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

 

# -*- 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, fsum_, hypot_, hypot2 # hypot 

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

_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 namedTuples 

from pygeodesy.namedTuples import LatLon4Tuple, Vector4Tuple, _xnamed 

from pygeodesy.props import deprecated_method, Property_RO, property_doc_ 

from pygeodesy.streprs import Fmt 

from pygeodesy.units import Height 

from pygeodesy.vector3d import Vector3d, _xyzhdn6 

 

from math import sqrt 

 

__all__ = () 

__version__ = '21.06.30' 

 

 

class CartesianBase(Vector3d): 

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

''' 

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

_height = 0 # height (L{Height}) 

 

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

'''New C{Cartesian...}. 

 

@arg xyz: An L{Ecef9Tuple}, L{Vector3Tuple}, L{Vector4Tuple} 

or the C{X} coordinate (C{scalar}). 

@arg y: The C{Y} coordinate (C{scalar}) if B{C{xyz}} C{scalar}. 

@arg z: The C{Z} coordinate (C{scalar}) if B{C{xyz}} C{scalar}. 

@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{xyz}}, B{C{y}} or B{C{z}} 

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

L{Vector3Tuple} or L{Vector4Tuple}. 

''' 

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

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

if h: 

self._height = Height(h) 

if d: 

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) 

 

@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}=None}. 

 

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

instance or if C{B{Cartesian}=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) 

 

@property_doc_(''' the height (C{meter}).''') 

def height(self): 

'''Get the height (C{meter}). 

''' 

return 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 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> 

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, -_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 

 

@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}=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}}. 

''' 

m = LatLon is None 

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=m) 

 

if not m: # class or .classof 

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

r = LatLon(r.lat, r.lon, **_xkwds(LatLon_kwds, 

datum=r.datum, height=h, 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}=None}. 

 

@return: An B{C{Xyz}} instance or if C{B{Xyz}=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}=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}=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) 2016-2021 -- 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.