Coverage for pygeodesy/cartesianBase.py: 92%

1 

2# -*- coding: utf-8 -*- 

3 

4u'''(INTERNAL) Private C{CartesianBase} class for elliposiodal, spherical and N-/vectorial 

5C{Cartesian}s and public functions L{rtp2xyz}, L{rtp2xyz_}, L{xyz2rtp} and L{xyz2rtp_}. 

6 

7After I{(C) Chris Veness 2011-2024} published under the same MIT Licence**, see 

8U{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 

13from pygeodesy.basics import _isin, _xinstanceof, typename 

14from pygeodesy.constants import EPS, EPS0, INT0, PI2, _isfinite, isnear0, \ 

15 _0_0, _1_0, _N_1_0, _2_0, _4_0, _6_0 

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

17 Transform, _WGS84 

18# from pygeodesy.ecef import EcefKarney # _MODS 

19from pygeodesy.ecefLocals import _EcefLocal 

20from pygeodesy.errors import _IsnotError, _TypeError, _ValueError, _xattr, \ 

21 _xdatum, _xkwds, _xkwds_get, _xkwds_pop2 

22from pygeodesy.fmath import cbrt, hypot, hypot_, hypot2, fabs, sqrt # hypot 

23# from pygeodesy.formy import _hartzell # _MODS 

24from pygeodesy.fsums import fsumf_, Fmt 

25# from pygeodesy.internals import typename # from .basics 

26from pygeodesy.interns import _COMMASPACE_, _datum_, _no_, _phi_ 

27from pygeodesy.interns import _ellipsoidal_, _spherical_ # PYCHOK used! 

28from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

29from pygeodesy.named import _name2__, _Pass 

30from pygeodesy.namedTuples import LatLon4Tuple, _NamedTupleTo, Vector3Tuple, \ 

31 Vector4Tuple 

32# from pygeodesy.nvectorBase import _N_Vector # _MODS 

33from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

34 property_doc_, property_RO, _update_all 

35# from pygeodesy import resections as _resections # _MODS.into 

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

37# from pygeodesy.triaxials import Triaxial_ # _MODS 

38from pygeodesy.units import Degrees, Height, _heigHt, _isMeter, Meter, Radians 

39from pygeodesy.utily import acos1, atan2, sincos2d, sincos2_, degrees, radians 

40from pygeodesy.vector3d import Vector3d, _xyzhdlln4 

41# from pygeodesy.vector3dBase import _xyz3 # _MODS 

42 

43# from math import degrees, fabs, radians, sqrt # from .fmath, .utily 

44 

45__all__ = _ALL_LAZY.cartesianBase 

46__version__ = '25.08.24' 

47 

48_r_ = 'r' 

49_resections = _MODS.into(resections=__name__) 

50_theta_ = 'theta' 

51 

52 

53class CartesianBase(Vector3d, _EcefLocal): 

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

55 ''' 

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

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

58 

59 def __init__(self, x_xyz, y=None, z=None, datum=None, **ll_name): 

60 '''New C{Cartesian...}. 

61 

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

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

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

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

66 @kwarg z: Cartesian Z coordinate (C{scalar}), like B{C{y}}. 

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

68 or L{a_f2Tuple}). 

69 @kwarg ll_name: Optional C{B{name}=NN} (C{str}) and optional, original 

70 latlon C{B{ll}=None} (C{LatLon}). 

71 

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

73 or B{C{x_xyz}} not a C{Cartesian}, L{Ecef9Tuple}, 

74 L{Vector3Tuple} or L{Vector4Tuple} or B{C{datum}} is 

75 not a L{Datum}. 

76 ''' 

77 h, d, ll, n = _xyzhdlln4(x_xyz, None, datum, **ll_name) 

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

79 if h is not None: 

80 self._height = Height(h) 

81 if d is not None: 

82 self.datum = d 

83 

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

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

86# ''' 

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

88# _NotImplemented(self, other) 

89 

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

91 '''3-Point resection between this and 2 other points using U{Cassini 

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

93 

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

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

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

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

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

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

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

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

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

103 force C{z=INT0} (C{bool}). 

