Coverage for pygeodesy/cartesianBase.py: 95%

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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, _spherical_datum, _WGS84, _xinstanceof 

17from pygeodesy.errors import _IsnotError, _ValueError, _xdatum, _xkwds 

18from pygeodesy.fmath import cbrt, hypot_, hypot2, sqrt # hypot 

19from pygeodesy.fsums import Fmt, fsumf_ 

20from pygeodesy.interns import NN, _COMMASPACE_, _height_, _not_ 

21from pygeodesy.interns import _ellipsoidal_, _spherical_ # PYCHOK used! 

22from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

23from pygeodesy.namedTuples import LatLon4Tuple, Vector4Tuple, \ 

24 Bearing2Tuple # PYCHOK .sphericalBase 

25from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

26 property_doc_, _update_all 

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

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

29from pygeodesy.units import Height, _heigHt 

30from pygeodesy.vector3d import Vector3d, _xyzhdn3 

31 

32# from math import sqrt # from .fmath 

33 

34__all__ = _ALL_LAZY.cartesianBase 

35__version__ = '23.06.02' 

36 

37 

38class CartesianBase(Vector3d): 

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

40 ''' 

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

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

43 

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

45 '''New C{Cartesian...}. 

46 

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

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

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

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

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

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

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

54 or L{a_f2Tuple}). 

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

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

57 

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

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

60 L{Vector3Tuple} or L{Vector4Tuple}. 

61 ''' 

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

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

64 if h is not None: 

65 self._height = Height(h) 

66 if d is not None: 

67 self.datum = d 

68 

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

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

71# ''' 

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

73# _NotImplemented(self, other) 

74 

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

76 '''3-Point resection between this and 2 other points using U{Cassini 

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

78 

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

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

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

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

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

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

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

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

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

88 force C{z=INT0} (C{bool}). 

89 

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

91 

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

93 

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

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

96 

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

98 

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

100 ''' 

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

102 useZ=useZ, datum=self.datum) 

103 

104 @deprecated_method 

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

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

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

108 

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

110 '''3-Point resection between this and 2 other points using U{Collins<https://Dokumen.tips/ 

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

112 

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

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

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

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

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

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

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

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

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

122 force C{z=INT0} (C{bool}). 

123 

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

125 

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

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

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

129 

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

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

132 

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

134 

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

136 ''' 

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

138 useZ=useZ, datum=self.datum) 

139 

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

141 def datum(self): 

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

143 ''' 

144 return self._datum 

145 

146 @datum.setter # PYCHOK setter! 

147 def datum(self, datum): 

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

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

150 

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

152 ''' 

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

154 if self._datum: # is not None 

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

156 raise _IsnotError(_ellipsoidal_, datum=datum) 

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

158 raise _IsnotError(_spherical_, datum=datum) 

159 if self._datum != d: 

160 _update_all(self) 

161 self._datum = d 

162 

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

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

165 

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

167 L{Ned} or L{Local9Tuple}). 

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

169 destination or C{None}. 

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

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

172 

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

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

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

176 

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

178 B{C{Cartesian_kwds}}. 

179 ''' 

180 if Cartesian is None: 

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

182 else: 

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

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

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

186 

187 @Property_RO 

188 def Ecef(self): 

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

190 ''' 

191 return _MODS.ecef.EcefKarney # default 

192 

193 @Property_RO 

194 def _ecef9(self): 

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

196 ''' 

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

198 

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

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

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

202 

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

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

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

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

207 this cartesian's C{datum} ellipsoid. 

208 

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

210 

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

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

213 outside the ellipsoid or in an opposite direction. 

214 

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

216 

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

218 ''' 

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

220 

221 @Property 

222 def height(self): 

223 '''Get the height (C{meter}). 

224 ''' 

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

226 

227 @height.setter # PYCHOK setter! 

228 def height(self, height): 

229 '''Set the height (C{meter}). 

230 

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

232 

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

234 ''' 

235 h = Height(height) 

236 if self._height != h: 

237 _update_all(self) 

238 self._height = h 

239 

240 @Property_RO 

241 def _height4(self): 

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

243 ''' 

244 try: 

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

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

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

248 return r 

249 

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

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

252 on this datum's ellipsoid surface. 

253 

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

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

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

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

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

259 ellipsoid's surface, otherwise the intersection of the 

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

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

262 (C{Cartesian}) or C{None}. 

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

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

265 

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

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

268 

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

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

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

272 

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

274 

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

276 

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

278 ''' 

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

280 if normal and d == self.datum: 

281 r = self._height4 

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

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

284 else: 

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

286 if Cartesian is not None: 

287 kwds = Cartesian_kwds.copy() 

288 h = kwds.pop(_height_, None) 

289 r = Cartesian(r, **kwds) 

290 if h is not None: 

291 r.height = Height(height=h) 

292 return r 

293 

294 @Property_RO 

295 def isEllipsoidal(self): 

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

297 ''' 

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

299 

300 @Property_RO 

301 def isSpherical(self): 

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

303 ''' 

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

305 

306 @Property_RO 

307 def latlon(self): 

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

309 ''' 

310 return self.toEcef().latlon 

311 

312 @Property_RO 

313 def latlonheight(self): 

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

315 ''' 

316 return self.toEcef().latlonheight 

317 

318 @Property_RO 

319 def latlonheightdatum(self): 

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

321 ''' 

322 return self.toEcef().latlonheightdatum 

323 

324 @Property_RO 

325 def _ltp(self): 

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

327 ''' 

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

329 

330 @Property_RO 

331 def _N_vector(self): 

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

333 ''' 

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

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

336 

337 def _n_xyzh4(self, datum): 

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

339 ''' 

340 def _ErrorEPS0(x): 

