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

 

# -*- coding: utf-8 -*- 

 

u'''(INTERNAL) Base classes for elliposiodal, spherical and N-/vectorial 

C{Cartesian}s. 

 

After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, 

see U{https://www.Movable-Type.co.UK/scripts/latlong.html}, 

U{https://www.Movable-Type.co.UK/scripts/latlong-vectors.html} and 

U{https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html}.. 

''' 

 

from pygeodesy.basics import isnear0, _xinstanceof 

from pygeodesy.datums import Datum, _spherical_datum, _WGS84 

from pygeodesy.errors import _datum_datum, _IsnotError, _ValueError, _xkwds 

from pygeodesy.fmath import cbrt, Fmt, fsum_, hypot_, hypot2 # hypot 

from pygeodesy.interns import EPS0, NN, _COMMASPACE_, _height_, _not_, \ 

_1_0, _N_1_0, _2_0, _4_0, _6_0 

from pygeodesy.interns import _ellipsoidal_, _spherical_ # PYCHOK used! 

from pygeodesy.lazily import _ALL_DOCS 

# from pygeodesy.named import _xnamed # from .vector3d 

from pygeodesy.namedTuples import Height, LatLon4Tuple, Vector4Tuple 

from pygeodesy.props import deprecated_method, Property, \ 

Property_RO, property_doc_ 

# from pygeodesy.streprs import Fmt # from .fmath 

# from pygeodesy.units import Height # from .namedTuples 

from pygeodesy.vector3d import Vector3d, _xnamed, _xyzhdn6 

 

from math import sqrt 

 

__all__ = () 

__version__ = '21.10.27' 

 

 

class CartesianBase(Vector3d): 

'''(INTERNAL) Base class for ellipsoidal and spherical C{Cartesian}. 

''' 

_datum = None # L{Datum}, to be overriden 

_height = None # height (L{Height}), set or approximated 

 

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

'''New C{Cartesian...}. 

 

@arg x_xyz: Cartesian X coordinate (C{scalar}) or a C{Cartesian}, 

L{Ecef9Tuple}, L{Vector3Tuple} or L{Vector4Tuple}. 

@kwarg y: Cartesian Y coordinate (C{scalar}), ignored if B{C{x_xyz}} 

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

@kwarg z: Cartesian Z coordinate (C{scalar}), ignored if B{C{x_xyz}} 

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

@kwarg datum: Optional datum (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: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}} 

coordinate or B{C{x_xyz}} not an L{Ecef9Tuple}, 

L{Vector3Tuple} or L{Vector4Tuple}. 

''' 

x, y, z, h, d, n = _xyzhdn6(x_xyz, y, z, None, datum, ll) 

Vector3d.__init__(self, x, y, z, ll=ll, name=name or n) 

if h is not None: 

self._height = Height(h) 

if d is not None: 

self.datum = d 

 

def _applyHelmert(self, transform, inverse=False, datum=None): 

'''(INTERNAL) Return a new cartesian by applying a Helmert 

transform to this cartesian. 

 

@arg transform: Transform to apply (L{Transform}). 

@kwarg inverse: Apply the inverse of the Helmert 

transform (C{bool}). 

@kwarg datum: Datum for the transformed point (L{Datum}), 

overriding this point's datum. 

 

@return: The transformed point (C{Cartesian}). 

 

@raise Valuerror: If C{B{inverse}=True} and B{C{datum}} 

is not L{Datums}C{.WGS84}. 

''' 

d = datum or self.datum 

if inverse and d != _WGS84: 

raise _ValueError(inverse=inverse, datum=d, 

txt=_not_(_WGS84.name)) 

 

xyz = transform.transform(*self.xyz, inverse=inverse) 

return self.classof(xyz, datum=d) 

 

def cassini(self, pointB, pointC, alpha, beta, useZ=False): 

'''3-Point resection between this and 2 other points using U{Cassini 

<https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>}'s method. 

 

@arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to 

B{C{pointC}} (C{degrees}, non-negative). 

@arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to 

B{C{pointC}} (C{degrees}, non-negative). 

@kwarg useZ: If C{True}, use and interpolate the Z component, otherwise 

force C{z=0} (C{bool}). 

 

@note: Typically, B{C{pointC}} is between this and B{C{pointB}}. 

 

@return: The survey point, an instance of this (sub-)class. 

