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

 

# -*- coding: utf-8 -*- 

 

u'''I{Local Tangent Plane} (LTP) and I{local} cartesian coordinates. 

 

I{Local cartesian} and I{local tangent plane} classes L{LocalCartesian} and L{Ltp}, 

L{LocalError} and L{Attitude} and L{Frustum}. 

 

@see: U{Local tangent plane coordinates<https://WikiPedia.org/wiki/Local_tangent_plane_coordinates>} 

and class L{LocalCartesian}, transcoded from I{Charles Karney}'s C++ classU{LocalCartesian 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1LocalCartesian.html>}. 

''' 

 

from pygeodesy.basics import isscalar, issubclassof, map1, _umod_360 

from pygeodesy.datums import _WGS84, _xinstanceof 

from pygeodesy.ecef import _EcefBase, EcefKarney, _llhn4, _xyzn4 

from pygeodesy.errors import _TypesError, _ValueError, _xkwds 

# from pygeodesy.fmath import fdot # from .vector3d 

from pygeodesy.fsums import fsum_, fsum1_ 

from pygeodesy.interns import EPS, NN, _COMMASPACE_, _lat0_, _lon0_, _ltp_, \ 

_M_, _name_, _0_, _0_0, _0_5, _2_0, _90_0, _180_0 

from pygeodesy.interns import _ecef_, _N_1_0 # PYCHOK used! 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.ltpTuples import Attitude4Tuple, Footprint5Tuple, Local9Tuple, \ 

_NamedBase, _XyzLocals4, _XyzLocals5, Xyz4Tuple 

# from pygeodesy.named import _NamedBase # from .ltpTuples 

# from pygeodesy.namedTuples import Vector3Tuple # from .vector3d 

from pygeodesy.props import Property, property_doc_, Property_RO 

from pygeodesy.streprs import Fmt, strs 

from pygeodesy.units import Bearing, Degrees, Meter 

from pygeodesy.utily import cotd, sincos2d, sincos2d_, tand, tand_, \ 

wrap180, wrap360 

from pygeodesy.vector3d import fdot, Vector3d, Vector3Tuple 

 

__all__ = _ALL_LAZY.ltp 

__version__ = '22.04.22' 

 

_Xyz_ = 'Xyz' 

 

 

def _fov_2(**fov): 

# Half a field-of-view in degrees 

f = Degrees(**fov) * _0_5 

if EPS < f < _90_0: 

return f 

raise _ValueError(**fov) 

 

 

class Attitude(_NamedBase): 

'''The orientation of a plane or camera in space. 

''' 

_alt = Meter( alt =_0_0) 

_roll = Degrees(roll=_0_0) 

_tilt = Degrees(tilt=_0_0) 

_yaw = Bearing(yaw =_0_0) 

 

def __init__(self, alt_attitude=0, tilt=0, yaw=0, roll=0, name=NN): 

'''New L{Attitude}. 

 

@kwarg alt_attitude: An altitude (C{meter}) above earth or an attitude 

(L{Attitude} or L{Attitude4Tuple}) with the 

C{B{alt}itude}, B{C{tilt}}, B{C{yaw}} and B{C{roll}}. 

@kwarg tilt: Pitch, elevation from horizontal (C{degrees180}), negative down 

(clockwise rotation along and around the x- or East axis). 

@kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North 

(counter-clockwise rotation along and around the z- or Up axis). 

@kwarg roll: Roll, bank (C{degrees180}), positive to the right and down 

(clockwise rotation along and around the y- or North axis). 

@kwarg name: Optional name C{str}). 

 

@raise AttitudeError: Invalid B{C{alt_attitude}}, B{C{tilt}}, B{C{yaw}} or 

B{C{roll}}. 

 

@see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>} and 

U{Yaw, pitch, and roll rotations<http://Planning.CS.UIUC.edu/node102.html>}. 

''' 

if isscalar(alt_attitude): 

t = Attitude4Tuple(alt_attitude, tilt, yaw, roll) 

else: 

try: 

t = alt_attitude.atyr 

except AttributeError: 

raise AttitudeError(alt=alt_attitude, tilt=tilt, yaw=yaw, rol=roll) 

for n, v in t.items(): 

if v: 

setattr(self, n, v) 

n = name or t.name 

if n: 

self.name = n 

 

@property_doc_(' altitude above earth in C{meter}.') 

def alt(self): 

return self._alt 

 

@alt.setter # PYCHOK setter! 

def alt(self, alt): # PYCHOK no cover 

a = Meter(alt=alt, Error=AttitudeError) 

self._update(a != self.alt) 

self._alt = a 

 

altitude = alt 

 

@Property_RO 

def atyr(self): 

'''Return this attitude's alt[itude], tilt, yaw and roll as an L{Attitude4Tuple}. 

