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

 

# -*- coding: utf-8 -*- 

 

u'''Ellipsoidal, C{N-vector}-based geodesy. 

 

Ellipsoidal classes geodetic (lat-/longitude) L{LatLon}, geocentric 

(ECEF) L{Cartesian}, L{Ned} and L{Nvector} and functions L{meanOf}, 

L{sumOf} and L{toNed}. 

 

Pure Python implementation of n-vector-based geodetic (lat-/longitude) 

methods by I{(C) Chris Veness 2011-2016} published under the same MIT 

Licence**, see U{Vector-based geodesy 

<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. 

 

These classes and functions work with: (a) geodesic (polar) lat-/longitude 

points on the earth's surface and (b) 3-D vectors used as n-vectors 

representing points on the earth's surface or vectors normal to the plane 

of a great circle. 

 

See also Kenneth Gade U{'A Non-singular Horizontal Position Representation' 

<https://www.NavLab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf>}, 

The Journal of Navigation (2010), vol 63, nr 3, pp 395-417. 

''' 

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

from __future__ import division 

 

from pygeodesy.basics import _xinstanceof 

from pygeodesy.datums import _ellipsoidal_datum, _spherical_datum, _WGS84 

from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, _TOL_M, \ 

LatLonEllipsoidalBase, _nearestOn 

from pygeodesy.errors import _xkwds 

from pygeodesy.fmath import fdot 

from pygeodesy.interns import NN, _Nv00_, _COMMASPACE_ 

from pygeodesy.interns import _down_, _east_, _north_, _pole_ # PYCHOK used! 

from pygeodesy.lazily import _ALL_LAZY, _ALL_OTHER 

from pygeodesy.ltpTuples import Aer as _Aer, Ned as _Ned 

from pygeodesy.named import _NamedTuple, _xnamed 

from pygeodesy.nvectorBase import NorthPole, LatLonNvectorBase, \ 

NvectorBase, sumOf as _sumOf 

from pygeodesy.props import deprecated_class, deprecated_function, \ 

deprecated_method, Property_RO 

from pygeodesy.streprs import Fmt, fstr, _xzipairs 

from pygeodesy.units import Bearing, Distance, Height, Meter, Scalar 

from pygeodesy.utily import sincos2d_ 

 

__all__ = _ALL_LAZY.ellipsoidalNvector 

__version__ = '21.10.05' 

 

 

class Cartesian(CartesianEllipsoidalBase): 

'''Extended to convert geocentric, L{Cartesian} points to 

L{Nvector} and n-vector-based, geodetic L{LatLon}. 

''' 

@Property_RO 

def Ecef(self): 

'''Get the ECEF I{class} (L{EcefVeness}), I{lazily}. 

''' 

from pygeodesy.ecef import EcefVeness 

return EcefVeness 

 

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

'''Convert this cartesian to an C{Nvector}-based geodetic point. 

 

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

keyword arguments. Use C{B{LatLon}=...} to 

override this L{LatLon} class or specify 

C{B{LatLon} is None}. 

 

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

to 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_and_kwds}}. 

''' 

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

return CartesianEllipsoidalBase.toLatLon(self, **kwds) 

 

def toNvector(self, **Nvector_and_kwds): # PYCHOK Datums.WGS84 

'''Convert this cartesian to L{Nvector} components, I{including height}. 

 

@kwarg Nvector_and_kwds: Optional L{Nvector}, B{C{datum}} and other 

keyword arguments. Use C{B{Nvector}=...} to 

override this L{Nvector} class or specify 

C{B{Nvector} is None}. 

 

@return: The C{n-vector} components (L{Nvector}) or if B{C{Nvector}} 

is set to C{None}, a L{Vector4Tuple}C{(x, y, z, h)} 

 

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

 

@example: 

 

>>> from ellipsoidalNvector import LatLon 

>>> c = Cartesian(3980581, 97, 4966825) 

>>> n = c.toNvector() # (0.62282, 0.000002, 0.78237, +0.24) 

''' 

kwds = _xkwds(Nvector_and_kwds, Nvector=Nvector, datum=self.datum) 

return CartesianEllipsoidalBase.toNvector(self, **kwds) 

 

 

class LatLon(LatLonNvectorBase, LatLonEllipsoidalBase): 

'''An n-vector-based, ellipsoidal L{LatLon} point. 

