Coverage for pygeodesy/cartesianBase.py: 92%

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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, _xattr, \ 

20 _xdatum, _xkwds, _xkwds_get, _xkwds_pop2 

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 _COMMASPACE_, _datum_, _no_, _phi_ 

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

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

27from pygeodesy.named import _name2__, _Pass 

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

29 Vector4Tuple, 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, pierlotx, \ 

34# tienstra7 # _MODS 

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

36# from pygeodesy.triaxials import Triaxial_ # _MODS 

37from pygeodesy.units import Degrees, Height, _heigHt, _isMeter, Meter, Radians 

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

39from pygeodesy.vector3d import Vector3d, _xyzhdlln4 

40# from pygeodesy.vector3dBase import _xyz3 # _MODS 

41# from pygeodesy import ltp # _MODS 

42 

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

44 

45__all__ = _ALL_LAZY.cartesianBase 

46__version__ = '24.06.10' 

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_name): 

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_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 _MODS.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 _MODS.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, **name_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}, L{Ned} 

187 or L{Local9Tuple}). 

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

189 or C{None}. 

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

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

192 C{B{Cartesian} is None}. 

193 

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

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

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

197 

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

199 item or C{datum} missing or incompatible. 

200 ''' 

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

202 if Cartesian is None: 

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

204 else: 

205 d = self.datum 

206 if not d: 

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

208 t = _xkwds_get(kwds, datum=d) 

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

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

211 c = self._Ltp._local2ecef(delta, nine=False) 

212 r = Cartesian(*c, **kwds) 

213 return r.renamed(n) if n else r 

214 

215 @property_RO 

216 def Ecef(self): 

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

218 ''' 

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

220 return E 

221 

222 @Property_RO 

223 def _ecef9(self): 

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

225 ''' 

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

227 

228 @property_RO 

229 def ellipsoidalCartesian(self): 

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

231 ''' 

232 return False 

233 

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

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

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

237 

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

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

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

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

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

243 C{datum} ellipsoid. 

244 

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

246 this C{pov}. 

247 

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

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

250 the ellipsoid. 

251 

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

253 

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

255 ''' 

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

257 

258 @Property 

259 def height(self): 

260 '''Get the height (C{meter}). 

261 ''' 

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

263 

264 @height.setter # PYCHOK setter! 

265 def height(self, height): 

266 '''Set the height (C{meter}). 

267 

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

269 

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

271 ''' 

272 h = Height(height) 

273 if self._height != h: 

274 _update_all(self) 

275 self._height = h 

276 

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

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

279 ''' 

280 if Cartesian is not None: 

281 r = Cartesian(r, **kwds) 

282 if datum is not None: 

283 r.datum = datum 

284 if height is not None: 

285 r.height = height # Height(height) 

286 return r 

287 

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

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

290 

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

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

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

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

295 cartesian's height. 

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

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

298 keyword arguments. 

299 

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

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

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

303 

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

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

306 

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

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

309 

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

311 

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

313 ''' 

314 n = self.height3.__name__ 

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

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

317 if h and d: 

318 R, r = self.Roc2(earth=d) 

319 if R > EPS0: 

320 R = (R + h) / R 

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

322 c = c.times_(R, R, r) 

323 

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

325 if Cartesian_and_kwds: 

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

327 return r 

328 

329 @Property_RO 

330 def _height4(self): 

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

332 ''' 

333 try: 

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

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

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

337 return r 

338 

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

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

341 this datum's ellipsoid surface. 

342 

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

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

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

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

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

348 ellipsoid's surface, otherwise the intersection of the 

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

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

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

352 arguments. 