''' 

return Attitude4Tuple(self.alt, self.tilt, self.yaw, self.roll, name=self.name) 

 

@Property_RO 

def matrix(self): 

'''Get the 3x3 rotation matrix C{R(yaw)·R(tilt)·R(roll)}, aka I{ZYX} (C{float}, row-order). 

 

@see: The matrix M of case 10 in U{Appendix A 

<https://ntrs.NASA.gov/api/citations/19770019231/downloads/19770019231.pdf>}. 

''' 

def _5to3(x, y, _y, z, _z): 

return x, fsum1_(y, _y), fsum1_(z, _z) 

 

r0, r1, r2 = self._rows3 

return _5to3(*r0), _5to3(*r1), r2 

 

@property_doc_(' roll/bank in C{degrees180}, positive to the right and down.') 

def roll(self): 

return self._roll 

 

@roll.setter # PYCHOK setter! 

def roll(self, roll): 

r = Degrees(roll=roll, wrap=wrap180, Error=AttitudeError) 

self._update(r != self.roll) 

self._roll = r 

 

bank = roll 

 

@Property_RO 

def _rows3(self): 

# to follow the definitions of rotation angles alpha, beta and gamma: 

# negate yaw since yaw is counter-clockwise around the z-axis, swap 

# tilt and roll since tilt is around the x- and roll around the y-axis 

sa, ca, sb, cb, sg, cg = sincos2d_(-self.yaw, self.roll, self.tilt) 

return ((ca * cb, ca * sb * sg, -sa * cg, ca * sb * cg, sa * sg), 

(sa * cb, sa * sb * sg, ca * cg, sa * sb * cg, -ca * sg), 

( -sb, cb * sg, cb * cg)) 

 

def rotate(self, x_xyz, y=None, z=None, Vector=None, **Vector_kwds): 

'''Transform a (local) cartesian by this attitude's matrix. 

 

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

(C{Cartesian}, L{Vector3d} or L{Vector3Tuple}). 

@kwarg y: Y component of vector (C{scalar}), same units as B{C{x}}. 

@kwarg z: Z component of vector (C{scalar}), same units as B{C{x}}. 

@kwarg Vector: Class to return transformed point (C{Cartesian}, 

L{Vector3d} or C{Vector3Tuple}) 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}} instance or a L{Vector3Tuple}C{(x, y, z)} if 

C{B{Vector}=None}. 

 

@see: U{Yaw, pitch, and roll rotations<http://Planning.CS.UIUC.edu/node102.html>}. 

''' 

try: 

x, y, z = map( float, x_xyz.xyz) 

except AttributeError: 

x, y, z = map1(float, x_xyz, y, z) 

 

r0, r1, r2 = self._rows3 

X = fdot(r0, x, y, y, z, z) 

Y = fdot(r1, x, y, y, z, z) 

Z = fdot(r2, x, y, z) 

return Vector3Tuple(X, Y, Z, name=self.name) if Vector is None else \ 

Vector(X, Y, Z, **_xkwds(Vector_kwds, name=self.name)) 

 

@property_doc_(' tilt/pitch/elevation from horizontal in C{degrees180}, negative down.') 

def tilt(self): 

return self._tilt 

 

@tilt.setter # PYCHOK setter! 

def tilt(self, tilt): 

t = Degrees(tilt=tilt, wrap=wrap180, Error=AttitudeError) 

self._update(t != self.tilt) 

self._tilt = t 

 

elevation = pitch = tilt 

 

def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature 

'''Format this attitude as string. 

 

@kwarg prec: The C{float} precision, number of decimal digits (0..9). 

Trailing zero decimals are stripped for B{C{prec}} values 

of 1 and above, but kept for negative B{C{prec}} values. 

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

 

@return: This attitude (C{str}). 

''' 

return self.atyr.toStr(prec=prec, sep=sep) 

 

@Property_RO 

def tyr3d(self): 

'''Get this attitude's (3-D) directional vector (L{Vector3d}). 

