Coverage for pygeodesy/cartesianBase.py: 91%

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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 2011-2015} 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 

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

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, _xinstanceof 

18# from pygeodesy.ecef import EcefKarney # _MODS 

19from pygeodesy.errors import _IsnotError, _TypeError, _ValueError, \ 

20 _xdatum, _xkwds 

21from pygeodesy.fmath import cbrt, hypot, hypot_, hypot2, fabs, sqrt # hypot 

22# from pygeodesy.formy import _hartzell # _MODS 

23from pygeodesy.fsums import fsumf_, Fmt 

24from pygeodesy.interns import NN, _COMMASPACE_, _phi_ # _not_ 

25from pygeodesy.interns import _ellipsoidal_, _spherical_ # PYCHOK used! 

26from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

27from pygeodesy.named import _NamedTuple, _Pass 

28from pygeodesy.namedTuples import LatLon4Tuple, Vector3Tuple, Vector4Tuple, \ 

29 Bearing2Tuple # PYCHOK .sphericalBase 

30# from pygeodesy.nvectorBase import _N_vector # _MODS 

31from pygeodesy.props import deprecated_method, Property, Property_RO, \ 

32 property_doc_, property_RO, _update_all 

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

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

35# from pygeodesy.triaxials import Triaxial_ # _MODS 

36from pygeodesy.units import Degrees, Height, _heigHt, _isMeter, Meter, \ 

37 Radians, _toDegrees, _toRadians 

38from pygeodesy.utily import acos1, sincos2d, sincos2_, atan2, degrees, radians 

39from pygeodesy.vector3d import Vector3d, _xyzhdn3 

40# from pygeodesy.vector3dBase import _xyz3 # _MODS 

41# from pygeodesy import ltp, resections # _MODS 

42 

43# from math import atan2, degrees, fabs, radians, sqrt # from .fmath, .utily 

44 

45__all__ = _ALL_LAZY.cartesianBase 

46__version__ = '24.02.22' 

47 

48_r_ = 'r' 

49_theta_ = 'theta' 

50 

51 

52class CartesianBase(Vector3d): 

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

54 ''' 

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

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

57 

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

59 '''New C{Cartesian...}. 

60 

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

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

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

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

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

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

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

68 or L{a_f2Tuple}). 

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

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

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, n = _xyzhdn3(x_xyz, None, datum, ll) 

78 Vector3d.__init__(self, x_xyz, y=y, z=z, ll=ll, name=name or 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 self._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 self._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 if self._datum: # is not None 

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

176 raise _IsnotError(_ellipsoidal_, datum=datum) 

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

178 raise _IsnotError(_spherical_, datum=datum) 

179 if self._datum != d: 

180 _update_all(self) 

181 self._datum = d 

182 

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

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

185 

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

187 L{Ned} or L{Local9Tuple}). 

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

189 destination or C{None}. 

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

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

192 

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

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

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

196 

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

198 B{C{Cartesian_kwds}}. 

199 ''' 

200 if Cartesian is None: 

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

202 else: 

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

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

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

206 

207 @property_RO 

208 def Ecef(self): 

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

210 ''' 

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

212 return E 

213 

214 @Property_RO 

215 def _ecef9(self): 

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

217 ''' 

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

219 

220 @property_RO 

221 def ellipsoidalCartesian(self): 

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

223 ''' 

224 return False 

225 

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

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

228 (pov) and this cartesian's ellipsoid surface. 

229 

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

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

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

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

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

235 C{datum} ellipsoid. 

236 

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

238 this C{pov}. 

239 

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

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

242 the ellipsoid. 

243 

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

245 

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

247 ''' 

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

249 

250 @Property 

251 def height(self): 

252 '''Get the height (C{meter}). 

253 ''' 

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

255 

256 @height.setter # PYCHOK setter! 

257 def height(self, height): 

258 '''Set the height (C{meter}). 

259 

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

261 

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

263 ''' 

264 h = Height(height) 

265 if self._height != h: 

266 _update_all(self) 

267 self._height = h 

268 

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

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

271 ''' 

272 if Cartesian is not None: 

273 r = Cartesian(r, **kwds) 

274 if datum is not None: 

275 r.datum = datum 

276 if height is not None: 

277 r.height = height # Height(height) 

278 return r 

279 

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

281 '''Compute the cartesian at a height above or below this certesian's ellipsoid. 

