Coverage for pygeodesy/cartesianBase.py: 94%

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1 

2# -*- coding: utf-8 -*- 

3 

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

5C{Cartesian}s. 

6 

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

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

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

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

11''' 

12 

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

14from pygeodesy.constants import EPS, EPS0, isnear0, _1_0, _N_1_0, \ 

15 _2_0, _4_0, _6_0 

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

17 _WGS84, _xinstanceof 

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

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

20from pygeodesy.fsums import Fmt, fsumf_ 

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

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

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

24from pygeodesy.namedTuples import LatLon4Tuple, Vector4Tuple, \ 

25 Bearing2Tuple # PYCHOK .sphericalBase 

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

27 property_doc_, property_RO, _update_all 

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

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

30from pygeodesy.units import Height, _heigHt 

31from pygeodesy.vector3d import Vector3d, _xyzhdn3 

32 

33# from math import sqrt # from .fmath 

34 

35__all__ = _ALL_LAZY.cartesianBase 

36__version__ = '23.12.18' 

37 

38 

39class 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 self._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 self._resections.collins5(self, pointB, pointC, alpha, beta, 

139 useZ=useZ, datum=self.datum) 

140 

141 @deprecated_method 

142 def convertDatum(self, datum2, **datum): 

143 '''DEPRECATED, use method L{toDatum}.''' 

144 return self.toDatum(datum2, **datum) 

145 

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

147 def datum(self): 

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

149 ''' 

150 return self._datum 

151 

152 @datum.setter # PYCHOK setter! 

153 def datum(self, datum): 

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

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

156 

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

158 ''' 

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

160 if self._datum: # is not None 

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

162 raise _IsnotError(_ellipsoidal_, datum=datum) 

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

164 raise _IsnotError(_spherical_, datum=datum) 

165 if self._datum != d: 

166 _update_all(self) 

167 self._datum = d 

168 

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

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

171 

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

173 L{Ned} or L{Local9Tuple}). 

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

175 destination or C{None}. 

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

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

178 

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

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

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

182 

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

184 B{C{Cartesian_kwds}}. 

185 ''' 

186 if Cartesian is None: 

187 r = self._Ltp._local2ecef(delta, nine=True) 

188 else: 

189 r = self._Ltp._local2ecef(delta, nine=False) 

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

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

192 

193 @property_RO 

194 def Ecef(self): 

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

196 ''' 

197 CartesianBase.Ecef = E = _MODS.ecef.EcefKarney # overwrite property_RO 

198 return E 

199 

200 @Property_RO 

201 def _ecef9(self): 

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

203 ''' 

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

205 

206 @property_RO 

207 def ellipsoidalCartesian(self): 

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

209 ''' 

210 return False 

211 

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

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

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

215 

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

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

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

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

220 this cartesian's C{datum} ellipsoid. 

221 

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

223 to the distance to this C{pov}. 

224 

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

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

227 outside or away from the ellipsoid. 

228 

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

230 

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

232 ''' 

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

234 

235 @Property 

236 def height(self): 

237 '''Get the height (C{meter}). 

238 ''' 

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

240 

241 @height.setter # PYCHOK setter! 

242 def height(self, height): 

243 '''Set the height (C{meter}). 

244 

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

246 

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

248 ''' 

249 h = Height(height) 

250 if self._height != h: 

251 _update_all(self) 

252 self._height = h 

253 

254 @Property_RO 

255 def _height4(self): 

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

257 ''' 

258 try: 

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

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

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

262 return r 

263 

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

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

266 on this datum's ellipsoid surface. 

267 

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

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

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

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

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

273 ellipsoid's surface, otherwise the intersection of the 

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

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

276 (C{Cartesian}) or C{None}. 

