Hide keyboard shortcuts

Hot-keys on this page

r m x p   toggle line displays

j k   next/prev highlighted chunk

0   (zero) top of page

1   (one) first highlighted chunk

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492

493

494

495

496

497

498

499

500

501

502

503

504

505

506

507

508

509

510

511

512

513

514

515

516

517

518

519

520

521

522

523

524

525

526

527

528

529

530

531

532

533

534

535

536

537

538

539

540

541

542

543

544

545

546

547

548

549

550

551

552

553

554

555

556

557

558

559

560

561

562

563

564

565

566

567

568

569

570

571

572

573

574

575

576

577

578

579

580

581

582

583

584

585

586

587

588

589

590

591

592

593

594

595

596

597

598

599

600

601

602

603

604

605

606

607

608

609

610

611

612

613

614

615

616

617

618

619

620

621

622

623

624

625

626

627

628

629

630

631

632

633

634

635

636

637

638

639

640

641

642

643

644

645

646

647

648

649

650

651

652

653

654

655

656

657

658

659

660

661

662

663

664

665

666

667

668

669

670

671

672

673

674

675

676

677

678

679

680

681

682

683

684

685

686

687

688

689

690

691

692

693

694

695

696

697

698

699

700

701

702

703

704

705

706

707

708

709

710

711

712

713

714

715

716

717

718

719

720

721

722

723

724

725

726

727

728

729

730

731

732

733

734

735

736

737

738

739

740

741

742

743

744

745

746

747

748

749

750

751

752

753

754

755

756

757

758

759

760

761

762

763

764

765

766

767

768

769

770

771

772

773

774

775

776

777

778

779

780

781

782

783

784

785

786

787

788

789

790

791

792

793

794

795

796

797

798

799

800

801

802

803

804

805

806

807

808

809

810

811

812

813

814

815

816

817

818

819

820

821

822

823

824

825

826

827

828

829

830

831

832

833

834

835

836

837

838

839

840

841

842

843

844

845

846

847

848

849

850

851

852

853

854

855

856

857

858

859

860

861

862

863

864

865

866

867

868

869

870

871

872

873

874

875

876

877

878

879

880

881

882

883

884

885

886

887

888

889

890

891

892

893

894

895

896

897

898

899

900

901

902

903

904

905

906

907

908

909

910

911

912

913

914

915

916

917

918

919

920

921

922

923

924

925

926

927

928

929

930

931

932

933

934

935

936

937

938

939

940

941

942

943

944

945

946

947

948

949

950

951

952

953

954

955

956

957

958

959

960

961

962

963

964

965

966

967

968

969

970

971

972

973

974

975

976

977

978

979

980

981

982

983

984

985

986

987

988

989

990

991

992

993

994

995

996

997

998

999

1000

1001

1002

1003

1004

1005

1006

1007

1008

1009

1010

1011

1012

1013

1014

1015

1016

1017

1018

1019

1020

1021

1022

1023

1024

1025

1026

1027

1028

1029

1030

1031

1032

1033

1034

1035

1036

1037

1038

1039

1040

1041

1042

1043

1044

1045

1046

1047

1048

1049

1050

1051

1052

1053

1054

1055

1056

1057

1058

1059

1060

1061

1062

1063

1064

1065

1066

1067

1068

1069

1070

1071

1072

1073

1074

1075

1076

1077

1078

1079

1080

1081

1082

1083

1084

1085

1086

1087

1088

1089

1090

1091

1092

1093

1094

1095

1096

1097

1098

1099

1100

1101

1102

1103

1104

1105

1106

1107

1108

1109

1110

1111

1112

1113

1114

1115

1116

1117

1118

1119

1120

1121

1122

1123

1124

1125

1126

1127

1128

1129

1130

1131

1132

1133

1134

1135

1136

1137

1138

1139

1140

1141

1142

1143

1144

1145

1146

1147

1148

1149

1150

1151

1152

1153

1154

1155

1156

1157

1158

1159

1160

1161

1162

1163

1164

1165

1166

1167

1168

1169

1170

1171

1172

1173

1174

1175

1176

1177

1178

1179

1180

1181

1182

1183

1184

1185

1186

1187

1188

1189

1190

1191

1192

1193

1194

1195

1196

1197

1198

1199

1200

1201

 

# -*- coding: utf-8 -*- 

 

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

 

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

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

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

 

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

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

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

TransverseMercatorProj.1.html>}. 

