1

2# -*- coding: utf-8 -*-

3

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

5

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

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

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

9

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

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

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

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

14 the results, see usage C{"python[3] -m pygeodesy.etm -h"}.

15

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

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

18 file C{Header}.

19

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

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

22 GeographicLib.SourceForge.io>} documentation.

23

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

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

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

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

28 suitable starting guess.

29

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

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

32 67-101. The C++ implementation and notation closely follow Lee, with the following

33 exceptions::

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

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

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

61 which 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

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

65

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

67 from 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, _90_0, isnear0, isnear90

70 from pygeodesy.constants import _4_0 # PYCHOK used!

71 from pygeodesy.datums import _ellipsoidal_datum, _WGS84, _EWGS84

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

73# from pygeodesy.elliptic import Elliptic # _MODS

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

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

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

77 from pygeodesy.interns import _COMMASPACE_, _near_, _SPACE_, _spherical_

78 from pygeodesy.karney import _K_2_4, _copyBit, _diff182, _fix90, \

79 _norm2, _norm180, _tand, _unsigned2

80# from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS # from .named

81 from pygeodesy.named import callername, _incompatible, _NamedBase, \

82 _ALL_LAZY, _MODS

83 from pygeodesy.namedTuples import Forward4Tuple, Reverse4Tuple

84 from pygeodesy.props import deprecated_method, deprecated_property_RO, \

85 Property_RO, property_RO, _update_all, \

86 property_doc_, _allPropertiesOf_n

87 from pygeodesy.streprs import Fmt, pairs, unstr

88 from pygeodesy.units import Degrees, Scalar_

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

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

91 _to7zBlldfn, Utm, UTMError

92

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

94

95__all__ = _ALL_LAZY.etm

96__version__ = '24.11.04'

97

98_OVERFLOW = _1_EPS**2 # ~2e+31

99_TAYTOL = pow(EPS, 0.6)

100_TAYTOL2 = _TAYTOL * _2_0

101_TOL_10 = EPS * _0_1

102_TRIPS = 21 # C++ 10

103

104

105 class ETMError(UTMError):

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

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

108 '''

109 pass

110

111

112 class Etm(Utm):

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

114 a Universal Transverse Mercator (UTM) coordinate using the

115 L{ExactTransverseMercator} projection for highest accuracy.

116

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

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

119

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

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

122 '''

123 _Error = ETMError # see utm.UTMError

124 _exactTM = None

125

126 __init__ = Utm.__init__

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

128

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

130 '''

131

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

133 def exactTM(self):

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

135 '''

136 if self._exactTM is None:

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

138 return self._exactTM

139

140 @exactTM.setter # PYCHOK setter!

141 def exactTM(self, exactTM):

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

143

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

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

146 '''

147 _xinstanceof(ExactTransverseMercator, exactTM=exactTM)

148

149 E = self.datum.ellipsoid

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

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

152 self._exactTM = exactTM

153 self._scale0 = exactTM.k0

154

155 def parse(self, strETM, **name):

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

157

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

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

160

161 @return: The instance (L{Etm}).

162

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

164

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

166 L{pygeodesy.parseUTMUPS5}.

167 '''

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

169 name=self._name__(name))

170

171 @deprecated_method

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

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

174 '''

175 return self.parse(strETM)

176

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

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

179

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

181 (C{LatLon}) or C{None}.

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

183

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

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

186

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

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

189

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

191 '''

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

193 self._toLLEB(unfalse=unfalse)

194 return self._latlon5(LatLon)

195

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

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

198 '''

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

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

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

202 t = repr(d.ellipsoid)

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

204

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

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

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

208

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

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

211

212 def toUtm(self): # PYCHOK signature

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

214

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

216 '''

217 return self._xcopy2(Utm)

218

219

220 class ExactTransverseMercator(_NamedBase):

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

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

223 a numerically exact transverse Mercator projection, abbreviated as C{TMExact}.

224 '''

225 _datum = _WGS84 # Datum

226 _E = _EWGS84 # Ellipsoid

227 _extendp = False # use extended domain

228# _iteration = None # _NameBase, ._sigmaInv2 and ._zetaInv2

229 _k0 = _K0_UTM # central scale factor

230 _lat0 = _0_0 # central parallel

231 _lon0 = _0_0 # central meridian

232 _mu = _EWGS84.e2 # 1st eccentricity squared

233 _mv = _EWGS84.e21 # 1 - ._mu

234 _raiser = False # throw Error

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

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

237

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

239 '''New L{ExactTransverseMercator} projection.

