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

 

# -*- coding: utf-8 -*- 

 

u'''Ellipsoidal classes geodetic (lat-/longitude) L{LatLon} and 

geocentric (ECEF) L{Cartesian} and functions L{areaOf}, 

L{intersections2}, L{isclockwise}, L{nearestOn} and L{perimeterOf}, 

all based on I{Charles Karney}'s Python U{geographiclib 

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

 

Here's an example usage of C{ellipsoidalKarney}: 

 

>>> from pygeodesy.ellipsoidalKarney import LatLon 

>>> Newport_RI = LatLon(41.49008, -71.312796) 

>>> Cleveland_OH = LatLon(41.499498, -81.695391) 

>>> Newport_RI.distanceTo(Cleveland_OH) 

866,455.4329098687 # meter 

 

You can change the ellipsoid model used by the Karney formulae 

as follows: 

 

>>> from pygeodesy import Datums 

>>> from pygeodesy.ellipsoidalKarney import LatLon 

>>> p = LatLon(0, 0, datum=Datums.OSGB36) 

 

or by converting to anothor datum: 

 

>>> p = p.convertDatum(Datums.OSGB36) 

 

@newfield example: Example, Examples 

''' 

 

from pygeodesy.basics import property_RO, _xkwds 

from pygeodesy.datums import Datums 

from pygeodesy.ecef import EcefKarney 

from pygeodesy.ellipsoidalBase import _TOL_M, _intersections2, \ 

CartesianEllipsoidalBase, \ 

LatLonEllipsoidalBase, _nearestOn 

from pygeodesy.errors import _ValueError, _xellipsoidal 

from pygeodesy.formy import points2 

from pygeodesy.lazily import _ALL_LAZY, _ALL_OTHER 

from pygeodesy.namedTuples import Bearing2Tuple, Destination2Tuple 

from pygeodesy.points import _areaError, ispolar # PYCHOK exported 

from pygeodesy.utily import unroll180, wrap90, wrap180, wrap360 

 

__all__ = _ALL_LAZY.ellipsoidalKarney 

__version__ = '20.10.08' 

 

 

class Cartesian(CartesianEllipsoidalBase): 

'''Extended to convert C{Karney}-based L{Cartesian} to 

C{Karney}-based L{LatLon} points. 

''' 

_Ecef = EcefKarney # preferred C{Ecef...} class 

 

def toLatLon(self, **LatLon_datum_kwds): # PYCHOK LatLon=LatLon, datum=None 

'''Convert this cartesian point to a C{Karney}-based 

geodetic point. 

 

@kwarg LatLon_datum_kwds: Optional L{LatLon}, B{C{datum}} and 

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

Use B{C{LatLon=...}} to override this L{LatLon} class 

or specify C{B{LatLon}=None}. 

 

@return: The geodetic point (L{LatLon}) or if B{C{LatLon}} 

is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, 

height, C, M, datum)} with C{C} and C{M} if available. 

 

@raise TypeError: Invalid B{C{LatLon}}, B{C{datum}} or other 

B{C{LatLon_datum_kwds}}. 

''' 

kwds = _xkwds(LatLon_datum_kwds, LatLon=LatLon, datum=self.datum) 

return CartesianEllipsoidalBase.toLatLon(self, **kwds) 

 

 

class LatLon(LatLonEllipsoidalBase): 

'''An ellipsoidal L{LatLon} similar to L{ellipsoidalVincenty.LatLon} 

but using I{Charles F. F. Karney}'s Python U{geographiclib 

<https://PyPI.org/project/geographiclib>} to compute the geodesic 

distance, initial and final bearing (azimuths) between two given 

points or the destination point given a start point and an initial 

bearing. 

 

@note: This L{LatLon}'s methods require the U{geographiclib 

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

''' 

_Ecef = EcefKarney # preferred C{Ecef...} class 

 

def bearingTo(self, other, wrap=False): # PYCHOK no cover 

'''DEPRECATED, use method C{initialBearingTo}. 

''' 

return self.initialBearingTo(other, wrap=wrap) 

 

def bearingTo2(self, other, wrap=False): 

'''Compute the initial and final bearing (forward and reverse 

azimuth) from this to an other point, using I{Karney}'s 

C{Inverse} method. See methods L{initialBearingTo} and 

L{finalBearingTo} for more details. 

 

@arg other: The other point (L{LatLon}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: A L{Bearing2Tuple}C{(initial, final)}. 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@raise TypeError: The B{C{other}} point is not L{LatLon}. 