 

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

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

file C{Header}. 

 

Copyright (C) U{Charles Karney<mailto:Charles@Karney.com>} (2008-2022) and licensed 

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

GeographicLib.SourceForge.io>} documentation. 

 

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

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

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

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

suitable starting guess. 

 

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

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

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

exceptions:: 

 

Lee here Description 

 

x/a xi Northing (unit Earth) 

 

y/a eta Easting (unit Earth) 

 

s/a sigma xi + i * eta 

 

y x Easting 

 

x y Northing 

 

k e Eccentricity 

 

k^2 mu Elliptic function parameter 

 

k'^2 mv Elliptic function complementary parameter 

 

m k Scale 

 

zeta zeta Complex longitude = Mercator = chi in paper 

 

s sigma Complex GK = zeta in paper 

 

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

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

which maintains accuracy near C{phi = pi/2}. Such changes are noted in the code. 

''' 

# make sure int/int division yields float quotient, see .basics 

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

 

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

from pygeodesy.constants import EPS, EPS02, PI_2, PI_4, _K0_UTM, \ 

_1_EPS, isnear0, _0_0, _0_1, _0_5, \ 

_1_0, _2_0, _3_0, _4_0, _90_0, _180_0 

from pygeodesy.datums import _ellipsoidal_datum, _WGS84 

from pygeodesy.elliptic import _ALL_LAZY, Elliptic 

# from pygeodesy.errors import _incompatible # from .named 

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

from pygeodesy.fsums import Fsum, fsum1_ 

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

_spherical_, _usage 

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

_tand, _unsigned2 

# from pygeodesy.lazily import _ALL_LAZY # from .elliptic 

from pygeodesy.named import callername, _incompatible, _NamedBase 

from pygeodesy.namedTuples import Forward4Tuple, Reverse4Tuple 

from pygeodesy.props import deprecated_method, deprecated_property_RO, \ 

Property_RO, property_RO, _update_all, \ 

property_doc_ 

from pygeodesy.streprs import Fmt, fstr, pairs, unstr 

from pygeodesy.units import Degrees, Scalar_ 

from pygeodesy.utily import atand, atan2d, sincos2 

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

_to7zBlldfn, Utm, UTMError 

 

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

 

__all__ = _ALL_LAZY.etm 

__version__ = '22.09.14' 

 

_OVERFLOW = _1_EPS**2 # about 2e+31 

_TAYTOL = pow(EPS, 0.6) 

_TAYTOL2 = _TAYTOL * _2_0 

_TOL_10 = EPS * _0_1 

_TRIPS = 21 # C++ 10 

 

 

def _overflow(x): 

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

''' 

return _copyBit(_OVERFLOW, x) 

 

 

class ETMError(UTMError): 

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

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

''' 

pass 

 

 

class Etm(Utm): 

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

a Universal Transverse Mercator (UTM) coordinate using the 

L{ExactTransverseMercator} projection for highest accuracy. 

 

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

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

 

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

html/classGeographicLib_1_1TransverseMercatorExact.html#details>}. 

''' 

_Error = ETMError # see utm.UTMError 

_exactTM = None 

 

def __init__(self, zone, hemisphere, easting, northing, band=NN, # PYCHOK expected 

datum=_WGS84, falsed=True, 

convergence=None, scale=None, name=NN): 

'''New L{Etm} coordinate. 

 

@arg zone: Longitudinal UTM zone (C{int}, 1..60) or zone with/-out 

I{latitudinal} Band letter (C{str}, '01C'|..|'60X'). 

