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

 

# -*- coding: utf-8 -*- 

 

u'''Equidistant, Equal-Area, and other Azimuthal projections. 

 

Classes L{Equidistant}, L{EquidistantExact}, L{EquidistantGeodSolve}, 

L{EquidistantKarney}, L{Gnomonic}, L{GnomonicExact}, L{GnomonicKarney}, 

L{LambertEqualArea}, L{Orthographic} and L{Stereographic}, classes 

L{AzimuthalError}, L{Azimuthal7Tuple} and functions L{equidistant} 

and L{gnomonic}. 

 

L{EquidistantExact} and L{GnomonicExact} are based on exact geodesic 

L{GeodesicExact} and L{GeodesicLineExact}, Python versions of I{Karney}'s 

C++ original U{GeodesicExact<https://GeographicLib.SourceForge.io/html/ 

classGeographicLib_1_1GeodesicExact.html>}, respectively U{GeodesicLineExact 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1GeodesicLineExact.html>}. 

 

Using L{EquidistantGeodSolve} requires I{Karney}'s utility U{GeodSolve 

<https://GeographicLib.SourceForge.io/html/GeodSolve.1.html>} to be 

available and set in env variable C{PYGEODESY_GEODSOLVE}, see module 

L{geodsolve} for more details. 

 

L{EquidistantKarney} and L{GnomonicKarney} require I{Charles Karney}'s Python 

U{geographiclib<https://PyPI.org/project/geographiclib/>} package to be installed. 

 

Other azimuthal classes implement only (**) U{Snyder's FORMULAS FOR THE SPHERE 

<https://Pubs.USGS.gov/pp/1395/report.pdf>} and use those for any datum, 

spherical and ellipsoidal. The radius used for the latter is the ellipsoid's 

I{mean radius of curvature} at the latitude of the projection center point. For 

further justification, see the first paragraph under U{Snyder's FORMULAS FOR THE 

ELLIPSOID, page 197<https://Pubs.USGS.gov/pp/1395/report.pdf>}. 

 

Page numbers in C{Snyder} references apply to U{John P. Snyder, "Map Projections 

-- A Working Manual", 1987<https://Pubs.USGS.gov/pp/1395/report.pdf>}. 

 

See also U{here<https://WikiPedia.org/wiki/Azimuthal_equidistant_projection>}, 

especially the U{Comparison of the Azimuthal equidistant projection and some 

azimuthal projections centred on 90° N at the same scale, ordered by projection 

altitude in Earth radii<https://WikiPedia.org/wiki/Azimuthal_equidistant_projection 

#/media/File:Comparison_azimuthal_projections.svg>}. 

''' 

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

from __future__ import division 

 

from pygeodesy.basics import copysign0, isnon0, _xinstanceof 

from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB 

from pygeodesy.datums import _spherical_datum, _WGS84 

from pygeodesy.errors import _datum_datum, _ValueError, _xkwds 

from pygeodesy.fmath import euclid, Fsum, hypot 

from pygeodesy.interns import EPS, EPS0, EPS1, _EPStol, NAN, NN, \ 

_azimuth_, _datum_, _lat_, _lon_, \ 

_no_, _scale_, _SPACE_, _x_, _y_, \ 

_0_0, _0_1, _0_5, _1_0, _2_0, _360_0 

from pygeodesy.karney import _norm180 

from pygeodesy.latlonBase import LatLonBase as _LLB 

from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _FOR_DOCS 

from pygeodesy.named import _NamedBase, _NamedTuple, notOverloaded, _Pass 

from pygeodesy.namedTuples import LatLon2Tuple, LatLon4Tuple 

from pygeodesy.props import deprecated_Property_RO, Property_RO, \ 

property_doc_, property_RO 

from pygeodesy.streprs import Fmt, _fstrLL0 

from pygeodesy.units import Bearing, Easting, Lat_, Lon_, \ 

Northing, Scalar, Scalar_ 

from pygeodesy.utily import asin1, atan2b, atan2d, sincos2, sincos2d 

 

from math import acos, atan, atan2, degrees, sin, sqrt 

 

__all__ = _ALL_LAZY.azimuthal 

__version__ = '21.07.03' 

 

_EPS_K = _EPStol * _0_1 # Karney's eps_ or _EPSmin * _0_1? 

_over_horizon_ = 'over horizon' 

_TRIPS = 21 # numit, 4 sufficient 

 

 

class _AzimuthalBase(_NamedBase): 

'''(INTERNAL) Base class for azimuthal projections. 

 

@see: I{Karney}'s C++ class U{AzimuthalEquidistant<https://GeographicLib.SourceForge.io/ 

html/classGeographicLib_1_1AzimuthalEquidistant.html>} and U{Gnomonic 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>} or the 

Python versions L{EquidistantKarney}, respectively L{GnomonicKarney}. 

''' 

_datum = _WGS84 # L{Datum} 

_iteration = None # iteration number for L{GnomonicKarney} 

_latlon0 = LatLon2Tuple(_0_0, _0_0) # lat0, lon0 (L{LatLon2Tuple}) 

_sc0 = (_0_0, _1_0) # 2-Tuple C{sincos2d(lat0)} 

 

def __init__(self, lat0, lon0, datum=None, name=NN): 

'''New azimuthal projection. 

 

@arg lat0: Latitude of the center point (C{degrees90}). 

@arg lon0: Longitude of the center point (C{degrees180}). 

@kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth 

radius (C{meter}). 

