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__ = '24.05.31' 

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 

180 point (C{LatLon}) or C{None}. 

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

182 C{falsed} (C{bool}). 

183 

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

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

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

187 

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

189 incompatible or no convergence transforming to 

190 lat- and longitude. 

191 

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

193 ''' 

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

195 self._toLLEB(unfalse=unfalse) 

196 return self._latlon5(LatLon) 

197 

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

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

200 ''' 

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

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

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

204 t = repr(d.ellipsoid) 

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

206 

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

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

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

210 

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

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

213 

214 def toUtm(self): # PYCHOK signature 

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

216 

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

218 ''' 

219 return self._xcopy2(Utm) 

220 

221 

222class ExactTransverseMercator(_NamedBase): 

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

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

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

226 ''' 

227 _datum = _WGS84 # Datum 

228 _E = _EWGS84 # Ellipsoid 

229 _extendp = False # use extended domain 

230# _iteration = None # ._sigmaInv2 and ._zetaInv2 

231 _k0 = _K0_UTM # central scale factor 

232 _lat0 = _0_0 # central parallel 

233 _lon0 = _0_0 # central meridian 

234 _mu = _EWGS84.e2 # 1st eccentricity squared 

235 _mv = _EWGS84.e21 # 1 - ._mu 

236 _raiser = False # throw Error 

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

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

239 

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

241 '''New L{ExactTransverseMercator} projection. 

242 

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

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

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

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

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

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

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

250 

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

252 or B{C{k0}}. 

253 

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

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

256 especially on B{X{extendp}}. 

257 

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

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

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

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

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

263 12.2 Monterey C{arm64} and C{"arm64_x86_64"}). 

264 ''' 

265 if extendp: 

266 self._extendp = True 

267 if name: 

268 self.name = name 

269 if raiser: 

270 self.raiser = True 

271 

272 TM = ExactTransverseMercator 

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

274 self.datum = datum # invokes ._resets 

275 if lon0 or lon0 != TM._lon0: 

276 self.lon0 = lon0 

277 if k0 is not TM._k0: 

278 self.k0 = k0 

279 

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

281 def datum(self): 

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

283 ''' 

284 return self._datum 

285 

286 @datum.setter # PYCHOK setter! 

287 def datum(self, datum): 

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

289 

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

291 ''' 

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

293 self._resets(d) 

294 self._datum = d 

295 

296 @Property_RO 

297 def _e(self): 

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

299 ''' 

300 return self._E.e 

301 

302 @Property_RO 

303 def _1_e_90(self): # PYCHOK no cover 

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

305 ''' 

306 return (_1_0 - self._e) * _90_0 

307 

308 @property_RO 

309 def ellipsoid(self): 

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

311 ''' 

312 return self._E 

313 

314 @Property_RO 

315 def _e_PI_2(self): 

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

317 ''' 

318 return self._e * PI_2 

319 

320 @Property_RO 

321 def _e_PI_4_(self): 

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

323 ''' 

324 return -self._e * PI_4 

325 

326 @Property_RO 

327 def _1_e_PI_2(self): 

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

329 ''' 

330 return (_1_0 - self._e) * PI_2 

331 

332 @Property_RO 

333 def _1_2e_PI_2(self): 

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

335 ''' 

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

337 

338 @property_RO 

339 def equatoradius(self): 

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

341 ''' 

342 return self._E.a 

343 

344 a = equatoradius 

345 

346 @Property_RO 

347 def _e_TAYTOL(self): 

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

349 ''' 

350 return self._e * _TAYTOL 

351 

352 @Property_RO 

353 def _Eu(self): 

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

355 ''' 

356 return Elliptic(self._mu) 

357 

358 @Property_RO 

359 def _Eu_cE(self): 

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

361 ''' 

362 return self._Eu.cE 

363 

364 def _Eu_2cE_(self, xi): 

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

366 ''' 

