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.

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, _4_0, _90_0, isnear0, isnear90

70 from pygeodesy.datums import _ellipsoidal_datum, _WGS84, _EWGS84

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

72 from pygeodesy.elliptic import _ALL_LAZY, Elliptic

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

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

75 from pygeodesy.fsums import Fsum, fsum1f_

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

77 _spherical_, _usage

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

79 _tand, _unsigned2

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

81 from pygeodesy.named import callername, _incompatible, _NamedBase

82 from pygeodesy.namedTuples import Forward4Tuple, Reverse4Tuple

83 from pygeodesy.props import deprecated_method, deprecated_property_RO, \

84 Property_RO, property_RO, _update_all, \

85 property_doc_

86 from pygeodesy.streprs import Fmt, pairs, unstr

87 from pygeodesy.units import Degrees, Scalar_

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

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

90 _to7zBlldfn, Utm, UTMError

91

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

93

94__all__ = _ALL_LAZY.etm

95__version__ = '23.12.03'

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

104 def _overflow(x):

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

106 '''

107 return _copyBit(_OVERFLOW, x)

108

109

110 class ETMError(UTMError):

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

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

113 '''

114 pass

115

116

117 class Etm(Utm):

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

119 a Universal Transverse Mercator (UTM) coordinate using the

120 L{ExactTransverseMercator} projection for highest accuracy.

121

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

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

124

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

126 html/classGeographicLib_1_1TransverseMercatorExact.html#details>}.

127 '''

128 _Error = ETMError # see utm.UTMError

129 _exactTM = None

130

131 __init__ = Utm.__init__

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

133

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

135 '''

136

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

138 def exactTM(self):

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

140 '''

141 if self._exactTM is None:

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

143 return self._exactTM

144

145 @exactTM.setter # PYCHOK setter!

146 def exactTM(self, exactTM):

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

148

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

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

151 '''

152 _xinstanceof(ExactTransverseMercator, exactTM=exactTM)

153

154 E = self.datum.ellipsoid

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

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

157 self._exactTM = exactTM

158 self._scale0 = exactTM.k0

159

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

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

162

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

164 see function L{parseETM5}.

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

166 overriding this name.

167

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

169

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

171

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

173 and L{pygeodesy.parseUTMUPS5}.

174 '''

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

176 name=name or self.name)

177

178 @deprecated_method

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

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

181 '''

182 return self.parse(strETM)

183

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

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

186

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

188 point (C{LatLon}) or C{None}.

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

190 C{falsed} (C{bool}).

191

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

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

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

195

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

197 incompatible or no convergence transforming to

198 lat- and longitude.

199

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

201 '''

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

203 self._toLLEB(unfalse=unfalse)

204 return self._latlon5(LatLon)

205

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

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

208 '''

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

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

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

212 t = repr(d.ellipsoid)

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

214

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

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

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

218

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

220 ll._gamma = g

221 ll._scale = k

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

223

224 def toUtm(self): # PYCHOK signature

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

226

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

228 '''

229 return self._xcopy2(Utm)

230

231

232 class ExactTransverseMercator(_NamedBase):

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

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

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

236 '''

237 _datum = _WGS84 # Datum

238 _E = _EWGS84 # Ellipsoid

239 _extendp = False # use extended domain

240# _iteration = None # ._sigmaInv2 and ._zetaInv2

241 _k0 = _K0_UTM # central scale factor

242 _lat0 = _0_0 # central parallel

243 _lon0 = _0_0 # central meridian

244 _mu = _EWGS84.e2 # 1st eccentricity squared

245 _mv = _EWGS84.e21 # 1 - ._mu

246 _raiser = False # throw Error

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

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

249

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

251 '''New L{ExactTransverseMercator} projection.

252

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

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

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

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

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

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

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

260

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

262 or B{C{k0}}.

263

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

265 html/classGeographicLib_1_1TransverseMercatorExact.html>} for more details,

266 especially on B{X{extendp}}.

267

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

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

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

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

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

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

274 '''

275 if extendp:

276 self._extendp = True

277 if name:

278 self.name = name

279 if raiser:

280 self.raiser = True

281

282 TM = ExactTransverseMercator

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

284 self.datum = datum # invokes ._resets

285 if lon0 or lon0 != TM._lon0:

286 self.lon0 = lon0

287 if k0 is not TM._k0:

288 self.k0 = k0

289

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

291 def datum(self):

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

293 '''

294 return self._datum

295

296 @datum.setter # PYCHOK setter!