282 

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

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

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

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

287 cartesian's height. 

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

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

290 keyword arguments. 

291 

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

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

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

295 

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

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

298 

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

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

301 

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

303 

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

305 ''' 

306 n = self.height3.__name__ 

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

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

309 if h and d: 

310 R, r = self.Roc2(earth=d) 

311 if R > EPS0: 

312 R = (R + h) / R 

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

314 c = c.times_(R, R, r) 

315 

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

317 if Cartesian_and_kwds: 

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

319 return r 

320 

321 @Property_RO 

322 def _height4(self): 

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

324 ''' 

325 try: 

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

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

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

329 return r 

330 

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

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

333 this datum's ellipsoid surface. 

334 

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

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

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

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

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

340 ellipsoid's surface, otherwise the intersection of the 

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

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

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

344 arguments. 

345 

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

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

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

349 

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

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

352 

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

354 

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

356 

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

358 ''' 

359 n = self.height4.__name__ 

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

361 if normal and d is self.datum: 

362 r = self._height4 

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

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

365 try: 

366 d = d.toEllipsoid(name=n) 

367 except (TypeError, ValueError): # TriaxialError 

368 d = None 

369 else: 

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

371 

372 if Cartesian_and_kwds: 

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

374 d = _spherical_datum(d, name=n) 

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

376 return r 

377 

378 @Property_RO 

379 def isEllipsoidal(self): 

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

381 ''' 

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

383 

384 @Property_RO 

385 def isSpherical(self): 

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

387 ''' 

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

389 

390 @Property_RO 

391 def latlon(self): 

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

393 ''' 

394 return self.toEcef().latlon 

395 

396 @Property_RO 

397 def latlonheight(self): 

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

399 ''' 

400 return self.toEcef().latlonheight 

401 

402 @Property_RO 

403 def latlonheightdatum(self): 

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

405 ''' 

406 return self.toEcef().latlonheightdatum 

407 

408 @property_RO 

409 def _ltp(self): 

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

411 ''' 

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

413 return m 

414 

415 @Property_RO 

416 def _Ltp(self): 

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

418 ''' 

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

420 

421 @Property_RO 

422 def _N_vector(self): 

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

424 ''' 

425 m = _MODS.nvectorBase 

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

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

428 

429 def _n_xyzh4(self, datum): 

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

431 ''' 

432 def _ErrorEPS0(x): 

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

434 

435 _xinstanceof(Datum, datum=datum) 

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

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

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

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

440 E = datum.ellipsoid 

441 x, y, z = self.xyz 

442 

443 # Kenneth Gade eqn 23 

444 p = hypot2(x, y) * E.a2_ 

445 q = z**2 * E.e21 * E.a2_ 

446 r = fsumf_(p, q, -E.e4) / _6_0 

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

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

449 if isnear0(t): 

450 raise _ErrorEPS0(t) 

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

452 v = sqrt(u**2 + E.e4 * q) 

453 t = v * _2_0 

454 if t < EPS0: # isnear0 

455 raise _ErrorEPS0(t) 

456 w = fsumf_(u, v, -q) * E.e2 / t 

457 k = sqrt(fsumf_(u, v, w**2)) - w 

458 if isnear0(k): 

459 raise _ErrorEPS0(k) 

460 t = k + E.e2 

461 if isnear0(t): 

462 raise _ErrorEPS0(t) 

463 e = k / t 

464# d = e * hypot(x, y) 

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

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

467 if t < EPS0: # isnear0 

468 raise _ErrorEPS0(t) 

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

470 s = e / t # == e * tmp 

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

472 

473 @Property_RO 

474 def philam(self): 

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

476 ''' 

477 return self.toEcef().philam 

478 

479 @Property_RO 

480 def philamheight(self): 

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

482 ''' 

483 return self.toEcef().philamheight 

484 

485 @Property_RO 

486 def philamheightdatum(self): 

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

488 ''' 

489 return self.toEcef().philamheightdatum 

490 

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

492 '''3-Point resection between this and two other points using U{Pierlot 

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

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

495 

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

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

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

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

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

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

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

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

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

505 (C{bool}). 