353 

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

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

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

357 

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

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

360 

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

362 

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

364 

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

366 ''' 

367 n = self.height4.__name__ 

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

369 if normal and d is self.datum: 

370 r = self._height4 

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

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

373 try: 

374 d = d.toEllipsoid(name=n) 

375 except (TypeError, ValueError): # TriaxialError 

376 d = None 

377 else: 

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

379 

380 if Cartesian_and_kwds: 

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

382 d = _spherical_datum(d, name=n) 

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

384 return r 

385 

386 @Property_RO 

387 def isEllipsoidal(self): 

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

389 ''' 

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

391 

392 @Property_RO 

393 def isSpherical(self): 

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

395 ''' 

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

397 

398 @Property_RO 

399 def latlon(self): 

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

401 ''' 

402 return self.toEcef().latlon 

403 

404 @Property_RO 

405 def latlonheight(self): 

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

407 ''' 

408 return self.toEcef().latlonheight 

409 

410 @Property_RO 

411 def latlonheightdatum(self): 

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

413 ''' 

414 return self.toEcef().latlonheightdatum 

415 

416 @Property_RO 

417 def _Ltp(self): 

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

419 ''' 

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

421 

422 @Property_RO 

423 def _N_vector(self): 

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

425 ''' 

426 _N = _MODS.nvectorBase._N_vector_ 

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

428 return _N(x, y, z, h=h, name=self.name) 

429 

430 def _n_xyzh4(self, datum): 

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

432 ''' 

433 def _ErrorEPS0(x): 

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

435 

436 _xinstanceof(Datum, datum=datum) 

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

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

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

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

441 E = datum.ellipsoid 

442 x, y, z = self.xyz 

443 

444 # Kenneth Gade eqn 23 

445 p = hypot2(x, y) * E.a2_ 

446 q = z**2 * E.e21 * E.a2_ 

447 r = fsumf_(p, q, -E.e4) / _6_0 

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

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

450 if isnear0(t): 

451 raise _ErrorEPS0(t) 

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

453 v = sqrt(u**2 + E.e4 * q) 

454 t = v * _2_0 

455 if t < EPS0: # isnear0 

456 raise _ErrorEPS0(t) 

457 w = fsumf_(u, v, -q) * E.e2 / t 

458 k = sqrt(fsumf_(u, v, w**2)) - w 

459 if isnear0(k): 

460 raise _ErrorEPS0(k) 

461 t = k + E.e2 

462 if isnear0(t): 

463 raise _ErrorEPS0(t) 

464 e = k / t 

465# d = e * hypot(x, y) 

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

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

468 if t < EPS0: # isnear0 

469 raise _ErrorEPS0(t) 

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

471 s = e / t # == e * tmp 

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

473 

474 @Property_RO 

475 def philam(self): 

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

477 ''' 

478 return self.toEcef().philam 

479 

480 @Property_RO 

481 def philamheight(self): 

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

483 ''' 

484 return self.toEcef().philamheight 

485 

486 @Property_RO 

487 def philamheightdatum(self): 

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

489 ''' 

490 return self.toEcef().philamheightdatum 

491 

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

493 '''3-Point resection between this and two other points using U{Pierlot 

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

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

496 

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

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

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

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

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

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

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

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

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

506 (C{bool}). 

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

508 

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

510 

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

512 

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

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

515 

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

517 

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

519 ''' 

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

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

522 

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

524 '''3-Point resection between this and two other points using U{Pierlot 

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

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

527 

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

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

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

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

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

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

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

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

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

537 

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

539 

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

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

542 

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

544 

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

546 ''' 

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

548 useZ=useZ, datum=self.datum) 

549 

550 def Roc2(self, earth=None): 

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

552 

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

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

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

556 

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

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

559 

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

561 ''' 

562 r = z = fabs( self.z) 

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

564 if R < _0: # polar 

565 R = z 

566 elif z > _0: # non-equatorial 

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

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

569 M = e.M # EcefMatrix 

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

571 if ca < _0: # polar 

572 R = z 

573 else: # prime-vertical, normal roc R 

574 R = R / ca # /= chokes PyChecker 

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

576 return R, r 

577 

578 @property_RO 

579 def sphericalCartesian(self): 

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

581 ''' 

582 return False 

583 

584 @deprecated_method 

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

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

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

588 

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

590 '''3-Point resection between this and two other points using U{Tienstra 

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

592 

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

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

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

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

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

598 non-negative). 

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

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

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

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

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

604 (C{bool}). 