297 def datum(self, datum):

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

299

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

301 '''

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

303 self._resets(d)

304 self._datum = d

305

306 @Property_RO

307 def _e(self):

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

309 '''

310 return self._E.e

311

312 @Property_RO

313 def _1_e_90(self): # PYCHOK no cover

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

315 '''

316 return (_1_0 - self._e) * _90_0

317

318 @property_RO

319 def ellipsoid(self):

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

321 '''

322 return self._E

323

324 @Property_RO

325 def _e_PI_2(self):

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

327 '''

328 return self._e * PI_2

329

330 @Property_RO

331 def _e_PI_4_(self):

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

333 '''

334 return -self._e * PI_4

335

336 @Property_RO

337 def _1_e_PI_2(self):

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

339 '''

340 return (_1_0 - self._e) * PI_2

341

342 @Property_RO

343 def _1_2e_PI_2(self):

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

345 '''

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

347

348 @property_RO

349 def equatoradius(self):

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

351 '''

352 return self._E.a

353

354 a = equatoradius

355

356 @Property_RO

357 def _e_TAYTOL(self):

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

359 '''

360 return self._e * _TAYTOL

361

362 @Property_RO

363 def _Eu(self):

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

365 '''

366 return Elliptic(self._mu)

367

368 @Property_RO

369 def _Eu_cE(self):

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

371 '''

372 return self._Eu.cE

373

374 def _Eu_2cE_(self, xi):

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

376 '''

377 return self._Eu_cE * _2_0 - xi

378

379 @Property_RO

380 def _Eu_cE_4(self):

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

382 '''

383 return self._Eu_cE / _4_0

384

385 @Property_RO

386 def _Eu_cK(self):

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

388 '''

389 return self._Eu.cK

390

391 @Property_RO

392 def _Eu_cK_cE(self):

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

394 '''

395 return self._Eu_cK / self._Eu_cE

396

397 @Property_RO

398 def _Eu_2cK_PI(self):

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

400 '''

401 return self._Eu_cK / PI_2

402

403 @Property_RO

404 def _Ev(self):

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

406 '''

407 return Elliptic(self._mv)

408

409 @Property_RO

410 def _Ev_cK(self):

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

412 '''

413 return self._Ev.cK

414

415 @Property_RO

416 def _Ev_cKE(self):

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

418 '''

419 return self._Ev.cKE

420

421 @Property_RO

422 def _Ev_3cKE_4(self):

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

424 '''

425 return self._Ev_cKE * 0.75 # _0_75

426

427 @Property_RO

428 def _Ev_5cKE_4(self):

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

430 '''

431 return self._Ev_cKE * 1.25 # _1_25

432

433 @Property_RO

434 def extendp(self):

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

436 '''

437 return self._extendp

438

439 @property_RO

440 def flattening(self):

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

442 '''

443 return self._E.f

444

445 f = flattening

446

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

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

449

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

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

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

453 the default if not C{None}.

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

455

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

457

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

459 real &x, real &y,

460 real &gamma, real &k)}.

461

462 @raise ETMError: No convergence, thrown iff property

463 C{B{raiser}=True}.

464 '''

465 lat = _fix90(lat - self._lat0)

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

467 if self.extendp:

468 backside = _lat = _lon = False

469 else: # enforce the parity

470 lat, _lat = _unsigned2(lat)

471 lon, _lon = _unsigned2(lon)

472 backside = lon > 90

473 if backside: # PYCHOK no cover

474 lon = _loneg(lon)

475 if lat == 0:

476 _lat = True

477

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

479 if lat == 90: # isnear90(lat)

480 u = self._Eu_cK

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

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

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

484 v = self._Ev_cK

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

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

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

488

489 sncndn6 = self._sncndn6(u, v)

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

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

492 self._zetaScaled(sncndn6, ll=False)

493

494 if backside:

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

496 y *= self._k0_a

497 x *= self._k0_a

498 if _lat:

499 y, g = neg_(y, g)

500 if _lon:

501 x, g = neg_(x, g)

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

503 name=name or self.name)

504

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

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

507 '''

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

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

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

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

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

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

514 s, c = sincos2(a)

515 h = hypot(psi, dlam)

516 r = cbrt(h * _3_mv_e)

517 u = r * c

518 v = r * s + self._Ev_cK

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

520 return u, v, h

521

522 @property_RO

523 def iteration(self):

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

525 or C{ExactTransverseMercator.reverse} iteration number

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

527 '''

528 return self._iteration

529

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

531 def k0(self):

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

533 '''

534 return self._k0 # aka scale0

535

536 @k0.setter # PYCHOK setter!