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

507 

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

509 

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

511 

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

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

514 

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

516 

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

518 ''' 

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

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

521 

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

523 '''3-Point resection between this and two other points using U{Pierlot 

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

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

526 

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

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

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

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

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

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

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

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

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

536 

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

538 

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

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

541 

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

543 

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

545 ''' 

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

547 useZ=useZ, datum=self.datum) 

548 

549 @property_RO 

550 def _resections(self): 

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

552 ''' 

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

554 return m 

555 

556 def Roc2(self, earth=None): 

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

558 

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

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

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

562 

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

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

565 

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

567 ''' 

568 r = z = fabs( self.z) 

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

570 if R < _0: # polar 

571 R = z 

572 elif z > _0: # non-equatorial 

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

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

575 M = e.M # EcefMatrix 

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

577 if ca < _0: # polar 

578 R = z 

579 else: # prime-vertical, normal roc R 

580 R = R / ca # /= chokes PyChecker 

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

582 return R, r 

583 

584 @property_RO 

585 def sphericalCartesian(self): 

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

587 ''' 

588 return False 

589 

590 @deprecated_method 

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

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

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

594 

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

596 '''3-Point resection between this and two other points using U{Tienstra 

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

598 

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

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

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

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

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

604 non-negative). 

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

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

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

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

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

610 (C{bool}). 

611 

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

613 

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

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

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

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

618 

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

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

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

622 

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

624 

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

626 ''' 

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

628 useZ=useZ, datum=self.datum) 

629 

630 @deprecated_method 

631 def to2ab(self): # PYCHOK no cover 

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

633 

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

635 ''' 

636 return self.philam 

637 

638 @deprecated_method 

639 def to2ll(self): # PYCHOK no cover 

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

641 

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

643 ''' 

644 return self.latlon 

645 

646 @deprecated_method 

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

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

649 

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

651 

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

653 as its name may suggest. 

654 ''' 

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

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

657 

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

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

660# ''' 

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

662# if LL is not None: 

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

664# for n, v in pairs.items(): 

665# setattr(r, n, v) 

666# return r 

667 

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

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

670 

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

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

673 

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

675 

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

677 invalid. 

678 ''' 

679 _xinstanceof(Datum, datum2=datum2) 

680 

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

682 self.toDatum(datum) 

683 

684 i, d = False, c.datum 

685 if d == datum2: 

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

687 

688 elif datum2.transform.isunity and \ 

689 d.transform.isunity: 

690 return c.dup(datum=datum2) 

691 

692 elif d == _WGS84: 

693 d = datum2 # convert from WGS84 to datum2 

694 

695 elif datum2 == _WGS84: 

696 i = True # convert to WGS84 by inverse transformation 

697 

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

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

700 d = datum2 

701 

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

703 

704 def toEcef(self): 

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

706 

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

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

709 

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

711 ''' 

712 return self._ecef9 

713 

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

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

716 

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

718 or L{a_f2Tuple}). 

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

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

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

722 (C{LatLon}) or C{None}. 

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

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

725 

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

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

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

729 

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

731 ''' 

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

733 if d == self.datum: 

734 r = self.toEcef() 

735 else: 

736 c = self.toDatum(d) 

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

738 

739 if LatLon: # class or .classof 

740 h = _heigHt(r, height) 

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

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

743 _xdatum(r.datum, d) 

744 return r 

745 

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

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

748 

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

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

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

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

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

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

755 

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

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

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

759 

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

761 ''' 

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

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

764 

765 def toLtp(self, Ecef=None): 

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

767 

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

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

770 ''' 

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

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

773 

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

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

776 

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

778 (C{Nvector}) or C{None}. 

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

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

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

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

783 

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

785 B{C{Nvector}} is C{None}. 

786 

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

788 B{C{datum}}. 

789 

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

791 ''' 

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

793 if datum is not None: 

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

795 if d != self.datum: 

796 r = self._n_xyzh4(d) 

797 

798 if Nvector is not None: 

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

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

801 return r 

802 

803 def toRtp(self): 

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

805 

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

807 and C{phi}, both in L{Degrees}. 