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

''' 

r = self._inverse(other, wrap) 

return self._xnamed(Bearing2Tuple(r.initial, r.final)) 

 

def destination(self, distance, bearing, height=None): 

'''Compute the destination point after having travelled 

for the given distance from this point along a geodesic 

given by an initial bearing, using I{Karney}'s C{Direct} 

method. See method L{destination2} for more details. 

 

@arg distance: Distance (C{meter}). 

@arg bearing: Initial bearing in (compass C{degrees360}). 

@kwarg height: Optional height, overriding the default 

height (C{meter}, same units as C{distance}). 

 

@return: The destination point (L{LatLon}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@example: 

 

>>> p = LatLon(-37.95103, 144.42487) 

>>> d = p.destination(54972.271, 306.86816) 

>>> d 

LatLon(37°39′10.14″S, 143°55′35.39″E) # 37.652818°S, 143.926498°E 

''' 

r = self._direct(distance, bearing, self.classof, height) 

return r.destination 

 

def destination2(self, distance, bearing, height=None): 

'''Compute the destination point and the final bearing (reverse 

azimuth) after having travelled for the given distance from 

this point along a geodesic given by an initial bearing, 

using I{Karney}'s C{Direct} method. 

 

The distance must be in the same units as this point's datum 

axes, conventionally C{meter}. The distance is measured on 

the surface of the ellipsoid, ignoring this point's height. 

 

The initial and final bearing (forward and reverse azimuth) 

are in compass C{degrees360}. 

 

The destination point's height and datum are set to this 

point's height and datum, unless the former is overridden. 

 

@arg distance: Distance (C{meter}). 

@arg bearing: Initial bearing (compass C{degrees360}). 

@kwarg height: Optional height, overriding the default 

height (C{meter}, same units as C{distance}). 

 

@return: A L{Destination2Tuple}C{(destination, final)}. 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@example: 

 

>>> p = LatLon(-37.95103, 144.42487) 

>>> d, f = p.destination2(54972.271, 306.86816) 

>>> d 

LatLon(37°39′10.14″S, 143°55′35.39″E) # 37.652818°S, 143.926498°E 

>>> f 

307.1736313846665 

''' 

r = self._direct(distance, bearing, self.classof, height) 

return self._xnamed(r) 

 

def distanceTo(self, other, wrap=False, **unused): # ignore radius=R_M 

'''Compute the distance between this and an other point 

along a geodesic, using I{Karney}'s C{Inverse} method. 

See method L{distanceTo3} for more details. 

 

@arg other: The other point (L{LatLon}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: Distance (C{meter}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@raise TypeError: The B{C{other}} point is not L{LatLon}. 

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

 

@example: 

 

>>> p = LatLon(50.06632, -5.71475) 

>>> q = LatLon(58.64402, -3.07009) 

>>> d = p.distanceTo(q) # 969,954.1663142084 m 

''' 

return self._inverse(other, wrap).distance 

 

def distanceTo3(self, other, wrap=False): 

'''Compute the distance, the initial and final bearing along a 

geodesic between this and an other point, using I{Karney}'s 

C{Inverse} method. 

 

The distance is in the same units as this point's datum axes, 

conventionally meter. The distance is measured on the surface 

of the ellipsoid, ignoring this point's height. 

 

The initial and final bearing (forward and reverse azimuth) 

are in compass C{degrees360} from North. 

 

@arg other: Destination point (L{LatLon}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: A L{Distance3Tuple}C{(distance, initial, final)}. 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@raise TypeError: The B{C{other}} point is not L{LatLon}. 

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

''' 

return self._xnamed(self._inverse(other, wrap)) 

 

def finalBearingOn(self, distance, bearing): 

'''Compute the final bearing (reverse azimuth) after having 

travelled for the given distance along a geodesic given 

by an initial bearing from this point, using I{Karney}'s 

C{Direct} method. See method L{destination2} for more details. 

 

@arg distance: Distance (C{meter}). 

@arg bearing: Initial bearing (compass C{degrees360}). 

 

@return: Final bearing (compass C{degrees360}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@example: 

 

>>> p = LatLon(-37.95103, 144.42487) 

>>> b = 306.86816 

>>> f = p.finalBearingOn(54972.271, b) # 307.1736313846665° 

''' 

return self._direct(distance, bearing, None, None).final 

 

def finalBearingTo(self, other, wrap=False): 

'''Compute the final bearing (reverse azimuth) after having 

travelled along a geodesic from this point to an other 

point, using I{Karney}'s C{Inverse} method. See method 

L{distanceTo3} for more details. 