367 return self._Eu_cE * _2_0 - xi 

368 

369 @Property_RO 

370 def _Eu_cE_4(self): 

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

372 ''' 

373 return self._Eu_cE / _4_0 

374 

375 @Property_RO 

376 def _Eu_cK(self): 

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

378 ''' 

379 return self._Eu.cK 

380 

381 @Property_RO 

382 def _Eu_cK_cE(self): 

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

384 ''' 

385 return self._Eu_cK / self._Eu_cE 

386 

387 @Property_RO 

388 def _Eu_2cK_PI(self): 

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

390 ''' 

391 return self._Eu_cK / PI_2 

392 

393 @Property_RO 

394 def _Ev(self): 

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

396 ''' 

397 return Elliptic(self._mv) 

398 

399 @Property_RO 

400 def _Ev_cK(self): 

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

402 ''' 

403 return self._Ev.cK 

404 

405 @Property_RO 

406 def _Ev_cKE(self): 

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

408 ''' 

409 return self._Ev.cKE 

410 

411 @Property_RO 

412 def _Ev_3cKE_4(self): 

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

414 ''' 

415 return self._Ev_cKE * 0.75 # _0_75 

416 

417 @Property_RO 

418 def _Ev_5cKE_4(self): 

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

420 ''' 

421 return self._Ev_cKE * 1.25 # _1_25 

422 

423 @Property_RO 

424 def extendp(self): 

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

426 ''' 

427 return self._extendp 

428 

429 @property_RO 

430 def flattening(self): 

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

432 ''' 

433 return self._E.f 

434 

435 f = flattening 

436 

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

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

439 

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

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

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

443 the default if not C{None}. 

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

445 

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

447 

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

449 real &x, real &y, 

450 real &gamma, real &k)}. 

451 

452 @raise ETMError: No convergence, thrown iff property 

453 C{B{raiser}=True}. 

454 ''' 

455 lat = _fix90(lat - self._lat0) 

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

457 if self.extendp: 

458 backside = _lat = _lon = False 

459 else: # enforce the parity 

460 lat, _lat = _unsigned2(lat) 

461 lon, _lon = _unsigned2(lon) 

462 backside = lon > 90 

463 if backside: # PYCHOK no cover 

464 lon = _loneg(lon) 

465 if lat == 0: 

466 _lat = True 

467 

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

469 if lat == 90: # isnear90(lat) 

470 u = self._Eu_cK 

471 v = self._iteration = self._zetaC = 0 

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

473 u = self._iteration = self._zetaC = 0 

474 v = self._Ev_cK 

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

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

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

478 

479 sncndn6 = self._sncndn6(u, v) 

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

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

482 self._zetaScaled(sncndn6, ll=False) 

483 

484 if backside: 

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

486 y *= self._k0_a 

487 x *= self._k0_a 

488 if _lat: 

489 y, g = neg_(y, g) 

490 if _lon: 

491 x, g = neg_(x, g) 

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

493 name=self._name__(name)) 

494 

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

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

497 ''' 

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

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

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

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

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

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

504 s, c = sincos2(a) 

505 h = hypot(psi, dlam) 

506 r = cbrt(h * _3_mv_e) 

507 u = r * c 

508 v = r * s + self._Ev_cK 

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

510 return u, v, h 

511 

512 @property_RO 

513 def iteration(self): 

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

515 or C{ExactTransverseMercator.reverse} iteration number 

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

517 ''' 

518 return self._iteration 

519 

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

521 def k0(self): 

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

523 ''' 

524 return self._k0 # aka scale0 

525 

526 @k0.setter # PYCHOK setter! 

527 def k0(self, k0): 

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

529 

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

531 ''' 

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

533 if self._k0 != k0: 

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

535 self._k0 = k0 

536 

537 @Property_RO 

538 def _k0_a(self): 

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

540 ''' 

541 return self.k0 * self.equatoradius 

542 

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

544 def lon0(self): 

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

546 ''' 

547 return self._lon0 

548 

549 @lon0.setter # PYCHOK setter! 

