1

2# -*- coding: utf-8 -*-

3

4 u'''(INTERNAL) Private base classes for elliposiodal, spherical and N-/vectorial

5 C{Cartesian}s.

6

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

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

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

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

11'''

12

13# from pygeodesy.basics import _xinstanceof # from .datums

14 from pygeodesy.constants import EPS0, isnear0, _1_0, _N_1_0, _2_0, _4_0, _6_0

15 from pygeodesy.datums import Datum, _spherical_datum, _WGS84, _xinstanceof

16 from pygeodesy.errors import _IsnotError, _ValueError, _xdatum, _xkwds

17 from pygeodesy.fmath import cbrt, hypot_, hypot2, sqrt # hypot

18 from pygeodesy.fsums import Fmt, fsumf_

19 from pygeodesy.interns import NN, _COMMASPACE_, _height_, _not_

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

21 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS

22 from pygeodesy.namedTuples import Bearing2Tuple, Height, LatLon4Tuple, Vector4Tuple, \

23 Vector3Tuple # PYCHOK .ellipsoidal-, .sphericalBase

24 from pygeodesy.props import deprecated_method, Property, Property_RO, \

25 property_doc_, _update_all

26# from pygeodesy.resections impoty cassini, collins5, pierlot, tienstra7

27# from pygeodesy.streprs import Fmt # from .fsums

28# from pygeodesy.units import Height # from .namedTuples

29 from pygeodesy.vector3d import Vector3d, _xyzhdn3

30

31# from math import sqrt # from .fmath

32

33__all__ = _ALL_LAZY.cartesianBase

34__version__ = '23.05.15'

35

36

37 class CartesianBase(Vector3d):

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

39 '''

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

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

42

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

44 '''New C{Cartesian...}.

45

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

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

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

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

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

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

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

53 or L{a_f2Tuple}).

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

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

56

57 @raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}}

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

59 L{Vector3Tuple} or L{Vector4Tuple}.

60 '''

61 h, d, n = _xyzhdn3(x_xyz, None, datum, ll)

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

63 if h is not None:

64 self._height = Height(h)

65 if d is not None:

66 self.datum = d

67

68# def __matmul__(self, other): # PYCHOK Python 3.5+

69# '''Return C{NotImplemented} for C{c_ = c @ datum} and C{c_ = c @ transform}.

70# '''

71# return NotImplemented if isinstance(other, (Datum, Transform)) else \

72# _NotImplemented(self, other)

73

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

75 '''3-Point resection between this and 2 other points using U{Cassini

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

77

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

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

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

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

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

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

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

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

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

87 force C{z=INT0} (C{bool}).

88

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

90

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

92

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

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

95

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

97

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

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

100 and function L{pygeodesy.cassini}.

101 '''

102 return _MODS.resections.cassini(self, pointB, pointC, alpha, beta,

103 useZ=useZ, datum=self.datum)

104

105 @deprecated_method

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

107 '''DEPRECATED, use method L{collins5}.'''

108 return self.collins5(pointB, pointC, alpha, beta, useZ=useZ)

109

110 def collins5(self, pointB, pointC, alpha, beta, useZ=False):

111 '''3-Point resection between this and 2 other points using U{Collins<https://Dokumen.tips/

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

113

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

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

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

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

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

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

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

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

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

123 force C{z=INT0} (C{bool}).

124

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

126

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

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

129 triangle sides C{a}, C{b} and C{c}.

130

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

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

133

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

135

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

137 and function L{pygeodesy.collins5}.

138 '''

139 return _MODS.resections.collins5(self, pointB, pointC, alpha, beta,

140 useZ=useZ, datum=self.datum)

141

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

143 def datum(self):

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

145 '''

146 return self._datum

147

148 @datum.setter # PYCHOK setter!

149 def datum(self, datum):

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

151 (L{Datum}), ellipsoidal or spherical.

152

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

154 '''

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

156 if self._datum: # is not None

157 if self._datum.isEllipsoidal and not d.isEllipsoidal:

158 raise _IsnotError(_ellipsoidal_, datum=datum)

159 elif self._datum.isSpherical and not d.isSpherical:

160 raise _IsnotError(_spherical_, datum=datum)

161 if self._datum != d:

162 _update_all(self)

163 self._datum = d

164

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

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

167

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

169 L{Ned} or L{Local9Tuple}).

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

171 destination or C{None}.

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

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

174

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

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

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

178

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

180 B{C{Cartesian_kwds}}.

181 '''

182 if Cartesian is None:

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

184 else:

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

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

187 return r._xnamed(r) if self.name else r

188

189 @Property_RO

190 def Ecef(self):

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

192 '''

193 return _MODS.ecef.EcefKarney # default

194

195 @Property_RO

196 def _ecef9(self):

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

198 '''

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

200

201 def hartzell(self, los=None, earth=None):

202 '''Compute the intersection of a Line-Of-Sight (los) from this certesian

203 Point-Of-View (pov) with this cartesian's ellipsoid surface.

204

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

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

207 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2},

208 L{a_f2Tuple} or C{scalar} radius in C{meter}) overriding

209 this cartesian's C{datum} ellipsoid.