240

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

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

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

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

245 @kwarg extendp: If C{True}, use the I{extended} domain, I{standard} otherwise (C{bool}).

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

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

248

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

250 or B{C{k0}}.

251

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

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

254 especially on B{X{extendp}}.

255

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

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

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

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

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

261 12.2 Monterey C{arm64} and C{"arm64_x86_64"}).

262 '''

263 if extendp:

264 self._extendp = True

265 if name:

266 self.name = name

267 if raiser:

268 self.raiser = True

269

270 TM = ExactTransverseMercator

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

272 self.datum = datum # invokes ._resets

273 if lon0 or lon0 != TM._lon0:

274 self.lon0 = lon0

275 if k0 is not TM._k0:

276 self.k0 = k0

277

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

279 def datum(self):

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

281 '''

282 return self._datum

283

284 @datum.setter # PYCHOK setter!

285 def datum(self, datum):

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

287

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

289 '''

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

291 self._resets(d)

292 self._datum = d

293

294 @Property_RO

295 def _e(self):

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

297 '''

298 return self._E.e

299

300 @Property_RO

301 def _1_e_90(self): # PYCHOK no cover

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

303 '''

304 return (_1_0 - self._e) * _90_0

305

306 @property_RO

307 def ellipsoid(self):

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

309 '''

310 return self._E

311

312 @Property_RO

313 def _e_PI_2(self):

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

315 '''

316 return self._e * PI_2

317

318 @Property_RO

319 def _e_PI_4_(self):

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

321 '''

322 return -self._e * PI_4

323

324 @Property_RO

325 def _1_e_PI_2(self):

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

327 '''

328 return (_1_0 - self._e) * PI_2

329

330 @Property_RO

331 def _1_2e_PI_2(self):

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

333 '''

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

335

336 @property_RO

337 def equatoradius(self):

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

339 '''

340 return self._E.a

341

342 a = equatoradius

343

344 @Property_RO

345 def _e_TAYTOL(self):

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

347 '''

348 return self._e * _TAYTOL

349

350 @Property_RO

351 def _Eu(self):

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

353 '''

354 return _MODS.elliptic.Elliptic(self._mu)

355

356 @Property_RO

357 def _Eu_cE(self):

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

359 '''

360 return self._Eu.cE

361

362 def _Eu_2cE_(self, xi):

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

364 '''

365 return self._Eu_cE * _2_0 - xi

366

367 @Property_RO

368 def _Eu_cE_4(self):

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

370 '''

371 return self._Eu_cE / _4_0

372

373 @Property_RO

374 def _Eu_cK(self):

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

376 '''

377 return self._Eu.cK

378

379 @Property_RO

380 def _Eu_cK_cE(self):

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

382 '''

383 return self._Eu_cK / self._Eu_cE

384

385 @Property_RO

386 def _Eu_2cK_PI(self):

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

388 '''

389 return self._Eu_cK / PI_2

390

391 @Property_RO

392 def _Ev(self):

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

394 '''

395 return _MODS.elliptic.Elliptic(self._mv)

396

397 @Property_RO

398 def _Ev_cK(self):

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

400 '''

401 return self._Ev.cK

402

403 @Property_RO

404 def _Ev_cKE(self):

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

406 '''

407 return self._Ev.cKE

408

409 @Property_RO

410 def _Ev_3cKE_4(self):

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

412 '''

413 return self._Ev_cKE * 0.75 # _0_75

414

415 @Property_RO

416 def _Ev_5cKE_4(self):

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

418 '''

419 return self._Ev_cKE * 1.25 # _1_25

420

421 @property_RO

422 def extendp(self):

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

424 '''

425 return self._extendp

426

427 @property_RO

428 def flattening(self):

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

430 '''

431 return self._E.f

432

433 f = flattening

434

435 def forward(self, lat, lon, lon0=None, jam=_K_2_4, **name): # MCCABE 13

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

437

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

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

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

441 the default if not C{None}.

442 @kwarg jam: If C{True}, use the C{Jacobi amplitude}

443 otherwise C{Bulirsch}' function (C{bool}).

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, jam=jam)

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 meridian (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 # lon0.setter

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 # E.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 # property_RO

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

669

670 self._E = E

671 self._mu = mu

672 self._mv = mv

673

674 def reverse(self, x, y, lon0=None, jam=_K_2_4, **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 jam: If C{True}, use the C{Jacobi amplitude}

682 otherwise C{Bulirsch}' function (C{bool}).

