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.fsums import Fsum # from .fmath

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

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

77 _spherical_

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__ = '24.06.11'

96

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

98_TAYTOL = pow(EPS, 0.6)

99_TAYTOL2 = _TAYTOL * _2_0

100_TOL_10 = EPS * _0_1

101_TRIPS = 21 # C++ 10

102

103

104 class 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

111 class Etm(Utm):

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

113 a Universal Transverse Mercator (UTM) coordinate using the

114 L{ExactTransverseMercator} projection for highest accuracy.

115

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

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

118

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

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

121 '''

122 _Error = ETMError # see utm.UTMError

123 _exactTM = None

124

125 __init__ = Utm.__init__

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

127

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

129 '''

130

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

132 def exactTM(self):

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

134 '''

135 if self._exactTM is None:

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

137 return self._exactTM

138

139 @exactTM.setter # PYCHOK setter!

140 def exactTM(self, exactTM):

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

142

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

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

145 '''

146 _xinstanceof(ExactTransverseMercator, exactTM=exactTM)

147

148 E = self.datum.ellipsoid

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

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

151 self._exactTM = exactTM

152 self._scale0 = exactTM.k0

153

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

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

156

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

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

159

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

161

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

163

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

165 L{pygeodesy.parseUTMUPS5}.

166 '''

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

168 name=self._name__(name))

169

170 @deprecated_method

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

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

173 '''

174 return self.parse(strETM)

175

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

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

178

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

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

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

182

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

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

185

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

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

188

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

190 '''

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

192 self._toLLEB(unfalse=unfalse)

193 return self._latlon5(LatLon)

194

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

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

197 '''

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

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

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

201 t = repr(d.ellipsoid)

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

203

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

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

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

207

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

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

210

211 def toUtm(self): # PYCHOK signature

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

213

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

215 '''

216 return self._xcopy2(Utm)

217

218

219 class ExactTransverseMercator(_NamedBase):

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

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

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

223 '''

224 _datum = _WGS84 # Datum

225 _E = _EWGS84 # Ellipsoid

226 _extendp = False # use extended domain

227# _iteration = None # ._sigmaInv2 and ._zetaInv2

228 _k0 = _K0_UTM # central scale factor

229 _lat0 = _0_0 # central parallel

230 _lon0 = _0_0 # central meridian

231 _mu = _EWGS84.e2 # 1st eccentricity squared

232 _mv = _EWGS84.e21 # 1 - ._mu

233 _raiser = False # throw Error

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

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

236

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

238 '''New L{ExactTransverseMercator} projection.

239

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

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

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

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

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

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

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

247

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

249 or B{C{k0}}.

250

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

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

253 especially on B{X{extendp}}.

254

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

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

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

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

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

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

261 '''

262 if extendp:

263 self._extendp = True

264 if name:

265 self.name = name

266 if raiser:

267 self.raiser = True

268

269 TM = ExactTransverseMercator

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

271 self.datum = datum # invokes ._resets

272 if lon0 or lon0 != TM._lon0:

273 self.lon0 = lon0

274 if k0 is not TM._k0:

275 self.k0 = k0

276

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

278 def datum(self):

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

280 '''

281 return self._datum

282

283 @datum.setter # PYCHOK setter!

284 def datum(self, datum):

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

286

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

288 '''

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

290 self._resets(d)

291 self._datum = d

292

293 @Property_RO

294 def _e(self):

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

296 '''

297 return self._E.e

298

299 @Property_RO

300 def _1_e_90(self): # PYCHOK no cover

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

302 '''

303 return (_1_0 - self._e) * _90_0

304

305 @property_RO

306 def ellipsoid(self):

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

308 '''

309 return self._E

310

311 @Property_RO

312 def _e_PI_2(self):

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

314 '''

315 return self._e * PI_2

316

317 @Property_RO

318 def _e_PI_4_(self):

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

320 '''