550 def lon0(self, lon0): 

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

552 

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

554 ''' 

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

556 

557 @deprecated_property_RO 

558 def majoradius(self): # PYCHOK no cover 

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

560 return self.equatoradius 

561 

562 @Property_RO 

563 def _1_mu_2(self): 

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

565 ''' 

566 return self._mu * _0_5 + _1_0 

567 

568 @Property_RO 

569 def _3_mv(self): 

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

571 ''' 

572 return _3_0 / self._mv 

573 

574 @Property_RO 

575 def _3_mv_e(self): 

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

577 ''' 

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

579 

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

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

582 

583 @return: 2-Tuple C{(u, v)}. 

584 

585 @raise ETMError: No convergence. 

586 ''' 

587 sca1, tol2 = _1_0, _TOL_10 

588 if psi: # _zetaInv2 

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

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

591 

592 _zeta3 = self._zeta3 

593 _zetaDwd2 = self._zetaDwd2 

594 else: # _sigmaInv2 

595 _zeta3 = self._sigma3 

596 _zetaDwd2 = self._sigmaDwd2 

597 

598 d2, r = tol2, self.raiser 

599 _U_2 = Fsum(u).fsum2f_ 

600 _V_2 = Fsum(v).fsum2f_ 

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

602 _hy2 = hypot2 

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

604 sncndn6 = self._sncndn6(u, v) 

605 du, dv = _zetaDwd2(*sncndn6) 

606 T, L, _ = _zeta3(v, *sncndn6) 

607 T = (taup - T) * sca1 

608 L -= lam 

609 u, dU = _U_2(T * du, L * dv) 

610 v, dV = _V_2(T * dv, -L * du) 

611 if d2 < tol2: 

612 r = False 

613 break 

614 d2 = _hy2(dU, dV) 

615 

616 self._iteration = i 

617 if r: # PYCHOK no cover 

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

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

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

621 return u, v 

622 

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

624 def raiser(self): 

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

626 ''' 

627 return self._raiser 

628 

629 @raiser.setter # PYCHOK setter! 

630 def raiser(self, raiser): 

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

632 for convergence failures. 

633 ''' 

634 self._raiser = bool(raiser) 

635 

636 def reset(self, lat0, lon0): 

637 '''Set the central parallel and meridian. 

638 

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

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

641 

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

643 parallel and meridian. 

644 

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

646 ''' 

647 t = self._lat0, self.lon0 

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

649 self. lon0 = lon0 

650 return t 

651 

652 def _resets(self, datum): 

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

654 

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

656 

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

658 ''' 

659 E = datum.ellipsoid 

660 mu = E.e2 # .eccentricity1st2 

661 mv = E.e21 # _1_0 - mu 

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

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

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

665 

666 if self._datum or self._E: 

667 _i = ExactTransverseMercator.iteration._uname 

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

669 

670 self._E = E 

671 self._mu = mu 

672 self._mv = mv 

673 

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

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

676 

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

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

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

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

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

682 

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

684 

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

686 real &lat, real &lon, 

687 real &gamma, real &k)} 

688 

689 @raise ETMError: No convergence, thrown iff property 

690 C{B{raiser}=True}. 

691 ''' 

692 # undoes the steps in .forward. 

693 xi = y / self._k0_a 

694 eta = x / self._k0_a 

695 if self.extendp: 

696 backside = _lat = _lon = False 

697 else: # enforce the parity 

698 eta, _lon = _unsigned2(eta) 

699 xi, _lat = _unsigned2(xi) 

700 backside = xi > self._Eu_cE 

701 if backside: # PYCHOK no cover 

702 xi = self._Eu_2cE_(xi) 

703 

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

705 if xi or eta != self._Ev_cKE: 

706 u, v = self._sigmaInv2(xi, eta) 

