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 EPS, EPS0, isnear0, _1_0, _N_1_0, \

15 _2_0, _4_0, _6_0

16 from pygeodesy.datums import Datum, _earth_ellipsoid, _spherical_datum, \

17 _WGS84, _xinstanceof

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

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

20 from pygeodesy.fsums import Fmt, fsumf_

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

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

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

24 from pygeodesy.namedTuples import LatLon4Tuple, Vector4Tuple, \

25 Bearing2Tuple # PYCHOK .sphericalBase

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

27 property_doc_, property_RO, _update_all

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

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

30 from pygeodesy.units import Height, _heigHt

31 from pygeodesy.vector3d import Vector3d, _xyzhdn3

32

33# from math import sqrt # from .fmath

34

35__all__ = _ALL_LAZY.cartesianBase

36__version__ = '23.10.29'

37

38

39 class CartesianBase(Vector3d):

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

41 '''

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

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

44

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

46 '''New C{Cartesian...}.

47

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

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

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

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

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

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

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

55 or L{a_f2Tuple}).

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

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

58

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

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

61 L{Vector3Tuple} or L{Vector4Tuple}.

62 '''

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

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

65 if h is not None:

66 self._height = Height(h)

67 if d is not None:

68 self.datum = d

69

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

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

72# '''

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

74# _NotImplemented(self, other)

75

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

77 '''3-Point resection between this and 2 other points using U{Cassini

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

79

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

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

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

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

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

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

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

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

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

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

90

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

92

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

94

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

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

97

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

99

100 @see: Function L{pygeodesy.cassini} for references and more details.

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: Function L{pygeodesy.collins5} for references and more details.

137 '''

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

139 useZ=useZ, datum=self.datum)

140

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

142 def datum(self):

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

144 '''

145 return self._datum

146

147 @datum.setter # PYCHOK setter!

148 def datum(self, datum):

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

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

151

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

153 '''

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

155 if self._datum: # is not None

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

157 raise _IsnotError(_ellipsoidal_, datum=datum)

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

159 raise _IsnotError(_spherical_, datum=datum)

160 if self._datum != d:

161 _update_all(self)

162 self._datum = d

163

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

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

166

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

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

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

170 destination or C{None}.

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

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

173

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

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

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

177

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

179 B{C{Cartesian_kwds}}.

180 '''

181 if Cartesian is None:

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

183 else:

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

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

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

187

188 @Property_RO

189 def Ecef(self):

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

191 '''

192 return _MODS.ecef.EcefKarney # default

193

194 @Property_RO

195 def _ecef9(self):

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

197 '''

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

199

200 @property_RO

201 def ellipsoidalCartesian(self):

202 '''Get the C{Cartesian type} iff ellipsoidal, overloaded in L{CartesianEllipsoidalBase}.

203 '''

204 return False

205

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

207 '''Compute the intersection of a Line-Of-Sight (los) from this cartesian

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

209

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

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

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

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

214 this cartesian's C{datum} ellipsoid.

215

216 @return: The ellipsoid intersection (C{Cartesian}) with C{.height} set

217 to the distance to this C{pov}.

218

219 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov}

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

221 points outside or away from the ellipsoid.

222

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

224

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

226 '''

227 return _MODS.formy._hartzell(self, los, earth)

228

229 @Property

230 def height(self):

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

232 '''

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

234

235 @height.setter # PYCHOK setter!

236 def height(self, height):

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

238

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

240

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

242 '''

243 h = Height(height)

244 if self._height != h:

245 _update_all(self)

246 self._height = h

247

248 @Property_RO

249 def _height4(self):

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

251 '''

252 try:

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

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

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

256 return r

257

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

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

260 on this datum's ellipsoid surface.

261

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

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

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

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

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

267 ellipsoid's surface, otherwise the intersection of the

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

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

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

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

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

273

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

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

276

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

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

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

280

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

282

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

284

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

286 '''

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

288 if normal and d is self.datum:

289 r = self._height4

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

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

292 else:

293 r = _earth_ellipsoid(d).height4(self, normal=normal)

294 if Cartesian is not None:

295 kwds = Cartesian_kwds.copy()

296 h = kwds.pop(_height_, None)

297 r = Cartesian(r, **kwds)

298 if h is not None:

299 r.height = Height(height=h)

300 return r

301

302 @Property_RO

303 def isEllipsoidal(self):

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

305 '''

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

307

308 @Property_RO

309 def isSpherical(self):

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

311 '''

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

313

314 @Property_RO

315 def latlon(self):

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

317 '''

318 return self.toEcef().latlon

319

320 @Property_RO

321 def latlonheight(self):

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

323 '''

324 return self.toEcef().latlonheight

325

326 @Property_RO

327 def latlonheightdatum(self):

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

329 '''

330 return self.toEcef().latlonheightdatum

331

332 @Property_RO

333 def _ltp(self):

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

335 '''

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

337

338 @Property_RO

339 def _N_vector(self):

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

341 '''

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

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

344

345 def _n_xyzh4(self, datum):

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

347 '''

348 def _ErrorEPS0(x):

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

350

351 _xinstanceof(Datum, datum=datum)

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

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

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

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

356 E = datum.ellipsoid

357 x, y, z = self.xyz

358

359 # Kenneth Gade eqn 23

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

361 q = z**2 * E.e21 * E.a2_

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

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

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

365 if isnear0(t):

366 raise _ErrorEPS0(t)

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

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

369 t = v * _2_0

370 if t < EPS0: # isnear0

371 raise _ErrorEPS0(t)

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

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

374 if isnear0(k):

375 raise _ErrorEPS0(k)