 

@arg other: The other point (L{LatLon}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: Final bearing (compass C{degrees360}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@raise TypeError: The B{C{other}} point is not L{LatLon}. 

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

 

@example: 

 

>>> p = new LatLon(50.06632, -5.71475) 

>>> q = new LatLon(58.64402, -3.07009) 

>>> f = p.finalBearingTo(q) # 11.297220414306684° 

 

>>> p = LatLon(52.205, 0.119) 

>>> q = LatLon(48.857, 2.351) 

>>> f = p.finalBearingTo(q) # 157.83449958372714° 

''' 

return self._inverse(other, wrap).final 

 

@property_RO 

def geodesic(self): 

'''Get this C{LatLon}'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 

 

def initialBearingTo(self, other, wrap=False): 

'''Compute the initial bearing (forward azimuth) to travel 

along a geodesic from this point to an other point, 

using I{Karney}'s C{Inverse} method. See method 

L{distanceTo3} for more details. 

 

@arg other: The other point (L{LatLon}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: Initial bearing (compass C{degrees360}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@raise TypeError: The B{C{other}} point is not L{LatLon}. 

 

@raise ValueError: If this and the B{C{other}} point's L{Datum} 

ellipsoids are not compatible. 

 

@example: 

 

>>> p = LatLon(50.06632, -5.71475) 

>>> q = LatLon(58.64402, -3.07009) 

>>> b = p.initialBearingTo(q) # 9.141877488906045° 

 

>>> p = LatLon(52.205, 0.119) 

>>> q = LatLon(48.857, 2.351) 

>>> b = p.initialBearingTo(q) # 156.1106404059787° 

 

@JSname: I{bearingTo}. 

''' 

return self._inverse(other, wrap).initial 

 

def intersections2(self, radius1, other, radius2, height=None, wrap=True, # PYCHOK expected 

tol=_TOL_M): 

'''Compute the intersection points of two circles each defined 

by a center point and a radius. 

 

@arg radius1: Radius of the this circle (C{meter}). 

@arg other: Center of the other circle (C{LatLon}). 

@arg radius2: Radius of the other circle (C{meter}). 

@kwarg height: Optional height for the intersection points, 

overriding the "radical height" at the "radical 

line" between both centers (C{meter}) or C{None}. 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

@kwarg tol: Convergence tolerance (C{meter}). 

 

@return: 2-Tuple of the intersection points, each a C{LatLon} 

instance. For abutting circles, the intersection 

points are the same instance. 

 

@raise IntersectionError: Concentric, antipodal, invalid or 

non-intersecting circles or no 

convergence. 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@raise TypeError: Invalid B{C{other}} or B{C{equidistant}}. 

 

@raise ValueError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}. 

''' 

self.others(other) 

return intersections2(self, radius1, other, radius2, height=height, wrap=wrap, 

tol=tol, LatLon=self.classof, datum=self.datum) 

 

def nearestOn(self, point1, point2, within=True, height=None, wrap=False, # PYCHOK expected 

tol=_TOL_M): 

'''Locate the closest point on the arc between two other points 

and this point. 

 

@arg point1: Start point of the arc (C{LatLon}). 

@arg point2: End point of the arc (C{LatLon}). 

@kwarg within: If C{True} return the closest point I{between} 

B{C{point1}} and B{C{point2}}, otherwise the 

closest point elsewhere on the arc (C{bool}). 

@kwarg height: Optional height for the closest point (C{meter}) 

or C{None}. 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

@kwarg tol: Convergence tolerance (C{meter}). 

 

@return: Closest point (B{C{LatLon}}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@raise TypeError: Invalid or non-ellipsoidal B{C{point1}} or B{C{point2}}. 

''' 

# use .nearestOn to get C{azimuthal.EquidistantKarney} or ImportError 

return nearestOn(self, point1, point2, within=within, height=height, wrap=wrap, 

tol=tol, LatLon=self.classof, datum=self.datum) 

 

def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None 

'''Convert this point to C{Karney}-based cartesian (ECEF) coordinates. 

 

@kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} 

and other keyword arguments, ignored if B{C{Cartesian=None}}. 

Use B{C{Cartesian=...}} to override this L{Cartesian} class 

or set B{C{Cartesian=None}}. 

 

@return: The cartesian (ECEF) coordinates (L{Cartesian}) or if 

B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, 

lat, lon, height, C, M, datum)} with C{C} and C{M} if 

available. 

