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

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

897 real &taup, real &lam)} 

898 ''' 

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

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

901 t1 = t2 = _overflow(snu) 

902 # Lee 54.17 but write 

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

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

905 d1 = cnu2 + mv * (snu * snv)**2 

906 if d1 > EPS02: # _EPSmin 

907 t1 = snu * dnv / sqrt(d1) 

908 else: 

909 d1 = 0 

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

911 if d2 > EPS02: # _EPSmin 

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

913 else: 

914 d2 = 0 

915 # psi = asinh(t1) - asinh(t2) 

916 # taup = sinh(psi) 

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

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

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

920 return taup, lam, d2 

921 

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

923 '''(INTERNAL) C{zetaDwd}. 

924 

925 @return: 2-Tuple C{(du, dv)}. 

926 

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

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

929 real &du, real &dv)}. 

930 ''' 

931 cnu2 = cnu**2 * self._mu 

932 cnv2 = cnv**2 

933 dnuv = dnu * dnv 

934 dnuv2 = dnuv**2 

935 snuv = snu * snv 

936 snuv2 = snuv**2 * self._mu 

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

938 # (1 - dnu^2 * snv^2) = (cnv^2 + _mu * snu^2 * snv^2) 

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

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

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

942 return du, neg(dv) 

943 

944 def _zetaInv2(self, taup, lam): 

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

946 

947 @return: 2-Tuple C{(u, v)}. 

948 

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

950 real &u, real &v)}. 

951 

952 @raise ETMError: No convergence. 

953 ''' 

954 psi = asinh(taup) 

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

956 if not t: 

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

958 return u, v 

959 

960 def _zetaInv04(self, psi, lam): 

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

962 

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

964 

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

966 real &u, real &v)}. 

967 ''' 

968 if lam > self._1_2e_PI_2: 

969 d = lam - self._1_e_PI_2 

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

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

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

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

974 # pole, where we have, approximately 

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

976 # Inverting this gives: 

977 e = self._e # eccentricity 

978 s, c = sincos2((PI_2 - lam) / e) 

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

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

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

982 return u, v, False, 1 

983 

984 elif psi < self._e_PI_2: 

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

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

987 # zeta' = zeta'' = 0 

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

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

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

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

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

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

994 

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

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

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

998 # corresponding to the north pole. 

999 s, c = sincos2(lam) 

1000 h, r = sinh(psi), self._Eu_2cK_PI 

1001 # But scale to put 90, 0 on the right place 

1002 u = r * atan2(h, c) 

1003 v = r * asinh(s / hypot(h, c)) 

1004 return u, v, False, 3 

1005 

1006 def _zetaScaled(self, sncndn6, ll=True): 

1007 '''(INTERNAL) Recompute (T, L) from (u, v) to improve accuracy of Scale. 

1008 

1009 @arg sncndn6: 6-Tuple C{(snu, cnu, dnu, snv, cnv, dnv)}. 

1010 

1011 @return: 2-Tuple C{(g, k)} if not C{B{ll}} else 

1012 4-tuple C{(g, k, lat, lon)}. 

1013 ''' 

1014 t, lam, d2 = self._zeta3(None, *sncndn6) 

1015 tau = self._E.es_tauf(t) 

1016 g_k = self._scaled2(tau, d2, *sncndn6) 

1017 if ll: 

1018 g_k += atan1d(tau), degrees(lam) 

1019 return g_k # or (g, k, lat, lon) 

1020 

1021 

1022def _overflow(x): 

1023 '''(INTERNAL) Like C{copysign0(OVERFLOW, B{x})}. 

1024 ''' 

1025 return _copyBit(_OVERFLOW, x) 

1026 

1027 

1028def parseETM5(strUTM, datum=_WGS84, Etm=Etm, falsed=True, **name): 

1029 '''Parse a string representing a UTM coordinate, consisting 

1030 of C{"zone[band] hemisphere easting northing"}. 

