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 impoty 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__ = '23.11.18' 

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 _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, once}. 

191 ''' 

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

193 return E 

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 @property_RO 

202 def ellipsoidalCartesian(self): 

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

204 ''' 

205 return False 

206 

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

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

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

210 

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

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

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

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

215 this cartesian's C{datum} ellipsoid. 

216 

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

218 to the distance to this C{pov}. 

219 

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

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

222 points outside or away from the ellipsoid. 

223 

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

225 

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

227 ''' 

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

229 

230 @Property 

231 def height(self): 

232 '''Get the height (C{meter}). 

233 ''' 

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

235 

236 @height.setter # PYCHOK setter! 

237 def height(self, height): 

238 '''Set the height (C{meter}). 

239 

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

241 

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

243 ''' 

244 h = Height(height) 

245 if self._height != h: 

246 _update_all(self) 

247 self._height = h 

248 

249 @Property_RO 

250 def _height4(self): 

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

252 ''' 

253 try: 

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

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

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

257 return r 

258 

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

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

261 on this datum's ellipsoid surface. 

262 

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

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

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

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

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

268 ellipsoid's surface, otherwise the intersection of the 

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

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

271 (C{Cartesian}) or C{None}. 

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

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

274 

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

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

277 

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

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

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

281 

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

283 

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

285 

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

287 ''' 

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

289 if normal and d is self.datum: 

290 r = self._height4 

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

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

293 else: 

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

295 if Cartesian is not None: 

296 kwds = Cartesian_kwds.copy() 

297 h = kwds.pop(_height_, None) 

298 r = Cartesian(r, **kwds) 

299 if h is not None: 

300 r.height = Height(height=h) 

301 return r 

302 

303 @Property_RO 

304 def isEllipsoidal(self): 

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

306 ''' 

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

308 

309 @Property_RO 

310 def isSpherical(self): 

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

312 ''' 

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

314 

315 @Property_RO 

316 def latlon(self): 

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

318 ''' 

319 return self.toEcef().latlon 

320 

321 @Property_RO 

322 def latlonheight(self): 

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

324 ''' 

325 return self.toEcef().latlonheight 

326 

327 @Property_RO 

328 def latlonheightdatum(self): 

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

330 ''' 

331 return self.toEcef().latlonheightdatum 

332 

333 @Property_RO 

334 def _ltp(self): 

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

336 ''' 

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

338 

339 @Property_RO 

340 def _N_vector(self): 

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

342 ''' 

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

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

345 

346 def _n_xyzh4(self, datum): 

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

348 ''' 

349 def _ErrorEPS0(x): 

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

351 

352 _xinstanceof(Datum, datum=datum) 

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

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

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

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

357 E = datum.ellipsoid 

358 x, y, z = self.xyz 

359 

360 # Kenneth Gade eqn 23 

361 p = hypot2(x, y) * E.a2_ 

362 q = z**2 * E.e21 * E.a2_ 

363 r = fsumf_(p, q, -E.e4) / _6_0 

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

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

366 if isnear0(t): 

367 raise _ErrorEPS0(t) 

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

369 v = sqrt(u**2 + E.e4 * q) 

370 t = v * _2_0 

371 if t < EPS0: # isnear0 

372 raise _ErrorEPS0(t) 

373 w = fsumf_(u, v, -q) * E.e2 / t 

374 k = sqrt(fsumf_(u, v, w**2)) - w 

375 if isnear0(k): 

376 raise _ErrorEPS0(k) 

377 t = k + E.e2 

378 if isnear0(t): 

379 raise _ErrorEPS0(t) 

380 e = k / t 

381# d = e * hypot(x, y) 

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

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

384 if t < EPS0: # isnear0 

385 raise _ErrorEPS0(t) 

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

387 s = e / t # == e * tmp 

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

389 

390 @Property_RO 

391 def philam(self): 

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

393 ''' 

394 return self.toEcef().philam 

395 

396 @Property_RO 

397 def philamheight(self): 

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

399 ''' 

400 return self.toEcef().philamheight 

401 

402 @Property_RO 

403 def philamheightdatum(self): 

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

405 ''' 

406 return self.toEcef().philamheightdatum 

407 

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

409 '''3-Point resection between this and two other points using U{Pierlot 

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

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

412 

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

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

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

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

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

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

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

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

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

422 (C{bool}). 