 

@raise ResectionError: Near-coincident, -colinear or -concyclic points 

or negative or invalid B{C{alpha}} or B{C{beta}}. 

 

@raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointM}}. 

 

@see: U{Three Point Resection Problem<https://Dokumen.tips/documents/ 

three-point-resection-problem-introduction-kaestner-burkhardt-method.html>} 

and function L{pygeodesy.cassini}. 

''' 

from pygeodesy.resections import cassini 

return cassini(self, pointB, pointC, alpha, beta, useZ=useZ, datum=self.datum) 

 

def collins(self, pointB, pointC, alpha, beta, useZ=False): 

'''3-Point resection between this and 2 other points using U{Collins<https://Dokumen.tips/ 

documents/three-point-resection-problem-introduction-kaestner-burkhardt-method.html>}' method. 

 

@arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to 

B{C{pointC}} (C{degrees}, non-negative). 

@arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to 

B{C{pointC}} (C{degrees}, non-negative). 

@kwarg useZ: If C{True}, use and interpolate the Z component, otherwise 

force C{z=0} (C{bool}). 

 

@note: Typically, B{C{pointC}} is between this and B{C{pointB}}. 

 

@return: L{Collins5Tuple}C{(pointP, pointH, a, b, c)} with survey C{pointP}, 

auxiliary C{pointH}, each an instance of this (sub-)class and 

triangle sides C{a}, C{b} and C{c}. 

 

@raise ResectionError: Near-coincident, -colinear or -concyclic points 

or negative or invalid B{C{alpha}} or B{C{beta}}. 

 

@raise TypeError: Invalid B{C{pointB}} or B{C{pointM}}. 

 

@see: U{Collins' methode<https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>} 

and function L{pygeodesy.collins}. 

''' 

from pygeodesy.resections import collins 

return collins(self, pointB, pointC, alpha, beta, useZ=useZ, datum=self.datum) 

 

@property_doc_(''' this cartesian's datum (L{Datum}).''') 

def datum(self): 

'''Get this cartesian's datum (L{Datum}). 

''' 

return self._datum 

 

@datum.setter # PYCHOK setter! 

def datum(self, datum): 

'''Set this cartesian's C{datum} I{without conversion}. 

 

@arg datum: New datum (L{Datum}), ellipsoidal or spherical. 

 

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

''' 

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

d = self.datum 

if d is not None: 

if d.isEllipsoidal and not datum.isEllipsoidal: 

raise _IsnotError(_ellipsoidal_, datum=datum) 

elif d.isSpherical and not datum.isSpherical: 

raise _IsnotError(_spherical_, datum=datum) 

self._update(datum != d) 

self._datum = datum 

 

def destinationXyz(self, delta, Cartesian=None, **Cartesian_kwds): 

'''Calculate the destination using a I{local} delta from this cartesian. 

 

@arg delta: Local delta to the destination (L{XyzLocal}, L{Enu}, 

L{Ned} or L{Local9Tuple}). 

@kwarg Cartesian: Optional (geocentric) class to return the 

destination or C{None}. 

@kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword 

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

 

@return: Destination as a C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} 

instance or if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y, 

z, lat, lon, height, C, M, datum)} with C{M=None} always. 

 

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

B{C{Cartesian_kwds}}. 

''' 

if Cartesian is None: 

r = self._ltp._local2ecef(delta, nine=True) 

else: 

r = self._ltp._local2ecef(delta, nine=False) 

r = Cartesian(*r, **_xkwds(Cartesian_kwds, datum=self.datum)) 

return _xnamed(r, self.name) 

 

@Property_RO 

def Ecef(self): 

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

''' 

from pygeodesy.ecef import EcefKarney 

return EcefKarney # default 

 

@Property_RO 

def _ecef9(self): 

'''(INTERNAL) Helper for L{toEcef}, L{toLocal} and L{toLtp} (L{Ecef9Tuple}). 

''' 

return self.Ecef(self.datum, name=self.name).reverse(self, M=True) 

 

def hartzell(self, los=None): 

'''Compute the intersection of a Line-Of-Sight from this certesian 

Point-Of-View (pov) with this C{datum}'s ellipsoid surface. 

 

@kwarg los: Line-Of-Sight, I{direction} to earth (L{Vector3d}) or 

C{None} to point to the ellipsoid's center. 

 

@return: The ellipsoid intersection (C{Cartesian}). 