1031 

1032 @arg strUTM: A UTM coordinate (C{str}). 

1033 @kwarg datum: Optional datum to use (L{Datum}, L{Ellipsoid}, 

1034 L{Ellipsoid2} or L{a_f2Tuple}). 

1035 @kwarg Etm: Optional class to return the UTM coordinate 

1036 (L{Etm}) or C{None}. 

1037 @kwarg falsed: Both easting and northing are C{falsed} (C{bool}). 

1038 @kwarg name: Optional B{C{Etm}} C{B{name}=NN} (C{str}). 

1039 

1040 @return: The UTM coordinate (B{C{Etm}}) or if C{B{Etm} is None}, a 

1041 L{UtmUps5Tuple}C{(zone, hemipole, easting, northing, band)} 

1042 with C{hemipole} is the hemisphere C{'N'|'S'}. 

1043 

1044 @raise ETMError: Invalid B{C{strUTM}}. 

1045 

1046 @raise TypeError: Invalid or near-spherical B{C{datum}}. 

1047 ''' 

1048 r = _parseUTM5(strUTM, datum, Etm, falsed, Error=ETMError, **name) 

1049 return r 

1050 

1051 

1052def toEtm8(latlon, lon=None, datum=None, Etm=Etm, falsed=True, 

1053 strict=True, zone=None, **name_cmoff): 

1054 '''Convert a geodetic lat-/longitude to an ETM coordinate. 

1055 

1056 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal) geodetic 

1057 C{LatLon} instance. 

1058 @kwarg lon: Optional longitude (C{degrees}), required if B{C{latlon}} 

1059 is C{degrees}, ignored otherwise. 

1060 @kwarg datum: Optional datum for the ETM coordinate, overriding 

1061 B{C{latlon}}'s datum (L{Datum}, L{Ellipsoid}, 

1062 L{Ellipsoid2} or L{a_f2Tuple}). 

1063 @kwarg Etm: Optional class to return the ETM coordinate (L{Etm}) or C{None}. 

1064 @kwarg falsed: False both easting and northing (C{bool}). 

1065 @kwarg strict: Restrict B{C{lat}} to UTM ranges (C{bool}). 

1066 @kwarg zone: Optional UTM zone to enforce (C{int} or C{str}). 

1067 @kwarg name_cmoff: Optional B{C{Etm}} C{B{name}=NN} (C{str}) and DEPRECATED 

1068 keyword argument C{B{cmoff}=True} to offset the longitude from 

1069 the zone's central meridian (C{bool}), use B{C{falsed}} instead. 

1070 

1071 @return: The ETM coordinate as B{C{Etm}} or if C{B{Etm} is None} or not B{C{falsed}}, 

1072 a L{UtmUps8Tuple}C{(zone, hemipole, easting, northing, band, datum, gamma, 

1073 scale)}. The C{hemipole} is the C{'N'|'S'} hemisphere. 

1074 

1075 @raise ETMError: No convergence transforming to ETM easting and northing. 

1076 

1077 @raise ETMError: Invalid B{C{zone}} or near-spherical or incompatible B{C{datum}} 

1078 or C{ellipsoid}. 

1079 

1080 @raise RangeError: If B{C{lat}} outside the valid UTM bands or if B{C{lat}} or B{C{lon}} 

1081 outside the valid range and L{rangerrors<pygeodesy.rangerrors>} is C{True}. 

1082 

1083 @raise TypeError: Invalid or near-spherical B{C{datum}} or B{C{latlon}} not ellipsoidal. 

1084 

1085 @raise ValueError: The B{C{lon}} value is missing or B{C{latlon}} is invalid. 