 

@see: U{Yaw, pitch, and roll rotations<http://Planning.CS.UIUC.edu/node102.html>}. 

''' 

def _r2d(r): 

return fsum_(_N_1_0, *r) 

 

return Vector3d(*map1(_r2d, *self._rows3), name=tyr3d.__name__) 

 

@property_doc_(' yaw/bearing/heading in compass C{degrees360}, clockwise from North.') 

def yaw(self): 

return self._yaw 

 

@yaw.setter # PYCHOK setter! 

def yaw(self, yaw): 

y = Bearing(yaw=yaw, Error=AttitudeError) 

self._update(y == self.yaw) 

self._yaw = y 

 

bearing = heading = yaw 

 

 

class AttitudeError(_ValueError): 

'''An L{Attitude} or L{Attitude4Tuple} issue. 

''' 

pass 

 

 

class Frustum(_NamedBase): 

'''A rectangular pyramid, typically representing a camera's I{field-of-view} 

(fov) and the intersection with (or projection to) a I{local tangent plane}. 

 

@see: U{Viewing frustum<https://WikiPedia.org/wiki/Viewing_frustum>}. 

''' 

_h_2 = _0_0 # half hfov in degrees 

_ltp = None # local tangent plane 

_tan_h_2 = _0_0 # tan(_h_2) 

_v_2 = _0_0 # half vfov in degrees 

 

def __init__(self, hfov, vfov, ltp=None): 

'''New L{Frustum}. 

 

@arg hfov: Horizontal field-of-view (C{degrees180}). 

@arg vfov: Vertical field-of-view (C{degrees180}). 

@kwarg ltp: Optional I{local tangent plane} (L{Ltp}). 

 

@raise UnitError: Invalid B{C{hfov}} or B{C{vfov}}. 

 

@raise ValueError: Invalid B{C{hfov}} or B{C{vfov}}. 

''' 

self._h_2 = h = _fov_2(hfov=hfov) 

self._v_2 = _fov_2(vfov=vfov) 

 

self._tan_h_2 = tand(h, fov_2=h) 

 

if ltp: 

self._ltp = _xLtp(ltp) 

 

def footprint5(self, alt_attitude, tilt=0, yaw=0, roll=0, z=_0_0, ltp=None): # MCCABE 15 

'''Compute the center and corners of the intersection with (or projection 

to) the I{local tangent plane} (LTP). 

 

@arg alt_attitude: An altitude (C{meter}) above I{local tangent plane} or 

an attitude (L{Attitude} or L{Attitude4Tuple}) with the 

C{B{alt}itude}, B{C{tilt}}, B{C{yaw}} and B{C{roll}}. 

@kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down 

(clockwise rotation along and around the x- or East axis). 

@kwarg yaw: Bearing, heading (compass C{degrees}), clockwise from North 

(counter-clockwise rotation along and around the z- or Up axis). 

@kwarg roll: Roll, bank (C{degrees}), positive to the right and down 

(clockwise rotation along and around the y- or North axis). 

@kwarg z: Optional height of the footprint (C{meter}) above I{local tangent plane}. 

@kwarg ltp: The I{local tangent plane} (L{Ltp}), overriding this 

frustum's C{ltp}. 

 

@return: A L{Footprint5Tuple}C{(center, upperleft, upperight, loweright, 

lowerleft)} with the C{center} and 4 corners each an L{Xyz4Tuple}. 

 

@raise TypeError: Invalid B{C{ltp}}. 

 

@raise UnitError: Invalid B{C{altitude}}, B{C{tilt}}, B{C{roll}} or B{C{z}}. 

 

@raise ValueError: If B{C{altitude}} too low, B{C{z}} too high or B{C{tilt}} 

or B{C{roll}} -including B{C{vfov}} respectively B{C{hfov}}- 

over the horizon. 

 

@see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>}. 