@arg hemisphere: Northern or southern hemisphere (C{str}, C{'N[orth]'} 

or C{'S[outh]'}). 

@arg easting: Easting, see B{C{falsed}} (C{meter}). 

@arg northing: Northing, see B{C{falsed}} (C{meter}). 

@kwarg band: Optional, I{latitudinal} band (C{str}, 'C'|..|'X'). 

@kwarg datum: Optional, this coordinate's datum (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}). 

@kwarg falsed: If C{True}, both B{C{easting}} and B{C{northing}} are 

C{falsed} (C{bool}). 

@kwarg convergence: Optional meridian convergence, bearing off grid North, 

clockwise from true North (C{degrees}) or C{None}. 

@kwarg scale: Optional grid scale factor (C{scalar}) or C{None}. 

@kwarg name: Optional name (C{str}). 

 

@raise ETMError: Invalid B{C{zone}}, B{C{hemishere}} or B{C{band}} 

or near-spherical B{C{datum}} or C{ellipsoid}. 

 

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

 

@example: 

 

>>> import pygeodesy 

>>> u = pygeodesy.Etm(31, 'N', 448251, 5411932) 

''' 

Utm.__init__(self, zone, hemisphere, easting, northing, 

band=band, datum=datum, falsed=falsed, 

convergence=convergence, scale=scale, 

name=name) 

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

 

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

def exactTM(self): 

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

''' 

return self._exactTM 

 

@exactTM.setter # PYCHOK setter! 

def exactTM(self, exactTM): 

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

 

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

with this ETM coordinate's C{datum}. 

''' 

_xinstanceof(ExactTransverseMercator, exactTM=exactTM) 

 

E = self.datum.ellipsoid 

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

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

self._exactTM = exactTM 

self._scale0 = exactTM.k0 

 

def parse(self, strETM, name=NN): 

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

 

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

see function L{parseETM5}. 

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

overriding this name. 

 

@return: The instance (L{Etm}). 

 

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

 

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

and L{pygeodesy.parseUTMUPS5}. 

''' 

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

name=name or self.name) 

 

@deprecated_method 

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

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

''' 

return self.parse(strETM) 

 

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

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

 

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

point (C{LatLon}) or C{None}. 

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

C{falsed} (C{bool}). 

 

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

L{LatLonDatum5Tuple}C{(lat, lon, datum, convergence, 

scale)} if B{C{LatLon}} is C{None}. 

 

@raise ETMError: No convergence transforming to lat- and longitude. 

 

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

incompatible. 

 

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

 

@example: 

 

>>> from pygeodesy import ellipsoidalVincenty as eV, Etm 

>>> u = Etm(31, 'N', 448251.795, 5411932.678) 

>>> ll = u.toLatLon(eV.LatLon) # 48°51′29.52″N, 002°17′40.20″E 

''' 

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

self._toLLEB(unfalse=unfalse) 

return self._latlon5(LatLon) 

 

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

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

''' 

xTM, d = self.exactTM, self.datum 

# double check that this and exactTM's ellipsoid match 

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

t = repr(d.ellipsoid) 

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

 

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

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

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

 

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

ll._convergence = g 

ll._scale = k 

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

 

def toUtm(self): # PYCHOK signature 

'''Copy this ETM to a UTM coordinate. 

 

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

''' 

return self._xcopy2(Utm) 

 

 

class ExactTransverseMercator(_NamedBase): 

'''A Python version of Karney's U{TransverseMercatorExact 

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

C++ class, a numerically exact transverse Mercator projection, here referred to as 

C{TMExact}. 

''' 

_datum = None # Datum 

_E = None # Ellipsoid 

_extendp = False # use extended domain 

# _iteration = None # ._sigmaInv2 and ._zetaInv2 

_k0 = _K0_UTM # central scale factor 

_lon0 = _0_0 # central meridian 

_mu = _0_0 # ._E.e2, 1st eccentricity squared 

_mv = _1_0 # _1_0 - ._mu 

_raiser = False # throw Error 

_sigmaC = None # _sigmaInv04 case 

_zetaC = None # _zetaInv04 case 

 

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

'''New L{ExactTransverseMercator} projection. 