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

684

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

686

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

688 real &lat, real &lon,

689 real &gamma, real &k)}

690

691 @raise ETMError: No convergence, thrown iff property

692 C{B{raiser}=True}.

693 '''

694 # undoes the steps in .forward.

695 xi = y / self._k0_a

696 eta = x / self._k0_a

697 if self.extendp:

698 backside = _lat = _lon = False

699 else: # enforce the parity

700 eta, _lon = _unsigned2(eta)

701 xi, _lat = _unsigned2(xi)

702 backside = xi > self._Eu_cE

703 if backside: # PYCHOK no cover

704 xi = self._Eu_2cE_(xi)

705

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

707 if xi or eta != self._Ev_cKE:

708 u, v = self._sigmaInv2(xi, eta)

709 else: # PYCHOK no cover

710 u = self._iteration = self._sigmaC = 0

711 v = self._Ev_cK

712

713 if v or u != self._Eu_cK:

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

715 else: # PYCHOK no cover

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

717

718 if backside: # PYCHOK no cover

719 lon, g = _loneg(lon), _loneg(g)

720 if _lat:

721 lat, g = neg_(lat, g)

722 if _lon:

723 lon, g = neg_(lon, g)

724 lat += self._lat0

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

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

727 iteration=self._iteration,

728 name=self._name__(name))

729

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

731 '''(INTERNAL) C{scaled}.

732

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

734 from C{._zeta3}.

735

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

737

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

739 real snu, real cnu, real dnu,

740 real snv, real cnv, real dnv,

741 real &gamma, real &k)}.

742 '''

743 mu, mv = self._mu, self._mv

744 cnudnv = cnu * dnv

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

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

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

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

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

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

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

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

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

754 # 9.1 as _mv + _mu * c^2 instead of 1 - _mu * sin(phi)^2

755 if d2 > 0:

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

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

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

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

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

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

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

763 if q2 > 0:

764 k2 = (tau**2 + _1_0) * mv + mu

765 if k2 > 0:

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

767 else:

768 k = _OVERFLOW

769 return g, k

770

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

772 '''(INTERNAL) C{sigma}.

773

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

775

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

777 real v, real snv, real cnv, real dnv,

778 real &xi, real &eta)}.

779

780 @raise ETMError: No convergence.

781 '''

782 mu = self._mu * cnu

783 mv = self._mv * cnv

784 # Lee 55.4 writing

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

786 d2 = cnu * mu + cnv * mv

787 mu *= snu * dnu

788 mv *= snv * dnv

789 if d2 > 0: # /= chokes PyChecker

790 mu = mu / d2

791 mv = mv / d2

792 else:

793 mu, mv = map1(_overflow, mu, mv)

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

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

796 return xi, v, d2

797

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

799 '''(INTERNAL) C{sigmaDwd}.

800

801 @return: 2-Tuple C{(du, dv)}.

802

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

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

805 real &du, real &dv)}.

806 '''

807 mu = self._mu

808 snuv = snu * snv

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

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

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

812 r = cnv * dnu * dnv

813 i = cnu * snuv * mu

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

815 dv = r * i * _2_0 / d

816 return du, neg(dv)

817

818 def _sigmaInv2(self, xi, eta):

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

820

821 @return: 2-Tuple C{(u, v)}.

822

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

824 real &u, real &v)}.

825

826 @raise ETMError: No convergence.

827 '''

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

829 if not t:

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

831 return u, v

832

833 def _sigmaInv04(self, xi, eta):

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

835

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

837

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

839 real &u, real &v)}.

840 '''

841 t = False

842 d = eta - self._Ev_cKE

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

844 # sigma as a simple pole at

845 # w = w0 = Eu.K() + i * Ev.K()

846 # and sigma is approximated by

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

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

849 u += self._Eu_cK

850 v += self._Ev_cK

851 C = 1

852

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

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

855 # sigma = sigma0 = i * Ev.KE()

856 # sigma' = sigma'' = 0

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

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

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

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

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

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

863 t = h < _TAYTOL2

864 C = 2

865

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

867 u = v = self._Eu_cK_cE

868 u *= xi

869 v *= eta

870 C = 3

871

872 return u, v, t, C

873

874 def _sncndn6(self, u, v, **jam):

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

876 '''

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

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

879 return self._Eu.sncndn(u, **jam) + \

880 self._Ev.sncndn(v, **jam)

881

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

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

884

885 @kwarg joined: Separator to join the attribute strings

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

887 @kwarg kwds: Optional, overriding keyword arguments.