321 return -self._e * PI_4

322

323 @Property_RO

324 def _1_e_PI_2(self):

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

326 '''

327 return (_1_0 - self._e) * PI_2

328

329 @Property_RO

330 def _1_2e_PI_2(self):

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

332 '''

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

334

335 @property_RO

336 def equatoradius(self):

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

338 '''

339 return self._E.a

340

341 a = equatoradius

342

343 @Property_RO

344 def _e_TAYTOL(self):

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

346 '''

347 return self._e * _TAYTOL

348

349 @Property_RO

350 def _Eu(self):

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

352 '''

353 return Elliptic(self._mu)

354

355 @Property_RO

356 def _Eu_cE(self):

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

358 '''

359 return self._Eu.cE

360

361 def _Eu_2cE_(self, xi):

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

363 '''

364 return self._Eu_cE * _2_0 - xi

365

366 @Property_RO

367 def _Eu_cE_4(self):

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

369 '''

370 return self._Eu_cE / _4_0

371

372 @Property_RO

373 def _Eu_cK(self):

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

375 '''

376 return self._Eu.cK

377

378 @Property_RO

379 def _Eu_cK_cE(self):

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

381 '''

382 return self._Eu_cK / self._Eu_cE

383

384 @Property_RO

385 def _Eu_2cK_PI(self):

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

387 '''

388 return self._Eu_cK / PI_2

389

390 @Property_RO

391 def _Ev(self):

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

393 '''

394 return Elliptic(self._mv)

395

396 @Property_RO

397 def _Ev_cK(self):

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

399 '''

400 return self._Ev.cK

401

402 @Property_RO

403 def _Ev_cKE(self):

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

405 '''

406 return self._Ev.cKE

407

408 @Property_RO

409 def _Ev_3cKE_4(self):

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

411 '''

412 return self._Ev_cKE * 0.75 # _0_75

413

414 @Property_RO

415 def _Ev_5cKE_4(self):

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

417 '''

418 return self._Ev_cKE * 1.25 # _1_25

419

420 @Property_RO

421 def extendp(self):

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

423 '''

424 return self._extendp

425

426 @property_RO

427 def flattening(self):

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

429 '''

430 return self._E.f

431

432 f = flattening

433

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

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

436

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

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

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

440 the default if not C{None}.

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

442

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

444

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

446 real &x, real &y,

447 real &gamma, real &k)}.

448

449 @raise ETMError: No convergence, thrown iff property

450 C{B{raiser}=True}.

451 '''

452 lat = _fix90(lat - self._lat0)

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

454 if self.extendp:

455 backside = _lat = _lon = False

456 else: # enforce the parity

457 lat, _lat = _unsigned2(lat)

458 lon, _lon = _unsigned2(lon)

459 backside = lon > 90

460 if backside: # PYCHOK no cover

461 lon = _loneg(lon)

462 if lat == 0:

463 _lat = True

464

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

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

467 u = self._Eu_cK

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

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

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

471 v = self._Ev_cK

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

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

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

475

476 sncndn6 = self._sncndn6(u, v)

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

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

479 self._zetaScaled(sncndn6, ll=False)

480

481 if backside:

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

483 y *= self._k0_a

484 x *= self._k0_a

485 if _lat:

486 y, g = neg_(y, g)

487 if _lon:

488 x, g = neg_(x, g)

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

490 name=self._name__(name))

491

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

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

494 '''

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

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

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

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

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

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

501 s, c = sincos2(a)

502 h = hypot(psi, dlam)

503 r = cbrt(h * _3_mv_e)

504 u = r * c

505 v = r * s + self._Ev_cK

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

507 return u, v, h

508

509 @property_RO

510 def iteration(self):

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

512 or C{ExactTransverseMercator.reverse} iteration number

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

514 '''

515 return self._iteration

516

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

518 def k0(self):

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

520 '''

521 return self._k0 # aka scale0

522

523 @k0.setter # PYCHOK setter!