''' 

def _xy2(a, e, h_2, tan_h_2, r): 

# left and right corners, or swapped 

if r < EPS: # no roll 

r = a * tan_h_2 

l = -r # PYCHOK l is ell 

else: # roll 

r, l = tand_(r - h_2, r + h_2, roll_hfov=r) # PYCHOK l is ell 

r *= -a # negate right positive 

l *= -a # PYCHOK l is ell 

y = a * cotd(e, tilt_vfov=e) 

return (l, y), (r, y) 

 

def _xyz5(b, xy5, z, ltp): 

# rotate (x, y)'s by bearing, clockwise 

s, c = sincos2d(b) 

for x, y in xy5: 

yield Xyz4Tuple(fsum1_(x * c, y * s), 

fsum1_(y * c, -x * s), z, ltp) 

 

try: 

a, t, y, r = alt_attitude.atyr 

except AttributeError: 

a, t, y, r = alt_attitude, tilt, yaw, roll 

 

a = Meter(altitude=a) 

if a < EPS: # too low 

raise _ValueError(altitude=a) 

if z: # PYCHOK no cover 

z = Meter(z=z) 

a -= z 

if a < EPS: # z above a 

raise _ValueError(altitude_z=a) 

else: 

z = _0_0 

 

b = Degrees(yaw=y, wrap=wrap360) # bearing 

e = -Degrees(tilt=t, wrap=wrap180) # elevation, pitch 

if not EPS < e < _180_0: 

raise _ValueError(tilt=t) 

if e > _90_0: 

e = _180_0 - e 

b = _umod_360(b + _180_0) 

 

r = Degrees(roll=r, wrap=wrap180) # roll center 

x = (-a * tand(r, roll=r)) if r else _0_0 

y = a * cotd(e, tilt=t) # ground range 

if abs(y) < EPS: 

y = _0_0 

 

# center and corners, clockwise from upperleft, rolled 

xy5 = ((x, y),) + _xy2(a, e - self._v_2, self._h_2, self._tan_h_2, r) \ 

+ _xy2(a, e + self._v_2, -self._h_2, -self._tan_h_2, r) # swapped 

# turn center and corners by yaw, clockwise 

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

return Footprint5Tuple(_xyz5(b, xy5, z, p)) # *_xyz5 

 

@Property_RO 

def hfov(self): 

'''Get the horizontal C{fov} (C{degrees}). 

''' 

return Degrees(hfov=self._h_2 * _2_0) 

 

@Property_RO 

def ltp(self): 

'''Get the I{local tangent plane} (L{Ltp}) or C{None}. 

''' 

return self._ltp 

 

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

'''Convert this frustum to a "hfov, vfov, ltp" string. 

 

@kwarg prec: Number of (decimal) digits, unstripped (0..8 or C{None}). 

@kwarg fmt: Optional, C{float} format (C{str}). 

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

 

@return: Frustum in the specified form (C{str}). 

''' 

t = self.hfov, self.vfov 

if self.ltp: 

t += self.ltp, 

t = strs(t, prec=prec, fmt=fmt) 

return sep.join(t) if sep else t 

 

@Property_RO 

def vfov(self): 

'''Get the vertical C{fov} (C{degrees}). 

''' 

return Degrees(vfov=self._v_2 * _2_0) 

 

 

class LocalError(_ValueError): 

'''A L{LocalCartesian} or L{Ltp} related issue. 

''' 

pass 

 

 

class LocalCartesian(_NamedBase): 

'''Conversion between geodetic C{(lat, lon, height)} and I{local cartesian} 

C{(x, y, z)} coordinates with I{geodetic} origin C{(lat0, lon0, height0)}, 

transcoded from I{Karney}'s C++ class U{LocalCartesian 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1LocalCartesian.html>}. 

 

The C{z} axis is normal to the ellipsoid, the C{y} axis points due 

North. The plane C{z = -height0} is tangent to the ellipsoid. 

 

The conversions all take place via geocentric coordinates using a 

geocentric L{EcefKarney}, by default the WGS84 datum/ellipsoid. 

 

@see: Class L{Ltp}. 

''' 

_ecef = EcefKarney(_WGS84) 

_t0 = None # origin (..., lat0, lon0, height0, ...) L{Ecef9Tuple} 

 

def __init__(self, latlonh0=0, lon0=0, height0=0, ecef=None, name=NN): 

'''New L{LocalCartesian} converter. 

 

@kwarg latlonh0: Either a C{LatLon}, L{Ltp}, L{Ecef9Tuple} or 

C{scalar} latitude of the (goedetic) origin 

(C{degrees}). 

@kwarg lon0: Optional C{scalar} longitude of the (goedetic) origin 

C{scalar} B{C{latlonh0}} (C{degrees}). 