210

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

212

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

214 is inside the ellipsoid or B{C{los}} points

215 outside the ellipsoid or in an opposite direction.

216

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

218

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

220 '''

221 return _MODS.formy.hartzell(self, los=los, earth=earth or self.datum)

222

223 @Property

224 def height(self):

225 '''Get the height (C{meter}).

226 '''

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

228

229 @height.setter # PYCHOK setter!

230 def height(self, height):

231 '''Set the height (C{meter}).

232

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

234

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

236 '''

237 h = Height(height)

238 if self._height != h:

239 _update_all(self)

240 self._height = h

241

242 @Property_RO

243 def _height4(self):

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

245 '''

246 try:

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

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

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

250 return r

251

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

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

254 on this datum's ellipsoid surface.

255

256 @kwarg earth: A datum, ellipsoid, triaxial ellipsoid or earth radius

257 I{overriding} this datum (L{Datum}, L{Ellipsoid},

258 L{Ellipsoid2}, L{a_f2Tuple}, L{Triaxial}, L{Triaxial_},

259 L{JacobiConformal} or C{meter}, conventionally).

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

261 ellipsoid's surface, otherwise the intersection of the

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

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

264 (C{Cartesian}) or C{None}.

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

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

267

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

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

270

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

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

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

274

275 @raise TriaxialError: No convergence in triaxial root finding.

276

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

278

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

280 '''

281 d = self.datum if earth is None else earth

282 if normal and d == self.datum:

283 r = self._height4

284 elif isinstance(d, _MODS.triaxials.Triaxial_):

285 r = d.height4(self, normal=normal)

286 else:

287 r = _spherical_datum(d).ellipsoid.height4(self, normal=normal)

288 if Cartesian is not None:

289 kwds = Cartesian_kwds.copy()

290 h = kwds.pop(_height_, None)

291 r = Cartesian(r, **kwds)

292 if h is not None:

293 r.height = Height(height=h)

294 return r

295

296 @Property_RO

297 def isEllipsoidal(self):

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

299 '''

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

301

302 @Property_RO

303 def isSpherical(self):

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

305 '''

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

307

308 @Property_RO

309 def latlon(self):

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

311 '''

312 return self.toEcef().latlon

313

314 @Property_RO

315 def latlonheight(self):

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

317 '''

318 return self.toEcef().latlonheight

319

320 @Property_RO

321 def latlonheightdatum(self):

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

323 '''

324 return self.toEcef().latlonheightdatum

325

326 @Property_RO

327 def _ltp(self):

328 '''(INTERNAL) Cache for L{toLtp}.

329 '''

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

331

332 @Property_RO

333 def _N_vector(self):

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

335 '''

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

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

338

339 def _n_xyzh4(self, datum):

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

341 '''

342 def _ErrorEPS0(x):

343 return _ValueError(origin=self, txt=Fmt.PARENTSPACED(EPS0=x))

344

345 _xinstanceof(Datum, datum=datum)

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

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

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

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

350 E = datum.ellipsoid

351 x, y, z = self.xyz

352

353 # Kenneth Gade eqn 23

354 p = hypot2(x, y) * E.a2_

355 q = (z**2 * E.e21) * E.a2_

356 r = fsumf_(p, q, -E.e4) / _6_0

357 s = (p * q * E.e4) / (_4_0 * r**3)

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

359 if isnear0(t):

360 raise _ErrorEPS0(t)

361

362 u = r * fsumf_(_1_0, t, _1_0 / t)

363 v = sqrt(u**2 + E.e4 * q)

364 t = v * _2_0

365 if t < EPS0: # isnear0

366 raise _ErrorEPS0(t)

367 w = E.e2 * fsumf_(u, v, -q) / t

368

369 k = sqrt(fsumf_(u, v, w**2)) - w

370 if isnear0(k):

371 raise _ErrorEPS0(k)

372 t = k + E.e2

373 if isnear0(t):

374 raise _ErrorEPS0(t)

375 e = k / t

376# d = e * hypot(x, y)

377

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

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

380 if t < EPS0: # isnear0

381 raise _ErrorEPS0(t)

382 h = fsumf_(k, E.e2, _N_1_0) / k * t

383 s = e / t # == e * tmp

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

385

386 @Property_RO

387 def philam(self):

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

389 '''

390 return self.toEcef().philam

391

392 @Property_RO

393 def philamheight(self):

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

395 '''

396 return self.toEcef().philamheight

397

398 @Property_RO

399 def philamheightdatum(self):

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

401 '''

402 return self.toEcef().philamheightdatum

403

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

405 '''3-Point resection between this and two other points using U{Pierlot

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

407

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

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

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

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

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

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

414 @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=INT0}

415 (C{bool}).

416

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

418

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

420

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

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

423

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

425

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

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

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

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

430 <http://www.Telecom.ULg.ac.Be/triangulation>} and functions

431 L{pygeodesy.pierlot}.

432 '''

433 return _MODS.resections.pierlot(self, point2, point3, alpha12, alpha23,

434 useZ=useZ, datum=self.datum)

435

436 @deprecated_method

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

438 '''DEPRECATED, use method L{tienstra7}.'''