 

@example: 

 

>>> from ellipsoidalNvector import LatLon 

>>> p = LatLon(52.205, 0.119) # height=0, datum=Datums.WGS84 

''' 

_Nv = None # cached toNvector (L{Nvector}) 

 

def _update(self, updated, *attrs): # PYCHOK args 

'''(INTERNAL) Zap cached attributes if updated. 

''' 

if updated: 

LatLonNvectorBase._update(self, updated, _Nv=self._Nv) # special case 

LatLonEllipsoidalBase._update(self, updated, *attrs) 

 

# def crossTrackDistanceTo(self, start, end, radius=R_M): 

# '''Return the (signed) distance from this point to the great 

# circle defined by a start point and an end point or bearing. 

# 

# @arg start: Start point of great circle path (L{LatLon}). 

# @arg end: End point of great circle path (L{LatLon}) or 

# initial bearing (compass C{degrees360}) at the 

# start point. 

# @kwarg radius: Mean earth radius (C{meter}). 

# 

# @return: Distance to great circle, negative if to left or 

# positive if to right of path (C{meter}, same units 

# as B{C{radius}}). 

# 

# @raise TypeError: If B{C{start}} or B{C{end}} point is not L{LatLon}. 

# 

# @example: 

# 

# >>> p = LatLon(53.2611, -0.7972) 

# 

# >>> s = LatLon(53.3206, -1.7297) 

# >>> b = 96.0 

# >>> d = p.crossTrackDistanceTo(s, b) # -305.7 

# 

# >>> e = LatLon(53.1887, 0.1334) 

# >>> d = p.crossTrackDistanceTo(s, e) # -307.5 

# ''' 

# self.others(start=start) 

# 

# if isscalar(end): # gc from point and bearing 

# gc = start.greatCircle(end) 

# else: # gc by two points 

# gc = start.toNvector().cross(end.toNvector()) 

# 

# # (signed) angle between point and gc normal vector 

# v = self.toNvector() 

# a = gc.angleTo(v, vSign=v.cross(gc)) 

# a = (-PI_2 - a) if a < 0 else (PI_2 - a) 

# return a * float(radius) 

 

def deltaTo(self, other): 

'''Calculate the local delta from this to an other point. 

 

The delta is returned as a North-East-Down (NED) vector. 

 

Note, this is a linear delta, unrelated to a geodesic 

on the ellipsoid. The points need not be defined on 

the same datum. 

 

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

 

@return: Delta of this point (L{Ned}). 

 

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

 

@raise ValueError: If ellipsoids are incompatible. 

 

@example: 

 

>>> a = LatLon(49.66618, 3.45063) 

>>> b = LatLon(48.88667, 2.37472) 

>>> delta = a.deltaTo(b) # [N:-86126, E:-78900, D:1069] 

>>> d = delta.length # 116807.681 m 

>>> b = delta.bearing # 222.493° 

>>> e = delta.elevation # -0.5245° 

''' 

self.ellipsoids(other) # throws TypeError and ValueError 

 

# get delta in cartesian frame 

dc = other.toCartesian().minus(self.toCartesian()) 

# rotate dc to get delta in n-vector reference 

# frame using the rotation matrix row vectors 

nv, ev, dv = self._rotation3 

return Ned(dc.dot(nv), dc.dot(ev), dc.dot(dv), name=self.name) 

 