808 

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

810 ''' 

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

812 

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

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

815 

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

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

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

819 

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

821 ''' 

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

823 

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

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

826 

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

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

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

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

831 

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

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

834 

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

836 ''' 

837 _xinstanceof(Transform, transform=transform) 

838 if transform.isunity: 

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

840 else: 

841 # if inverse and d != _WGS84: 

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

843 # txt=_not_(_WGS84.name)) 

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

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

846 return c 

847 

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

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

850 

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

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

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

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

855 

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

857 B{C{Vector}} is C{None}. 

858 

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

860 ''' 

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

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

863 

864 

865class RadiusThetaPhi3Tuple(_NamedTuple): 

866 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination 

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

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

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

870 ''' 

871 _Names_ = (_r_, _theta_, _phi_) 

872 _Units_ = ( Meter, _Pass, _Pass) 

873 

874 def toCartesian(self, name=NN, **Cartesian_and_kwds): 

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

876 

877 @kwarg name: Optional name (C{str}), overriding this name. 

878 @kwarg Cartesian_and_kwds: Optional C{B{Cartesian}=None} class and additional 

879 C{B{Cartesian}} keyword arguments. 

880 

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

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

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

884 

885 @see: Function L{rtp2xyz_}. 

886 ''' 

887 r, t, p = self 

888 t, p, _ = _toRadians(self, t, p) 

889 return rtp2xyz_(r, t, p, name=name or self.name, **Cartesian_and_kwds) 

890 

891 def toDegrees(self, name=NN): 

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

893 

894 @kwarg name: Optional name (C{str}), overriding this name. 

895 

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

897 and C{phi} both in L{Degrees}. 

898 ''' 

899 r, t, p = self 

900 t, p, _ = _toDegrees(self, t, p) 

901 return _ or self.classof(r, Degrees(theta=t), Degrees(phi=p), 

902 name=name or self.name) 

903 

904 def toRadians(self, name=NN): 

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

906 

907 @kwarg name: Optional name (C{str}), overriding this name. 

908 

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

910 and C{phi} both in L{Radians}. 

911 ''' 

912 r, t, p = self 

913 t, p, _ = _toRadians(self, t, p) 

914 return _ or self.classof(r, Radians(theta=t), Radians(phi=p), 

915 name=name or self.name) 

916 

917 

918def rtp2xyz(r_rtp, *theta_phi, **name_Cartesian_and_kwds): 

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

920 

921 @arg r_rtp: Radial distance (C{scalar}, conventially C{meter}) or a previous 

922 L{RadiusThetaPhi3Tuple} instance. 

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

924 and azimuthal angle B{C{phi}} (C{degrees}), ignored if C{B{r_rtp}} is a 

925 L{RadiusThetaPhi3Tuple}. 

926 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN} (C{str}), a C{B{Cartesian}=None} 

927 class to return the coordinates and additional C{B{Cartesian}} 

928 keyword arguments. 

929 

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

931 is given a L{Vector3Tuple}C{(x, y, z)}, with C{x}, C{y} and C{z} in the same 

932 units as radius C{r}, C{meter} conventionally. 

933 

934 @raise TypeError: Invalid B{C{r_rtp}}. 

935 

936 @see: Functions L{rtp2xyz_} and L{xyz2rtp}. 

937 ''' 

938 if isinstance(r_rtp, RadiusThetaPhi3Tuple): 

939 c = r_rtp.toCartesian(**name_Cartesian_and_kwds) 

940 else: 

941 c = rtp2xyz_(r_rtp, *map(radians, theta_phi), **name_Cartesian_and_kwds) 

942 return c 

943 

944 

945def rtp2xyz_(r_rtp, *theta_phi, **name_Cartesian_and_kwds): 

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

947 

948 @arg r_rtp: Radial distance (C{scalar}, conventially C{meter}) or a previous 

949 L{RadiusThetaPhi3Tuple} instance. 

950 @arg theta_phi: Inclination B{C{theta}} (C{radians} with respect to the positive z-axis) 

951 and azimuthal angle B{C{phi}} (C{degrees}), ignored is C{B{r_rtp}} is a 

952 L{RadiusThetaPhi3Tuple}. 

953 @kwarg name_Cartesian_and_kwds: Optional C{B{name}=NN} (C{str}), a C{B{Cartesian}=None} 

954 class to return the coordinates and additional C{B{Cartesian}} 

955 keyword arguments. 