439 return self.tienstra7(pointB, pointC, alpha, beta=beta, gamma=gamma, useZ=useZ)

440

441 def tienstra7(self, pointB, pointC, alpha, beta=None, gamma=None, useZ=False):

442 '''3-Point resection between this and two other points using U{Tienstra

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

444

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

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

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

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

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

450 non-negative).

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

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

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

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

455 @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=INT0}

456 (C{bool}).

457

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

459

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

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

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

463 triangle sides C{a}, C{b} and C{c}.

464

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

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

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

468

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

470

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

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

473 <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree/>},

474 U{18 Triangulation Algorithms...<http://www.Telecom.ULg.ac.Be/triangulation/>}

475 and function L{pygeodesy.tienstra7}.

476 '''

477 return _MODS.resections.tienstra7(self, pointB, pointC, alpha, beta, gamma,

478 useZ=useZ, datum=self.datum)

479

480 @deprecated_method

481 def to2ab(self): # PYCHOK no cover

482 '''DEPRECATED, use property C{philam}.

483

484 @return: A L{PhiLam2Tuple}C{(phi, lam)}.

485 '''

486 return self.philam

487

488 @deprecated_method

489 def to2ll(self): # PYCHOK no cover

490 '''DEPRECATED, use property C{latlon}.

491

492 @return: A L{LatLon2Tuple}C{(lat, lon)}.

493 '''

494 return self.latlon

495

496 @deprecated_method

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

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

499

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

501

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

503 as its name may suggest.

504 '''

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

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

507

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

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

510# '''

511# r = self.to3llh(datum) # LatLon3Tuple

512# if LL is not None:

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

514# for n, v in pairs.items():

515# setattr(r, n, v)

516# return r

517

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

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

520

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

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

523

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

525

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

527 invalid.

528 '''

529 _xinstanceof(Datum, datum2=datum2)

530

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

532 self.toDatum(datum)

533

534 i, d = False, c.datum

535 if d == datum2:

536 return c.copy() if c is self else c

537

538 elif d == _WGS84:

539 d = datum2 # convert from WGS84 to datum2

540

541 elif datum2 == _WGS84:

542 i = True # convert to WGS84 by inverse transformation

543

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

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

546 d = datum2

547

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

549

550 convertDatum = toDatum # for backward compatibility

551

552 def toEcef(self):

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

554

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

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

557

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

559 '''

560 return self._ecef9

561

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

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

564

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

566 or L{a_f2Tuple}).

567 @kwarg height: Optional height, overriding the converted height

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

569 @kwarg LatLon: Optional class to return the geodetic point

570 (C{LatLon}) or C{None}.

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

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

573

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

575 is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon,

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

577

578 @raise TypeError: Invalid B{C{datum}} or B{C{LatLon_kwds}}.

579 '''

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

581 if d == self.datum:

582 r = self.toEcef()

583 else:

584 c = self.toDatum(d)

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

586

587 if LatLon: # class or .classof

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

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

590 **_xkwds(LatLon_kwds, name=r.name))

591 _xdatum(r.datum, d)

592 return r

593

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

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

596

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

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

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

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

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

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

603

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

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

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

607

608 @raise TypeError: Invalid B{C{ltp}}.

609 '''

610 p = _MODS.ltp._xLtp(ltp, self._ltp)

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

612

613 def toLtp(self, Ecef=None):

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

615

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

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

618 '''

619 return self._ltp if Ecef in (None, self.Ecef) else _MODS.ltp.Ltp(

620 self._ecef9, ecef=Ecef(self.datum), name=self.name)

621

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

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

624

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

626 components (C{Nvector}) or C{None}.

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

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

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

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

631

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

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

634

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

636

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

638

639 @example:

640

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

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

643 '''

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

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

646

647 if Nvector is not None:

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

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

650 return r

651

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

653 '''Return the string representation of this cartesian.

654

655 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).

656 @kwarg fmt: Enclosing backets format (string).

657 @kwarg sep: Separator to join (string).

658

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

660 '''

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

662

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

664 '''Return a new cartesian by applying a Helmert transform

665 to this cartesian.

666

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

668 @kwarg inverse: Apply the inverse of the Helmert

669 transform (C{bool}).

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

671 overriding this cartesian's datum.

672

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

674

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

676 is not L{Datums}C{.WGS84}.

677 '''

678 d = datum or self.datum

679 if inverse and d != _WGS84:

680 raise _ValueError(inverse=inverse, datum=d,

681 txt=_not_(_WGS84.name))

682

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

684 return self.classof(xyz, datum=d)

685

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

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

688

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

690 components (L{Vector3d}) or C{None}.

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

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

693

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

695 B{C{Vector}} is C{None}.

696

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

698 '''

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

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

701

702

703__all__ += _ALL_DOCS(CartesianBase)

704

705# **) MIT License

706#

707# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

708#

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

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

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

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

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

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

715#

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

717# in all copies or substantial portions of the Software.

718#

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

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

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

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

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

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

725# OTHER DEALINGS IN THE SOFTWARE.