104 

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

106 

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

108 

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

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

111 

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

113 

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

115 ''' 

116 return _resections.cassini(self, pointB, pointC, alpha, beta, 

117 useZ=useZ, datum=self.datum) 

118 

119 @deprecated_method 

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

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

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

123 

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

125 '''3-Point resection between this and 2 other points using U{Collins<https://Dokumen.tips/ 

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

127 

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

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

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

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

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

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

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

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

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

137 force C{z=INT0} (C{bool}). 

138 

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

140 

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

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

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

144 

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

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

147 

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

149 

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

151 ''' 

152 return _resections.collins5(self, pointB, pointC, alpha, beta, 

153 useZ=useZ, datum=self.datum) 

154 

155 @deprecated_method 

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

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

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

159 

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

161 def datum(self): 

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

163 ''' 

164 return self._datum 

165 

166 @datum.setter # PYCHOK setter! 

167 def datum(self, datum): 

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

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

170 

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

172 ''' 

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

174 D = self._datum 

175 if D: # is not None 

176 if d.isEllipsoidal and not D.isEllipsoidal: 

177 raise _IsnotError(_ellipsoidal_, datum=datum) 

178 elif d.isSpherical and not D.isSpherical: 

179 raise _IsnotError(_spherical_, datum=datum) 

180 if D != d: # or (D and D.name != d.name) 

181 _update_all(self) 

182 self._datum = d 

183 

184 def destinationXyz(self, delta, Cartesian=None, **name_Cartesian_kwds): 

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

186 

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

188 or L{Local9Tuple}). 

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

190 or C{None}. 

191 @kwarg name_Cartesian_kwds: Optional C{B{name}=NN} (C{str}) and optionally, 

192 additional B{C{Cartesian}} keyword arguments, ignored if 

193 C{B{Cartesian} is None}. 

194 

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

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

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

198 

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

200 item or C{datum} missing or incompatible. 

201 ''' 

202 n, kwds = _name2__(name_Cartesian_kwds, _or_nameof=self) 

203 if Cartesian is None: 

204 r = self._ltp._local2ecef(delta, nine=True) # _EcefLocal._ltp 

205 else: 

206 d = self.datum 

207 if not d: 

208 raise _TypeError(delta=delta, txt=_no_(_datum_)) 

209 t = _xkwds_get(kwds, datum=d) 

210 if _xattr(t, ellipsoid=None) != d.ellipsoid: 

211 raise _TypeError(datum=t, txt=str(d)) 

212 c = self._ltp._local2ecef(delta, nine=False) # _EcefLocal._ltp 

213 r = Cartesian(*c, **kwds) 

214 return r.renamed(n) if n else r 

215 

216 @Property_RO 

217 def _ecef9(self): 

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

219 ''' 

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

221 

222 @property_RO 

223 def ellipsoidalCartesian(self): 

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

225 ''' 

226 return False 

227 

228 def hartzell(self, los=False, earth=None): 

229 '''Compute the intersection of a Line-Of-Sight from this cartesian Point-Of-View 

230 (pov) and this cartesian's C{datum} ellipsoid surface. 

231 

232 @kwarg los: Line-Of-Sight, I{direction} to the ellipsoid (L{Los}, L{Vector3d}), 

233 C{True} for the I{normal, plumb} onto the surface or I{False} or 

234 C{None} to point to the center of the ellipsoid. 

235 @kwarg earth: The earth model (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} 

236 or C{scalar} radius in C{meter}), overriding this cartesian's 

237 datum. 

238 

239 @return: The intersection (C{Cartesian}) with C{.height} set to the distance to 

240 this C{pov}. 

241 

242 @raise IntersectionError: Null or bad C{pov} or B{C{los}}, this C{pov} is inside 

243 the ellipsoid or B{C{los}} points outside or away from 

244 the ellipsoid. 

245 

246 @raise TypeError: Invalid B{C{los}} or invalid or undefined B{C{earth}} or C{datum}. 

247 

248 @see: Function L{hartzell<pygeodesy.formy.hartzell>} for further details. 

249 ''' 

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

251 

252 @Property 

253 def height(self): 

254 '''Get the height (C{meter}). 

255 ''' 

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

257 

258 @height.setter # PYCHOK setter! 

259 def height(self, height): 

260 '''Set the height (C{meter}). 

261 

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

263 

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

265 ''' 

266 h = Height(height) 

267 if self._height != h: 

268 _update_all(self) 

269 self._height = h 

270 

271 def _height2C(self, r, Cartesian=None, datum=None, height=INT0, **kwds): 

272 '''(INTERNAL) Helper for methods C{.height3} and C{.height4}. 