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

 

@raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or (spherical) B{C{datum}}. 

 

@raise TypeError: Invalid B{C{datum}}. 

''' 

if datum not in (None, self._datum): 

self._datum = _spherical_datum(datum, name=name) 

if name: 

self.name = name 

 

if lat0 or lon0: # often both 0 

self.reset(lat0, lon0) 

 

@Property_RO 

def datum(self): 

'''Get the datum (L{Datum}). 

''' 

return self._datum 

 

@Property_RO 

def equatoradius(self): 

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

''' 

return self.datum.ellipsoid.a 

 

@property_RO 

def iteration(self): 

'''Get the iteration number (C{int}) or C{None} if not available/applicable. 

''' 

return self._iteration 

 

@Property_RO 

def flattening(self): 

'''Get the geodesic's flattening (C{float}). 

''' 

return self.datum.ellipsoid.f 

 

def forward(self, lat, lon, name=NN): 

'''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. 

''' 

notOverloaded(self, lat, lon, name=name) 

 

def _forward(self, lat, lon, name, _k_t_2): 

'''(INTERNAL) Azimuthal (spherical) forward C{lat, lon} to C{x, y}. 

''' 

lat, lon = Lat_(lat), Lon_(lon) 

sa, ca, sb, cb = sincos2d(lat, lon - self.lon0) 

s0, c0 = self._sc0 

 

k, t = _k_t_2(s0 * sa + c0 * ca * cb) 

if t: 

r = k * self.radius 

x = Easting(x=r * ca * sb) 

y = Northing(y=r * (c0 * sa - s0 * ca * cb)) 

z = atan2b(x, y) # (x, y) for azimuth from true North 

else: # 0 or 180 

x = y = z = _0_0 

 

t = Azimuthal7Tuple(x, y, lat, lon, z, k, self.datum, 

name=name or self.name) 

return t 

 

@Property_RO 

def lat0(self): 

'''Get the center latitude (C{degrees90}). 

''' 

return self._latlon0.lat 

 

@property 

def latlon0(self): 

'''Get the center lat- and longitude (L{LatLon2Tuple}C{(lat, lon)}) in (C{degrees90}, C{degrees180}). 

''' 

return self._latlon0 

 

@latlon0.setter # PYCHOK setter! 

def latlon0(self, latlon0): 

'''Set the center lat- and longitude (C{LatLon}, L{LatLon2Tuple} or L{LatLon4Tuple}). 

 

@raise AzimuthalError: Invalid B{C{lat0}} or B{C{lon0}} or ellipsoidal mismatch 

of B{C{latlon0}} and this projection. 

''' 

B = _LLEB if self.datum.isEllipsoidal else _LLB 

_xinstanceof(B, LatLon2Tuple, LatLon4Tuple, latlon0=latlon0) 

if hasattr(latlon0, _datum_): 

_datum_datum(self.datum, latlon0.datum, Error=AzimuthalError) 

self.reset(latlon0.lat, latlon0.lon) 

 

@Property_RO 

def lon0(self): 

'''Get the center longitude (C{degrees180}). 

''' 

return self._latlon0.lon 

 

@deprecated_Property_RO 

def majoradius(self): # PYCHOK no cover 

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

return self.equatoradius 

 

@Property_RO 

def radius(self): 

'''Get this projection's mean radius of curvature (C{meter}). 

''' 

return self.datum.ellipsoid.rocMean(self.lat0) 

 

def reset(self, lat0, lon0): 

'''Set or reset the center point of this azimuthal projection. 

 

@arg lat0: Center point latitude (C{degrees90}). 

@arg lon0: Center point longitude (C{degrees180}). 

 

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

''' 

self._update(True) # force reset 

self._latlon0 = LatLon2Tuple(Lat_(lat0=lat0, Error=AzimuthalError), 

Lon_(lon0=lon0, Error=AzimuthalError)) 

self._sc0 = tuple(sincos2d(self.lat0)) 

 

def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): 

'''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. 

''' 

notOverloaded(self, x, y, name=name, LatLon=LatLon, **LatLon_kwds) 

 

def _reverse(self, x, y, name, LatLon, LatLon_kwds, _c_t, lea): 

'''(INTERNAL) Azimuthal (spherical) reverse C{x, y} to C{lat, lon}. 

''' 

x = Easting(x=x) 

y = Northing(y=y) 

 

r = hypot(x, y) 

c, t = _c_t(r / self.radius) 

if t: 

s0, c0 = self._sc0 

sc, cc = sincos2(c) 

k = c / sc 

z = atan2b(x, y) # (x, y) for azimuth from true North 

 

t = s0 * cc 

if r > EPS0: 

t += c0 * sc * (y / r) 

lat = degrees(asin1(t)) 

if lea or abs(c0) > EPS: 

lon = atan2d(x * sc, c0 * cc * r - s0 * sc * y) 

else: 

lon = atan2d(x, (y if s0 < 0 else -y)) 

lon = _norm180(self.lon0 + lon) 

else: 

k, z = _1_0, _0_0 

lat, lon = self.latlon0 

 

r = Azimuthal7Tuple(x, y, lat, lon, z, k, self.datum, 

name=name or self.name) if LatLon is None else \ 

self._toLatLon(lat, lon, LatLon, LatLon_kwds, name) 

return r 

 

def _reverse2(self, x, y): 

'''(INTERNAL) See iterating functions .ellipsoidalBaseDI._intersect3, 

.ellipsoidalBaseDI._intersects2 and .ellipsoidalBaseDI._nearestOne. 