888 '''

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

890 k0=self.k0, extendp=self.extendp)

891 if self.name:

892 d.update(name=self.name)

893 t = pairs(d, **kwds)

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

895

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

897 '''(INTERNAL) C{zeta}.

898

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

900

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

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

903 real &taup, real &lam)}

904 '''

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

906 # Lee 54.17 but write

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

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

909 d1 = cnu2 + (snu * snv)**2 * mv

910 if d1 > EPS02: # _EPSmin

911 t1 = snu * dnv / sqrt(d1)

912 else: # like atan(overflow) = pi/2

913 t1, d1 = _overflow(snu), 0

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

915 if d2 > EPS02: # _EPSmin

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

917 else:

918 t2, d2 = _overflow(snu), 0

919 # psi = asinh(t1) - asinh(t2)

920 # taup = sinh(psi)

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

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

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

924 return taup, lam, d2

925

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

927 '''(INTERNAL) C{zetaDwd}.

928

929 @return: 2-Tuple C{(du, dv)}.

930

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

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

933 real &du, real &dv)}.

934 '''

935 cnu2 = cnu**2 * self._mu

936 cnv2 = cnv**2

937 dnuv = dnu * dnv

938 dnuv2 = dnuv**2

939 snuv = snu * snv

940 snuv2 = snuv**2 * self._mu

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

942 # (1 - dnu^2 * snv^2) = (cnv^2 + _mu * snu^2 * snv^2)

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

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

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

946 return du, neg(dv)

947

948 def _zetaInv2(self, taup, lam):

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

950

951 @return: 2-Tuple C{(u, v)}.

952

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

954 real &u, real &v)}.

955

956 @raise ETMError: No convergence.

957 '''

958 psi = asinh(taup)

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

960 if not t:

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

962 return u, v

963

964 def _zetaInv04(self, psi, lam):

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

966

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

968

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

970 real &u, real &v)}.

971 '''

972 if lam > self._1_2e_PI_2:

973 d = lam - self._1_e_PI_2

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

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

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

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

978 # pole, where we have, approximately

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

980 # Inverting this gives:

981 e = self._e # eccentricity

982 s, c = sincos2((PI_2 - lam) / e)

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

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

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

986 return u, v, False, 1

987

988 elif psi < self._e_PI_2:

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

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

991 # zeta' = zeta'' = 0

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

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

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

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

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

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

998

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

1000 # cosh(psi)) = asinh(sin(lam) / hypot(cos(lam), sinh(psi)))}.

1001 # This takes care of the log singularity at C{zeta = Eu.K()},

1002 # corresponding to the north pole.

1003 s, c = sincos2(lam)

1004 h, r = sinh(psi), self._Eu_2cK_PI

1005 # But scale to put 90, 0 on the right place

1006 u = r * atan2(h, c)

1007 v = r * asinh(s / hypot(h, c))

1008 return u, v, False, 3

1009

1010 def _zetaScaled(self, sncndn6, ll=True):

1011 '''(INTERNAL) Recompute (T, L) from (u, v) to improve accuracy of Scale.

1012

1013 @arg sncndn6: 6-Tuple C{(snu, cnu, dnu, snv, cnv, dnv)}.

1014

1015 @return: 2-Tuple C{(g, k)} if not C{B{ll}} else

1016 4-tuple C{(g, k, lat, lon)}.

1017 '''

1018 t, lam, d2 = self._zeta3(None, *sncndn6)

1019 tau = self._E.es_tauf(t)

1020 g_k = self._scaled2(tau, d2, *sncndn6)

1021 if ll:

1022 g_k += atan1d(tau), degrees(lam)

1023 return g_k # or (g, k, lat, lon)

1024

1025_allPropertiesOf_n(22, ExactTransverseMercator, Property_RO) # PYCHOK assert

1026 del _0_1, _allPropertiesOf_n, EPS, _1_EPS, _EWGS84

1027

1028

1029 def _overflow(x):

1030 '''(INTERNAL) Like C{copysign0(OVERFLOW, B{x})}.