376 t = k + E.e2

377 if isnear0(t):

378 raise _ErrorEPS0(t)

379 e = k / t

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

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

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

383 if t < EPS0: # isnear0

384 raise _ErrorEPS0(t)

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

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

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

388

389 @Property_RO

390 def philam(self):

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

392 '''

393 return self.toEcef().philam

394

395 @Property_RO

396 def philamheight(self):

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

398 '''

399 return self.toEcef().philamheight

400

401 @Property_RO

402 def philamheightdatum(self):

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

404 '''

405 return self.toEcef().philamheightdatum

406

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

408 '''3-Point resection between this and two other points using U{Pierlot

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

410 I{approximate} limits for the (pseudo-)singularities.

411

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

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

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

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

416 @arg alpha12: Angle subtended from this point to B{C{point2}} or

417 B{C{alpha2 - alpha}} (C{degrees}).

418 @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} or

419 B{C{alpha3 - alpha2}} (C{degrees}).

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

421 (C{bool}).

422 @kwarg eps: Tolerance for C{cot} (pseudo-)singularities (C{float}).

423

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

425

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

427

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

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

430

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

432

433 @see: Function L{pygeodesy.pierlot} for references and more details.

434 '''

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

436 useZ=useZ, eps=eps, datum=self.datum)

437

438 def pierlotx(self, point2, point3, alpha1, alpha2, alpha3, useZ=False):

439 '''3-Point resection between this and two other points using U{Pierlot

440 <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree>}'s

441 method C{ToTal} with I{exact} limits for the (pseudo-)singularities.

442

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

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

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

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

447 @arg alpha1: Angle at B{C{point1}} (C{degrees}).

448 @arg alpha2: Angle at B{C{point2}} (C{degrees}).

449 @arg alpha3: Angle at B{C{point3}} (C{degrees}).

450 @kwarg useZ: If C{True}, interpolate the survey point's Z component,

451 otherwise use C{z=INT0} (C{bool}).

452

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

454

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

456 invalid B{C{alpha1}}, B{C{alpha2}} or B{C{alpha3}}.

457

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

459

460 @see: Function L{pygeodesy.pierlotx} for references and more details.

461 '''

462 return _MODS.resections.pierlotx(self, point2, point3, alpha1, alpha2, alpha3,

463 useZ=useZ, datum=self.datum)

464

465 @property_RO

466 def sphericalCartesian(self):

467 '''Get the C{Cartesian type} iff spherical, overloaded in L{CartesianSphericalBase}.

468 '''

469 return False

470

471 @deprecated_method

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

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

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

475

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

477 '''3-Point resection between this and two other points using U{Tienstra

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

479

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

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

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

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

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

485 non-negative).

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

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

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

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

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

491 (C{bool}).

492

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

494

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

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

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

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

499

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

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

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

503

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

505

506 @see: Function L{pygeodesy.tienstra7} for references and more details.

507 '''

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

509 useZ=useZ, datum=self.datum)

510

511 @deprecated_method

512 def to2ab(self): # PYCHOK no cover

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

514

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

516 '''

517 return self.philam

518

519 @deprecated_method

520 def to2ll(self): # PYCHOK no cover

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

522

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

524 '''

525 return self.latlon

526

527 @deprecated_method

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

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

530

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

532

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

534 as its name may suggest.

535 '''

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

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

538

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

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

541# '''

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

543# if LL is not None:

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

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

546# setattr(r, n, v)

547# return r

548

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

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

551

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

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

554

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

556

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

558 invalid.

559 '''

560 _xinstanceof(Datum, datum2=datum2)

561

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

563 self.toDatum(datum)

564

565 i, d = False, c.datum

566 if d == datum2:

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

568

569 elif d == _WGS84:

570 d = datum2 # convert from WGS84 to datum2

571

572 elif datum2 == _WGS84:

573 i = True # convert to WGS84 by inverse transformation

574

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

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

577 d = datum2

578

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

580

581 convertDatum = toDatum # for backward compatibility

582

583 def toEcef(self):

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

585

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

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

588

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

590 '''

591 return self._ecef9

592

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

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

595

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

597 or L{a_f2Tuple}).

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

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

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

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

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

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

604

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

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

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

608

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

610 '''

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

612 if d == self.datum:

613 r = self.toEcef()

614 else:

615 c = self.toDatum(d)

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

617

618 if LatLon: # class or .classof

619 h = _heigHt(r, height)

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

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

622 _xdatum(r.datum, d)

623 return r

624

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

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

627

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

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

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

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

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

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

634

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

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

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

638

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

640 '''

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

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

643

644 def toLtp(self, Ecef=None):

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

646

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

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

649 '''

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

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

652

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

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

655

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

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

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

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

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

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

662

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

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

665

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

667

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

669

670 @example:

671

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

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

674 '''

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

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

677

678 if Nvector is not None:

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

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

681 return r

682

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

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

685

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

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

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

689

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

691 '''

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

693

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

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

696 to this cartesian.

697

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

699 @kwarg inverse: Apply the inverse of the Helmert

700 transform (C{bool}).

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

702 overriding this cartesian's datum.

703

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

705

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

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

708 '''

709 d = datum or self.datum

710 if inverse and d != _WGS84:

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

712 txt=_not_(_WGS84.name))

713

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

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

716

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

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

719

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

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

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

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

724

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

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

727

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

729 '''

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

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

732

733

734__all__ += _ALL_DOCS(CartesianBase)

735

736# **) MIT License

737#

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

739#

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

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

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

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

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

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

746#

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

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

749#

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

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

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

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

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

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

756# OTHER DEALINGS IN THE SOFTWARE.