524 def k0(self, k0):

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

526

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

528 '''

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

530 if self._k0 != k0:

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

532 self._k0 = k0

533

534 @Property_RO

535 def _k0_a(self):

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

537 '''

538 return self.k0 * self.equatoradius

539

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

541 def lon0(self):

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

543 '''

544 return self._lon0

545

546 @lon0.setter # PYCHOK setter!

547 def lon0(self, lon0):

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

549

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

551 '''

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

553

554 @deprecated_property_RO

555 def majoradius(self): # PYCHOK no cover

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

557 return self.equatoradius

558

559 @Property_RO

560 def _1_mu_2(self):

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

562 '''

563 return self._mu * _0_5 + _1_0

564

565 @Property_RO

566 def _3_mv(self):

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

568 '''

569 return _3_0 / self._mv

570

571 @Property_RO

572 def _3_mv_e(self):

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

574 '''

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

576

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

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

579

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

581

582 @raise ETMError: No convergence.

583 '''

584 sca1, tol2 = _1_0, _TOL_10

585 if psi: # _zetaInv2

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

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

588

589 _zeta3 = self._zeta3

590 _zetaDwd2 = self._zetaDwd2

591 else: # _sigmaInv2

592 _zeta3 = self._sigma3

593 _zetaDwd2 = self._sigmaDwd2

594

595 d2, r = tol2, self.raiser

596 _U_2 = Fsum(u).fsum2f_

597 _V_2 = Fsum(v).fsum2f_

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

599 _hy2 = hypot2

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

601 sncndn6 = self._sncndn6(u, v)

602 du, dv = _zetaDwd2(*sncndn6)

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

604 T = (taup - T) * sca1

605 L -= lam

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

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

608 if d2 < tol2:

609 r = False

610 break

611 d2 = _hy2(dU, dV)

612

613 self._iteration = i

614 if r: # PYCHOK no cover

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

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

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

618 return u, v

619

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

621 def raiser(self):

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

623 '''

624 return self._raiser

625

626 @raiser.setter # PYCHOK setter!

627 def raiser(self, raiser):

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

629 for convergence failures.

630 '''

631 self._raiser = bool(raiser)

632

633 def reset(self, lat0, lon0):

634 '''Set the central parallel and meridian.

635

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

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

638

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

640 parallel and meridian.

641

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

643 '''

644 t = self._lat0, self.lon0

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

646 self. lon0 = lon0

647 return t

648

649 def _resets(self, datum):

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

651

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

653

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

655 '''

656 E = datum.ellipsoid

657 mu = E.e2 # .eccentricity1st2

658 mv = E.e21 # _1_0 - mu

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

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

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

662

663 if self._datum or self._E:

664 _i = ExactTransverseMercator.iteration._uname

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

666

667 self._E = E

668 self._mu = mu

669 self._mv = mv

670

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

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

673

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

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

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

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

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

679

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

681

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

683 real &lat, real &lon,

684 real &gamma, real &k)}

685

686 @raise ETMError: No convergence, thrown iff property

687 C{B{raiser}=True}.

688 '''

689 # undoes the steps in .forward.

690 xi = y / self._k0_a

691 eta = x / self._k0_a

692 if self.extendp:

693 backside = _lat = _lon = False

694 else: # enforce the parity

695 eta, _lon = _unsigned2(eta)

696 xi, _lat = _unsigned2(xi)

697 backside = xi > self._Eu_cE

698 if backside: # PYCHOK no cover

699 xi = self._Eu_2cE_(xi)

700

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

702 if xi or eta != self._Ev_cKE:

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

704 else: # PYCHOK no cover

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

706 v = self._Ev_cK

707

708 if v or u != self._Eu_cK:

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

710 else: # PYCHOK no cover

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

712

713 if backside: # PYCHOK no cover

714 lon, g = _loneg(lon), _loneg(g)

715 if _lat:

716 lat, g = neg_(lat, g)

717 if _lon:

718 lon, g = neg_(lon, g)

719 lat += self._lat0

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

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

722 iteration=self._iteration,

723 name=self._name__(name))

724

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

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

727

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

729 from C{._zeta3}.