707 else: # PYCHOK no cover 

708 u = self._iteration = self._sigmaC = 0 

709 v = self._Ev_cK 

710 

711 if v or u != self._Eu_cK: 

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

713 else: # PYCHOK no cover 

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

715 

716 if backside: # PYCHOK no cover 

717 lon, g = _loneg(lon), _loneg(g) 

718 if _lat: 

719 lat, g = neg_(lat, g) 

720 if _lon: 

721 lon, g = neg_(lon, g) 

722 lat += self._lat0 

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

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

725 iteration=self._iteration, 

726 name=self._name__(name)) 

727 

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

729 '''(INTERNAL) C{scaled}. 

730 

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

732 from C{._zeta3}. 

733 

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

735 

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

737 real snu, real cnu, real dnu, 

738 real snv, real cnv, real dnv, 

739 real &gamma, real &k)}. 

740 ''' 

741 mu, mv = self._mu, self._mv 

742 cnudnv = cnu * dnv 

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

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

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

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

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

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

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

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

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

752 # 9.1 as _mv + _mu * c^2 instead of 1 - _mu * sin(phi)^2 

753 if d2 > 0: 

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

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

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

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

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

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

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

761 if q2 > 0: 

762 k2 = (tau**2 + _1_0) * mv + mu 

763 if k2 > 0: 

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

765 else: 

766 k = _OVERFLOW 

767 return g, k 

768 

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

770 '''(INTERNAL) C{sigma}. 

771 

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

773 

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

775 real v, real snv, real cnv, real dnv, 

776 real &xi, real &eta)}. 

777 

778 @raise ETMError: No convergence. 

779 ''' 

780 mu = self._mu * cnu 

781 mv = self._mv * cnv 

782 # Lee 55.4 writing 

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

784 d2 = cnu * mu + cnv * mv 

785 mu *= snu * dnu 

786 mv *= snv * dnv 

787 if d2 > 0: # /= chokes PyChecker 

788 mu = mu / d2 

789 mv = mv / d2 

790 else: 

791 mu, mv = map1(_overflow, mu, mv) 

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

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

794 return xi, v, d2 

795 

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

797 '''(INTERNAL) C{sigmaDwd}. 

798 

799 @return: 2-Tuple C{(du, dv)}. 

800 

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

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

803 real &du, real &dv)}. 

804 ''' 

805 mu = self._mu 

806 snuv = snu * snv 

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

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

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

810 r = cnv * dnu * dnv 

811 i = cnu * snuv * mu 

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

813 dv = neg(r * i * _2_0 / d) 

814 return du, dv 

815 

816 def _sigmaInv2(self, xi, eta): 

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

818 

819 @return: 2-Tuple C{(u, v)}. 

820 

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

822 real &u, real &v)}. 

823 

824 @raise ETMError: No convergence. 

825 ''' 

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

827 if not t: 

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

829 return u, v 

830 

831 def _sigmaInv04(self, xi, eta): 

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

833 

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

835 

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

837 real &u, real &v)}. 

838 ''' 

839 t = False 

840 d = eta - self._Ev_cKE 

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

842 # sigma as a simple pole at 

843 # w = w0 = Eu.K() + i * Ev.K() 

844 # and sigma is approximated by 

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

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

847 u += self._Eu_cK 

848 v += self._Ev_cK 

849 C = 1 

850 

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

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

853 # sigma = sigma0 = i * Ev.KE() 

854 # sigma' = sigma'' = 0 

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

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

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

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

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

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

861 t = h < _TAYTOL2 

862 C = 2 

863 

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

865 u = v = self._Eu_cK_cE 

866 u *= xi 

867 v *= eta 

868 C = 3 

869 

870 return u, v, t, C 

871 

872 def _sncndn6(self, u, v): 

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

874 ''' 

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

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

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

878 

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

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

881 

882 @kwarg joined: Separator to join the attribute strings 

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

884 @kwarg kwds: Optional, overriding keyword arguments. 