1031 '''

1032 return _copyBit(_OVERFLOW, x)

1033

1034

1035 def parseETM5(strUTM, datum=_WGS84, Etm=Etm, falsed=True, **name):

1036 '''Parse a string representing a UTM coordinate, consisting

1037 of C{"zone[band] hemisphere easting northing"}.

1038

1039 @arg strUTM: A UTM coordinate (C{str}).

1040 @kwarg datum: Optional datum to use (L{Datum}, L{Ellipsoid},

1041 L{Ellipsoid2} or L{a_f2Tuple}).

1042 @kwarg Etm: Optional class to return the UTM coordinate

1043 (L{Etm}) or C{None}.

1044 @kwarg falsed: Both easting and northing are C{falsed} (C{bool}).

1045 @kwarg name: Optional B{C{Etm}} C{B{name}=NN} (C{str}).

1046

1047 @return: The UTM coordinate (B{C{Etm}}) or if C{B{Etm} is None}, a

1048 L{UtmUps5Tuple}C{(zone, hemipole, easting, northing, band)}

1049 with C{hemipole} is the hemisphere C{'N'|'S'}.

1050

1051 @raise ETMError: Invalid B{C{strUTM}}.

1052

1053 @raise TypeError: Invalid or near-spherical B{C{datum}}.

1054 '''

1055 r = _parseUTM5(strUTM, datum, Etm, falsed, Error=ETMError, **name)

1056 return r

1057

1058

1059 def toEtm8(latlon, lon=None, datum=None, Etm=Etm, falsed=True,

1060 strict=True, zone=None, **name_cmoff):

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

1062

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

1064 C{LatLon} instance.

1065 @kwarg lon: Optional longitude (C{degrees}), required if B{C{latlon}}

1066 is C{degrees}, ignored otherwise.

1067 @kwarg datum: Optional datum for the ETM coordinate, overriding

1068 B{C{latlon}}'s datum (L{Datum}, L{Ellipsoid},

1069 L{Ellipsoid2} or L{a_f2Tuple}).

1070 @kwarg Etm: Optional class to return the ETM coordinate (L{Etm}) or C{None}.

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

1072 @kwarg strict: Restrict B{C{lat}} to UTM ranges (C{bool}).

1073 @kwarg zone: Optional UTM zone to enforce (C{int} or C{str}).

1074 @kwarg name_cmoff: Optional B{C{Etm}} C{B{name}=NN} (C{str}) and DEPRECATED

1075 keyword argument C{B{cmoff}=True} to offset the longitude from

1076 the zone's central meridian (C{bool}), use B{C{falsed}} instead.

1077

1078 @return: The ETM coordinate as B{C{Etm}} or if C{B{Etm} is None} or not B{C{falsed}},

1079 a L{UtmUps8Tuple}C{(zone, hemipole, easting, northing, band, datum, gamma,

1080 scale)}. The C{hemipole} is the C{'N'|'S'} hemisphere.

1081

1082 @raise ETMError: No convergence transforming to ETM easting and northing.

1083

1084 @raise ETMError: Invalid B{C{zone}} or near-spherical or incompatible B{C{datum}}

1085 or C{ellipsoid}.

1086

1087 @raise RangeError: If B{C{lat}} outside the valid UTM bands or if B{C{lat}} or B{C{lon}}

1088 outside the valid range and L{rangerrors<pygeodesy.rangerrors>} is C{True}.

1089

1090 @raise TypeError: Invalid or near-spherical B{C{datum}} or B{C{latlon}} not ellipsoidal.

1091

1092 @raise ValueError: The B{C{lon}} value is missing or B{C{latlon}} is invalid.

1093 '''

1094 z, B, lat, lon, d, f, n = _to7zBlldfn(latlon, lon, datum,

1095 falsed, zone, strict,

1096 ETMError, **name_cmoff)

1097 lon0 = _cmlon(z) if f else None

1098 x, y, g, k = d.exactTM.forward(lat, lon, lon0=lon0)

1099

1100 return _toXtm8(Etm, z, lat, x, y, B, d, g, k, f,

1101 n, latlon, d.exactTM, Error=ETMError)

1102

1103

1104 if __name__ == '__main__': # MCCABE 16

1105

1106 def _main():

1107

1108 from pygeodesy import fstr, KTransverseMercator

1109 from pygeodesy.interns import _BAR_, _COLONSPACE_, _DASH_, NN

1110 from pygeodesy.internals import printf, _usage

1111 from sys import argv, exit as _exit

1112

1113 def _error(why, _a=NN):