273 ''' 

274 if Cartesian is not None: 

275 r = Cartesian(r, **kwds) 

276 if datum is not None: 

277 r.datum = datum 

278 if height is not None: 

279 r.height = height # Height(height) 

280 return r 

281 

282 def height3(self, earth=None, height=None, **Cartesian_and_kwds): 

283 '''Compute the cartesian at a height above or below this certesian's 

284 C{datum} ellipsoid surface. 

285 

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

287 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid}, 

288 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally). 

289 @kwarg height: The height (C{meter}, conventionally), overriding this 

290 cartesian's height. 

291 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return 

292 the cartesian I{at height} and additional B{C{Cartesian}} 

293 keyword arguments. 

294 

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

296 a L{Vector3Tuple}C{(x, y, z)} with the C{x}, C{y} and C{z} 

297 coordinates I{at height} in C{meter}, conventionally. 

298 

299 @note: This cartesian's coordinates are returned if B{C{earth}} and this 

300 datum or B{C{height}} and/or this height are C{None} or undefined. 

301 

302 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}} 

303 does not accept a B{C{datum}} keyword agument. 

304 

305 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}. 

306 ''' 

307 n = typename(self.height3) 

308 d = self.datum if earth is None else _spherical_datum(earth, name=n) 

309 c, h = self, _heigHt(self, height) 

310 if h and d: 

311 R, r = self.Roc2(earth=d) 

312 if R > EPS0: 

313 R = (R + h) / R 

314 r = ((r + h) / r) if r > EPS0 else _1_0 

315 c = c.times_(R, R, r) 

316 

317 r = Vector3Tuple(c.x, c.y, c.z, name=n) 

318 if Cartesian_and_kwds: 

319 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d)) 

320 return r 

321 

322 @Property_RO 

323 def _height4(self): 

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

325 ''' 

326 try: 

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

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

329 r = Vector4Tuple(self.x, self.y, self.z, 0, name__=self.height4) 

330 return r 

331 

332 def height4(self, earth=None, normal=True, **Cartesian_and_kwds): 

333 '''Compute the projection of this point on and the height above or below 

334 this datum's ellipsoid surface. 

335 

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

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

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

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

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

341 ellipsoid's surface, otherwise the intersection of the 

342 radial line to the ellipsoid's center and surface C{bool}). 

343 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class to return 

344 the I{projection} and additional B{C{Cartesian}} keyword 

345 arguments. 

346 

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

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

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

350 

351 @note: Include keyword argument C{B{datum}=None} if class B{C{Cartesian}} 

352 does not accept a B{C{datum}} keyword agument. 

353 

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

355 

356 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}. 

357 

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

359 ''' 

360 n = typename(self.height4) 

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

362 if normal and d is self.datum: 

363 r = self._height4 

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

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

366 try: 

367 d = d.toEllipsoid(name=n) 

368 except (TypeError, ValueError): # TriaxialError 

369 d = None 

370 else: 

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

372 

373 if Cartesian_and_kwds: 

374 if d and not isinstance(d, Datum): 

375 d = _spherical_datum(d, name=n) 

376 r = self._height2C(r, **_xkwds(Cartesian_and_kwds, datum=d)) 

377 return r 

378 

379 @Property_RO 

380 def isEllipsoidal(self): 

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

382 ''' 

383 return _xattr(self.datum, isEllipsoidal=None) 

384 

385 @Property_RO 

386 def isSpherical(self): 

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

388 ''' 

389 return _xattr(self.datum, isSpherical=None) 

390 

391 @Property_RO 

392 def latlon(self): 

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

394 ''' 

395 return self.toEcef().latlon 

396 

397 @Property_RO 

398 def latlonheight(self): 

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

400 ''' 

401 return self.toEcef().latlonheight 

402 

403 @Property_RO 

404 def latlonheightdatum(self): 

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

406 ''' 

407 return self.toEcef().latlonheightdatum 

408 

409 @Property_RO 

410 def _N_vector(self): 

411 '''(INTERNAL) Get the (C{nvectorBase._N_Vector}). 