537 def k0(self, k0):

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

539

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

541 '''

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

543 if self._k0 != k0:

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

545 self._k0 = k0

546

547 @Property_RO

548 def _k0_a(self):

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

550 '''

551 return self.k0 * self.equatoradius

552

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

554 def lon0(self):

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

556 '''

557 return self._lon0

558

559 @lon0.setter # PYCHOK setter!

560 def lon0(self, lon0):

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

562

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

564 '''

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

566

567 @deprecated_property_RO

568 def majoradius(self): # PYCHOK no cover

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

570 return self.equatoradius

571

572 @Property_RO

573 def _1_mu_2(self):

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

575 '''

576 return self._mu * _0_5 + _1_0

577

578 @Property_RO

579 def _3_mv(self):

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

581 '''

582 return _3_0 / self._mv

583

584 @Property_RO

585 def _3_mv_e(self):

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

587 '''

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

589

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

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

592

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

594

595 @raise ETMError: No convergence.

596 '''

597 sca1, tol2 = _1_0, _TOL_10

598 if psi: # _zetaInv2

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

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

601

602 _zeta3 = self._zeta3

603 _zetaDwd2 = self._zetaDwd2

604 else: # _sigmaInv2

605 _zeta3 = self._sigma3

606 _zetaDwd2 = self._sigmaDwd2

607

608 d2, r = tol2, self.raiser

609 _U_2 = Fsum(u).fsum2_

610 _V_2 = Fsum(v).fsum2_

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

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

613 sncndn6 = self._sncndn6(u, v)

614 du, dv = _zetaDwd2(*sncndn6)

615 T, L, _ = _zeta3(v, *sncndn6)

616 T = (taup - T) * sca1

617 L -= lam

618 u, dU = _U_2(T * du, L * dv)

619 v, dV = _V_2(T * dv, -L * du)

620 if d2 < tol2:

621 r = False

622 break

623 d2 = hypot2(dU, dV)

624

625 self._iteration = i

626 if r: # PYCHOK no cover

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

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

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

630 return u, v

631

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

633 def raiser(self):

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

635 '''

636 return self._raiser

637

638 @raiser.setter # PYCHOK setter!

639 def raiser(self, raiser):

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

641 for convergence failures.

642 '''

643 self._raiser = bool(raiser)

644

645 def reset(self, lat0, lon0):

646 '''Set the central parallel and meridian.

647

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

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

650

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

652 parallel and meridian.

653

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

655 '''

656 t = self._lat0, self.lon0

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

658 self. lon0 = lon0

659 return t

660

661 def _resets(self, datum):

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

663

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

665

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

667 '''

668 E = datum.ellipsoid

669 mu = E.e2 # .eccentricity1st2

670 mv = E.e21 # _1_0 - mu

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

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

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

674

675 if self._datum or self._E:

676 _i = ExactTransverseMercator.iteration._uname

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

678

679 self._E = E

680 self._mu = mu

681 self._mv = mv

682

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

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

685

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

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

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

689 the default if not C{None}.

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

691

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

693

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

695 real &lat, real &lon,

696 real &gamma, real &k)}

697

698 @raise ETMError: No convergence, thrown iff property

699 C{B{raiser}=True}.

700 '''

701 # undoes the steps in .forward.

702 xi = y / self._k0_a

703 eta = x / self._k0_a

704 if self.extendp:

705 backside = _lat = _lon = False

706 else: # enforce the parity

707 eta, _lon = _unsigned2(eta)

708 xi, _lat = _unsigned2(xi)

709 backside = xi > self._Eu_cE

710 if backside: # PYCHOK no cover

711 xi = self._Eu_2cE_(xi)

712

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

714 if xi or eta != self._Ev_cKE:

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

716 else: # PYCHOK no cover

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

718 v = self._Ev_cK

719

720 if v or u != self._Eu_cK:

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

722 else: # PYCHOK no cover

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

724

725 if backside: # PYCHOK no cover

726 lon, g = _loneg(lon), _loneg(g)

727 if _lat:

728 lat, g = neg_(lat, g)

729 if _lon:

730 lon, g = neg_(lon, g)

731 lat += self._lat0

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

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

734 iteration=self._iteration,

735 name=name or self.name)

736

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

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

739

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

741 from C{._zeta3}.