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

424 

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

426 

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

428 

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

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

431 

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

433 

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

435 ''' 

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

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

438 

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

440 '''3-Point resection between this and two other points using U{Pierlot 

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

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

443 

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

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

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

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

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

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

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

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

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

453 

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

455 

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

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

458 

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

460 

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

462 ''' 

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

464 useZ=useZ, datum=self.datum) 

465 

466 @property_RO 

467 def sphericalCartesian(self): 

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

469 ''' 

470 return False 

471 

472 @deprecated_method 

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

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

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

476 

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

478 '''3-Point resection between this and two other points using U{Tienstra 

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

480 

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

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

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

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

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

486 non-negative). 

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

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

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

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

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

492 (C{bool}). 

493 

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

495 

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

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

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

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

500 

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

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

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

504 

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

506 

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

508 ''' 

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

510 useZ=useZ, datum=self.datum) 

511 

512 @deprecated_method 

513 def to2ab(self): # PYCHOK no cover 

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

515 

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

517 ''' 

518 return self.philam 

519 

520 @deprecated_method 

521 def to2ll(self): # PYCHOK no cover 

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

523 

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

525 ''' 

526 return self.latlon 

527 

528 @deprecated_method 

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

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

531 

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

533 

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

535 as its name may suggest. 

536 ''' 

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

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

539 

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

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

542# ''' 

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

544# if LL is not None: 

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

546# for n, v in pairs.items(): 

547# setattr(r, n, v) 

548# return r 

549 

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

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

552 

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

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

555 

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

557 

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

559 invalid. 

560 ''' 

561 _xinstanceof(Datum, datum2=datum2) 

562 

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

564 self.toDatum(datum) 

565 

566 i, d = False, c.datum 

567 if d == datum2: 

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

569 

570 elif d == _WGS84: 

571 d = datum2 # convert from WGS84 to datum2 

572 

573 elif datum2 == _WGS84: 

574 i = True # convert to WGS84 by inverse transformation 

575 

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

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

578 d = datum2 

579 

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

581 

582 convertDatum = toDatum # for backward compatibility 

583 

584 def toEcef(self): 

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

586 

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

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

589 

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

591 ''' 

592 return self._ecef9 

593 

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

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

596 

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

598 or L{a_f2Tuple}). 

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

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

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

602 (C{LatLon}) or C{None}. 

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

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

605 

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

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

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

609 

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

611 ''' 

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

613 if d == self.datum: 

614 r = self.toEcef() 

615 else: 

616 c = self.toDatum(d) 

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

618 

619 if LatLon: # class or .classof 

620 h = _heigHt(r, height) 

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

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

623 _xdatum(r.datum, d) 

624 return r 

625 

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

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

628 

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

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

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

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

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

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

635 

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

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

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

639 

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

641 ''' 

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

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

644 

645 def toLtp(self, Ecef=None): 

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

647 

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

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

650 ''' 

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

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

653 

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

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

656 

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

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

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

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

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

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

663 

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

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

666 

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

668 

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

670 

671 @example: 

672 

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

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

675 ''' 

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

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

678 

679 if Nvector is not None: 

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

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

682 return r 

683 

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

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

686 

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

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

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

690 

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

692 ''' 

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

694 

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

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

697 to this cartesian. 

698 

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

700 @kwarg inverse: Apply the inverse of the Helmert 

701 transform (C{bool}). 

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

703 overriding this cartesian's datum. 

704 

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

706 

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

708 is not L{Datums}C{.WGS84}. 

709 ''' 

710 d = datum or self.datum 

711 if inverse and d != _WGS84: 

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

713 txt=_not_(_WGS84.name)) 

714 

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

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

717 

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

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

720 

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

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

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

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

725 

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

727 B{C{Vector}} is C{None}. 

728 

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

730 ''' 

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

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

733 

734 

735__all__ += _ALL_DOCS(CartesianBase) 

736 

737# **) MIT License 

738# 

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

740# 

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

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

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

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

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

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

747# 

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

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

750# 

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

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

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

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

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

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

757# OTHER DEALINGS IN THE SOFTWARE.