412 ''' 

413 _N = _MODS.nvectorBase._N_Vector 

414 return self._n_xyzh4(self.datum, Vector=_N) 

415 

416 def _n_xyzh4(self, datum, Vector=Vector4Tuple): 

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

418 ''' 

419 def _ErrorEPS0(x): 

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

421 

422 _xinstanceof(Datum, datum=datum) 

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

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

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

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

427 E = datum.ellipsoid 

428 x, y, z = self.xyz3 

429 

430 # Kenneth Gade eqn 23 

431 p = hypot2(x, y) * E.a2_ 

432 q = z**2 * E.e21 * E.a2_ 

433 r = fsumf_(p, q, -E.e4) / _6_0 

434 if isnear0(r): 

435 raise _ErrorEPS0(r) 

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

437 if s < 0: 

438 raise _ErrorEPS0(s) 

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

440 if isnear0(t): 

441 raise _ErrorEPS0(t) 

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

443 v = sqrt(u**2 + E.e4 * q) 

444 t = v * _2_0 

445 if t < EPS0: # isnear0 

446 raise _ErrorEPS0(t) 

447 w = fsumf_(u, v, -q) * E.e2 / t 

448 k = sqrt(fsumf_(u, v, w**2)) - w 

449 if isnear0(k): 

450 raise _ErrorEPS0(k) 

451 t = k + E.e2 

452 if isnear0(t): 

453 raise _ErrorEPS0(t) 

454 e = k / t 

455# d = e * hypot(x, y) 

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

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

458 if t < EPS0: # isnear0 

459 raise _ErrorEPS0(t) 

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

461 s = e / t # == e * tmp 

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

463 

464 @Property_RO 

465 def philam(self): 

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

467 ''' 

468 return self.toEcef().philam 

469 

470 @Property_RO 

471 def philamheight(self): 

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

473 ''' 

474 return self.toEcef().philamheight 

475 

476 @Property_RO 

477 def philamheightdatum(self): 

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

479 ''' 

480 return self.toEcef().philamheightdatum 

481 

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

483 '''3-Point resection between this and two other points using U{Pierlot 

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

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

486 

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

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

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

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

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

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

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

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

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

496 (C{bool}). 

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

498 

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

500 

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

502 

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

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

505 

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

507 

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

509 ''' 

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

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

512 

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

514 '''3-Point resection between this and two other points using U{Pierlot 

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

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

517 

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

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

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

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

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

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

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

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

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

527 

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

529 

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

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

532 

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

534 

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

536 ''' 

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

538 useZ=useZ, datum=self.datum) 

539 

540 def Roc2(self, earth=None): 

541 '''Compute this cartesian's I{normal} and I{pseudo, z-based} radius of curvature. 

542 

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

544 I{overriding} this cartesian's datum (L{Datum}, L{Ellipsoid}, 

545 L{Ellipsoid2}, L{a_f2Tuple} or C{meter}, conventionally). 

546 

547 @return: 2-Tuple C{(R, r)} with the I{normal} and I{pseudo, z-based} radius of 

548 curvature C{R} respectively C{r}, both in C{meter} conventionally. 

549 

550 @raise TypeError: Invalid or undefined B{C{earth}} or C{datum}. 

551 ''' 

552 r = z = fabs( self.z) 

553 R, _0 = hypot(self.x, self.y), EPS0 

554 if R < _0: # polar 

555 R = z 

556 elif z > _0: # non-equatorial 

557 d = self.datum if earth is None else _spherical_datum(earth) 

558 e = self.toLatLon(datum=d, height=0, LatLon=None) # Ecef9Tuple 

559 M = e.M # EcefMatrix 

560 sa, ca = map(fabs, (M._2_2_, M._2_1_) if M else sincos2d(e.lat)) 

561 if ca < _0: # polar 

562 R = z 

563 else: # prime-vertical, normal roc R 

564 R = R / ca # /= chokes PyChecker 

565 r = R if sa < _0 else (r / sa) # non-/equatorial 

566 return R, r 

567 

568 @property_RO 

569 def sphericalCartesian(self): 

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

571 ''' 

572 return False 

573 

574 @deprecated_method 

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

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

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

578 

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

580 '''3-Point resection between this and two other points using U{Tienstra 

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

582 

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

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

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

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

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

588 non-negative). 

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

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

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

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

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

594 (C{bool}). 