742

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

744

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

746 real snu, real cnu, real dnu,

747 real snv, real cnv, real dnv,

748 real &gamma, real &k)}.

749 '''

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

751 cnudnv = cnu * dnv

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

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

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

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

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

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

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

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

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

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

762 if d2 > 0:

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

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

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

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

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

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

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

770 if q2 > 0:

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

772 if k2 > 0:

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

774 else:

775 k = _OVERFLOW

776 return g, k

777

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

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

780

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

782

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

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

785 real &xi, real &eta)}.

786

787 @raise ETMError: No convergence.

788 '''

789 mu = self._mu * cnu

790 mv = self._mv * cnv

791 # Lee 55.4 writing

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

793 d2 = cnu * mu + cnv * mv

794 mu *= snu * dnu

795 mv *= snv * dnv

796 if d2 > 0: # /= chokes PyChecker

797 mu = mu / d2

798 mv = mv / d2

799 else:

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

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

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

803 return xi, v, d2

804

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

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

807

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

809

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

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

812 real &du, real &dv)}.

813 '''

814 snuv = snu * snv

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

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

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

818 r = cnv * dnu * dnv

819 i = cnu * snuv * self._mu

820 du = (r**2 - i**2) / d

821 dv = neg(r * i * _2_0 / d)

822 return du, dv

823

824 def _sigmaInv2(self, xi, eta):

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

826

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

828

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

830 real &u, real &v)}.

831

832 @raise ETMError: No convergence.

833 '''

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

835 if not t:

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

837 return u, v

838

839 def _sigmaInv04(self, xi, eta):

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

841

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

843

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

845 real &u, real &v)}.

846 '''

847 t = False

848 d = eta - self._Ev_cKE

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

850 # sigma as a simple pole at

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

852 # and sigma is approximated by

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

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

855 u += self._Eu_cK

856 v += self._Ev_cK

857 C = 1

858

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

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

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

862 # sigma' = sigma'' = 0

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

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

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

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

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

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

869 t = h < _TAYTOL2

870 C = 2

871

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

873 u = v = self._Eu_cK_cE

874 u *= xi

875 v *= eta

876 C = 3

877

878 return u, v, t, C

879

880 def _sncndn6(self, u, v):

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

882 '''

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

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

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

886

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

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

889

890 @kwarg joined: Separator to join the attribute strings

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

892 @kwarg kwds: Optional, overriding keyword arguments.

893 '''

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

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

896 if self.name:

897 d.update(name=self.name)

898 t = pairs(d, **kwds)

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

900

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

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

903

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

905

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

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

908 real &taup, real &lam)}

909 '''

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

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

912 t1 = t2 = _overflow(snu)

913 # Lee 54.17 but write

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

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

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

917 if d1 > EPS02: # _EPSmin

918 t1 = snu * dnv / sqrt(d1)

919 else:

920 d1 = 0

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

922 if d2 > EPS02: # _EPSmin

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

924 else:

925 d2 = 0

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

927 # taup = sinh(psi)

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

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

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

931 return taup, lam, d2

932

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

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

935

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

937

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

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

940 real &du, real &dv)}.

941 '''

942 cnu2 = cnu**2 * self._mu

943 cnv2 = cnv**2

944 dnuv = dnu * dnv

945 dnuv2 = dnuv**2

946 snuv = snu * snv

947 snuv2 = snuv**2 * self._mu

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

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

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

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

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

953 return du, neg(dv)

954

955 def _zetaInv2(self, taup, lam):

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

957

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

959

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

961 real &u, real &v)}.

962

963 @raise ETMError: No convergence.

964 '''

965 psi = asinh(taup)

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

967 if not t:

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

969 return u, v

970

971 def _zetaInv04(self, psi, lam):

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

973

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

975

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

977 real &u, real &v)}.

978 '''

979 if lam > self._1_2e_PI_2:

980 d = lam - self._1_e_PI_2

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

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

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

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

985 # pole, where we have, approximately

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

987 # Inverting this gives:

988 e = self._e # eccentricity

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

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

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

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

993 return u, v, False, 1

994

995 elif psi < self._e_PI_2:

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

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

998 # zeta' = zeta'' = 0

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

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

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

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

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

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

1005

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

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

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

1009 # corresponding to the north pole.