1086 ''' 

1087 z, B, lat, lon, d, f, n = _to7zBlldfn(latlon, lon, datum, 

1088 falsed, zone, strict, 

1089 ETMError, **name_cmoff) 

1090 lon0 = _cmlon(z) if f else None 

1091 x, y, g, k = d.exactTM.forward(lat, lon, lon0=lon0) 

1092 

1093 return _toXtm8(Etm, z, lat, x, y, B, d, g, k, f, 

1094 n, latlon, d.exactTM, Error=ETMError) 

1095 

1096 

1097if __name__ == '__main__': # MCCABE 13 

1098 

1099 from pygeodesy import fstr, KTransverseMercator, printf 

1100 from pygeodesy.internals import _usage 

1101 from sys import argv, exit as _exit 

1102 

1103 # mimick some of I{Karney}'s utility C{TransverseMercatorProj} 

1104 _f = _r = _s = _t = False 

1105 _p = -6 

1106 _as = argv[1:] 

1107 while _as and _as[0].startswith(_DASH_): 

1108 _a = _as.pop(0) 

1109 if len(_a) < 2: 

1110 _exit('%s: option %r invalid' % (_usage(*argv), _a)) 

1111 elif '-forward'.startswith(_a): 

1112 _f, _r = True, False 

1113 elif '-reverse'.startswith(_a): 

1114 _f, _r = False, True 

1115 elif '-precision'.startswith(_a): 

1116 _p = int(_as.pop(0)) 

1117 elif '-series'.startswith(_a): 

1118 _s, _t = True, False 

1119 elif _a == '-t': 

1120 _s, _t = False, True 

1121 elif '-help'.startswith(_a): 

1122 _exit(_usage(argv[0], '[-s | -t ]', 

1123 '[-p[recision] <ndigits>', 

1124 '[-f[orward] <lat> <lon>', 

1125 '|-r[everse] <easting> <northing>', 

1126 '|<lat> <lon>]', 

1127 '|-h[elp]')) 

1128 else: 

1129 _exit('%s: option %r not supported' % (_usage(*argv), _a)) 

1130 if len(_as) > 1: 

1131 f2 = map1(float, *_as[:2]) 

1132 else: 

1133 _exit('%s ...: incomplete' % (_usage(*argv),)) 

1134 

1135 if _s: # -series 

1136 tm = KTransverseMercator() 

1137 else: 

1138 tm = ExactTransverseMercator(extendp=_t) 

1139 

1140 if _f: 

1141 t = tm.forward(*f2) 

1142 elif _r: 

1143 t = tm.reverse(*f2) 

1144 else: 

1145 t = tm.forward(*f2) 

1146 printf('%s: %s', tm.classname, fstr(t, prec=_p, sep=_SPACE_)) 

1147 t = tm.reverse(t.easting, t.northing) 

1148 printf('%s: %s', tm.classname, fstr(t, prec=_p, sep=_SPACE_)) 

1149 

1150 

1151# % python3 -m pygeodesy.etm -p 12 33.33 44.44 

1152# ExactTransverseMercator: 4276926.11480390653 4727193.767015309073 28.375536563148 1.233325101778 

1153# ExactTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778 

1154 

1155# % python3 -m pygeodesy.etm -s -p 12 33.33 44.44 

1156# KTransverseMercator: 4276926.114803904667 4727193.767015310004 28.375536563148 1.233325101778 

1157# KTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778 

1158 

1159# % echo 33.33 44.44 | .../bin/TransverseMercatorProj 

1160# 4276926.114804 4727193.767015 28.375536563148 1.233325101778 

1161 

1162# **) MIT License 

1163# 

1164# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1165# 

1166# Permission is hereby granted, free of charge, to any person obtaining a 

1167# copy of this software and associated documentation files (the "Software"), 

1168# to deal in the Software without restriction, including without limitation 

1169# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1170# and/or sell copies of the Software, and to permit persons to whom the 

1171# Software is furnished to do so, subject to the following conditions: 

1172# 

1173# The above copyright notice and this permission notice shall be included 

1174# in all copies or substantial portions of the Software. 

1175# 

1176# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1177# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1178# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1179# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1180# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1181# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1182# OTHER DEALINGS IN THE SOFTWARE.