 

@raise IntersectionError: Null C{pov} or B{C{los}} vector, 

this C{pov} is inside the ellipsoid or 

B{C{los}} points outside the ellipsoid 

or in an opposite direction. 

 

@raise TypeError: Invalid B{C{los}} or no B{C{datum}}. 

 

@see: Function C{hartzell} for further details. 

''' 

from pygeodesy.formy import hartzell 

return hartzell(self, los=los, earth=self.datum) 

 

@Property 

def height(self): 

'''Get the height (C{meter}). 

''' 

return self._height4.h if self._height is None else self._height 

 

@height.setter # PYCHOK setter! 

def height(self, height): 

'''Set the height. 

 

@arg height: New height (C{meter}). 

 

@raise TypeError: Invalid B{C{height}} C{type}. 

 

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

''' 

h = Height(height) 

self._update(h != self.height) 

self._height = h 

 

@Property_RO 

def _height4(self): 

'''(INTERNAL) Get this C{height4}-tuple. 

''' 

try: 

r = self.datum.ellipsoid.height4(self, normal=True) 

except (AttributeError, ValueError): # no datum, null cartesian, 

r = Vector4Tuple(self.x, self.y, self.z, 0, name=self.height4.__name__) 

return r 

 

def height4(self, earth=None, normal=True, Cartesian=None, **Cartesian_kwds): 

'''Compute the height of this cartesian above or below and the projection 

on this datum's ellipsoid surface. 

 

@kwarg earth: A datum, ellipsoid or earth radius I{overriding} this 

datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} 

or C{meter}, conventionally). 

@kwarg normal: If C{True} the projection is the nearest point on the 

ellipsoid's surface, otherwise the intersection of the 

radial line to the center and the ellipsoid's surface. 

@kwarg Cartesian: Optional class to return the height and projection 

(C{Cartesian}) or C{None}. 

@kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword 

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

 

@note: Use keyword argument C{height=0} to override C{B{Cartesian}.height} 

to {0} or any other C{scalar}, conventionally in C{meter}. 

 

@return: An instance of B{C{Cartesian}} or if C{B{Cartesian} is None}, a 

L{Vector4Tuple}C{(x, y, z, h)} with the I{projection} C{x}, C{y} 

and C{z} coordinates and height C{h} in C{meter}, conventionally. 

 

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

 

@see: L{Ellipsoid.height4} for more information. 

''' 

r = self._height4 if normal and earth in (None, self.datum) else \ 

_spherical_datum(earth).ellipsoid.height4(self, normal=normal) 

if Cartesian is not None: 

kwds = Cartesian_kwds.copy() 

h = kwds.pop(_height_, None) 

r = Cartesian(r, **kwds) 

if h is not None: 

r.height = Height(height=h) 

return r 

 

@Property_RO 

def isEllipsoidal(self): 

'''Check whether this cartesian is ellipsoidal (C{bool} or C{None} if unknown). 

''' 

return self.datum.isEllipsoidal if self._datum else None 

 

@Property_RO 

def isSpherical(self): 

'''Check whether this cartesian is spherical (C{bool} or C{None} if unknown). 

''' 

return self.datum.isSpherical if self._datum else None 

 

@Property_RO 

def latlon(self): 

'''Get this cartesian's (geodetic) lat- and longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). 

''' 

return self.toEcef().latlon 

 

@Property_RO 

def latlonheight(self): 

'''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height (L{LatLon3Tuple}C{(lat, lon, height)}). 

''' 

return self.toEcef().latlonheight 

 

@Property_RO 

def latlonheightdatum(self): 

'''Get this cartesian's (geodetic) lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}). 

''' 

return self.toEcef().latlonheightdatum 

 

@Property_RO 

def _ltp(self): 

'''(INTERNAL) Cache for L{toLtp}. 

''' 

from pygeodesy.ltp import Ltp 

return Ltp(self._ecef9, ecef=self.Ecef(self.datum), name=self.name) 

 

@Property_RO 

def _N_vector(self): 

'''(INTERNAL) Get the (C{nvectorBase._N_vector_}). 

''' 

from pygeodesy.nvectorBase import _N_vector_ 

x, y, z, h = self._n_xyzh4(self.datum) 

return _N_vector_(x, y, z, h=h, name=self.name) 

 

def _n_xyzh4(self, datum): 

'''(INTERNAL) Get the n-vector components as L{Vector4Tuple}. 