1114 if _a:

1115 why = 'option %r %s' % (_a, why)

1116 _exit(_COLONSPACE_(_usage(*argv), why))

1117

1118 def _help(*why):

1119 if why:

1120 printf(_COLONSPACE_(_usage(*argv), *why))

1121 _exit(_usage(argv[0], '[-s[eries]', _BAR_, '-t]',

1122 '[-p[recision] <ndigits>]',

1123 '[-f[orward] <lat> <lon>', _BAR_,

1124 '-r[everse] <easting> <northing>', _BAR_,

1125 '<lat> <lon>]', _BAR_,

1126 '-h[elp]'))

1127

1128 def _result(t4):

1129 printf(_COLONSPACE_(tm.classname, fstr(t4, prec=_p, sep=_SPACE_)))

1130

1131 # mimick some of I{Karney}'s utility C{TransverseMercatorProj}

1132 _f = _r = _s = _t = False

1133 _p = -6

1134 args = argv[1:]

1135 while args and args[0].startswith(_DASH_):

1136 _a = args.pop(0)

1137 if len(_a) < 2:

1138 _error('invalid', _a)

1139 elif '-forward'.startswith(_a):

1140 _f, _r = True, False

1141 elif '-reverse'.startswith(_a):

1142 _f, _r = False, True

1143 elif '-precision'.startswith(_a) and args:

1144 _p = int(args.pop(0))

1145 elif '-series'.startswith(_a):

1146 _s, _t = True, False

1147 elif _a == '-t':

1148 _s, _t = False, True

1149 elif '-help'.startswith(_a):

1150 _help()

1151 else:

1152 _error('not supported', _a)

1153 if len(args) < 2:

1154 _help('incomplete')

1155

1156 f2 = map1(float, *args[:2])

1157 tm = KTransverseMercator() if _s else \

1158 ExactTransverseMercator(extendp=_t)

1159 if _f:

1160 t = tm.forward(*f2)

1161 elif _r:

1162 t = tm.reverse(*f2)

1163 else:

1164 t = tm.forward(*f2)

1165 _result(t)

1166 t = tm.reverse(t.easting, t.northing)

1167 _result(t)

1168

1169 _main()

1170

1171# % python3.13 -m pygeodesy.etm -p 12 33.33 44.44

1172# ExactTransverseMercator: 4276926.114803905599 4727193.767015309073 28.375536563148 1.233325101778

1173# ExactTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778

1174

1175# % python3.13 -m pygeodesy.etm -s -p 12 33.33 44.44

1176# KTransverseMercator: 4276926.114803904667 4727193.767015310004 28.375536563148 1.233325101778

1177# KTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778

1178

1179# % python3.12 -m pygeodesy.etm -p 12 33.33 44.44

1180# ExactTransverseMercator: 4276926.11480390653 4727193.767015309073 28.375536563148 1.233325101778

1181# ExactTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778

1182

1183# % python3.12 -m pygeodesy.etm -s -p 12 33.33 44.44

1184# KTransverseMercator: 4276926.114803904667 4727193.767015310004 28.375536563148 1.233325101778

1185# KTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778

1186

1187# % python2 -m pygeodesy.etm -p 12 33.33 44.44

1188# ExactTransverseMercator: 4276926.11480390653 4727193.767015309073 28.375536563148 1.233325101778

1189# ExactTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778

1190

1191# % python2 -m pygeodesy.etm -s -p 12 33.33 44.44

1192# KTransverseMercator: 4276926.114803904667 4727193.767015310004 28.375536563148 1.233325101778

1193# KTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778

1194

1195# % echo 33.33 44.44 | .../bin/TransverseMercatorProj

1196# 4276926.114804 4727193.767015 28.375536563148 1.233325101778

1197

1198# **) MIT License

1199#

1200# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1201#

1202# Permission is hereby granted, free of charge, to any person obtaining a

1203# copy of this software and associated documentation files (the "Software"),

1204# to deal in the Software without restriction, including without limitation

1205# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1206# and/or sell copies of the Software, and to permit persons to whom the

1207# Software is furnished to do so, subject to the following conditions:

1208#

1209# The above copyright notice and this permission notice shall be included

1210# in all copies or substantial portions of the Software.

1211#

1212# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1213# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1214# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1215# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1216# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1217# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1218# OTHER DEALINGS IN THE SOFTWARE.