885 ''' 

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

887 k0=self.k0, extendp=self.extendp) 

888 if self.name: 

889 d.update(name=self.name) 

890 t = pairs(d, **kwds) 

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

892 

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

894 '''(INTERNAL) C{zeta}. 

895 

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

897 

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

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

900 real &taup, real &lam)} 

901 ''' 

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

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

904 t1 = t2 = _overflow(snu) 

905 # Lee 54.17 but write 

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

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

908 d1 = cnu2 + mv * (snu * snv)**2 

909 if d1 > EPS02: # _EPSmin 

910 t1 = snu * dnv / sqrt(d1) 

911 else: 

912 d1 = 0 

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

914 if d2 > EPS02: # _EPSmin 

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

916 else: 

917 d2 = 0 

918 # psi = asinh(t1) - asinh(t2) 

919 # taup = sinh(psi) 

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

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

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

923 return taup, lam, d2 

924 

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

926 '''(INTERNAL) C{zetaDwd}. 

927 

928 @return: 2-Tuple C{(du, dv)}. 

929 

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

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

932 real &du, real &dv)}. 

933 ''' 

934 cnu2 = cnu**2 * self._mu 

935 cnv2 = cnv**2 

936 dnuv = dnu * dnv 

937 dnuv2 = dnuv**2 

938 snuv = snu * snv 

939 snuv2 = snuv**2 * self._mu 

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

941 # (1 - dnu^2 * snv^2) = (cnv^2 + _mu * snu^2 * snv^2) 

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

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

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

945 return du, neg(dv) 

946 

947 def _zetaInv2(self, taup, lam): 

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

949 

950 @return: 2-Tuple C{(u, v)}. 

951 

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

953 real &u, real &v)}. 

954 

955 @raise ETMError: No convergence. 

956 ''' 

957 psi = asinh(taup) 

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

959 if not t: 

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

961 return u, v 

962 

963 def _zetaInv04(self, psi, lam): 

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

965 

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

967 

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

969 real &u, real &v)}. 

970 ''' 

971 if lam > self._1_2e_PI_2: 

972 d = lam - self._1_e_PI_2 

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

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

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

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

977 # pole, where we have, approximately 

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

979 # Inverting this gives: 

980 e = self._e # eccentricity 

981 s, c = sincos2((PI_2 - lam) / e) 

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

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

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

985 return u, v, False, 1 

986 

987 elif psi < self._e_PI_2: 

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

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

990 # zeta' = zeta'' = 0 

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

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

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

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

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

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

997 

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

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

1000 # This takes care of the log singularity at C{zeta = Eu.K()}, 

1001 # corresponding to the north pole. 

1002 s, c = sincos2(lam) 

1003 h, r = sinh(psi), self._Eu_2cK_PI 

1004 # But scale to put 90, 0 on the right place 

1005 u = r * atan2(h, c) 

1006 v = r * asinh(s / hypot(h, c)) 

1007 return u, v, False, 3 

1008 

1009 def _zetaScaled(self, sncndn6, ll=True): 

1010 '''(INTERNAL) Recompute (T, L) from (u, v) to improve accuracy of Scale. 

1011 

1012 @arg sncndn6: 6-Tuple C{(snu, cnu, dnu, snv, cnv, dnv)}. 

1013 

1014 @return: 2-Tuple C{(g, k)} if not C{B{ll}} else 

1015 4-tuple C{(g, k, lat, lon)}. 

1016 ''' 

1017 t, lam, d2 = self._zeta3(None, *sncndn6) 

1018 tau = self._E.es_tauf(t) 

1019 g_k = self._scaled2(tau, d2, *sncndn6) 

1020 if ll: 

1021 g_k += atan1d(tau), degrees(lam) 

1022 return g_k # or (g, k, lat, lon) 

1023 

1024 

1025def _overflow(x): 

1026 '''(INTERNAL) Like C{copysign0(OVERFLOW, B{x})}. 