''' 

_xinstanceof(Datum, datum=datum) 

# <https://www.Movable-Type.co.UK/scripts/geodesy/docs/ 

# latlon-nvector-ellipsoidal.js.html#line309>, 

# <https://GitHub.com/pbrod/nvector>/src/nvector/core.py> 

# _equation23 and <https://www.NavLab.net/nvector> 

E = datum.ellipsoid 

x, y, z = self.xyz 

 

# Kenneth Gade eqn 23 

p = hypot2(x, y) * E.a2_ 

q = (z**2 * E.e12) * E.a2_ 

r = fsum_(p, q, -E.e4) / _6_0 

s = (p * q * E.e4) / (_4_0 * r**3) 

t = cbrt(fsum_(_1_0, s, sqrt(s * (_2_0 + s)))) 

if isnear0(t): 

raise _ValueError(origin=self, txt=Fmt.EPS0(t)) 

 

u = r * fsum_(_1_0, t, _1_0 / t) 

v = sqrt(u**2 + E.e4 * q) 

t = v * _2_0 

if t < EPS0: # isnear0 

raise _ValueError(origin=self, txt=Fmt.EPS0(t)) 

w = E.e2 * fsum_(u, v, -q) / t 

 

k = sqrt(fsum_(u, v, w**2)) - w 

if isnear0(k): 

raise _ValueError(origin=self, txt=Fmt.EPS0(k)) 

t = k + E.e2 

if isnear0(t): 

raise _ValueError(origin=self, txt=Fmt.EPS0(t)) 

e = k / t 

# d = e * hypot(x, y) 

 

# tmp = 1 / hypot(d, z) == 1 / hypot(e * hypot(x, y), z) 

t = hypot_(x * e, y * e, z) # == 1 / tmp 

if t < EPS0: # isnear0 

raise _ValueError(origin=self, txt=Fmt.EPS0(t)) 

h = fsum_(k, E.e2, _N_1_0) / k * t 

s = e / t # == e * tmp 

return Vector4Tuple(x * s, y * s, z / t, h, name=self.name) 

 

@Property_RO 

def philam(self): 

'''Get this cartesian's (geodetic) lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}). 

''' 

return self.toEcef().philam 

 

@Property_RO 

def philamheight(self): 

'''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height (L{PhiLam3Tuple}C{(phi, lam, height)}). 

''' 

return self.toEcef().philamheight 

 

@Property_RO 

def philamheightdatum(self): 

'''Get this cartesian's (geodetic) lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}). 

''' 

return self.toEcef().philamheightdatum 

 

def pierlot(self, point2, point3, alpha12, alpha23, useZ=False): 

'''3-Point resection between this and two other points using U{Pierlot 

<http://www.Telecom.ULg.ac.BE/triangulation>}'s method C{ToTal}. 

 

@arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, 

C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). 

@arg alpha12: Angle subtended from this point to B{C{point2}} (C{degrees}). 

@arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} (C{degrees}). 

@kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=0} 

(C{bool}). 

 

@note: This point, B{C{point2}} and B{C{point3}} are ordered counter-clockwise. 

 

@return: The survey (or robot) point, an instance of this (sub-)class. 

 

@raise ResectionError: Near-coincident, -colinear or -concyclic points 

or invalid B{C{alpha12}} or B{C{alpha23}}. 

 

@raise TypeError: Invalid B{C{point2}} or B{C{point3}}. 

 

@see: U{V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation 

Algorithm for Mobile Robot Positioning"<https://ORBi.ULiege.BE/ 

bitstream/2268/157469/1/Pierlot2014ANewThree.pdf>}, U{18 Triangulation 

Algorithms for 2D Positioning (also known as the Resection Problem) 

<http://Telecom.ULg.ac.BE/triangulation>} and functions 

L{pygeodesy.pierlot}. 

''' 

from pygeodesy.resections import pierlot 

return pierlot(self, point2, point3, alpha12, alpha23, useZ=useZ, datum=self.datum) 

 

def tienstra(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False): 

'''3-Point resection between this and two other points using U{Tienstra 

<https://WikiPedia.org/wiki/Tienstra_formula>}'s formula. 

 

@arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or 

C{Vector2Tuple} if C{B{useZ}=False}). 

@arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or 

C{Vector2Tuple} if C{B{useZ}=False}). 

@arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees}, 

non-negative). 