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

# '''Return the destination point after traveling from this 

# point the given distance on the given initial bearing. 

# 

# @arg distance: Distance traveled (C{meter}, same units as 

# given earth B{C{radius}}). 

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

# @kwarg radius: Mean earth radius (C{meter}). 

# @kwarg height: Optional height at destination point, 

# overriding default (C{meter}, same units 

# as B{C{radius}}). 

# 

# @return: Destination point (L{LatLon}). 

# 

# @example: 

# 

# >>> p = LatLon(51.4778, -0.0015) 

# >>> q = p.destination(7794, 300.7) 

# >>> q.toStr() # '51.5135°N, 000.0983°W' ? 

# ''' 

# r = _angular(distance, radius) # angular distance in radians 

# # great circle by starting from this point on given bearing 

# gc = self.greatCircle(bearing) 

# 

# v1 = self.toNvector() 

# x = v1.times(cos(r)) # component of v2 parallel to v1 

# y = gc.cross(v1).times(sin(r)) # component of v2 perpendicular to v1 

# 

# v2 = x.plus(y).unit() 

# return v2.toLatLon(height=self.height if height is C{None} else height) 

 

def destinationNed(self, delta): 

'''Calculate the destination point using the supplied NED delta 

from this point. 

 

@arg delta: Delta from this to the other point in the local 

tangent plane (LTP) of this point (L{Ned}). 

 

@return: Destination point (L{LatLon}). 

 

@raise TypeError: If B{C{delta}} is not L{Ned}. 

 

@example: 

 

>>> a = LatLon(49.66618, 3.45063) 

>>> delta = Ned(-86126, -78900, 1069) # from Aer(222.493, -0.5245, 116807.681) 

>>> b = a.destinationNed(delta) # 48.886669°N, 002.374721°E or 48°53′12.01″N, 002°22′29.0″E +0.20m 

 

@JSname: I{destinationPoint}. 

''' 

_xinstanceof(Ned, delta=delta) 

 

nv, ev, dv = self._rotation3 

# convert NED delta to standard coordinate frame of n-vector 

dn = delta.ned 

# rotate dn to get delta in cartesian (ECEF) coordinate 

# reference frame using the rotation matrix column vectors 

dc = Cartesian(fdot(dn, nv.x, ev.x, dv.x), 

fdot(dn, nv.y, ev.y, dv.y), 

fdot(dn, nv.z, ev.z, dv.z)) 

 

# apply (cartesian) delta to this Cartesian to obtain destination as cartesian 

v = self.toCartesian().plus(dc) 

return v.toLatLon(datum=self.datum, LatLon=self.classof) # Cartesian(v.x, v.y, v.z).toLatLon(...) 

 

def distanceTo(self, other, radius=None, wrap=False): 

'''I{Approximate} the distance from this to an other point. 

 

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

@kwarg radius: Mean earth radius, ellipsoid or datum 

(C{meter}, L{Ellipsoid}, L{Ellipsoid2}, 

L{Datum} or L{a_f2Tuple}), overriding the 

mean radius C{R1} of this point's datum.. 

@kwarg wrap: Wrap/unroll the angular distance (C{bool}). 

 

@return: Distance (C{meter}, same units as B{C{radius}}). 

 

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

 

@raise ValueError: Invalid B{C{radius}}. 

 

@example: 

 

>>> p = LatLon(52.205, 0.119) 

>>> q = LatLon(48.857, 2.351); 

>>> d = p.distanceTo(q) # 404300 

''' 

self.others(other) 

 

a = self._N_vector.angleTo(other._N_vector, wrap=wrap) 

d = self.datum if radius is None else _spherical_datum(radius) 

return abs(a) * d.ellipsoid.R1 # see .utily.radians2m 

 

@Property_RO 

def Ecef(self): 

'''Get the ECEF I{class} (L{EcefVeness}), I{lazily}. 

''' 

from pygeodesy.ecef import EcefVeness 

return EcefVeness 

 

@deprecated_method 

def equals(self, other, eps=None): # PYCHOK no cover 

'''DEPRECATED, use method L{isequalTo}. 

''' 

return self.isequalTo(other, eps=eps) 

 

def isequalTo(self, other, eps=None): 

'''Compare this point with an other point. 