@kwarg height0: Optional origin height (C{meter}), vertically 

above (or below) the surface of the ellipsoid. 

@kwarg ecef: An ECEF converter (L{EcefKarney}). 

@kwarg name: Optional name (C{str}). 

 

@raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{Ecef9Tuple}, 

C{scalar} or invalid or if B{C{lon0}} not 

C{scalar} for C{scalar} B{C{latlonh0}} or 

invalid or if B{C{height0}} invalid. 

 

@raise TypeError: Invalid B{C{ecef}}, not L{EcefKarney}. 

 

@note: If BC{latlonh0} is L{Ltp}, only the lat-, longitude and 

height are duplicated, I{not} the ECEF converter. 

''' 

if isinstance(latlonh0, LocalCartesian): 

self._ecef = latlonh0.ecef 

self._t0 = latlonh0._t0 

self.name = name or latlonh0.name 

else: 

self.reset(latlonh0, lon0, height0, name=name) 

if ecef: # PYCHOK no cover 

_xinstanceof(EcefKarney, ecef=ecef) 

self._ecef = ecef 

 

def __eq__(self, other): 

'''Compare this and an other instance. 

 

@arg other: The other ellipsoid (L{LocalCartesian} or L{Ltp}). 

 

@return: C{True} if equal, C{False} otherwise. 

''' 

return other is self or (isinstance(other, self.__class__) and 

self.ecef == other.ecef and 

self._t0 == other._t0) 

 

@Property_RO 

def datum(self): 

'''Get the ECEF converter's datum (L{Datum}). 

''' 

return self.ecef.datum 

 

@Property_RO 

def ecef(self): 

'''Get the ECEF converter (L{EcefKarney}). 

''' 

return self._ecef 

 

def _ecef2local(self, ecef, Xyz, Xyz_kwds): 

'''(INTERNAL) Convert geocentric/geodetic to local, like I{forward}. 

 

@arg ecef: Geocentric (and geodetic) (L{Ecef9Tuple}). 

@arg Xyz: An L{XyzLocal}, L{Enu} or L{Ned} I{class} or C{None}. 

@arg Xyz_kwds: B{C{Xyz}} keyword arguments, ignored if C{B{Xyz} is None}. 

 

@return: An C{B{Xyz}(x, y, z, ltp, **B{Xyz_kwds}} instance or if 

C{B{Xyz} is None}, an L{Local9Tuple}C{(x, y, z, lat, lon, 

height, ltp, ecef, M)} with this C{ltp}, B{C{ecef}} 

(L{Ecef9Tuple}) converted to this C{datum} and C{M=None}, 

always. 

''' 

ltp = self 

if ecef.datum != ltp.datum: 

ecef = ecef.toDatum(ltp.datum) 

x, y, z = self.M.rotate(ecef.xyz, *ltp._xyz0) 

r = Local9Tuple(x, y, z, ecef.lat, ecef.lon, ecef.height, 

ltp, ecef, None, name=ecef.name) 

if Xyz: 

if not issubclassof(Xyz, *_XyzLocals4): # Vector3d 

raise _TypesError(_Xyz_, Xyz, *_XyzLocals4) 

r = r.toXyz(Xyz=Xyz, **Xyz_kwds) 

return r 

 

def forward(self, latlonh, lon=None, height=0, M=False, name=NN): 

'''Convert I{geodetic} C{(lat, lon, height)} to I{local} cartesian 

C{(x, y, z)}. 

 

@arg latlonh: Either a C{LatLon}, a L{Ltp}, an L{Ecef9Tuple} or 

C{scalar} (geodetic) latitude (C{degrees}). 

@kwarg lon: Optional C{scalar} (geodetic) longitude for C{scalar} 

B{C{latlonh}} (C{degrees}). 

@kwarg height: Optional height (C{meter}), vertically above (or below) 

the surface of the ellipsoid. 

@kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}). 

@kwarg name: Optional name (C{str}). 

 

@return: A L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} 

with I{local} C{x}, C{y}, C{z}, I{geodetic} C{(lat}, C{lon}, 

C{height}, this C{ltp}, C{ecef} (L{Ecef9Tuple}) with 

I{geocentric} C{x}, C{y}, C{z} (and I{geodetic} C{lat}, 

C{lon}, C{height}) and the I{concatenated} rotation matrix 

C{M} (L{EcefMatrix}) if requested. 