''' 

t = self.reverse(x, y) # LatLon=None 

d = euclid(t.lat - self.lat0, t.lon - self.lon0) 

return t, d 

 

def _toLatLon(self, lat, lon, LatLon, LatLon_kwds, name): 

'''(INTERNAL) Check B{C{LatLon}} and return an instance. 

''' 

kwds = _xkwds(LatLon_kwds, datum=self.datum) 

r = self._xnamed(LatLon(lat, lon, **kwds), name=name) # handle .classof 

B = _LLEB if self.datum.isEllipsoidal else _LLB 

_xinstanceof(B, LatLon=r) 

return r 

 

def toRepr(self, prec=6, **unused): # PYCHOK expected 

'''Return a string representation of this projection. 

 

@kwarg prec: Optional number of decimals, unstripped (C{int}). 

 

@return: This projection as C{"<classname>(lat0, lon0, ...)"} 

(C{str}). 

''' 

return _fstrLL0(self, prec, True) 

 

def toStr(self, prec=6, sep=_SPACE_, **unused): # PYCHOK expected 

'''Return a string representation of this projection. 

 

@kwarg prec: Optional number of decimal, unstripped (C{int}). 

@kwarg sep: Optional separator to join (C{str}). 

 

@return: This projection as C{"lat0 lon0"} (C{str}). 

''' 

t = _fstrLL0(self, prec, False) 

return t if sep is None else sep.join(t) 

 

 

class AzimuthalError(_ValueError): 

'''An azimuthal L{Equidistant}, L{EquidistantKarney}, L{Gnomonic}, 

L{LambertEqualArea}, L{Orthographic}, L{Stereographic} or 

L{Azimuthal7Tuple} issue. 

''' 

pass 

 

 

class Azimuthal7Tuple(_NamedTuple): 

'''7-Tuple C{(x, y, lat, lon, azimuth, scale, datum)}, in C{meter}, C{meter}, 

C{degrees90}, C{degrees180}, compass C{degrees}, C{scalar} and C{Datum} 

where C{(x, y)} is the easting and northing of a projected point, C{(lat, 

lon)} the geodetic location, C{azimuth} the azimuth, clockwise from true 

North and C{scale} is the projection scale, either C{1 / reciprocal} or 

C{1} or C{-1} in the L{Equidistant} case. 

''' 

_Names_ = (_x_, _y_, _lat_, _lon_, _azimuth_, _scale_, _datum_) 

_Units_ = ( Easting, Northing, Lat_, Lon_, Bearing, Scalar, _Pass) 

 

 

class Equidistant(_AzimuthalBase): 

'''Azimuthal equidistant projection for the sphere**, see U{Snyder, pp 195-197 

<https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram 

<https://MathWorld.Wolfram.com/AzimuthalEquidistantProjection.html>}. 

 

@note: Results from this L{Equidistant} and an L{EquidistantExact}, 

L{EquidistantGeodSolve} or L{EquidistantKarney} projection 

C{may differ} by 10% or more. For an example, see method 

C{testDiscrepancies} in module C{testAzimuthal.py}. 

''' 

if _FOR_DOCS: 

__init__ = _AzimuthalBase.__init__ 

 

def forward(self, lat, lon, name=NN): 

'''Convert a geodetic location to azimuthal equidistant east- and northing. 

 

@arg lat: Latitude of the location (C{degrees90}). 

@arg lon: Longitude of the location (C{degrees180}). 

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

 

@return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} 

with easting C{x} and northing C{y} of point in C{meter} and C{lat} 

and C{lon} in C{degrees} and C{azimuth} clockwise from true North. 

The C{scale} of the projection is C{1} in I{radial} direction and 

is C{1 / reciprocal} in the direction perpendicular to this. 

 

@raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. 

 

@note: The C{scale} will be C{-1} if B{C{(lat, lon)}} is antipodal to 

the projection center C{(lat0, lon0)}. 

''' 

def _k_t(c): 

t = abs(c) < EPS1 

if t: 

c = acos(c) 

k = c / sin(c) 

else: 

k = copysign0(_1_0, c) 

return k, t 

 

return self._forward(lat, lon, name, _k_t) 

 

def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): 

'''Convert an azimuthal equidistant location to geodetic lat- and longitude. 

 

@arg x: Easting of the location (C{meter}). 

@arg y: Northing of the location (C{meter}). 

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

@kwarg LatLon: Class to use (C{LatLon}) or C{None}. 

@kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword 

arguments, ignored if C{B{LatLon}=None}. 

 

@return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an 

L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. 

 

@note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} 

in the range C{[-180..180] degrees}. The C{scale} of the 

projection is C{1} in I{radial} direction, C{azimuth} clockwise 

from true North and is C{1 / reciprocal} in the direction 

perpendicular to this. 

''' 

def _c_t(c): 

return c, (c > EPS) 

 

return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) 

 

 

def equidistant(lat0, lon0, datum=_WGS84, exact=False, geodsolve=False, name=NN): 

'''Return an L{EquidistantExact}, L{EquidistantGeodSolve} or (if I{Karney}'s 

U{geographiclib<https://PyPI.org/project/geographiclib>} package is 

installed) an L{EquidistantKarney}, otherwise an L{Equidistant} instance. 

 

@arg lat0: Latitude of center point (C{degrees90}). 

@arg lon0: Longitude of center point (C{degrees180}). 

@kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth 

radius (C{meter}). 

@kwarg exact: Return an L{EquidistantExact} instance. 

@kwarg geodsolve: Return an L{EquidistantGeodSolve} instance. 

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

 

@return: An L{EquidistantExact}, L{EquidistantGeodSolve}, 

L{EquidistantKarney} or L{Equidistant} instance. 

 

@raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or (spherical) B{C{datum}}. 

 

@raise TypeError: Invalid B{C{datum}}. 

''' 

if exact: 

return EquidistantExact(lat0, lon0, datum=datum, name=name) 

elif geodsolve: 

return EquidistantGeodSolve(lat0, lon0, datum=datum, name=name) # PYCHOK types 

try: 

return EquidistantKarney(lat0, lon0, datum=datum, name=name) # PYCHOK types 

except ImportError: 

return Equidistant(lat0, lon0, datum=datum, name=name) # PYCHOK types 

 

 

class _AzimuthalGeodesic(_AzimuthalBase): 

'''(INTERNAL) Base class for azimuthal projections using U{Karney Geodesic 

<https://GeographicLib.SourceForge.io/html/python/code.html>} or 

exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact}. 

''' 

_mask = 0 

 

@Property_RO 

def geodesic(self): 

'''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. 

''' 

notOverloaded(self) 

 

def _7Tuple(self, x, y, r, M=None, name=NN): 

'''(INTERNAL) Return an C{Azimuthal7Tuple}. 

''' 

s = M if M is not None else ( # reciprocal, azimuthal scale 

(r.m12 / r.s12) if r.a12 > _EPS_K else _1_0) 

z = (r.azi2 + _360_0) % _360_0 # -180 <= r.azi2 < 180 

return Azimuthal7Tuple(x, y, r.lat2, r.lon2, z, s, self.datum, 

name=name or self.name) 

 

 

class _EquidistantBase(_AzimuthalGeodesic): 

'''(INTERNAL) Base for classes L{EquidistantExact}, L{EquidistantGeodSolve} 

and L{EquidistantKarney}. 

''' 

def __init__(self, lat0, lon0, datum=_WGS84, name=NN): 

'''New azimuthal L{EquidistantExact}, L{EquidistantGeodSolve} or 

L{EquidistantKarney} projection. 

''' 

_AzimuthalGeodesic.__init__(self, lat0, lon0, datum=datum, name=name) 

 

g = self.geodesic 

# g.STANDARD = g.AZIMUTH | g.DISTANCE | g.LATITUDE | g.LONGITUDE 

self._mask = g.REDUCEDLENGTH | g.STANDARD # | g.LONG_UNROLL 

 

def forward(self, lat, lon, name=NN): 

'''Convert an (ellipsoidal) geodetic location to azimuthal equidistant east- and northing. 

 

@arg lat: Latitude of the location (C{degrees90}). 

@arg lon: Longitude of the location (C{degrees180}). 

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

 

@return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} 

with easting C{x} and northing C{y} of point in C{meter} and C{lat} 

and C{lon} in C{degrees} and C{azimuth} clockwise from true North. 

The C{scale} of the projection is C{1} in I{radial} direction and 

is C{1 / reciprocal} in the direction perpendicular to this. 

 

@raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. 

 

@note: A call to C{.forward} followed by a call to C{.reverse} will return 

the original C{lat, lon} to within roundoff. 

''' 

r = self.geodesic.Inverse(self.lat0, self.lon0, 

Lat_(lat), Lon_(lon), self._mask) 

x, y = sincos2d(r.azi1) 

return self._7Tuple(x * r.s12, y * r.s12, r, name=name) 

 

def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): 

'''Convert an azimuthal equidistant location to (ellipsoidal) geodetic lat- and longitude. 

 

@arg x: Easting of the location (C{meter}). 

@arg y: Northing of the location (C{meter}). 

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

@kwarg LatLon: Class to use (C{LatLon}) or C{None}. 

@kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword 

arguments, ignored if C{B{LatLon}=None}. 

 

@return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an 

L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. 

 

@note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} 

in the range C{[-180..180] degrees}. The scale of the projection 

is C{1} in I{radial} direction, C{azimuth} clockwise from true 

North and is C{1 / reciprocal} in the direction perpendicular 

to this. 

''' 

x = Easting(x=x) 

y = Northing(y=y) 

 

z = atan2d(x, y) # (x, y) for azimuth from true North 

s = hypot( x, y) 

 

r = self.geodesic.Direct(self.lat0, self.lon0, z, s, self._mask) 

return self._7Tuple(x, y, r, name=name) if LatLon is None else \ 

self._toLatLon(r.lat2, r.lon2, LatLon, LatLon_kwds, name) 

 

 

class EquidistantExact(_EquidistantBase): 

'''Azimuthal equidistant projection, a Python version of I{Karney}'s C++ class U{AzimuthalEquidistant 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1AzimuthalEquidistant.html>}, 

based on exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact}. 

 

An azimuthal equidistant projection is centered at an arbitrary position on the ellipsoid. 

For a point in projected space C{(x, y)}, the geodesic distance from the center position 

is C{hypot(x, y)} and the C{azimuth} of the geodesic from the center point is C{atan2(x, y)}, 

clockwise from true North. 

 

The C{.forward} and C{.reverse} methods also return the C{azimuth} of the geodesic at C{(x, 

y)} and the C{scale} in the azimuthal direction which, together with the basic properties 

of the projection, serve to specify completely the local affine transformation between 

geographic and projected coordinates. 