 

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

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

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

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

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

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

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

 

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

B{C{lon0}} or B{C{k0}}. 

 

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

 

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

html/classGeographicLib_1_1TransverseMercatorExact.html} for more details, 

especially on B{X{extendp}}. 

 

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

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

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

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

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

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

''' 

if extendp: 

self._extendp = True 

if name: 

self.name = name 

if raiser: 

self.raiser = True 

 

self.datum = datum # invokes ._reset 

self.k0 = k0 

self.lon0 = lon0 

 

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

def datum(self): 

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

''' 

return self._datum 

 

@datum.setter # PYCHOK setter! 

def datum(self, datum): 

'''Set the datum and ellipsoid (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}). 

 

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

 

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

''' 

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

self._reset(d) 

self._datum = d 

 

@Property_RO 

def _e(self): 

'''(INTERNAL) Get and cache C{_e}. 

''' 

return self._E.e 

 

@Property_RO 

def _1_e_90(self): # PYCHOK no cover 

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

''' 

return (_1_0 - self._e) * _90_0 

 

@property_RO 

def ellipsoid(self): 

'''Get the ellipsoid (L{Ellipsoid}). 

''' 

return self._E 

 

@Property_RO 

def _e_PI_2(self): 

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

''' 

return self._e * PI_2 

 

@Property_RO 

def _e_PI_4_(self): 

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

''' 

return -self._e * PI_4 

 

@Property_RO 

def _1_e_PI_2(self): 

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

''' 

return (_1_0 - self._e) * PI_2 

 

@Property_RO 

def _1_2e_PI_2(self): 

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

''' 

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

 

@property_RO 

def equatoradius(self): 

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

''' 

return self._E.a 

 

a = equatoradius 

 

@Property_RO 

def _e_TAYTOL(self): 

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

''' 

return self._e * _TAYTOL 

 

@Property_RO 

def _Eu(self): 

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

''' 

return Elliptic(self._mu) 

 

@Property_RO 

def _Eu_cE(self): 

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

''' 

return self._Eu.cE 

 

def _Eu_2cE_(self, xi): 

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

''' 

return self._Eu_cE * _2_0 - xi 

 

@Property_RO 

def _Eu_cE_4(self): 

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

''' 

return self._Eu_cE / _4_0 

 

@Property_RO 

def _Eu_cK(self): 

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

''' 

return self._Eu.cK 

 

@Property_RO 

def _Eu_cK_cE(self): 

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

''' 

return self._Eu_cK / self._Eu_cE 

 

@Property_RO 

def _Eu_2cK_PI(self): 

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

''' 

return self._Eu_cK / PI_2 

 

@Property_RO 

def _Ev(self): 

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

''' 

return Elliptic(self._mv) 

 

@Property_RO 

def _Ev_cK(self): 

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

''' 

return self._Ev.cK 

 

@Property_RO 

def _Ev_cKE(self): 

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

''' 

return self._Ev.cKE 

 

@Property_RO 

def _Ev_3cKE_4(self): 

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

''' 

return self._Ev_cKE * 0.75 

 

@Property_RO 

def _Ev_5cKE_4(self): 

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

''' 

return self._Ev_cKE * 1.25 

 

@Property_RO 

def extendp(self): 

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

''' 

return self._extendp 

 

@property_RO 

def flattening(self): 

'''Get this C{ellipsoid}'s flattening (C{float}). 

''' 

return self._E.f 

 

f = flattening 

 

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

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

 

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

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

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

the default if not C{None}. 

@kwarg name: Optional name (C{str}). 

 

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

 

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

real &x, real &y, 

real &gamma, real &k)}. 