 

@raise LocalError: If B{C{latlonh}} not C{scalar}, C{LatLon}, L{Ltp}, 

L{Ecef9Tuple} or invalid or if B{C{lon}} not 

C{scalar} for C{scalar} B{C{latlonh}} or invalid 

or if B{C{height}} invalid. 

''' 

lat, lon, h, n = _llhn4(latlonh, lon, height, Error=LocalError, name=name) 

t = self.ecef._forward(lat, lon, h, n, M=M) 

x, y, z = self.M.rotate(t.xyz, *self._xyz0) 

m = self.M.multiply(t.M) if M else None 

return Local9Tuple(x, y, z, lat, lon, h, self, t, m, name=n or self.name) 

 

@Property_RO 

def height0(self): 

'''Get origin's height (C{meter}). 

''' 

return self._t0.height 

 

@Property_RO 

def lat0(self): 

'''Get origin's latitude (C{degrees}). 

''' 

return self._t0.lat 

 

def _local2ecef(self, local, nine=False, M=False): 

'''(INTERNAL) Convert I{local} to geocentric/geodetic, like I{.reverse}. 

 

@arg local: Local (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer} or L{Local9Tuple}). 

@kwarg nine: Return 3- or 9-tuple (C{bool}). 

@kwarg M: Include the rotation matrix (C{bool}). 

 

@return: A I{geocentric} 3-tuple C{(x, y, z)} or if C{B{nine}=True}, 

an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}, 

optionally including rotation matrix C{M} or C{None}. 

''' 

t = self.M.unrotate(local.xyz, *self._xyz0) 

if nine: 

t = self.ecef.reverse(*t, M=M) 

return t 

 

@Property_RO 

def lon0(self): 

'''Get origin's longitude (C{degrees}). 

''' 

return self._t0.lon 

 

@Property_RO 

def M(self): 

'''Get the rotation matrix (C{EcefMatrix}). 

''' 

return self._t0.M 

 

def reset(self, latlonh0=0, lon0=0, height0=0, name=NN): 

'''Reset the (geodetic) origin. 

 

@kwarg latlonh0: Either a C{LatLon}, an L{Ecef9Tuple} or C{scalar} 

latitude of the origin (C{degrees}). 

@kwarg lon0: Optional C{scalar} longitude of the origin for 

C{scalar} B{C{latlonh0}} (C{degrees}). 

@kwarg height0: Optional origin height (C{meter}), vertically 

above (or below) the surface of the ellipsoid. 

@kwarg name: Optional, new name (C{str}). 

 

@raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{Ecef9Tuple}, 

C{scalar} or invalid or if B{C{lon0}} not 

C{scalar} for C{scalar} B{C{latlonh0}} or 

invalid or if B{C{height0}} invalid. 

''' 

self._update(True) # force reset 

 

lat0, lon0, height0, n = _llhn4(latlonh0, lon0, height0, 

suffix=_0_, Error=LocalError, name=name) 

if n: 

self.rename(n) 

else: 

n = self.name 

self._t0 = self.ecef._forward(lat0, lon0, height0, n, M=True) 

 

def reverse(self, xyz, y=None, z=None, M=False, name=NN): 

'''Convert I{local} C{(x, y, z)} to I{geodetic} C{(lat, lon, height)}. 

 

@arg xyz: A I{local} (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer}, L{Local9Tuple}) or 

local C{x} coordinate (C{scalar}). 

@kwarg y: Local C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}). 

@kwarg z: Local C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}). 

@kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix}, 

I{iff avaialble} (C{bool}). 

@kwarg name: Optional name (C{str}). 

 

@return: An L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} with 

I{local} C{x}, C{y}, C{z}, I{geodetic} C{lat}, C{lon}, C{height}, 

this C{ltp}, an C{ecef} (L{Ecef9Tuple}) with the I{geocentric} C{x}, 

C{y}, C{z} (and I{geodetic} C{lat}, C{lon}, C{height}) and the 

I{concatenated} rotation matrix C{M} (L{EcefMatrix}) if requested. 

 

@raise LocalError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}} 

not C{scalar} for C{scalar} B{C{xyz}}. 