''' 

def __init__(self, lat0, lon0, datum=_WGS84, name=NN): 

'''New azimuthal L{EquidistantExact} projection. 

 

@arg lat0: Latitude of center point (C{degrees90}). 

@arg lon0: Longitude of center point (C{degrees180}). 

@kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth 

radius (C{meter}). 

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

 

@raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or B{C{datum}}. 

''' 

_EquidistantBase.__init__(self, lat0, lon0, datum=datum, name=name) 

 

if _FOR_DOCS: 

forward = _EquidistantBase.forward 

reverse = _EquidistantBase.reverse 

 

@Property_RO 

def geodesic(self): 

'''Get this projection's exact geodesic (L{GeodesicExact}). 

''' 

return self.datum.ellipsoid.geodesicx 

 

 

class EquidistantGeodSolve(_EquidistantBase): 

'''Azimuthal equidistant projection, a Python version of I{Karney}'s C++ class U{AzimuthalEquidistant 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1AzimuthalEquidistant.html>}, 

based on (exact) geodesic I{wrappers} L{GeodesicSolve} and L{GeodesicLineSolve} and intended 

I{for testing purposes only}. 

 

@see: L{EquidistantExact} and module L{geodsolve}. 

''' 

def __init__(self, lat0, lon0, datum=_WGS84, name=NN): 

'''New azimuthal L{EquidistantGeodSolve} projection. 

 

@arg lat0: Latitude of center point (C{degrees90}). 

@arg lon0: Longitude of center point (C{degrees180}). 

@kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth 

radius (C{meter}). 

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

 

@raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or B{C{datum}}. 

''' 

_EquidistantBase.__init__(self, lat0, lon0, datum=datum, name=name) 

 

if _FOR_DOCS: 

forward = _EquidistantBase.forward 

reverse = _EquidistantBase.reverse 

 

@Property_RO 

def geodesic(self): 

'''Get this projection's (exact) geodesic (L{GeodesicSolve}). 

''' 

return self.datum.ellipsoid.geodsolve 

 

 

class EquidistantKarney(_EquidistantBase): 

'''Azimuthal equidistant projection, a Python version of I{Karney}'s C++ class U{AzimuthalEquidistant 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1AzimuthalEquidistant.html>}, 

requiring package U{geographiclib<https://PyPI.org/project/geographiclib>} to be installed. 

 

@see: L{EquidistantExact}. 

''' 

def __init__(self, lat0, lon0, datum=_WGS84, name=NN): 

'''New azimuthal L{EquidistantKarney} projection. 

 

@arg lat0: Latitude of center point (C{degrees90}). 

@arg lon0: Longitude of center point (C{degrees180}). 

@kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth 

radius (C{meter}). 

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

 

@raise ImportError: Package U{geographiclib<https://PyPI.org/project/geographiclib>} 

not installed or not found. 

 

@raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or B{C{datum}}. 

''' 

_EquidistantBase.__init__(self, lat0, lon0, datum=datum, name=name) 

 

if _FOR_DOCS: 

forward = _EquidistantBase.forward 

reverse = _EquidistantBase.reverse 

 

@Property_RO 

def geodesic(self): 

'''Get this projection's I{wrapped} U{Karney Geodesic 

<https://GeographicLib.SourceForge.io/html/python/code.html>}, 

provided package U{geographiclib 

<https://PyPI.org/project/geographiclib>} is installed. 

''' 

return self.datum.ellipsoid.geodesic 

 

 

_Equidistants = (Equidistant, EquidistantExact, EquidistantGeodSolve, 

EquidistantKarney) # PYCHOK in .ellipsoidalBaseDI 

 

 

class Gnomonic(_AzimuthalBase): 

'''Azimuthal gnomonic projection for the sphere**, see U{Snyder, pp 164-168 

<https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram 

<https://MathWorld.Wolfram.com/GnomonicProjection.html>}. 

''' 

if _FOR_DOCS: 

__init__ = _AzimuthalBase.__init__ 

 

def forward(self, lat, lon, name=NN): 

'''Convert a geodetic location to azimuthal equidistant east- and northing. 

 

@arg lat: Latitude of the location (C{degrees90}). 

@arg lon: Longitude of the location (C{degrees180}). 

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

 

@return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} 

with easting C{x} and northing C{y} of point in C{meter} and C{lat} 

and C{lon} in C{degrees} and C{azimuth} clockwise from true North. 

The C{scale} of the projection is C{1} in I{radial} direction and 

is C{1 / reciprocal} in the direction perpendicular to this. 

 

@raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. 

''' 

def _k_t(c): 

t = c > EPS 

k = (_1_0 / c) if t else _1_0 

return k, t 

 

return self._forward(lat, lon, name, _k_t) 

 

def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): 

'''Convert an azimuthal equidistant location to geodetic lat- and longitude. 

 

@arg x: Easting of the location (C{meter}). 

@arg y: Northing of the location (C{meter}). 

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

@kwarg LatLon: Class to use (C{LatLon}) or C{None}. 

@kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword 

arguments, ignored if C{B{LatLon}=None}. 

 

@return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an 

L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. 

 

@note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} 

in the range C{[-180..180] degrees}. The C{scale} of the 

projection is C{1} in I{radial} direction, C{azimuth} clockwise 

from true North and C{1 / reciprocal} in the direction 

perpendicular to this. 