@kwarg beta: Angle subtended by triangle side C{b} from this to B{C{pointC}} (C{degrees}, 

non-negative) or C{None} if C{B{gamma} is not None}. 

@kwarg gamma: Angle subtended by triangle side C{c} from this to B{C{pointB}} (C{degrees}, 

non-negative) or C{None} if C{B{beta} is not None}. 

@kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=0} 

(C{bool}). 

 

@note: This point, B{C{pointB}} and B{C{pointC}} are ordered clockwise. 

 

@return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP}, 

an instance of this (sub-)class and triangle angle C{A} at this point, 

C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and 

triangle sides C{a}, C{b} and C{c}. 

 

@raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of 

B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or 

negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}. 

 

@raise TypeError: Invalid B{C{pointB}} or B{C{pointC}}. 

 

@see: U{3-Point Resection Solver<http://MesaMike.org/geocache/GC1B0Q9/tienstra/>}, 

U{V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation..." 

<http://Telecom.ULG.ac.BE/publi/publications/pierlot/Pierlot2014ANewThree/>}, 

U{18 Triangulation Algorithms...<http://Telecom.ULG.ac.BE/triangulation/>} and 

function L{pygeodesy.tienstra}. 

''' 

from pygeodesy.resections import tienstra 

return tienstra(self, pointB, pointC, alpha, beta, gamma, useZ=useZ, datum=self.datum) 

 

@deprecated_method 

def to3llh(self, datum=None): # PYCHOK no cover 

'''DEPRECATED, use property L{latlonheightdatum} or L{latlonheight}. 

 

@return: A L{LatLon4Tuple}C{(lat, lon, height, datum)}. 

 

@note: This method returns a B{C{-4Tuple}} I{and not a} C{-3Tuple} 

as its name may suggest. 

''' 

t = self.toLatLon(datum=datum, LatLon=None) 

return LatLon4Tuple(t.lat, t.lon, t.height, t.datum, name=self.name) 

 

# def _to3LLh(self, datum, LL, **pairs): # OBSOLETE 

# '''(INTERNAL) Helper for C{subclass.toLatLon} and C{.to3llh}. 

# ''' 

# r = self.to3llh(datum) # LatLon3Tuple 

# if LL is not None: 

# r = LL(r.lat, r.lon, height=r.height, datum=datum, name=self.name) 

# for n, v in pairs.items(): 

# setattr(r, n, v) 

# return r 

 

def toDatum(self, datum2, datum=None): 

'''Convert this cartesian from one datum to an other. 

 

@arg datum2: Datum to convert I{to} (L{Datum}). 

@kwarg datum: Datum to convert I{from} (L{Datum}). 

 

@return: The converted point (C{Cartesian}). 

 

@raise TypeError: B{C{datum2}} or B{C{datum}} 

invalid. 

''' 

_xinstanceof(Datum, datum2=datum2) 

 

c = self if datum in (None, self.datum) else \ 

self.toDatum(datum) 

 

i, d = False, c.datum 

if d == datum2: 

return c.copy() if c is self else c 

 

elif d == _WGS84: 

d = datum2 # convert from WGS84 to datum2 

 

elif datum2 == _WGS84: 

i = True # convert to WGS84 by inverse transformation 

 

else: # neither datum2 nor c.datum is WGS84, invert to WGS84 first 

c = c._applyHelmert(d.transform, inverse=True, datum=_WGS84) 

d = datum2 

 

return c._applyHelmert(d.transform, inverse=i, datum=datum2) 

 

convertDatum = toDatum # for backward compatibility 

 

def toEcef(self): 

'''Convert this cartesian to I{geodetic} (lat-/longitude) coordinates. 

 

@return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, 

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

 

@raise EcefError: A C{.datum} or an ECEF issue. 

''' 

return self._ecef9 

 

def toLatLon(self, datum=None, height=None, LatLon=None, **LatLon_kwds): # see .ecef.Ecef9Tuple.toDatum 

'''Convert this cartesian to a geodetic (lat-/longitude) point. 

 

@kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} 

or L{a_f2Tuple}). 

@kwarg height: Optional height, overriding the converted height 

(C{meter}), iff B{C{LatLon}} is not C{None}. 

@kwarg LatLon: Optional class to return the geodetic point 

(C{LatLon}) or C{None}. 

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

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

 

@return: The geodetic point (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 TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}. 