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

342 

343 _xinstanceof(Datum, datum=datum) 

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

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

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

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

348 E = datum.ellipsoid 

349 x, y, z = self.xyz 

350 

351 # Kenneth Gade eqn 23 

352 p = hypot2(x, y) * E.a2_ 

353 q = z**2 * E.e21 * E.a2_ 

354 r = fsumf_(p, q, -E.e4) / _6_0 

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

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

357 if isnear0(t): 

358 raise _ErrorEPS0(t) 

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

360 v = sqrt(u**2 + E.e4 * q) 

361 t = v * _2_0 

362 if t < EPS0: # isnear0 

363 raise _ErrorEPS0(t) 

364 w = fsumf_(u, v, -q) * E.e2 / t 

365 k = sqrt(fsumf_(u, v, w**2)) - w 

366 if isnear0(k): 

367 raise _ErrorEPS0(k) 

368 t = k + E.e2 

369 if isnear0(t): 

370 raise _ErrorEPS0(t) 

371 e = k / t 

372# d = e * hypot(x, y) 

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

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

375 if t < EPS0: # isnear0 

376 raise _ErrorEPS0(t) 

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

378 s = e / t # == e * tmp 

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

380 

381 @Property_RO 

382 def philam(self): 

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

384 ''' 

385 return self.toEcef().philam 

386 

387 @Property_RO 

388 def philamheight(self): 

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

390 ''' 

391 return self.toEcef().philamheight 

392 

393 @Property_RO 

394 def philamheightdatum(self): 

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

396 ''' 

397 return self.toEcef().philamheightdatum 

398 

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

400 '''3-Point resection between this and two other points using U{Pierlot 

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

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

403 

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

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

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

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

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

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

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

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

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

413 (C{bool}). 

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

415 

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

417 

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

419 

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

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

422 

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

424 

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

426 ''' 

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

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

429 

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

431 '''3-Point resection between this and two other points using U{Pierlot 

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

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

434 

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

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

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

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

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

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

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

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

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

444 

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

446 

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

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

449 

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

451 

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

453 ''' 

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

455 useZ=useZ, datum=self.datum) 

456 

457 @deprecated_method 

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

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

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

461 

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

463 '''3-Point resection between this and two other points using U{Tienstra 

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

465 

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

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

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

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

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

471 non-negative). 

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

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

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

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

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

477 (C{bool}). 

478 

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

480 

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

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

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

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

485 

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

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

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

489 

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

491 

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

493 ''' 

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

495 useZ=useZ, datum=self.datum) 

496 

497 @deprecated_method 

498 def to2ab(self): # PYCHOK no cover 

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

500 

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

502 ''' 

503 return self.philam 

504 

505 @deprecated_method 

506 def to2ll(self): # PYCHOK no cover 

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

508 

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

510 ''' 

511 return self.latlon 

512 

513 @deprecated_method 

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

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

516 

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

518 

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

520 as its name may suggest. 

521 ''' 

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

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

524 

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

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

527# ''' 

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

529# if LL is not None: 

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

531# for n, v in pairs.items(): 

532# setattr(r, n, v) 

533# return r 

534 

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

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

537 

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

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

540 

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

542 

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

544 invalid. 

545 ''' 

546 _xinstanceof(Datum, datum2=datum2) 

547 

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

549 self.toDatum(datum) 

550 

551 i, d = False, c.datum 

552 if d == datum2: 

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

554 

555 elif d == _WGS84: 

556 d = datum2 # convert from WGS84 to datum2 

557 

558 elif datum2 == _WGS84: 

559 i = True # convert to WGS84 by inverse transformation 

560 

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

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

563 d = datum2 

564 

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

566 

567 convertDatum = toDatum # for backward compatibility 

568 

569 def toEcef(self): 

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

571 

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

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

574 

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

576 ''' 

577 return self._ecef9 

578 

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

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

581 

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

583 or L{a_f2Tuple}). 

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

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

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

587 (C{LatLon}) or C{None}. 

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

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

590 

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

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

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

594 

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

596 ''' 

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

598 if d == self.datum: 

599 r = self.toEcef() 

600 else: 

601 c = self.toDatum(d) 

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

603 

604 if LatLon: # class or .classof 

605 h = _heigHt(r, height) 

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

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

608 _xdatum(r.datum, d) 

609 return r 

610 

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

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

613 

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

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

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

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

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

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

620 

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

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

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

624 

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

626 ''' 

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

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

629 

630 def toLtp(self, Ecef=None): 

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

632 

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

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

635 ''' 

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

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

638 

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

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

641 

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

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

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

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

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

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

648 

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

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

651 

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

653 

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

655 

656 @example: 

657 

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

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

660 ''' 

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

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

663 

664 if Nvector is not None: 

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

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

667 return r 

668 

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

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

671 

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

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

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

675 

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

677 ''' 

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

679 

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

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

682 to this cartesian. 

683 

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

685 @kwarg inverse: Apply the inverse of the Helmert 

686 transform (C{bool}). 

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

688 overriding this cartesian's datum. 

689 

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

691 

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

693 is not L{Datums}C{.WGS84}. 

694 ''' 

695 d = datum or self.datum 

696 if inverse and d != _WGS84: 

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

698 txt=_not_(_WGS84.name)) 

699 

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

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

702 

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

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

705 

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

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

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

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

710 

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

712 B{C{Vector}} is C{None}. 

713 

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

715 ''' 

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

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

718 

719 

720__all__ += _ALL_DOCS(CartesianBase) 

721 

722# **) MIT License 

723# 

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

725# 

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

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

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

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

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

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

732# 

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

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

735# 

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

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

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

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

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

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

742# OTHER DEALINGS IN THE SOFTWARE.