595 

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

597 

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

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

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

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

602 

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

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

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

606 

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

608 

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

610 ''' 

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

612 useZ=useZ, datum=self.datum) 

613 

614 @deprecated_method 

615 def to2ab(self): # PYCHOK no cover 

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

617 

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

619 ''' 

620 return self.philam 

621 

622 @deprecated_method 

623 def to2ll(self): # PYCHOK no cover 

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

625 

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

627 ''' 

628 return self.latlon 

629 

630 @deprecated_method 

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

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

633 

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

635 

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

637 as its name may suggest. 

638 ''' 

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

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

641 

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

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

644# ''' 

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

646# if LL is not None: 

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

648# for n, v in pairs.items(): 

649# setattr(r, n, v) 

650# return r 

651 

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

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

654 

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

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

657 

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

659 

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

661 invalid. 

662 ''' 

663 _xinstanceof(Datum, datum2=datum2) 

664 

665 c = self if _isin(datum, None, self.datum) else \ 

666 self.toDatum(datum) 

667 

668 i, d = False, c.datum 

669 if d == datum2: 

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

671 

672 elif d is None or (d.transform.isunity and 

673 datum2.transform.isunity): 

674 return c.dup(datum=datum2) 

675 

676 elif d == _WGS84: 

677 d = datum2 # convert from WGS84 to datum2 

678 

679 elif datum2 == _WGS84: 

680 i = True # convert to WGS84 by inverse transformation 

681 

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

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

684 d = datum2 

685 

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

687 

688 def toEcef(self): 

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

690 

691 @return: An L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} 

692 with C{C} and C{M} if available. 

693 

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

695 ''' 

696 return self._ecef9 

697 

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

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

700 

701 @kwarg datum: Optional datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). 

702 @kwarg height: Optional height, overriding the converted height (C{meter}), only if 

703 C{B{LatLon} is not None}. 

704 @kwarg LatLon: Optional class to return the geodetic point (C{LatLon}) or C{None}. 

705 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if 

706 C{B{LatLon} is None}. 

707 

708 @return: The geodetic point (B{C{LatLon}}) or if C{B{LatLon}is None}, an 

709 L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} 

710 and C{M} if available. 

711 

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

713 ''' 

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

715 if d == self.datum: 

716 r = self.toEcef() 

717 else: 

718 c = self.toDatum(d) 

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

720 

721 if LatLon: # class or .classof 

722 h = _heigHt(r, height) 

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

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

725 _xdatum(r.datum, d) 

726 return r 

727 

728 def toNvector(self, Nvector=None, datum=None, **name_Nvector_kwds): 

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

730 

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

732 (C{Nvector}) or C{None}. 

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

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

735 @kwarg name_Nvector_kwds: Optional C{B{name}=NN} (C{str}) and optionally, 

736 additional B{C{Nvector}} keyword arguments, ignored if 

737 C{B{Nvector} is None}. 

738 

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

740 C{B{Nvector} is None}. 

741 

742 @raise TypeError: Invalid B{C{Nvector}}, B{C{datum}} or 

743 B{C{name_Nvector_kwds}} item. 

744 

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

746 ''' 

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

748 if datum is not None: 

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

750 if d != self.datum: 

751 r = self._n_xyzh4(d) 

752 

753 if Nvector is None: 

754 n, _ = _name2__(name_Nvector_kwds, _or_nameof=self) 

755 if n: 

756 r = r.dup(name=n) 

757 else: 

758 kwds = _xkwds(name_Nvector_kwds, h=r.h, datum=d) 

759 r = Nvector(r.x, r.y, r.z, **self._name1__(kwds)) 

760 return r 

761 

762 def toRtp(self): 

763 '''Convert this cartesian to I{spherical, polar} coordinates. 

764 

765 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} 

766 and C{phi}, both in L{Degrees}. 

767 

768 @see: Function L{xyz2rtp_} and class L{RadiusThetaPhi3Tuple}. 

769 ''' 

770 return _rtp3(self.toRtp, Degrees, self, name=self.name) 

771 

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

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

774 

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

776 @kwarg fmt: Enclosing backets format (C{letter}). 

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

778 

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

780 ''' 

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

782 

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

784 '''Apply a Helmert transform to this cartesian. 

785 

786 @arg transform: Transform to apply (L{Transform} or L{TransformXform}). 