 

@raise ETMError: No convergence, thrown if property C{raiser} set, 

''' 

lat = _fix90(lat) 

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

if self.extendp: 

backside = _lat = _lon = False 

else: # enforce the parity 

lat, _lat = _unsigned2(lat) 

lon, _lon = _unsigned2(lon) 

backside = lon > 90 

if backside: # PYCHOK no cover 

lon = _180_0 - lon 

if lat == 0: 

_lat = True 

 

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

if lat == 90: 

u = self._Eu_cK 

v = self._iteration = self._zetaC = 0 

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

u = self._iteration = self._zetaC = 0 

v = self._Ev_cK 

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

tau, lam = _tand(lat), radians(lon) 

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

 

sncndn6 = self._sncndn6(u, v) 

y, x, _ = self._sigma3(v, *sncndn6) 

g, k = self._zetaScaled(sncndn6, ll=False) \ 

if lat != 90 else (lon, self.k0) 

if backside: 

y, g = self._Eu_2cE_(y), (_180_0 - g) 

y *= self._k0_a 

x *= self._k0_a 

if _lat: 

y, g = neg_(y, g) 

if _lon: 

x, g = neg_(x, g) 

 

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

name=name or self.name) 

 

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

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

''' 

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

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

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

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

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

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

s, c = sincos2(a) 

h = hypot(psi, dlam) 

r = cbrt(h * _3_mv_e) 

u = r * c 

v = r * s + self._Ev_cK 

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

return u, v, h 

 

@property_RO 

def iteration(self): 

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

or C{ExactTransverseMercator.reverse} iteration number 

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

''' 

return self._iteration 

 

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

def k0(self): 

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

''' 

return self._k0 # aka scale0 

 

@k0.setter # PYCHOK setter! 

def k0(self, k0): 

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

 

@raise ETMError: Invalid B{C{k0}}. 

''' 

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

if self._k0 != k0: 

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

self._k0 = k0 

 

@Property_RO 

def _k0_a(self): 

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

''' 

return self.k0 * self.equatoradius 

 

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

def lon0(self): 

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

''' 

return self._lon0 

 

@lon0.setter # PYCHOK setter! 

def lon0(self, lon0): 

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

 

@raise ETMError: Invalid B{C{lon0}}. 

''' 

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

 

@deprecated_property_RO 

def majoradius(self): # PYCHOK no cover 

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

return self.equatoradius 

 

@Property_RO 

def _1_mu_2(self): 

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

''' 

return _1_0 + self._mu * _0_5 

 

@Property_RO 

def _3_mv(self): 

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

''' 

return _3_0 / self._mv 

 

@Property_RO 

def _3_mv_e(self): 

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

''' 

return _3_0 / (self._mv * self._e) 

 

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

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

 

@return: 2-Tuple C{(u, v)}. 

 

@raise ETMError: No convergence. 

''' 

sca1, tol2 = _1_0, _TOL_10 

if psi: # _zetaInv2 

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

tol2 = tol2 / max(psi[0], _1_0)**2 

 

_zeta3 = self._zeta3 

_zetaDwd2 = self._zetaDwd2 

else: # _sigmaInv2 

_zeta3 = self._sigma3 

_zetaDwd2 = self._sigmaDwd2 

 

d2, r = tol2, self.raiser 

_U_2_ = Fsum(u).fsum2_ 

_V_2_ = Fsum(v).fsum2_ 

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

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

sncndn6 = self._sncndn6(u, v) 

du, dv = _zetaDwd2(*sncndn6) 

T, L, _ = _zeta3(v, *sncndn6) 

T = (taup - T) * sca1 

L -= lam 

u, dU = _U_2_(T * du, L * dv) 

v, dV = _V_2_(T * dv, -L * du) 

if d2 < tol2: 

r = False 

break 

d2 = hypot2(dU, dV) 

 

self._iteration = i 

if r: # PYCHOK no cover 

i = callername(up=2, underOK=True) 

t = unstr(i, taup, lam, u, v, C=C) 

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

return u, v 

 

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

def raiser(self): 

'''Get the error setting (C{bool}). 