 

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

@kwarg eps: Optional margin (C{float}). 

 

@return: C{True} if points are identical, including 

datum, I{ignoring height}, C{False} otherwise. 

 

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

 

@raise ValueError: Invalid B{C{eps}}. 

 

@see: Method C{isequalTo3} to include I{height}. 

 

@example: 

 

>>> p = LatLon(52.205, 0.119) 

>>> q = LatLon(52.205, 0.119) 

>>> e = p.isequalTo(q) # True 

''' 

return LatLonEllipsoidalBase.isequalTo(self, other, eps=eps) \ 

if self.datum == other.datum else False 

 

# def greatCircle(self, bearing): 

# '''Return the great circle heading on the given bearing 

# from this point. 

# 

# Direction of vector is such that initial bearing vector 

# b = c × p, where p is representing this point. 

# 

# @arg bearing: Bearing from this point (compass C{degrees360}). 

# 

# @return: N-vector representing great circle (L{Nvector}). 

# 

# @example: 

# 

# >>> p = LatLon(53.3206, -1.7297) 

# >>> g = p.greatCircle(96.0) 

# >>> g.toStr() # '(-0.794, 0.129, 0.594)' 

# ''' 

# a, b, _ = self.philamheight 

# t = radians(bearing) 

# 

# sa, ca, sb, cb, st, ct = sincos2_(a, b, t) 

# return self._xnamed(Nvector(sb * ct - sa * cb * st, 

# -cb * ct - sa * sb * st, 

# ca * st) 

 

# def initialBearingTo(self, other): 

# '''Return the initial bearing (forward azimuth) from this 

# to an other point. 

# 

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

# 

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

# 

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

# 

# @example: 

# 

# >>> p1 = LatLon(52.205, 0.119) 

# >>> p2 = LatLon(48.857, 2.351) 

# >>> b = p1.bearingTo(p2) # 156.2 

# 

# @JSname: I{bearingTo}. 

# ''' 

# self.others(other) 

# 

# v1 = self.toNvector() 

# v2 = other.toNvector() 

# 

# gc1 = v1.cross(v2) # gc through v1 & v2 

# gc2 = v1.cross(_NP3) # gc through v1 & North pole 

# 

# # bearing is (signed) angle between gc1 & gc2 

# return degrees360(gc1.angleTo(gc2, vSign=v1)) 

 

def intermediateTo(self, other, fraction, height=None, **unused): # wrap=False 

'''Return the point at given fraction between this and 

an other point. 

 

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

@arg fraction: Fraction between both points (C{scalar}, 

0.0 at this to 1.0 at the other point. 

@kwarg height: Optional height, overriding the fractional 

height (C{meter}). 

 

@return: Intermediate point (L{LatLon}). 

 

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

 

@example: 

 

>>> p = LatLon(52.205, 0.119) 

>>> q = LatLon(48.857, 2.351) 

>>> p = p.intermediateTo(q, 0.25) # 51.3721°N, 000.7073°E 

 

@JSname: I{intermediatePointTo}. 

''' 

self.others(other) 

 

f = Scalar(fraction=fraction) 

i = self.toNvector().intermediateTo(other.toNvector(), f) 

 

h = self._havg(other, f=f) if height is None else Height(height) 

return i.toLatLon(height=h, LatLon=self.classof) # Nvector(i.x, i.y, i.z).toLatLon(...) 

 

@Property_RO 

def _rotation3(self): 

'''(INTERNAL) Get the rotation matrix from n-vector coordinate frame axes. 

''' 

nv = self.toNvector() # local (n-vector) coordinate frame 

 

dv = nv.negate() # down, opposite to n-vector 

ev = NorthPole.cross(nv, raiser=_pole_).unit() # east, pointing perpendicular to the plane 

nv = ev.cross(dv) # north, by right hand rule 

return nv, ev, dv # matrix rows 

 

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

'''Convert this point to an C{Nvector}-based geodetic point. 