1010 s, c = sincos2(lam)

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

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

1013 u = r * atan2(h, c)

1014 v = r * asinh(s / hypot(h, c))

1015 return u, v, False, 3

1016

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

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

1019

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

1021

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

1023 4-tuple C{(g, k, lat, lon)}.

1024 '''

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

1026 tau = self._E.es_tauf(t)

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

1028 if ll:

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

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

1031

1032

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

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

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

1036

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

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

1039 L{Ellipsoid2} or L{a_f2Tuple}).

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

1041 (L{Etm}) or C{None}.

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

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

1044

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

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

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

1048 C{'N'|'S'}.

1049

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

1051

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

1053 '''

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

1055 return r

1056

1057

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

1059 name=NN, strict=True,

1060 zone=None, **cmoff):

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

1062

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

1064 geodetic C{LatLon} instance.

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

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

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

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

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

1070 (L{Etm}) or C{None}.

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

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

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

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

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

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

1077

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

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

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

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

1082 hemisphere.

1083

1084 @raise ETMError: No convergence transforming to ETM easting

1085 and northing.

1086

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

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

1089

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

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

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

1093

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

1095 B{C{latlon}} not ellipsoidal.

1096

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

1098 is invalid.

1099 '''

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

1101 falsed, name, zone,

1102 strict, ETMError, **cmoff)

1103 lon0 = _cmlon(z) if f else None

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

1105

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

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

1108

1109

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

1111

1112 from pygeodesy import fstr, KTransverseMercator, printf

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 _as = argv[1:]

1118 while _as and _as[0].startswith(_DASH_):

1119 _a = _as.pop(0)

1120 if len(_a) < 2:

1121 _exit('%s: option %r invalid' % (_usage(*argv), _a))

1122 elif '-forward'.startswith(_a):

1123 _f, _r = True, False

1124 elif '-reverse'.startswith(_a):

1125 _f, _r = False, True

1126 elif '-series'.startswith(_a):

1127 _s, _t = True, False

1128 elif _a == '-t':

1129 _s, _t = False, True

1130 elif '-help'.startswith(_a):

1131 _exit(_usage(argv[0], '[-s | -t]',

1132 '[-f[orward] <lat> <lon>',

1133 '| -r[everse] <easting> <northing>',

1134 '| <lat> <lon>]',

1135 '| -h[elp]'))

1136 else:

1137 _exit('%s: option %r not supported' % (_usage(*argv), _a))

1138 if len(_as) > 1:

1139 f2 = map1(float, *_as[:2])

1140 else:

1141 _exit('%s ...: incomplete' % (_usage(*argv),))

1142

1143 if _s: # -series

1144 tm = KTransverseMercator()

1145 else:

1146 tm = ExactTransverseMercator(extendp=_t)

1147

1148 if _f:

1149 t = tm.forward(*f2)

1150 elif _r:

1151 t = tm.reverse(*f2)

1152 else:

1153 t = tm.forward(*f2)

1154 printf('%s: %s', tm.classname, fstr(t, sep=_SPACE_))

1155 t = tm.reverse(t.easting, t.northing)

1156 printf('%s: %s', tm.classname, fstr(t, sep=_SPACE_))

1157

1158

1159# % python3 -m pygeodesy.etm 33.33 44.44

1160# ExactTransverseMercator: 4276926.114804 4727193.767015 28.375537 1.233325

1161# ExactTransverseMercator: 33.33 44.44 28.375537 1.233325

1162

1163# % python3 -m pygeodesy.etm -s 33.33 44.44

1164# KTransverseMercator: 4276926.114804 4727193.767015 28.375537 1.233325

1165# KTransverseMercator: 33.33 44.44 28.375537 1.233325

1166

1167# % echo 33.33 44.44 | .../bin/TransverseMercatorProj

1168# 4276926.114804 4727193.767015 28.375536563148 1.233325101778

1169

1170# **) MIT License

1171#

1172# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1173#

1174# Permission is hereby granted, free of charge, to any person obtaining a

1175# copy of this software and associated documentation files (the "Software"),

1176# to deal in the Software without restriction, including without limitation

1177# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1178# and/or sell copies of the Software, and to permit persons to whom the

1179# Software is furnished to do so, subject to the following conditions:

1180#

1181# The above copyright notice and this permission notice shall be included

1182# in all copies or substantial portions of the Software.

1183#

1184# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1185# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1186# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1187# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1188# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1189# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1190# OTHER DEALINGS IN THE SOFTWARE.