''' 

return self._raiser 

 

@raiser.setter # PYCHOK setter! 

def raiser(self, raiser): 

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

for convergence failures. 

''' 

self._raiser = bool(raiser) 

 

def _reset(self, datum): 

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

 

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

 

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

''' 

E = datum.ellipsoid 

mu = E.e2 # .eccentricity1st2 

mv = E.e21 # _1_0 - mu 

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

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

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

 

if self._datum or self._E: 

_i = ExactTransverseMercator.iteration._uname 

_update_all(self, _i, '_sigmaC', '_zetaC') 

 

self._E = E 

self._mu = mu 

self._mv = mv 

 

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

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

 

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

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

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

the default if not C{None}. 

@kwarg name: Optional name (C{str}). 

 

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

 

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

real &lat, real &lon, 

real &gamma, real &k)} 

 

@raise ETMError: No convergence, thrown if property C{raiser} set, 

''' 

# undoes the steps in .forward. 

xi = y / self._k0_a 

eta = x / self._k0_a 

if self.extendp: 

backside = _lat = _lon = False 

else: # enforce the parity 

eta, _lon = _unsigned2(eta) 

xi, _lat = _unsigned2(xi) 

backside = xi > self._Eu_cE 

if backside: # PYCHOK no cover 

xi = self._Eu_2cE_(xi) 

 

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

if xi or eta != self._Ev_cKE: 

u, v = self._sigmaInv2(xi, eta) 

else: # PYCHOK no cover 

u = self._iteration = self._sigmaC = 0 

v = self._Ev_cK 

 

if v or u != self._Eu_cK: 

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

else: # PYCHOK no cover 

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

 

if backside: # PYCHOK no cover 

lon, g = (_180_0 - lon), (_180_0 - g) 

if _lat: 

lat, g = neg_(lat, g) 

if _lon: 

lon, g = neg_(lon, g) 

 

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

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

iteration=self._iteration, 

name=name or self.name) 

 

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

'''(INTERNAL) C{scaled}. 

 

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

from C{._zeta3}. 

 

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

 

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

real snu, real cnu, real dnu, 

real snv, real cnv, real dnv, 

real &gamma, real &k)}. 

''' 

mu, mv = self._mu, self._mv 

cnudnv = cnu * dnv 

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

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

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

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

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

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

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

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

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

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

if d2 > 0: 

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

# d2 = (mu * cnu**2 + mv * cnv**2) 

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

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

# = sqrt(mv * sec2 + mu) * sqrt(q2) 

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

k2 = fsum1_(mu, mv, mv * tau**2) 

q2 = (mv * snv**2 + cnudnv**2) / d2 

k = (sqrt(k2) * sqrt(q2) * self.k0) if \ 

(k2 > 0 and q2 > 0) else _0_0 

else: 

k = _OVERFLOW 

return g, k 

 

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

'''(INTERNAL) C{sigma}. 

 

@return: 3-Tuple C{(xi, eta, d2)}. 

 

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

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

real &xi, real &eta)}. 

 

@raise ETMError: No convergence. 

''' 

mu = self._mu * cnu 

mv = self._mv * cnv 

# Lee 55.4 writing 

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

d2 = cnu * mu + cnv * mv 

mu *= snu * dnu 

mv *= snv * dnv 

if d2 > 0: # /= chokes PyChecker 

mu = mu / d2 

mv = mv / d2 

else: 

mu, mv = map1(_overflow, mu, mv) 

xi = self._Eu.fE(snu, cnu, dnu) - mu 

v -= self._Ev.fE(snv, cnv, dnv) - mv 

return xi, v, d2 

 

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

'''(INTERNAL) C{sigmaDwd}. 

 

@return: 2-Tuple C{(du, dv)}. 

 

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

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

real &du, real &dv)}. 

''' 

snuv = snu * snv 

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

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

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

r = cnv * dnu * dnv 

i = cnu * snuv * self._mu 

du = (r**2 - i**2) / d 

dv = neg(_2_0 * i * r / d) 

return du, dv 

 

def _sigmaInv2(self, xi, eta): 

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

 

@return: 2-Tuple C{(u, v)}. 