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

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

279 

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

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

282 

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

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

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

286 

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

288 

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

290 

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

292 ''' 

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

294 if normal and d is self.datum: 

295 r = self._height4 

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

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

298 else: 

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

300 if Cartesian is not None: 

301 kwds = Cartesian_kwds.copy() 

302 h = kwds.pop(_height_, None) 

303 r = Cartesian(r, **kwds) 

304 if h is not None: 

305 r.height = Height(height=h) 

306 return r 

307 

308 @Property_RO 

309 def isEllipsoidal(self): 

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

311 ''' 

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

313 

314 @Property_RO 

315 def isSpherical(self): 

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

317 ''' 

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

319 

320 @Property_RO 

321 def latlon(self): 

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

323 ''' 

324 return self.toEcef().latlon 

325 

326 @Property_RO 

327 def latlonheight(self): 

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

329 ''' 

330 return self.toEcef().latlonheight 

331 

332 @Property_RO 

333 def latlonheightdatum(self): 

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

335 ''' 

336 return self.toEcef().latlonheightdatum 

337 

338 @property_RO 

339 def _ltp(self): 

340 '''(INTERNAL) Get module C{.ltp}, I{once}. 

341 ''' 

342 CartesianBase._ltp = m = _MODS.ltp # overwrite property_RO 

343 return m 

344 

345 @Property_RO 

346 def _Ltp(self): 

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

348 ''' 

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

350 

351 @Property_RO 

352 def _N_vector(self): 

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

354 ''' 

355 m = _MODS.nvectorBase 

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

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

358 

359 def _n_xyzh4(self, datum): 

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

361 ''' 

362 def _ErrorEPS0(x): 

363 return _ValueError(origin=self, txt=Fmt.PARENSPACED(EPS0=x)) 

364 

365 _xinstanceof(Datum, datum=datum) 

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

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

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

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

370 E = datum.ellipsoid 

371 x, y, z = self.xyz 

372 

373 # Kenneth Gade eqn 23 

374 p = hypot2(x, y) * E.a2_ 

375 q = z**2 * E.e21 * E.a2_ 

376 r = fsumf_(p, q, -E.e4) / _6_0 

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

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

379 if isnear0(t): 

380 raise _ErrorEPS0(t) 

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

382 v = sqrt(u**2 + E.e4 * q) 

383 t = v * _2_0 

384 if t < EPS0: # isnear0 

385 raise _ErrorEPS0(t) 

386 w = fsumf_(u, v, -q) * E.e2 / t 

387 k = sqrt(fsumf_(u, v, w**2)) - w 

388 if isnear0(k): 

389 raise _ErrorEPS0(k) 

390 t = k + E.e2 

391 if isnear0(t): 

392 raise _ErrorEPS0(t) 

393 e = k / t 

394# d = e * hypot(x, y) 

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

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

397 if t < EPS0: # isnear0 

398 raise _ErrorEPS0(t) 

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

400 s = e / t # == e * tmp 

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

402 

403 @Property_RO 

404 def philam(self): 

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

406 ''' 

407 return self.toEcef().philam 

408 

409 @Property_RO 

410 def philamheight(self): 

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

412 ''' 

413 return self.toEcef().philamheight 

414 

415 @Property_RO 

416 def philamheightdatum(self): 

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

418 ''' 

419 return self.toEcef().philamheightdatum 

420 

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

422 '''3-Point resection between this and two other points using U{Pierlot 

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

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

425 

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

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

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

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

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

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

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

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

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

435 (C{bool}). 

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

437 

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

439 

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

441 

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

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

444 

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

446 

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

448 ''' 

449 return self._resections.pierlot(self, point2, point3, alpha12, alpha23, 

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

451 

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

453 '''3-Point resection between this and two other points using U{Pierlot 

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

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

456 

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

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

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

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

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

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

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

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

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

466 

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

468 

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

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

471 

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

473 

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

475 ''' 

476 return self._resections.pierlotx(self, point2, point3, alpha1, alpha2, alpha3, 

477 useZ=useZ, datum=self.datum) 

478 

479 @property_RO 

480 def _resections(self): 

481 '''(INTERNAL) Import the C{.resections} module, I{once}. 

482 ''' 

483 CartesianBase._resections = m = _MODS.resections # overwrite property_RO 

484 return m 

485 

486 @property_RO 

487 def sphericalCartesian(self): 

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

489 ''' 

490 return False 

491 

492 @deprecated_method 

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

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

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

496 

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

498 '''3-Point resection between this and two other points using U{Tienstra 

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

500 

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

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

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

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

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

506 non-negative). 

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

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

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

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

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

512 (C{bool}). 