 

@raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other 

B{C{Cartesian_datum_kwds}}. 

''' 

kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, 

datum=self.datum) 

return LatLonEllipsoidalBase.toCartesian(self, **kwds) 

 

def _direct(self, distance, bearing, LL, height): 

'''(INTERNAL) I{Karney}'s C{Direct} method. 

 

@return: A L{Destination2Tuple}C{(destination, final)} or 

a L{Destination3Tuple}C{(lat, lon, final)} if 

B{C{LL}} is C{None}. 

''' 

g = self.datum.ellipsoid.geodesic 

r = g.Direct3(self.lat, self.lon, bearing, distance) 

if LL: 

h = self.height if height is None else height 

d = LL(wrap90(r.lat), wrap180(r.lon), height=h, datum=self.datum) 

r = Destination2Tuple(self._xnamed(d), wrap360(r.final)) 

return r 

 

def _inverse(self, other, wrap): 

'''(INTERNAL) I{Karney}'s C{Inverse} method. 

 

@return: A L{Distance3Tuple}C{(distance, initial, final)}. 

 

@raise TypeError: The B{C{other}} point is not L{LatLon}. 

 

@raise ValueError: If this and the B{C{other}} point's 

L{Datum} ellipsoids are not compatible. 

''' 

g = self.ellipsoids(other).geodesic 

_, lon = unroll180(self.lon, other.lon, wrap=wrap) 

return g.Inverse3(self.lat, self.lon, other.lat, lon) 

 

 

def _geodesic(datum, points, closed, line, wrap): 

# Compute the area or perimeter of a polygon, 

# using the geographiclib package, iff installed 

g = datum.ellipsoid.geodesic 

 

if not wrap: # capability LONG_UNROLL can't be off 

raise _ValueError(wrap=wrap) 

 

_, points = points2(points, closed=closed) # base=LatLonEllipsoidalBase(0, 0) 

 

g = g.Polygon(line) 

 

# note, lon deltas are unrolled, by default 

for p in points: 

g.AddPoint(p.lat, p.lon) 

if closed and line: 

p = points[0] 

g.AddPoint(p.lat, p.lon) 

 

# g.Compute returns (number_of_points, perimeter, signed area) 

return g.Compute(False, True)[1 if line else 2] 

 

 

def areaOf(points, datum=Datums.WGS84, wrap=True): 

'''Compute the area of a (n ellipsoidal) polygon. 

 

@arg points: The polygon points (L{LatLon}[]). 

@kwarg datum: Optional datum (L{Datum}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: Area (C{meter}, same as units of the B{C{datum}} 

ellipsoid, squared). 

 

@raise ImportError: Package U{geographiclib 

<https://PyPI.org/project/geographiclib>} missing. 

 

@raise TypeError: Some B{C{points}} are not L{LatLon}. 

 

@raise PointsError: Insufficient number of B{C{points}}. 

 

@raise ValueError: Invalid B{C{wrap}}, longitudes not 

wrapped, unrolled. 

 

@note: This function requires installation of the U{geographiclib 

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

 

@see: L{pygeodesy.areaOf}, L{sphericalNvector.areaOf} and 

L{sphericalTrigonometry.areaOf}. 

''' 

return abs(_geodesic(datum, points, True, False, wrap)) 

 

 

def intersections2(center1, radius1, center2, radius2, height=None, wrap=True, 

equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): 

'''Iteratively compute the intersection points of two circles each defined 

by an (ellipsoidal) center point and a radius. 

 

@arg center1: Center of the first circle (L{LatLon}). 

@arg radius1: Radius of the first circle (C{meter}). 

@arg center2: Center of the second circle (L{LatLon}). 

@arg radius2: Radius of the second circle (C{meter}). 

@kwarg height: Optional height for the intersection points, 

overriding the "radical height" at the "radical 

line" between both centers (C{meter}) or C{None}. 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

@kwarg equidistant: An azimuthal equidistant projection class 

(L{Equidistant} or L{equidistant}) 

or C{None} for L{EquidistantKarney}. 

@kwarg tol: Convergence tolerance (C{meter}). 

@kwarg LatLon: Optional class to return the intersection points 

(L{LatLon}) or C{None}. 

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

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

 

@return: 2-Tuple of the intersection points, each a B{C{LatLon}} 

instance or L{LatLon4Tuple}C{(lat, lon, height, datum)} 

if B{C{LatLon}} is C{None}. For abutting circles, the 

intersection points are the same instance. 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@raise IntersectionError: Concentric, antipodal, invalid or 

non-intersecting circles or no 

convergence for the B{C{tol}}. 