''' 

d = _spherical_datum(datum or self.datum, name=self.name) 

if d == self.datum: 

r = self.toEcef() 

else: 

c = self.toDatum(d) 

r = c.Ecef(d, name=self.name).reverse(c, M=LatLon is None) 

 

if LatLon: # class or .classof 

h = r.height if height is None else Height(height) 

r = LatLon(r.lat, r.lon, datum=r.datum, height=h, 

**_xkwds(LatLon_kwds, name=r.name)) 

_datum_datum(r.datum, d) 

return r 

 

def toLocal(self, Xyz=None, ltp=None, **Xyz_kwds): 

'''Convert this I{geocentric} cartesian to I{local} C{X}, C{Y} and C{Z}. 

 

@kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} 

(L{XyzLocal}, L{Enu}, L{Ned}) or C{None}. 

@kwarg ltp: The I{local tangent plane} (LTP) to use, 

overriding this cartesian's LTP (L{Ltp}). 

@kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword 

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

 

@return: An B{C{Xyz}} instance or if C{B{Xyz} is None}, 

a L{Local9Tuple}C{(x, y, z, lat, lon, height, 

ltp, ecef, M)} with C{M=None} always. 

 

@raise TypeError: Invalid B{C{ltp}}. 

''' 

p = self._ltp if ltp is None else self._xLtp(ltp) 

return p._ecef2local(self._ecef9, Xyz, Xyz_kwds) 

 

def toLtp(self, Ecef=None): 

'''Return the I{local tangent plane} (LTP) for this cartesian. 

 

@kwarg Ecef: Optional ECEF I{class} (L{EcefKarney}, ... 

L{EcefYou}), overriding this cartesian's C{Ecef}. 

''' 

if Ecef in (None, self.Ecef): 

r = self._ltp 

else: 

from pygeodesy.ltp import Ltp 

r = Ltp(self._ecef9, ecef=Ecef(self.datum), name=self.name) 

return r 

 

def toNvector(self, Nvector=None, datum=None, **Nvector_kwds): 

'''Convert this cartesian to C{n-vector} components. 

 

@kwarg Nvector: Optional class to return the C{n-vector} 

components (C{Nvector}) or C{None}. 

@kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} 

or L{a_f2Tuple}) overriding this cartesian's datum. 

@kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword 

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

 

@return: The C{unit, n-vector} components (B{C{Nvector}}) or a 

L{Vector4Tuple}C{(x, y, z, h)} if B{C{Nvector}} is C{None}. 

 

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

 

@raise ValueError: The B{C{Cartesian}} at origin. 

 

@example: 

 

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

>>> n = c.toNvector() # (x=0.622818, y=0.00002, z=0.782367, h=0.242887) 

''' 

d = _spherical_datum(datum or self.datum, name=self.name) 

r = self._N_vector.xyzh if d == self.datum else self._n_xyzh4(d) 

 

if Nvector is not None: 

kwds = _xkwds(Nvector_kwds, h=r.h, datum=d) 

r = self._xnamed(Nvector(r.x, r.y, r.z, **kwds)) 

return r 

 

def toStr(self, prec=3, fmt=Fmt.SQUARE, sep=_COMMASPACE_): # PYCHOK expected 

'''Return the string representation of this cartesian. 

 

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

@kwarg fmt: Optional enclosing backets format (string). 

@kwarg sep: Optional separator to join (string). 

 

@return: Cartesian represented as "[x, y, z]" (string). 

''' 

return Vector3d.toStr(self, prec=prec, fmt=fmt, sep=sep) 

 

def toVector(self, Vector=None, **Vector_kwds): 

'''Return this cartesian's components as vector. 

 

@kwarg Vector: Optional class to return the C{n-vector} 

components (L{Vector3d}) or C{None}. 

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

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

 

@return: A B{C{Vector}} or an L{Vector3Tuple}C{(x, y, z)} 

if B{C{Vector}} is C{None}. 

 

@raise TypeError: Invalid B{C{Vector}} or B{C{Vector_kwds}}. 

''' 

return self.xyz if Vector is None else self._xnamed( 

Vector(self.x, self.y, self.z, **Vector_kwds)) 

 

@Property_RO 

def _xLtp(self): 

'''(INTERNAL) Import and cache function C{ltp._xLtp}. 

''' 

from pygeodesy.ltp import _xLtp 

return _xLtp 

 

 

__all__ += _ALL_DOCS(CartesianBase) 

 

# **) 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.