''' 

x, y, z, n = _xyzn4(xyz, y, z, _XyzLocals5, Error=LocalError, name=name) 

c = self.M.unrotate((x, y, z), *self._xyz0) 

t = self.ecef.reverse(*c, M=M) 

m = self.M.multiply(t.M) if M else None 

return Local9Tuple(x, y, z, t.lat, t.lon, t.height, self, t, m, name=n or self.name) 

 

def toStr(self, prec=9, **unused): # PYCHOK signature 

'''Return this L{LocalCartesian} as a string. 

 

@kwarg prec: Precision, number of (decimal) digits (0..9). 

 

@return: This L{LocalCartesian} representation (C{str}). 

''' 

return self.attrs(_lat0_, _lon0_, 'height0', _M_, 'ecef', _name_, prec=prec) 

 

@Property_RO 

def _xyz0(self): 

'''(INTERNAL) Get C{(x0, y0, z0)} as L{Vector3Tuple}. 

''' 

return self._t0.xyz 

 

 

class Ltp(LocalCartesian): 

'''A I{local tangent plan} LTP, a sub-class of C{LocalCartesian} with 

configurable ECEF converter and without optional rotation matrix. 

''' 

def __init__(self, latlonh0=0, lon0=0, height0=0, ecef=None, name=NN): 

'''New C{Ltp}. 

 

@kwarg latlonh0: Either a C{LatLon}, L{Ltp}, L{Ecef9Tuple} or 

C{scalar} latitude of the (goedetic) origin 

(C{degrees}). 

@kwarg lon0: Optional C{scalar} longitude of the (goedetic) origin 

for C{scalar} B{C{latlonh0}} (C{degrees}). 

@kwarg height0: Optional origin height (C{meter}), vertically 

above (or below) the surface of the ellipsoid. 

@kwarg ecef: Optional ECEF converter (L{EcefKarney}, l{EcefFarrell21}, 

L{EcefFarrell22}, L{EcefSudano}, L{EcefVeness} or 

L{EcefYou} I{instance}), overriding default 

L{EcefKarney}C{(datum=Datums.WGS84)}. 

@kwarg name: Optional name (C{str}). 

 

@return: New instance (C{Ltp}). 

 

@raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{Ecef9Tuple}, 

C{scalar} or invalid or if B{C{lon0}} not 

C{scalar} for C{scalar} B{C{latlonh0}} or 

invalid or if B{C{height0}} invalid. 

 

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

''' 

LocalCartesian.__init__(self, latlonh0, lon0=lon0, height0=height0, name=name) 

if ecef: 

self.ecef = ecef 

 

@Property 

def ecef(self): 

'''Get this LTP's ECEF converter (C{Ecef...} I{instance}). 

''' 

return self._ecef 

 

@ecef.setter # PYCHOK setter! 

def ecef(self, ecef): 

'''Set this LTP's ECEF converter. 

 

@arg ecef: New ECEF converter (C{Ecef...} I{instance}). 

 

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

''' 

_xinstanceof(_EcefBase, ecef=ecef) 

if ecef != self._ecef: # PYCHOK no cover 

self._ecef = ecef 

self.reset(self._t0) 

 

 

def tyr3d(tilt=0, yaw=0, roll=0, Vector=Vector3d, **Vector_kwds): 

'''Convert an attitude oriention into a (3-D) direction vector. 

 

@kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down 

(clockwise rotation along and around the x-axis). 

@kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North 

(counter-clockwise rotation along and around the z-axis). 

@kwarg roll: Roll, bank (C{degrees}), positive to the right and down 

(clockwise rotation along and around the y-axis). 

 

@return: A named B{C{Vector}} instance or if B{C{Vector}} is C{None}, 

a named L{Vector3Tuple}C{(x, y, z)}. 

 

@see: U{Yaw, pitch, and roll rotations<http://Planning.CS.UIUC.edu/node102.html>} 

and function L{pygeodesy.hartzell} argument C{los}. 

''' 

d = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d 

return d if Vector is Vector3d else ( 

Vector3Tuple(d.x, d.y, d.z, name=d.name) if Vector is None else 

Vector(d.x, d.y, d.z, **_xkwds(Vector_kwds, name=d.name))) # PYCHOK indent 

 

 

def _xLtp(ltp): 

'''(INTERNAL) Validate B{C{ltp}}. 

''' 

if isinstance(ltp, (LocalCartesian, Ltp)): 

return ltp 

raise _TypesError(_ltp_, ltp, Ltp, LocalCartesian) 

 

# **) 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.