''' 

def _c_t(c): 

return atan(c), (c > EPS) 

 

return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) 

 

 

def gnomonic(lat0, lon0, datum=_WGS84, exact=False, geodsolve=False, name=NN): 

'''Return a L{GnomonicExact} or (if I{Karney}'s U{geographiclib 

<https://PyPI.org/project/geographiclib>} package is installed) 

a L{GnomonicKarney}, otherwise a L{Gnomonic} instance. 

 

@arg lat0: Latitude of center point (C{degrees90}). 

@arg lon0: Longitude of center point (C{degrees180}). 

@kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth 

radius (C{meter}). 

@kwarg exact: Return a L{GnomonicExact} instance. 

@kwarg geodsolve: Return an L{GnomonicGeodSolve} instance. 

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

 

@return: A L{GnomonicExact}, L{GnomonicGeodSolve}, 

L{GnomonicKarney} or L{Gnomonic} instance. 

 

@raise AzimuthalError: Invalid B{C{lat0}}, B{C{lon0}} or (spherical) B{C{datum}}. 

 

@raise TypeError: Invalid B{C{datum}}. 

''' 

if exact: 

return GnomonicExact(lat0, lon0, datum=datum, name=name) 

elif geodsolve: 

return GnomonicGeodSolve(lat0, lon0, datum=datum, name=name) # PYCHOK types 

try: 

return GnomonicKarney(lat0, lon0, datum=datum, name=name) # PYCHOK types 

except ImportError: 

return Gnomonic(lat0, lon0, datum=datum, name=name) # PYCHOK types 

 

 

class _GnomonicBase(_AzimuthalGeodesic): 

'''(INTERNAL) Base for classes L{GnomonicExact} and L{GnomonicKarney}. 

''' 

def __init__(self, lat0, lon0, datum=_WGS84, name=NN): 

'''New azimuthal L{GnomonicExact} or L{GnomonicKarney} projection. 

''' 

_AzimuthalGeodesic.__init__(self, lat0, lon0, datum=datum, name=name) 

 

g = self.geodesic 

self._mask = g.ALL # | g.LONG_UNROLL 

 

def forward(self, lat, lon, name=NN, raiser=True): # PYCHOK signature 

'''Convert an (ellipsoidal) geodetic location to azimuthal gnomonic east- and northing. 

 

@arg lat: Latitude of the location (C{degrees90}). 

@arg lon: Longitude of the location (C{degrees180}). 

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

@kwarg raiser: Do or don't throw an error (C{bool}) if 

the location lies over the horizon. 

 

@return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} 

with easting C{x} and northing C{y} of point in C{meter} and C{lat} 

and C{lon} in C{degrees} and C{azimuth} clockwise from true North. 

The C{scale} of the projection is C{1 / reciprocal**2} in I{radial} 

direction and C{1 / reciprocal} in the direction perpendicular to 

this. Both C{x} and C{y} will be C{NAN} if the (geodetic) location 

lies over the horizon and C{B{raiser}=False}. 

 

@raise AzimuthalError: Invalid B{C{lat}}, B{C{lon}} or the location lies 

over the horizon and C{B{raiser}=True}. 

''' 

self._iteration = 0 

 

r = self.geodesic.Inverse(self.lat0, self.lon0, 

Lat_(lat), Lon_(lon), self._mask) 

M = r.M21 

if M > EPS0: 

q = r.m12 / M # .M12 

x, y = sincos2d(r.azi1) 

x *= q 

y *= q 

elif raiser: 

raise AzimuthalError(lat=lat, lon=lon, txt=_over_horizon_) 

else: 

x = y = NAN 

 

t = self._7Tuple(x, y, r, M=M, name=name) 

t._iteraton = self._iteration # = 0 

return t 

 

def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): 

'''Convert an azimuthal gnomonic location to (ellipsoidal) geodetic lat- and longitude. 

 

@arg x: Easting of the location (C{meter}). 

@arg y: Northing of the location (C{meter}). 

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

@kwarg LatLon: Class to use (C{LatLon}) or C{None}. 

@kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword 

arguments, ignored if C{B{LatLon}=None}. 

 

@return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an 

L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. 

 

@raise AzimuthalError: No convergence. 

 

@note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} 

in the range C{[-180..180] degrees}. The C{azimuth} is clockwise 

from true North. The scale is C{1 / reciprocal**2} in C{radial} 

direction and C{1 / reciprocal} in the direction perpendicular 

to this. 

''' 

x = Easting(x=x) 

y = Northing(y=y) 

 

z = atan2d(x, y) # (x, y) for azimuth from true North 

q = hypot( x, y) 

 

d = e = self.equatoradius 

s = e * atan(q / e) 

if q > e: 

def _d(r, q): 

return (r.M12 - q * r.m12) * r.m12 # negated 

q = _1_0 / q 

else: # little == True 

def _d(r, q): # PYCHOK _d 

return (q * r.M12 - r.m12) * r.M12 # negated 

e *= _EPS_K 

 

m = self._mask 

g = self.geodesic._Line(self.lat0, self.lon0, z, m) 

P = g.Position 

S = Fsum(s) 

for self._iteration in range(1, _TRIPS): 

r = P(s, m) 

if abs(d) < e: 

break 

s, d = S.fsum2_(_d(r, q)) 

else: 

raise AzimuthalError(x=x, y=y, txt=_no_(Fmt.convergence(e))) 

 

t = self._7Tuple(x, y, r, M=r.M12, name=name) if LatLon is None else \ 

self._toLatLon(r.lat2, r.lon2, LatLon, LatLon_kwds, name) 

t._iteration = self._iteration 

return t 

 

 

class GnomonicExact(_GnomonicBase): 

'''Azimuthal gnomonic projection, a Python version of I{Karney}'s C++ class U{Gnomonic 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>}, 

based on exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact}. 