730

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

732

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

734 real snu, real cnu, real dnu,

735 real snv, real cnv, real dnv,

736 real &gamma, real &k)}.

737 '''

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

739 cnudnv = cnu * dnv

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

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

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

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

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

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

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

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

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

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

750 if d2 > 0:

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

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

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

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

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

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

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

758 if q2 > 0:

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

760 if k2 > 0:

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

762 else:

763 k = _OVERFLOW

764 return g, k

765

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

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

768

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

770

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

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

773 real &xi, real &eta)}.

774

775 @raise ETMError: No convergence.

776 '''

777 mu = self._mu * cnu

778 mv = self._mv * cnv

779 # Lee 55.4 writing

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

781 d2 = cnu * mu + cnv * mv

782 mu *= snu * dnu

783 mv *= snv * dnv

784 if d2 > 0: # /= chokes PyChecker

785 mu = mu / d2

786 mv = mv / d2

787 else:

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

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

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

791 return xi, v, d2

792

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

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

795

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

797

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

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

800 real &du, real &dv)}.

801 '''

802 mu = self._mu

803 snuv = snu * snv

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

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

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

807 r = cnv * dnu * dnv

808 i = cnu * snuv * mu

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

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

811 return du, dv

812

813 def _sigmaInv2(self, xi, eta):

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

815

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

817

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

819 real &u, real &v)}.

820

821 @raise ETMError: No convergence.

822 '''

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

824 if not t:

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

826 return u, v

827

828 def _sigmaInv04(self, xi, eta):

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

830

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

832

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

834 real &u, real &v)}.

835 '''

836 t = False

837 d = eta - self._Ev_cKE

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

839 # sigma as a simple pole at

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

841 # and sigma is approximated by

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

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

844 u += self._Eu_cK

845 v += self._Ev_cK

846 C = 1

847

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

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

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

851 # sigma' = sigma'' = 0

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

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

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

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

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

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

858 t = h < _TAYTOL2

859 C = 2

860

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

862 u = v = self._Eu_cK_cE

863 u *= xi

864 v *= eta

865 C = 3

866

867 return u, v, t, C

868

869 def _sncndn6(self, u, v):

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

871 '''

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

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

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

875

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

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

878

879 @kwarg joined: Separator to join the attribute strings

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

881 @kwarg kwds: Optional, overriding keyword arguments.

882 '''

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

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

885 if self.name:

886 d.update(name=self.name)

887 t = pairs(d, **kwds)

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

889

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

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

892

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

894

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

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

897 real &taup, real &lam)}

898 '''

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

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

901 t1 = t2 = _overflow(snu)

902 # Lee 54.17 but write

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

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

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

906 if d1 > EPS02: # _EPSmin

907 t1 = snu * dnv / sqrt(d1)

908 else:

909 d1 = 0

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

911 if d2 > EPS02: # _EPSmin

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

913 else:

914 d2 = 0

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

916 # taup = sinh(psi)

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

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

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

920 return taup, lam, d2

921

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

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

924

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

926

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

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

929 real &du, real &dv)}.

930 '''

931 cnu2 = cnu**2 * self._mu

932 cnv2 = cnv**2

933 dnuv = dnu * dnv

934 dnuv2 = dnuv**2

935 snuv = snu * snv

936 snuv2 = snuv**2 * self._mu

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

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

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

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

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

942 return du, neg(dv)

943

944 def _zetaInv2(self, taup, lam):

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

946

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

948

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

950 real &u, real &v)}.

951

952 @raise ETMError: No convergence.

953 '''

954 psi = asinh(taup)

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

956 if not t:

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

958 return u, v

959

960 def _zetaInv04(self, psi, lam):

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

962

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

964

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

966 real &u, real &v)}.