 

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

real &u, real &v)}. 

 

@raise ETMError: No convergence. 

''' 

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

if not t: 

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

return u, v 

 

def _sigmaInv04(self, xi, eta): 

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

 

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

 

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

real &u, real &v)}. 

''' 

t = False 

d = eta - self._Ev_cKE 

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

# sigma as a simple pole at 

# w = w0 = Eu.K() + i * Ev.K() 

# and sigma is approximated by 

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

u, v = _norm2(xi - self._Eu_cE, -d) 

u += self._Eu_cK 

v += self._Ev_cK 

C = 1 

 

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

# At w = w0 = i * Ev.K(), we have 

# sigma = sigma0 = i * Ev.KE() 

# sigma' = sigma'' = 0 

# including the next term in the Taylor series gives: 

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

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

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

# [-pi/2, -pi/6] to [-pi/2, pi/2] 

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

t = h < _TAYTOL2 

C = 2 

 

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

u = v = self._Eu_cK_cE 

u *= xi 

v *= eta 

C = 3 

 

return u, v, t, C 

 

def _sncndn6(self, u, v): 

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

''' 

# snu, cnu, dnu = self._Eu.sncndn(u) 

# snv, cnv, dnv = self._Ev.sncndn(v) 

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

 

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

'''Return a C{str} representation. 

 

@kwarg joined: Separator to join the attribute strings 

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

@kwarg kwds: Optional, overriding keyword arguments. 

''' 

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

k0=self.k0, extendp=self.extendp) 

if self.name: 

d.update(name=self.name) 

t = pairs(d, **kwds) 

return joined.join(t) if joined else t 

 

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

'''(INTERNAL) C{zeta}. 

 

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

 

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

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

real &taup, real &lam)} 

''' 

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

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

t1 = t2 = _overflow(snu) 

# Lee 54.17 but write 

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

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

d1 = cnu2 + mv * (snu * snv)**2 

if d1 > EPS02: # _EPSmin 

t1 = snu * dnv / sqrt(d1) 

else: 

d1 = 0 

d2 = self._mu * cnu2 + mv * cnv**2 

if d2 > EPS02: # _EPSmin 

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

else: 

d2 = 0 

# psi = asinh(t1) - asinh(t2) 

# taup = sinh(psi) 

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

lam = (atan2(dnu * snv, cnu * cnv) - 

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

return taup, lam, d2 

 

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

'''(INTERNAL) C{zetaDwd}. 

 

@return: 2-Tuple C{(du, dv)}. 

 

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

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

real &du, real &dv)}. 

''' 

cnu2 = cnu**2 * self._mu 

cnv2 = cnv**2 

dnuv = dnu * dnv 

dnuv2 = dnuv**2 

snuv = snu * snv 

snuv2 = snuv**2 * self._mu 

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

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

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

du = cnu * dnuv * (cnv2 - snuv2) / d 

dv = cnv * snuv * (cnu2 + dnuv2) / d 

return du, neg(dv) 

 

def _zetaInv2(self, taup, lam): 

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

 

@return: 2-Tuple C{(u, v)}. 

 

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

real &u, real &v)}. 

 

@raise ETMError: No convergence. 

''' 

psi = asinh(taup) 

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

if not t: 

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

return u, v 

 

def _zetaInv04(self, psi, lam): 

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

 

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

 

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

real &u, real &v)}. 