1027 ''' 

1028 return _copyBit(_OVERFLOW, x) 

1029 

1030 

1031def parseETM5(strUTM, datum=_WGS84, Etm=Etm, falsed=True, **name): 

1032 '''Parse a string representing a UTM coordinate, consisting 

1033 of C{"zone[band] hemisphere easting northing"}. 

1034 

1035 @arg strUTM: A UTM coordinate (C{str}). 

1036 @kwarg datum: Optional datum to use (L{Datum}, L{Ellipsoid}, 

1037 L{Ellipsoid2} or L{a_f2Tuple}). 

1038 @kwarg Etm: Optional class to return the UTM coordinate 

1039 (L{Etm}) or C{None}. 

1040 @kwarg falsed: Both easting and northing are C{falsed} (C{bool}). 

1041 @kwarg name: Optional B{C{Etm}} C{B{name}=NN} (C{str}). 

1042 

1043 @return: The UTM coordinate (B{C{Etm}}) or if B{C{Etm}} is 

1044 C{None}, a L{UtmUps5Tuple}C{(zone, hemipole, easting, 

1045 northing, band)}. The C{hemipole} is the hemisphere 

1046 C{'N'|'S'}. 

1047 

1048 @raise ETMError: Invalid B{C{strUTM}}. 

1049 

1050 @raise TypeError: Invalid or near-spherical B{C{datum}}. 

1051 ''' 

1052 r = _parseUTM5(strUTM, datum, Etm, falsed, Error=ETMError, **name) 

1053 return r 

1054 

1055 

1056def toEtm8(latlon, lon=None, datum=None, Etm=Etm, falsed=True, 

1057 strict=True, zone=None, **name_cmoff): 

1058 '''Convert a geodetic lat-/longitude to an ETM coordinate. 

1059 

1060 @arg latlon: Latitude (C{degrees}) or an (ellipsoidal) 

1061 geodetic C{LatLon} instance. 

1062 @kwarg lon: Optional longitude (C{degrees}), required 

1063 if B{C{latlon}} is in C{degrees}. 

1064 @kwarg datum: Optional datum for the ETM coordinate, 

1065 overriding B{C{latlon}}'s datum (L{Datum}, 

1066 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). 

1067 @kwarg Etm: Optional class to return the ETM coordinate 

1068 (L{Etm}) or C{None}. 

1069 @kwarg falsed: False both easting and northing (C{bool}). 

1070 @kwarg strict: Restrict B{C{lat}} to UTM ranges (C{bool}). 

1071 @kwarg zone: Optional UTM zone to enforce (C{int} or C{str}). 

1072 @kwarg name_cmoff: Optional B{C{Etm}} C{B{name}=NN} (C{str}) 

1073 and DEPRECATED keyword argument C{B{cmoff}=True} 

1074 to offset the longitude from the zone's central 

1075 meridian (C{bool}), use B{C{falsed}} instead. 

1076 

1077 @return: The ETM coordinate as an B{C{Etm}} instance or a 

1078 L{UtmUps8Tuple}C{(zone, hemipole, easting, northing, 

1079 band, datum, gamma, scale)} if B{C{Etm}} is C{None} 

1080 or not B{C{falsed}}. The C{hemipole} is the C{'N'|'S'} 

1081 hemisphere. 

1082 

1083 @raise ETMError: No convergence transforming to ETM easting 

1084 and northing. 

1085 

1086 @raise ETMError: Invalid B{C{zone}} or near-spherical or 

1087 incompatible B{C{datum}} or C{ellipsoid}. 

1088 

1089 @raise RangeError: If B{C{lat}} outside the valid UTM bands or 

1090 if B{C{lat}} or B{C{lon}} outside the valid 

1091 range and L{pygeodesy.rangerrors} set to C{True}. 

1092 

1093 @raise TypeError: Invalid or near-spherical B{C{datum}} or 

1094 B{C{latlon}} not ellipsoidal. 

1095 

1096 @raise ValueError: The B{C{lon}} value is missing or B{C{latlon}} 

1097 is invalid. 