513 

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

515 

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

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

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

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

520 

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

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

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

524 

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

526 

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

528 ''' 

529 return self._resections.tienstra7(self, pointB, pointC, alpha, beta, gamma, 

530 useZ=useZ, datum=self.datum) 

531 

532 @deprecated_method 

533 def to2ab(self): # PYCHOK no cover 

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

535 

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

537 ''' 

538 return self.philam 

539 

540 @deprecated_method 

541 def to2ll(self): # PYCHOK no cover 

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

543 

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

545 ''' 

546 return self.latlon 

547 

548 @deprecated_method 

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

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

551 

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

553 

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

555 as its name may suggest. 

556 ''' 

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

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

559 

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

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

562# ''' 

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

564# if LL is not None: 

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

566# for n, v in pairs.items(): 

567# setattr(r, n, v) 

568# return r 

569 

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

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

572 

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

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

575 

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

577 

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

579 invalid. 

580 ''' 

581 _xinstanceof(Datum, datum2=datum2) 

582 

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

584 self.toDatum(datum) 

585 

586 i, d = False, c.datum 

587 if d == datum2: 

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

589 

590 elif d == _WGS84: 

591 d = datum2 # convert from WGS84 to datum2 

592 

593 elif datum2 == _WGS84: 

594 i = True # convert to WGS84 by inverse transformation 

595 

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

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

598 d = datum2 

599 

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

601 

602 def toEcef(self): 

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

604 

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

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

607 

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

609 ''' 

610 return self._ecef9 

611 

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

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

614 

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

616 or L{a_f2Tuple}). 

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

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

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

620 (C{LatLon}) or C{None}. 

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

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

623 

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

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

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

627 

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

629 ''' 

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

631 if d == self.datum: 

632 r = self.toEcef() 

633 else: 

634 c = self.toDatum(d) 

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

636 

637 if LatLon: # class or .classof 

638 h = _heigHt(r, height) 

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

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

641 _xdatum(r.datum, d) 

642 return r 

643 

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

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

646 

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

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

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

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

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

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

653 

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

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

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

657 

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

659 ''' 

660 p = self._ltp._xLtp(ltp, self._Ltp) 

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

662 

663 def toLtp(self, Ecef=None): 

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

665 

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

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

668 ''' 

669 return self._Ltp if Ecef in (None, self.Ecef) else self._ltp.Ltp( 

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

671 

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

673 '''Convert this cartesian to C{n-vector} components, I{including height}. 

674 

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

676 (C{Nvector}) or C{None}. 

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

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

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

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

681 

682 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if 

683 B{C{Nvector}} is C{None}. 

684 

685 @raise TypeError: Invalid B{C{Nvector}}, B{C{Nvector_kwds}} or 

686 B{C{datum}}. 

687 

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

689 ''' 

690 r, d = self._N_vector.xyzh, self.datum 

691 if datum is not None: 

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

693 if d != self.datum: 

694 r = self._n_xyzh4(d) 

695 

696 if Nvector is not None: 

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

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

699 return r 

700 

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

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

703 

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

705 @kwarg fmt: Enclosing backets format (C{str}). 

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

707 

708 @return: Cartesian represented as "[x, y, z]" (C{str}). 

709 ''' 

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

711 

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

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

714 to this cartesian. 

715 

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

717 @kwarg inverse: Apply the inverse of the Helmert 

718 transform (C{bool}). 

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

720 overriding this cartesian's datum. 

721 

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

723 

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

725 is not L{Datums}C{.WGS84}. 

726 ''' 

727 d = datum or self.datum 

728 if inverse and d != _WGS84: 

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

730 txt=_not_(_WGS84.name)) 

731 

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

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

734 

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

736 '''Return this cartesian's I{geocentric} components as vector. 

737 

738 @kwarg Vector: Optional class to return the I{geocentric} 

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

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

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

742 

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

744 B{C{Vector}} is C{None}. 

745 

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

747 ''' 

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

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

750 

751 

752__all__ += _ALL_DOCS(CartesianBase) 

753 

754# **) MIT License 

755# 

756# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

757# 

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

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

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

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

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

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

764# 

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

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

767# 

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

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

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

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

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

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

774# OTHER DEALINGS IN THE SOFTWARE.