''' 

if lam > self._1_2e_PI_2: 

d = lam - self._1_e_PI_2 

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

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

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

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

# pole, where we have, approximately 

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

# Inverting this gives: 

e = self._e # eccentricity 

s, c = sincos2((PI_2 - lam) / e) 

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

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

v = self._Ev_cK - r * atan2(c, h) 

return u, v, False, 1 

 

elif psi < self._e_PI_2: 

# At w = w0 = i * Ev.K(), we have 

# zeta = zeta0 = i * (1 - _e) * pi/2 

# zeta' = zeta'' = 0 

# including the next term in the Taylor series gives: 

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

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

# to arg(zeta - zeta0) = [-90, 180] 

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

return u, v, (h < self._e_TAYTOL), 2 

 

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

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

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

# corresponding to the north pole. 

s, c = sincos2(lam) 

h, r = sinh(psi), self._Eu_2cK_PI 

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

u = r * atan2(h, c) 

v = r * asinh(s / hypot(h, c)) 

return u, v, False, 3 

 

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

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

 

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

 

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

4-tuple C{(g, k, lat, lon)}. 

''' 

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

tau = self._E.es_tauf(t) 

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

if ll: 

g_k += atand(tau), degrees(lam) 

return g_k # or (g, k, lat, lon) 

 

 

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

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

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

 

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

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

L{Ellipsoid2} or L{a_f2Tuple}). 

@kwarg Etm: Optional class to return the UTM coordinate 

(L{Etm}) or C{None}. 

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

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

 

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

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

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

C{'N'|'S'}. 

 

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

 

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

 

@example: 

 

>>> u = parseETM5('31 N 448251 5411932') 

>>> u.toRepr() # [Z:31, H:N, E:448251, N:5411932] 

>>> u = parseETM5('31 N 448251.8 5411932.7') 

>>> u.toStr() # 31 N 448252 5411933 

''' 

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

return r 

 

 

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

name=NN, strict=True, 

zone=None, **cmoff): 

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

 

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

geodetic C{LatLon} point. 

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

@kwarg datum: Optional datum for this ETM coordinate, 

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

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

@kwarg Etm: Optional class to return the ETM coordinate 

(L{Etm}) or C{None}. 

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

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

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

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

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

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

 

@return: The ETM coordinate (B{C{Etm}}) or a 

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

band, datum, convergence, scale)} if B{C{Etm}} is 

C{None} or not B{C{falsed}}. The C{hemipole} is the 

C{'N'|'S'} hemisphere. 

 

@raise ETMError: No convergence transforming to ETM east- 

and northing. 

 

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

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

 

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

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

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

 

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

B{C{latlon}} not ellipsoidal. 

 

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

is invalid. 

''' 

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

falsed, name, zone, 

strict, ETMError, **cmoff) 

lon0 = _cmlon(z) if f else None 

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

 

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

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

 

 

if __name__ == '__main__': # MCCABE 13 

 

from sys import argv, exit as _exit 

 

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

_f = _r = _s = _t = False 

_as = argv[1:] 

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

_a = _as.pop(0) 

if len(_a) < 2: 

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

elif '-forward'.startswith(_a): 

_f, _r = True, False 

elif '-reverse'.startswith(_a): 

_f, _r = False, True 

elif '-series'.startswith(_a): 

_s, _t = True, False 

elif _a == '-t': 

_s, _t = False, True 

elif '-help'.startswith(_a): 

_exit(_usage(argv[0], '[-s | -t]', 

'[-f[orward] <lat> <lon>', 

'| -r[everse] <easting> <northing>', 

'| <lat> <lon>]', 

'| -h[elp]')) 

else: 

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

if len(_as) > 1: 

f2 = map1(float, *_as[:2]) 

else: 

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

 

if _s: 

from pygeodesy.ktm import KTransverseMercator 

tm = KTransverseMercator() 

else: 

tm = ExactTransverseMercator(extendp=_t) 

 

if _f: 

t = tm.forward(*f2) 

elif _r: 

t = tm.reverse(*f2) 

else: 

t = tm.forward(*f2) 

print(fstr(t, sep=_SPACE_)) 

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

print(fstr(t, sep=_SPACE_)) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2022 -- mrJean1 at Gmail -- All Rights Reserved. 

# 

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

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

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

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

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

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

# 

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

# in all copies or substantial portions of the Software. 

# 

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

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

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

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

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

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

# OTHER DEALINGS IN THE SOFTWARE.