1098 ''' 

1099 z, B, lat, lon, d, f, n = _to7zBlldfn(latlon, lon, datum, 

1100 falsed, zone, strict, 

1101 ETMError, **name_cmoff) 

1102 lon0 = _cmlon(z) if f else None 

1103 x, y, g, k = d.exactTM.forward(lat, lon, lon0=lon0) 

1104 

1105 return _toXtm8(Etm, z, lat, x, y, B, d, g, k, f, 

1106 n, latlon, d.exactTM, Error=ETMError) 

1107 

1108 

1109if __name__ == '__main__': # MCCABE 13 

1110 

1111 from pygeodesy import fstr, KTransverseMercator, printf 

1112 from pygeodesy.internals import _usage 

1113 from sys import argv, exit as _exit 

1114 

1115 # mimick some of I{Karney}'s utility C{TransverseMercatorProj} 

1116 _f = _r = _s = _t = False 

1117 _p = -6 

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 '-precision'.startswith(_a): 

1128 _p = int(_as.pop(0)) 

1129 elif '-series'.startswith(_a): 

1130 _s, _t = True, False 

1131 elif _a == '-t': 

1132 _s, _t = False, True 

1133 elif '-help'.startswith(_a): 

1134 _exit(_usage(argv[0], '[-s | -t ]', 

1135 '[-p[recision] <ndigits>', 

1136 '[-f[orward] <lat> <lon>', 

1137 '|-r[everse] <easting> <northing>', 

1138 '|<lat> <lon>]', 

1139 '|-h[elp]')) 

1140 else: 

1141 _exit('%s: option %r not supported' % (_usage(*argv), _a)) 

1142 if len(_as) > 1: 

1143 f2 = map1(float, *_as[:2]) 

1144 else: 

1145 _exit('%s ...: incomplete' % (_usage(*argv),)) 

1146 

1147 if _s: # -series 

1148 tm = KTransverseMercator() 

1149 else: 

1150 tm = ExactTransverseMercator(extendp=_t) 

1151 

1152 if _f: 

1153 t = tm.forward(*f2) 

1154 elif _r: 

1155 t = tm.reverse(*f2) 

1156 else: 

1157 t = tm.forward(*f2) 

1158 printf('%s: %s', tm.classname, fstr(t, prec=_p, sep=_SPACE_)) 

1159 t = tm.reverse(t.easting, t.northing) 

1160 printf('%s: %s', tm.classname, fstr(t, prec=_p, sep=_SPACE_)) 

1161 

1162 

1163# % python3 -m pygeodesy.etm -p 12 33.33 44.44 

1164# ExactTransverseMercator: 4276926.11480390653 4727193.767015309073 28.375536563148 1.233325101778 

1165# ExactTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778 

1166 

1167# % python3 -m pygeodesy.etm -s -p 12 33.33 44.44 

1168# KTransverseMercator: 4276926.114803904667 4727193.767015310004 28.375536563148 1.233325101778 

1169# KTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778 

1170 

1171# % echo 33.33 44.44 | .../bin/TransverseMercatorProj 

1172# 4276926.114804 4727193.767015 28.375536563148 1.233325101778 

1173 

1174# **) MIT License 

1175# 

1176# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1177# 

1178# Permission is hereby granted, free of charge, to any person obtaining a 

1179# copy of this software and associated documentation files (the "Software"), 

1180# to deal in the Software without restriction, including without limitation 

1181# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1182# and/or sell copies of the Software, and to permit persons to whom the 

1183# Software is furnished to do so, subject to the following conditions: 

1184# 

1185# The above copyright notice and this permission notice shall be included 

1186# in all copies or substantial portions of the Software. 

1187# 

1188# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1189# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1190# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1191# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1192# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1193# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1194# OTHER DEALINGS IN THE SOFTWARE.