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

 

# -*- coding: utf-8 -*- 

 

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

L{Cartesian} classed and functions L{areaOf}, L{isclockwise} and 

L{perimeterOf}, all based on I{Charles Karney's} Python implementation 

of 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.datum import Datums 

from pygeodesy.ecef import EcefKarney 

from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \ 

LatLonEllipsoidalBase 

from pygeodesy.formy import points2 

from pygeodesy.lazily import _ALL_LAZY, _2kwds 

from pygeodesy.named import Bearing2Tuple, Destination2Tuple, Distance3Tuple 

from pygeodesy.points import ispolar # PYCHOK exported 

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

 

# all public contants, classes and functions 

__all__ = _ALL_LAZY.ellipsoidalKarney + ( 

'Cartesian', 'LatLon', # classes 

'areaOf', 'isclockwise', 'ispolar', 'perimeterOf') # functions 

__version__ = '19.10.19' 

 

 

class Cartesian(CartesianEllipsoidalBase): 

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

C{Karney}-based L{LatLon} points. 

''' 

_Ecef = EcefKarney #: (INTERNAL) Preferred C{Ecef...} class. 

 

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

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

geodetic point. 

 

@keyword kwds: Optional, additional B{C{LatLon}} keyword 

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

For example, use C{LatLon=...} to override 

the L{LatLon} (sub-)class or specify 

C{B{LatLon}=None}. 

 

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

C{B{LatLon}=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 B{C{kwds}}. 

''' 

kwds = _2kwds(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 #: (INTERNAL) Preferred C{Ecef...} class. 

 

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

'''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 Karney's 

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

L{finalBearingTo} for more details. 

 

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

@keyword 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 = Bearing2Tuple(*self._inverse(other, True, wrap)[1:]) 

return self._xnamed(r) 

 

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 Karney's C{Direct} 

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

 

@param distance: Distance (C{meter}). 

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

@keyword 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 

''' 

return self._direct(distance, bearing, True, height=height)[0] 

 

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 Karney's C{Direct} method. 

 

The distance must be 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 degrees. 

 

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

point's height and datum. 

 

@param distance: Distance (C{meter}). 

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

@keyword 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 = Destination2Tuple(*self._direct(distance, bearing, True, 

height=height)[:2]) 

return self._xnamed(r) 

 

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

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

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

See method L{distanceTo3} for more details. 

 

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

@keyword 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, False, wrap) 

 

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

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

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

C{Inverse} method. 

 

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

conventially 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 degrees from North. 

 

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

@keyword 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. 

''' 

r = Distance3Tuple(*self._inverse(other, True, wrap)) 

return self._xnamed(r) 

 

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 Karney's 

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

 

@param distance: Distance (C{meter}). 

@param 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, False) 

 

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 Karney's C{Inverse} method. See method 

L{distanceTo3} for more details. 

 

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

@keyword 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, True, wrap)[2] 

 

@property_RO 

def geodesic(self): 

'''Get this C{LatLon}'s U{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 Karney's C{Inverse} method. See method 

L{distanceTo3} for more details. 

 

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

@keyword 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, True, wrap)[1] 

 

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

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

coordinates. 

 

@keyword kwds: Optional, additional B{C{Cartesian}} keyword 

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

For example, use C{Cartesian=...} to override 

the L{Cartesian} (sub-)class or specify 

C{B{Cartesian}=None}. 

 

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

C{B{Cartesian}=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 B{C{kwds}}. 

''' 

kwds = _2kwds(kwds, Cartesian=Cartesian, datum=self.datum) 

return LatLonEllipsoidalBase.toCartesian(self, **kwds) 

 

def _direct(self, distance, bearing, llr, height=None): 

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

''' 

g = self.datum.ellipsoid.geodesic 

m = g.AZIMUTH 

if llr: 

m |= g.LATITUDE | g.LONGITUDE 

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

t = wrap360(r['azi2']) 

if llr: 

a, b = wrap90(r['lat2']), wrap180(r['lon2']) 

h = self.height if height is None else height 

t = self.classof(a, b, height=h, datum=self.datum), t 

return t 

 

def _inverse(self, other, azis, wrap): 

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

 

@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 

m = g.DISTANCE 

if azis: 

m |= g.AZIMUTH 

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

r = g.Inverse(self.lat, self.lon, other.lat, lon, m) 

t = r['s12'] 

if azis: # forward and reverse azimuth 

t = t, wrap360(r['azi1']), wrap360(r['azi2']) 

return t 

 

 

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('%s invalid: %s' % ('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 line and closed: 

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. 

 

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

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

@keyword 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 ValueError: Insufficient number of B{C{points}} or longitudes 

not wrapped, unrolled, B{C{wrap}} is C{False}. 

 

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

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

 

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

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

@keyword 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 ValueError: Insufficient number of B{C{points}} or 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 ValueError('polar or zero area: %r' % (points,)) 

 

 

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

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

 

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

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

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

@keyword 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 ValueError: Insufficient number of B{C{points}} or longitudes 

not wrapped, unrolled, B{C{wrap}} is C{False}. 

 

@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) 

 

# **) 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.