 

@kwarg Cartesian_and_kwds: Optional L{Cartesian}, B{C{datum}} and other 

keyword arguments. Use C{B{Cartesian}=...} 

to override this L{Cartesian} class or specify 

C{B{Cartesian} is None}. 

 

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

to 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}} or other B{C{Cartesian_and_kwds}}. 

''' 

kwds = _xkwds(Cartesian_and_kwds, Cartesian=Cartesian, datum=self.datum) 

return LatLonEllipsoidalBase.toCartesian(self, **kwds) 

 

def toNvector(self, **Nvector_and_kwds): # PYCHOK signature 

'''Convert this point to L{Nvector} components, I{including height}. 

 

@kwarg Nvector_and_kwds: Optional L{Nvector}, B{C{datum}} and other 

keyword arguments. Use C{B{Nvector}=...} 

to override this L{Nvector} class or specify 

C{B{Nvector} is None}. 

 

@return: The C{n-vector} components (L{Nvector}) or if B{C{Nvector}} 

is set to C{None}, a L{Vector4Tuple}C{(x, y, z, h)}. 

 

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

 

@example: 

 

>>> p = LatLon(45, 45) 

>>> n = p.toNvector() 

>>> n.toStr() # [0.50, 0.50, 0.70710] 

''' 

kwds = _xkwds(Nvector_and_kwds, Nvector=Nvector, datum=self.datum) 

return LatLonNvectorBase.toNvector(self, **kwds) 

 

 

class Ned(_Ned): 

'''DEPRECATED, use L{pygeodesy.Ned}.''' 

 

def __init__(self, north, east, down, name=NN): 

deprecated_class(self.__class__) 

_Ned.__init__(self, north, east, down, name=name) 

 

@deprecated_method # PYCHOK expected 

def toRepr(self, prec=None, fmt=Fmt.SQUARE, sep=_COMMASPACE_, **unused): 

'''DEPRECATED, use L{ltpTuples.Aer}. 

 

Return a string representation of this NED vector as 

length, bearing and elevation. 

 

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

@kwarg fmt: Optional enclosing backets format (C{str}). 

@kwarg sep: Optional separator between NEDs (C{str}). 

 

@return: This Ned as "[L:f, B:degrees360, E:degrees90]" (C{str}). 

''' 

from pygeodesy.dms import F_D, toDMS 

t = (fstr(self.slantrange, prec=3 if prec is None else prec), 

toDMS(self.azimuth, form=F_D, prec=prec, ddd=0), 

toDMS(self.elevation, form=F_D, prec=prec, ddd=0)) 

return _xzipairs('LBE', t, sep=sep, fmt=fmt) 

 

 

class Ned3Tuple(_NamedTuple): # @see: .ltpTuples 

'''3-Tuple C{(north, east, down)}. DEPRECATED, use L{pygeodesy.Ned4Tuple}. 

''' 

_Names_ = (_north_, _east_, _down_) 

_Units_ = ( Meter, Meter, Meter) 

 

def __new__(cls, north, east, down, name=NN): 

deprecated_class(cls) 

return _NamedTuple.__new__(cls, north, east, down, name=name) 

 

 

_Nvll = LatLon(0, 0, name=_Nv00_) # reference instance (L{LatLon}) 

 

 

class Nvector(NvectorBase): 

'''An n-vector is a position representation using a (unit) vector 

normal to the earth ellipsoid. Unlike lat-/longitude points, 

n-vectors have no singularities or discontinuities. 

 

For many applications, n-vectors are more convenient to work 

with than other position representations like lat-/longitude, 

earth-centred earth-fixed (ECEF) vectors, UTM coordinates, etc. 

 

Note commonality with L{sphericalNvector.Nvector}. 

''' 

_datum = _WGS84 # default datum (L{Datum}) 

 

def __init__(self, x_xyz, y=None, z=None, h=0, datum=None, ll=None, name=NN): 

'''New n-vector normal to the earth's surface. 