787 @kwarg inverse: Apply the inverse of the C{B{transform}} (C{bool}). 

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

789 this cartesian's datum but I{not} taken it into account. 

790 

791 @return: A transformed cartesian (C{Cartesian}) or a copy of this 

792 cartesian if C{B{transform}.isunity}. 

793 

794 @raise TypeError: Invalid B{C{transform}}. 

795 ''' 

796 _xinstanceof(Transform, transform=transform) 

797 if transform.isunity: 

798 c = self.dup(datum=datum or self.datum) 

799 else: 

800 # if inverse and d != _WGS84: 

801 # raise _ValueError(inverse=inverse, datum=d, 

802 # txt_not_=_WGS84.name) 

803 xyz = transform.transform(*self.xyz3, inverse=inverse) 

804 c = self.dup(xyz=xyz, datum=datum or self.datum) 

805 return c 

806 

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

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

809 

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

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

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

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

814 

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

816 C{B{Vector} is None}. 

817 

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

819 ''' 

820 return self.xyz if Vector is None else Vector( 

821 self.x, self.y, self.z, **self._name1__(Vector_kwds)) 

822 

823 

824class RadiusThetaPhi3Tuple(_NamedTupleTo): 

825 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination 

826 C{theta} (with respect to the positive z-axis) and azimuthal angle C{phi} in 

827 L{Degrees} I{or} L{Radians} representing a U{spherical, polar position 

828 <https://WikiPedia.org/wiki/Spherical_coordinate_system>}. 

829 ''' 

830 _Names_ = (_r_, _theta_, _phi_) 

831 _Units_ = ( Meter, _Pass, _Pass) 

832 

833 def toCartesian(self, **name_Cartesian_and_kwds): 

834 '''Convert this L{RadiusThetaPhi3Tuple} to a cartesian C{(x, y, z)} vector. 

835 

836 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN}, overriding this 

837 name and optional class C{B{Cartesian}=None} and additional 

838 C{B{Cartesian}} keyword arguments. 

839 

840 @return: A C{B{Cartesian}(x, y, z)} instance or if no C{B{Cartesian}} keyword 

841 argument is given, a L{Vector3Tuple}C{(x, y, z)} with C{x}, C{y} 

842 and C{z} in the same units as radius C{r}, C{meter} conventionally. 

843 

844 @see: Function L{rtp2xyz_}. 

845 ''' 

846 r, t, p = self 

847 t, p, _ = _NamedTupleTo._Radians3(self, t, p) 

848 return rtp2xyz_(r, t, p, **name_Cartesian_and_kwds) 

849 

850 def toDegrees(self, **name): 

851 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Degrees}. 

852 

853 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name. 

854 

855 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} 

856 and C{phi} both in L{Degrees}. 

857 ''' 

858 return self._toX3U(_NamedTupleTo._Degrees3, Degrees, name) 

859 

860 def toRadians(self, **name): 

861 '''Convert this L{RadiusThetaPhi3Tuple}'s angles to L{Radians}. 

862 

863 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name. 

864 

865 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} 

866 and C{phi} both in L{Radians}. 

867 ''' 

868 return self._toX3U(_NamedTupleTo._Radians3, Radians, name) 

869 

870 def _toU(self, U): 

871 M = RadiusThetaPhi3Tuple._Units_[0] # Meter 

872 return self.reUnit(M, U, U).toUnits() 

873 

874 def _toX3U(self, _X3, U, name): 

875 r, t, p = self 

876 t, p, s = _X3(self, t, p) 

877 if s is None or name: 

878 n = self._name__(name) 

879 s = self.classof(r, t, p, name=n)._toU(U) 

880 return s 

881 

882 

883def rtp2xyz(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds): 

884 '''Convert I{spherical, polar} C{(r, theta, phi)} to cartesian C{(x, y, z)} coordinates. 

885 

886 @arg theta: Inclination B{C{theta}} (C{degrees} with respect to the positive z-axis), 

887 required if C{B{r_rtp}} is C{scalar}, ignored otherwise. 

888 @arg phi: Azimuthal angle B{C{phi}} (C{degrees}), like B{C{theta}}. 

889 

890 @see: Function L{rtp2xyz_} for further details. 

891 ''' 

892 if isinstance(r_rtp, RadiusThetaPhi3Tuple): 

893 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)