967 '''

968 if lam > self._1_2e_PI_2:

969 d = lam - self._1_e_PI_2

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

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

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

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

974 # pole, where we have, approximately

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

976 # Inverting this gives:

977 e = self._e # eccentricity

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

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

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

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

982 return u, v, False, 1

983

984 elif psi < self._e_PI_2:

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

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

987 # zeta' = zeta'' = 0

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

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

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

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

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

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

994

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

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

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

998 # corresponding to the north pole.

999 s, c = sincos2(lam)

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

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

1002 u = r * atan2(h, c)

1003 v = r * asinh(s / hypot(h, c))

1004 return u, v, False, 3

1005

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

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

1008

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

1010

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

1012 4-tuple C{(g, k, lat, lon)}.

1013 '''

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

1015 tau = self._E.es_tauf(t)

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

1017 if ll:

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

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

1020

1021

1022 def _overflow(x):

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

1024 '''

1025 return _copyBit(_OVERFLOW, x)

1026

1027

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

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

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

1031

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

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

1034 L{Ellipsoid2} or L{a_f2Tuple}).

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

1036 (L{Etm}) or C{None}.

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

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

1039

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

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

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

1043

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

1045

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

1047 '''

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

1049 return r

1050

1051

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

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

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

1055

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

1057 C{LatLon} instance.

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

1059 is C{degrees}, ignored otherwise.

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

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

1062 L{Ellipsoid2} or L{a_f2Tuple}).

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

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

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

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

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

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

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

1070

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

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

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

1074

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

1076

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

1078 or C{ellipsoid}.

1079

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

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

1082

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

1084

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

1086 '''

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

1088 falsed, zone, strict,

1089 ETMError, **name_cmoff)

1090 lon0 = _cmlon(z) if f else None

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

1092

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

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

1095

1096

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

1098

1099 from pygeodesy import fstr, KTransverseMercator, printf

1100 from pygeodesy.internals import _usage

1101 from sys import argv, exit as _exit

1102

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

1104 _f = _r = _s = _t = False

1105 _p = -6

1106 _as = argv[1:]

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

1108 _a = _as.pop(0)

1109 if len(_a) < 2:

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

1111 elif '-forward'.startswith(_a):

1112 _f, _r = True, False

1113 elif '-reverse'.startswith(_a):

1114 _f, _r = False, True

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

1116 _p = int(_as.pop(0))

1117 elif '-series'.startswith(_a):

1118 _s, _t = True, False

1119 elif _a == '-t':

1120 _s, _t = False, True

1121 elif '-help'.startswith(_a):

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

1123 '[-p[recision] <ndigits>',

1124 '[-f[orward] <lat> <lon>',

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

1126 '|<lat> <lon>]',

1127 '|-h[elp]'))

1128 else:

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

1130 if len(_as) > 1:

1131 f2 = map1(float, *_as[:2])

1132 else:

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

1134

1135 if _s: # -series

1136 tm = KTransverseMercator()

1137 else:

1138 tm = ExactTransverseMercator(extendp=_t)

1139

1140 if _f:

1141 t = tm.forward(*f2)

1142 elif _r:

1143 t = tm.reverse(*f2)

1144 else:

1145 t = tm.forward(*f2)

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

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

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

1149

1150

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

1152# ExactTransverseMercator: 4276926.11480390653 4727193.767015309073 28.375536563148 1.233325101778

1153# ExactTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778

1154

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

1156# KTransverseMercator: 4276926.114803904667 4727193.767015310004 28.375536563148 1.233325101778

1157# KTransverseMercator: 33.33 44.44 28.375536563148 1.233325101778

1158

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

1160# 4276926.114804 4727193.767015 28.375536563148 1.233325101778

1161

1162# **) MIT License

1163#

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

1165#

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

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

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

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

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

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

1172#

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

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

1175#

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

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

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

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

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

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

1182# OTHER DEALINGS IN THE SOFTWARE.