 

@arg x_xyz: X component of vector (C{scalar}) or (3-D) vector 

(C{Nvector}, L{Vector3d}, L{Vector3Tuple} or 

L{Vector4Tuple}). 

@kwarg y: Y component of vector (C{scalar}), ignored if B{C{x_xyz}} 

is not C{scalar}, otherwise same units as B{C{x_xyz}}. 

@kwarg z: Z component of vector (C{scalar}), ignored if B{C{x_xyz}} 

is not C{scalar}, otherwise same units as B{C{x_xyz}}. 

@kwarg h: Optional height above model surface (C{meter}). 

@kwarg datum: Optional datum this n-vector is defined in 

(L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or 

L{a_f2Tuple}). 

@kwarg ll: Optional, original latlon (C{LatLon}). 

@kwarg name: Optional name (C{str}). 

 

@raise TypeError: If B{C{datum}} is not a L{Datum}. 

 

@example: 

 

>>> from ellipsoidalNvector import Nvector 

>>> v = Nvector(0.5, 0.5, 0.7071, 1) 

>>> v.toLatLon() # 45.0°N, 045.0°E, +1.00m 

''' 

NvectorBase.__init__(self, x_xyz, y=y, z=z, h=h, ll=ll, name=name) 

if datum not in (None, self._datum): 

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

 

@Property_RO 

def datum(self): 

'''Get this n-vector's datum (L{Datum}). 

''' 

return self._datum 

 

def toCartesian(self, **Cartesian_and_kwds): # PYCHOK Cartesian=Cartesian 

'''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates. 

 

@kwarg Cartesian_and_kwds: Optional L{Cartesian}, B{C{h}}, B{C{datum}} and 

other keyword arguments. Use C{B{Cartesian}=...} 

to override this L{Cartesian} class or specify 

C{B{Cartesian} is None}. 

 

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

to 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_and_kwds}}. 

 

@example: 

 

>>> v = Nvector(0.5, 0.5, 0.7071) 

>>> c = v.toCartesian() # [3194434, 3194434, 4487327] 

>>> p = c.toLatLon() # 45.0°N, 45.0°E 

''' 

kwds = _xkwds(Cartesian_and_kwds, h=self.h, Cartesian=Cartesian, 

datum=self.datum) 

return NvectorBase.toCartesian(self, **kwds) # class or .classof 

 

def toLatLon(self, **LatLon_and_kwds): # PYCHOK height=None, LatLon=LatLon 

'''Convert this n-vector to an C{Nvector}-based geodetic point. 

 

@kwarg LatLon_and_kwds: Optional L{LatLon}, B{C{height}}, B{C{datum}} 

and other keyword arguments. Use C{B{LatLon}=...} 

to override this L{LatLon} class or specify 

C{B{LatLon} is None}. 

 

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

to 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_and_kwds}}. 

 

@example: 

 

>>> v = Nvector(0.5, 0.5, 0.7071) 

>>> p = v.toLatLon() # 45.0°N, 45.0°E 

''' 

kwds = _xkwds(LatLon_and_kwds, height=self.h, datum=self.datum, LatLon=LatLon) 

return NvectorBase.toLatLon(self, **kwds) # class or .classof 

 

def unit(self, ll=None): 

'''Normalize this vector to unit length. 

 

@kwarg ll: Optional, original latlon (C{LatLon}). 

 

@return: Normalised vector (L{Nvector}). 

''' 

u = NvectorBase.unit(self, ll=ll) 

if u.datum != self.datum: 

u._overwrite(datum=self.datum) 

return u 

 

 

def meanOf(points, datum=_WGS84, height=None, LatLon=LatLon, 

**LatLon_kwds): 

'''Compute the geographic mean of several points. 

 

@arg points: Points to be averaged (L{LatLon}[]). 

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

@kwarg height: Optional height at mean point, overriding 

the mean height (C{meter}). 

@kwarg LatLon: Optional class to return the mean point 

(L{LatLon}) or C{None}. 

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

keyword arguments, ignored if 

C{B{LatLon} is None}. 