 

@raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}} 

or invalid B{C{equidistant}}. 

 

@raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}. 

 

@see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ 

calculating-intersection-of-two-circles>}, U{Karney's paper 

<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section 14 I{Maritime Boundaries}, 

U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and 

U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>} 

intersections. 

''' 

from pygeodesy.azimuthal import EquidistantKarney 

E = EquidistantKarney if equidistant is None else equidistant 

return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap, 

equidistant=E, tol=tol, LatLon=LatLon, **LatLon_kwds) 

 

 

def isclockwise(points, datum=Datums.WGS84, wrap=True): 

'''Determine the direction of a path or polygon. 

 

@arg points: The path or polygon points (C{LatLon}[]). 

@kwarg datum: Optional datum (L{Datum}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: C{True} if B{C{points}} are clockwise, C{False} otherwise. 

 

@raise TypeError: Some B{C{points}} are not C{LatLon}. 

 

@raise PointsError: Insufficient number of B{C{points}}. 

 

@raise ValueError: The B{C{points}} enclose a pole or zero 

area. 

 

@note: This function requires installation of the U{geographiclib 

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

 

@see: L{pygeodesy.isclockwise}. 

''' 

a = _geodesic(datum, points, True, False, wrap) 

if a > 0: 

return True 

elif a < 0: 

return False 

raise _areaError(points) 

 

 

def nearestOn(point, point1, point2, within=True, height=None, wrap=False, 

equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): 

'''Locate the closest point on the arc between two other points. 

 

@arg point: Reference point (C{LatLon}). 

@arg point1: Start point of the arc (C{LatLon}). 

@arg point2: End point of the arc (C{LatLon}). 

@kwarg within: If C{True} return the closest point I{between} 

B{C{point1}} and B{C{point2}}, otherwise the 

closest point elsewhere on the arc (C{bool}). 

@kwarg height: Optional height for the closest point (C{meter}) 

or C{None}. 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

@kwarg equidistant: An azimuthal equidistant projection class 

(L{Equidistant} or L{EquidistantKarney}), 

function L{azimuthal.equidistant} will be 

invoked if left unspecified. 

@kwarg tol: Convergence tolerance (C{meter}). 

@kwarg LatLon: Optional class to return the closest point 

(L{LatLon}) or C{None}. 

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

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

 

@return: Closest point (B{C{LatLon}}). 

 

@raise ImportError: Package U{geographiclib 

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

not installed or not found. 

 

@raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}} 

or B{C{point2}} or invalid B{C{equidistant}}. 

''' 

from pygeodesy.azimuthal import EquidistantKarney 

p = _xellipsoidal(point=point) 

p1 = p.others(point1=point1) 

p2 = p.others(point2=point2) 

E = EquidistantKarney if equidistant is None else equidistant 

return _nearestOn(p, p1, p2, within=within, height=height, wrap=wrap, 

equidistant=E, tol=tol, LatLon=LatLon, **LatLon_kwds) 

 

 

def perimeterOf(points, closed=False, datum=Datums.WGS84, wrap=True): 

'''Compute the perimeter of a (n ellipsoidal) polygon. 

 

@arg points: The polygon points (L{LatLon}[]). 

@kwarg closed: Optionally, close the polygon (C{bool}). 

@kwarg datum: Optional datum (L{Datum}). 

@kwarg wrap: Wrap and unroll longitudes (C{bool}). 

 

@return: Perimeter (C{meter}, same as units of the B{C{datum}} 

ellipsoid). 

 

@raise ImportError: Package U{geographiclib 

<https://PyPI.org/project/geographiclib>} missing. 

 

@raise TypeError: Some B{C{points}} are not L{LatLon}. 

 

@raise PointsError: Insufficient number of B{C{points}}. 

 

@raise ValueError: Invalid B{C{wrap}}, longitudes not 

wrapped, unrolled. 

 

@note: This function requires installation of the U{geographiclib 

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

 

@see: L{pygeodesy.perimeterOf} and L{sphericalTrigonometry.perimeterOf}. 

''' 

return _geodesic(datum, points, closed, True, wrap) 

 

 

__all__ += _ALL_OTHER(Cartesian, LatLon, # classes 

areaOf, intersections2, isclockwise, ispolar, # functions 

nearestOn, perimeterOf) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2020 -- 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.