 

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

classGeographicLib_1_1Gnomonic.html>}, especially the B{Warning}. 

''' 

def __init__(self, lat0, lon0, datum=_WGS84, name=NN): 

'''New azimuthal L{GnomonicExact} projection. 

 

@arg lat0: Latitude of center point (C{degrees90}). 

@arg lon0: Longitude of center point (C{degrees180}). 

@kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth 

radius (C{meter}). 

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

 

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

''' 

_GnomonicBase.__init__(self, lat0, lon0, datum=datum, name=name) 

 

if _FOR_DOCS: 

forward = _GnomonicBase.forward 

reverse = _GnomonicBase.reverse 

 

@Property_RO 

def geodesic(self): 

'''Get this projection's exact geodesic (L{GeodesicExact}). 

''' 

return self.datum.ellipsoid.geodesicx 

 

 

class GnomonicGeodSolve(_GnomonicBase): 

'''Azimuthal gnomonic projection, a Python version of I{Karney}'s C++ class U{Gnomonic 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>}, 

based on (exact) geodesic I{wrappers} L{GeodesicSolve} and L{GeodesicLineSolve} and 

intended I{for testing purposes only}. 

 

@see: L{GnomonicExact} and module L{geodsolve}. 

''' 

def __init__(self, lat0, lon0, datum=_WGS84, name=NN): 

'''New azimuthal L{GnomonicGeodSolve} projection. 

 

@arg lat0: Latitude of center point (C{degrees90}). 

@arg lon0: Longitude of center point (C{degrees180}). 

@kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth 

radius (C{meter}). 

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

 

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

''' 

_GnomonicBase.__init__(self, lat0, lon0, datum=datum, name=name) 

 

if _FOR_DOCS: 

forward = _GnomonicBase.forward 

reverse = _GnomonicBase.reverse 

 

@Property_RO 

def geodesic(self): 

'''Get this projection's (exact) geodesic (L{GeodesicSolve}). 

''' 

return self.datum.ellipsoid.geodsolve 

 

 

class GnomonicKarney(_GnomonicBase): 

'''Azimuthal gnomonic projection, a Python version of I{Karney}'s C++ class U{Gnomonic 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>}, 

requiring package U{geographiclib<https://PyPI.org/project/geographiclib>} to be installed. 

 

@see: L{GnomonicExact}. 

''' 

def __init__(self, lat0, lon0, datum=_WGS84, name=NN): 

'''New azimuthal L{GnomonicKarney} projection. 

 

@arg lat0: Latitude of center point (C{degrees90}). 

@arg lon0: Longitude of center point (C{degrees180}). 

@kwarg datum: Optional datum or ellipsoid (L{Datum}, L{Ellipsoid}, 

L{Ellipsoid2} or L{a_f2Tuple}) or I{scalar} earth 

radius (C{meter}). 

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

 

@raise ImportError: Package U{geographiclib<https://PyPI.org/project/geographiclib>} 

not installed or not found. 

 

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

''' 

_GnomonicBase.__init__(self, lat0, lon0, datum=datum, name=name) 

 

if _FOR_DOCS: 

forward = _GnomonicBase.forward 

reverse = _GnomonicBase.reverse 

 

@Property_RO 

def geodesic(self): 

'''Get this projection's I{wrapped} U{Karney Geodesic 

<https://GeographicLib.SourceForge.io/html/python/code.html>}, 

provided package U{geographiclib 

<https://PyPI.org/project/geographiclib>} is installed. 

''' 

return self.datum.ellipsoid.geodesic 

 

 

class LambertEqualArea(_AzimuthalBase): 

'''Lambert-equal-area projection for the sphere** (aka U{Lambert zenithal equal-area 

projection<https://WikiPedia.org/wiki/Lambert_azimuthal_equal-area_projection>}, see 

U{Snyder, pp 185-187<https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram 

<https://MathWorld.Wolfram.com/LambertAzimuthalEqual-AreaProjection.html>}. 

''' 

if _FOR_DOCS: 

__init__ = _AzimuthalBase.__init__ 

 

def forward(self, lat, lon, name=NN): 

'''Convert a geodetic location to azimuthal Lambert-equal-area east- and northing. 

 

@arg lat: Latitude of the location (C{degrees90}). 

@arg lon: Longitude of the location (C{degrees180}). 

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

 

@return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} 

with easting C{x} and northing C{y} of point in C{meter} and C{lat} 

and C{lon} in C{degrees} and C{azimuth} clockwise from true North. 

The C{scale} of the projection is C{1} in I{radial} direction and 

is C{1 / reciprocal} in the direction perpendicular to this. 

 

@raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. 

''' 

def _k_t(c): 

c = c + _1_0 

t = c > EPS0 

k = sqrt(_2_0 / c) if t else _1_0 

return k, t 

 

return self._forward(lat, lon, name, _k_t) 

 

def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): 

'''Convert an azimuthal Lambert-equal-area location to geodetic lat- and longitude. 

 

@arg x: Easting of the location (C{meter}). 

@arg y: Northing of the location (C{meter}). 

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

@kwarg LatLon: Class to use (C{LatLon}) or C{None}. 

@kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword 

arguments, ignored if C{B{LatLon}=None}. 

 

@return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an 

L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. 

 

@note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} 

in the range C{[-180..180] degrees}. The C{scale} of the 

projection is C{1} in I{radial} direction, C{azimuth} clockwise 

from true North and is C{1 / reciprocal} in the direction 

perpendicular to this. 

''' 

def _c_t(c): 

c = c * _0_5 

t = c > EPS 

if t: 

c = _2_0 * asin1(c) 

return c, t 

 

return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, True) 

 

 

class Orthographic(_AzimuthalBase): 

'''Orthographic projection for the sphere**, see U{Snyder, pp 148-153 

<https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram 

<https://MathWorld.Wolfram.com/OrthographicProjection.html>}. 

''' 

if _FOR_DOCS: 

__init__ = _AzimuthalBase.__init__ 

 

def forward(self, lat, lon, name=NN): 

'''Convert a geodetic location to azimuthal orthographic east- and northing. 

 

@arg lat: Latitude of the location (C{degrees90}). 

@arg lon: Longitude of the location (C{degrees180}). 

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

 

@return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} 

with easting C{x} and northing C{y} of point in C{meter} and C{lat} 

and C{lon} in C{degrees} and C{azimuth} clockwise from true North. 

The C{scale} of the projection is C{1} in I{radial} direction and 

is C{1 / reciprocal} in the direction perpendicular to this. 

 

@raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. 

''' 

def _k_t(c): 

return _1_0, (c >= 0) 

 

return self._forward(lat, lon, name, _k_t) 

 

def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): 

'''Convert an azimuthal orthographic location to geodetic lat- and longitude. 

 

@arg x: Easting of the location (C{meter}). 

@arg y: Northing of the location (C{meter}). 

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

@kwarg LatLon: Class to use (C{LatLon}) or C{None}. 

@kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword 

arguments, ignored if C{B{LatLon}=None}. 

 

@return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an 

L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. 

 

@note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} 

in the range C{[-180..180] degrees}. The C{scale} of the 

projection is C{1} in I{radial} direction, C{azimuth} clockwise 

from true North and is C{1 / reciprocal} in the direction 

perpendicular to this. 

''' 

def _c_t(c): 

t = c > EPS 

if t: 

c = asin1(c) 

return c, t 

 

return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) 

 

 

class Stereographic(_AzimuthalBase): 

'''Stereographic projection for the sphere**, see U{Snyder, pp 157-160 

<https://Pubs.USGS.gov/pp/1395/report.pdf>} and U{MathWorld-Wolfram 

<https://MathWorld.Wolfram.com/StereographicProjection.html>}. 

''' 

_k0 = _1_0 # central scale factor (C{scalar}) 

 

if _FOR_DOCS: 

__init__ = _AzimuthalBase.__init__ 

 

def forward(self, lat, lon, name=NN): 

'''Convert a geodetic location to azimuthal stereographic east- and northing. 

 

@arg lat: Latitude of the location (C{degrees90}). 

@arg lon: Longitude of the location (C{degrees180}). 

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

 

@return: An L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)} 

with easting C{x} and northing C{y} of point in C{meter} and C{lat} 

and C{lon} in C{degrees} and C{azimuth} clockwise from true North. 

The C{scale} of the projection is C{1} in I{radial} direction and 

is C{1 / reciprocal} in the direction perpendicular to this. 

 

@raise AzimuthalError: Invalid B{C{lat}} or B{C{lon}}. 

''' 

def _k_t(c): 

c = c + _1_0 

t = isnon0(c) 

k = (_2_0 * self._k0 / c) if t else _1_0 

return k, t 

 

return self._forward(lat, lon, name, _k_t) 

 

@property_doc_('''optional, central scale factor (C{scalar}).''') 

def k0(self): 

'''Get the central scale factor (C{scalar}). 

''' 

return self._k0 

 

@k0.setter # PYCHOK setter! 

def k0(self, factor): 

'''Set the central scale factor (C{scalar}). 

''' 

n = Stereographic.k0.fget.__name__ 

self._k0 = Scalar_(factor, name=n, low=EPS, high=2) # XXX high=1, 2, other? 

 

def reverse(self, x, y, name=NN, LatLon=None, **LatLon_kwds): 

'''Convert an azimuthal stereographic location to geodetic lat- and longitude. 

 

@arg x: Easting of the location (C{meter}). 

@arg y: Northing of the location (C{meter}). 

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

@kwarg LatLon: Class to use (C{LatLon}) or C{None}. 

@kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword 

arguments, ignored if C{B{LatLon}=None}. 

 

@return: The geodetic (C{LatLon}) or if B{C{LatLon}} is C{None} an 

L{Azimuthal7Tuple}C{(x, y, lat, lon, azimuth, scale, datum)}. 

 

@note: The C{lat} will be in the range C{[-90..90] degrees} and C{lon} 

in the range C{[-180..180] degrees}. The C{scale} of the 

projection is C{1} in I{radial} direction, C{azimuth} clockwise 

from true North and is C{1 / reciprocal} in the direction 

perpendicular to this. 

''' 

def _c_t(c): 

t = c > EPS 

if t: 

c = _2_0 * atan2(c, 2 * self._k0) 

return c, t 

 

return self._reverse(x, y, name, LatLon, LatLon_kwds, _c_t, False) 

 

 

__all__ += _ALL_DOCS(_AzimuthalBase) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2021 -- 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.