956 

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

958 is given a L{Vector3Tuple}C{(x, y, z)}, with C{x}, C{y} and C{z} in the same 

959 units as radius C{r}, C{meter} conventionally. 

960 

961 @raise TypeError: Invalid B{C{r_rtp}} or B{C{theta_phi}}. 

962 

963 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>} 

964 (ISO 80000-2:2019). 

965 ''' 

966 if _isMeter(r_rtp) and len(theta_phi) == 2: 

967 r = r_rtp 

968 if r and _isfinite(r): 

969 s, z, y, x = sincos2_(*theta_phi) 

970 s *= r 

971 z *= r 

972 y *= s 

973 x *= s 

974 else: 

975 x = y = z = r 

976 

977 def _n_C_kwds3(name=NN, Cartesian=None, **kwds): 

978 return name, Cartesian, kwds 

979 

980 n, C, kwds = _n_C_kwds3(**name_Cartesian_and_kwds) 

981 c = Vector3Tuple(x, y, z, name=n) if C is None else \ 

982 C(x, y, z, name=n, **kwds) 

983 

984 elif isinstance(r_rtp, RadiusThetaPhi3Tuple): 

985 c = r_rtp.toCartesian(**name_Cartesian_and_kwds) 

986 else: 

987 raise _TypeError(r_rtp=r_rtp, theta_phi=theta_phi) 

988 return c 

989 

990 

991def _rtp3(where, Unit, *x_y_z, **name): 

992 '''(INTERNAL) Helper for C{.toRtp}, C{xyz2rtp} and C{xyz2rtp_}. 

993 ''' 

994 x, y, z = _MODS.vector3dBase._xyz3(where, *x_y_z) 

995 r = hypot_(x, y, z) 

996 if r > 0: 

997 t = acos1(z / r) 

998 p = atan2(y, x) 

999 while p < 0: 

1000 p += PI2 

1001 if Unit is Degrees: 

1002 t = degrees(t) 

1003 p = degrees(p) 

1004 else: 

1005 t = p = _0_0 

1006 return RadiusThetaPhi3Tuple(r, Unit(theta=t), Unit(phi=p), **name) 

1007 

1008 

1009def xyz2rtp(x_xyz, *y_z, **name): 

1010 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates. 

1011 

1012 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} and C{phi}, 

1013 both in L{Degrees}. 

1014 

1015 @see: Function L{xyz2rtp_} and class L{RadiusThetaPhi3Tuple}. 

1016 ''' 

1017 return _rtp3(xyz2rtp, Degrees, x_xyz, *y_z, **name) 

1018 

1019 

1020def xyz2rtp_(x_xyz, *y_z, **name): 

1021 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates. 

1022 

1023 @arg x_xyz: X component (C{scalar}) or a cartesian (C{Cartesian}, L{Ecef9Tuple}, 

1024 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a 

1025 C{tuple} or C{list} of 3+ C{scalar} items) if no C{y_z} specified. 

1026 @arg y_z: Y and Z component (C{scalar}s), ignored if C{x_xyz} is not a C{scalar}. 

1027 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1028 

1029 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with radial distance C{r} 

1030 (C{meter}, same units as C{x}, C{y} and C{z}), inclination C{theta} 

1031 (with respect to the positive z-axis) and azimuthal angle C{phi}, 

1032 both in L{Radians}. 

1033 

1034 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>} 

1035 (ISO 80000-2:2019). 

1036 ''' 

1037 return _rtp3(xyz2rtp_, Radians, x_xyz, *y_z, **name) 

1038 

1039 

1040__all__ += _ALL_DOCS(CartesianBase) 

1041 

1042# **) MIT License 

1043# 

1044# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1045# 

1046# Permission is hereby granted, free of charge, to any person obtaining a 

1047# copy of this software and associated documentation files (the "Software"), 

1048# to deal in the Software without restriction, including without limitation 

1049# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1050# and/or sell copies of the Software, and to permit persons to whom the 

1051# Software is furnished to do so, subject to the following conditions: 

1052# 

1053# The above copyright notice and this permission notice shall be included 

1054# in all copies or substantial portions of the Software. 

1055# 

1056# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1057# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1058# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1059# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1060# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1061# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1062# OTHER DEALINGS IN THE SOFTWARE.