 

@return: Geographic mean point and mean height (B{C{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 ValueError: Insufficient number of B{C{points}}. 

''' 

Ps = _Nvll.PointsIter(points) 

# geographic mean 

m = sumOf(p._N_vector for p in Ps.iterate(closed=False)) 

kwds = _xkwds(LatLon_kwds, height=height, datum=datum, 

LatLon=LatLon, name=meanOf.__name__) 

return m.toLatLon(**kwds) 

 

 

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

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

'''Iteratively locate the closest point on the geodesic between 

two other (ellipsoidal) 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}, 

conventionally) or C{None} or C{False} for the 

interpolated height. If C{False}, the closest 

takes the heights of the points into account. 

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

@kwarg equidistant: An azimuthal equidistant projection (I{class} 

or function L{pygeodesy.equidistant}) or C{None} 

for the preferred C{B{point}.Equidistant}. 

@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} is None}. 

 

@return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon} 

is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}. 

 

@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}}. 

 

@raise ValueError: No convergence for the B{C{tol}}. 

 

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

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

<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME 

BOUNDARIES} for more details about the iteration algorithm. 

''' 

return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap, 

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

 

 

def sumOf(nvectors, Vector=Nvector, h=None, **Vector_kwds): 

'''Return the vectorial sum of two or more n-vectors. 

 

@arg nvectors: Vectors to be added (L{Nvector}[]). 

@kwarg Vector: Optional class for the vectorial sum (L{Nvector}). 

@kwarg h: Optional height, overriding the mean height (C{meter}). 

@kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword 

arguments, ignored if C{B{Vector} is None}. 

 

@return: Vectorial sum (B{C{Vector}}). 

 

@raise VectorError: No B{C{nvectors}}. 

''' 

return _sumOf(nvectors, Vector=Vector, h=h, **Vector_kwds) 

 

 

@deprecated_function 

def toNed(distance, bearing, elevation, Ned=Ned, name=NN): 

'''DEPRECATED, use L{pygeodesy.Aer}C{(bearing, elevation, 

distance).xyzLocal.toNed(B{Ned}, name=B{name})} or 

L{XyzLocal}C{(pygeodesy.Aer(bearing, elevation, 

distance)).toNed(B{Ned}, name=B{name})}. 

 

Create an NED vector from distance, bearing and elevation 

(in local coordinate system). 

 

@arg distance: NED vector length (C{meter}). 

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

@arg elevation: NED vector elevation from local coordinate 

frame horizontal (C{degrees}). 

@kwarg Ned: Optional class to return the NED (C{Ned}) or 

C{None}. 

@kwarg name: Optional name (C{str}). 

 

@return: An NED vector equivalent to this B{C{distance}}, 

B{C{bearing}} and B{C{elevation}} (DEPRECATED L{Ned}) 

or a DEPRECATED L{Ned3Tuple}C{(north, east, down)} 

if C{B{Ned} is None}. 

 

@raise ValueError: Invalid B{C{distance}}, B{C{bearing}} 

or B{C{elevation}}. 

 

@JSname: I{fromDistanceBearingElevation}. 

''' 

if True: # use new Aer class 

n, e, d, _ = _Aer(bearing, elevation, distance).xyz4 

else: # DEPRECATED 

d = Distance(distance) 

 

sb, cb, se, ce = sincos2d_(Bearing(bearing), 

Height(elevation=elevation)) 

n = cb * d * ce 

e = sb * d * ce 

d *= se 

 

r = Ned3Tuple(n, e, -d) if Ned is None else \ 

Ned(n, e, -d) 

return _xnamed(r, name) 

 

 

__all__ += _ALL_OTHER(Cartesian, LatLon, Ned, Nvector, # classes 

meanOf, sumOf, toNed) 

 

# **) MIT License 

# 

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

# 

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

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

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

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

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

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

# 

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

# in all copies or substantial portions of the Software. 

# 

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

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

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

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

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

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

# OTHER DEALINGS IN THE SOFTWARE.