605 

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

607 

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

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

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

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

612 

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

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

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

616 

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

618 

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

620 ''' 

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

622 useZ=useZ, datum=self.datum) 

623 

624 @deprecated_method 

625 def to2ab(self): # PYCHOK no cover 

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

627 

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

629 ''' 

630 return self.philam 

631 

632 @deprecated_method 

633 def to2ll(self): # PYCHOK no cover 

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

635 

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

637 ''' 

638 return self.latlon 

639 

640 @deprecated_method 

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

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

643 

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

645 

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

647 as its name may suggest. 

648 ''' 

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

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

651 

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

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

654# ''' 

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

656# if LL is not None: 

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

658# for n, v in pairs.items(): 

659# setattr(r, n, v) 

660# return r 

661 

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

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

664 

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

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

667 

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

669 

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

671 invalid. 

672 ''' 

673 _xinstanceof(Datum, datum2=datum2) 

674 

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

676 self.toDatum(datum) 

677 

678 i, d = False, c.datum 

679 if d == datum2: 

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

681 

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

683 datum2.transform.isunity): 

684 return c.dup(datum=datum2) 

685 

686 elif d == _WGS84: 

687 d = datum2 # convert from WGS84 to datum2 

688 

689 elif datum2 == _WGS84: 

690 i = True # convert to WGS84 by inverse transformation 

691 

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

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

694 d = datum2 

695 

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

697 

698 def toEcef(self): 

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

700 

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

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

703 

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

705 ''' 

706 return self._ecef9 

707 

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

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

710 

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

712 or L{a_f2Tuple}). 

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

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

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

716 (C{LatLon}) or C{None}. 

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

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

719 

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

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

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

723 

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

725 ''' 

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

727 if d == self.datum: 

728 r = self.toEcef() 

729 else: 

730 c = self.toDatum(d) 

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

732 

733 if LatLon: # class or .classof 

734 h = _heigHt(r, height) 

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

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

737 _xdatum(r.datum, d) 

738 return r 

739 

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

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

742 

743 @kwarg Xyz: Optional class to return C{X}, C{Y} and C{Z} (L{XyzLocal}, 

744 L{Enu}, L{Ned}) or C{None}. 

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

746 cartesian's LTP (L{Ltp}). 

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

748 ignored if C{B{Xyz} is None}. 

749 

750 @return: An B{C{Xyz}} instance or a L{Local9Tuple}C{(x, y, z, lat, lon, 

751 height, ltp, ecef, M)} if C{B{Xyz} is None} (with C{M=None}). 

752 

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

754 ''' 

755 return _MODS.ltp._toLocal(self, ltp, Xyz, Xyz_kwds) # self._ecef9 

756 

757 def toLtp(self, Ecef=None, **name): 

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

759 

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

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

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

763 ''' 

764 return _MODS.ltp._toLtp(self, Ecef, self._ecef9, name) # self._Ltp 

765 

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

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

768 

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

770 (C{Nvector}) or C{None}. 

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

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

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

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

775 C{B{Nvector} is None}. 

776 

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

778 B{C{Nvector}} is C{None}. 

779 

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

781 B{C{name_Nvector_kwds}} item. 

782 

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

784 ''' 

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

786 if datum is not None: 

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

788 if d != self.datum: 

789 r = self._n_xyzh4(d) 

790 

791 if Nvector is None: 

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

793 if n: 

794 r = r.dup(name=n) 

795 else: 

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

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

798 return r 

799 

800 def toRtp(self): 

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

802 

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

804 and C{phi}, both in L{Degrees}. 

805 

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

807 ''' 

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

809 

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

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

812 

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

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

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

816 

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

818 ''' 

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

820 

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

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

823 

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

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

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

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

828 

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

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

831 

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

833 ''' 

834 _xinstanceof(Transform, transform=transform) 

835 if transform.isunity: 

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

837 else: 

838 # if inverse and d != _WGS84: 

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

840 # txt_not_=_WGS84.name) 

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

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

843 return c 

844 

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

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

847 

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

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

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

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

852 

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

854 B{C{Vector}} is C{None}. 

855 

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

857 ''' 

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

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

860 

861 

862class RadiusThetaPhi3Tuple(_NamedTupleTo): 

863 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination 

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

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

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

867 ''' 

868 _Names_ = (_r_, _theta_, _phi_) 

869 _Units_ = ( Meter, _Pass, _Pass) 

870 

871 def toCartesian(self, **name_Cartesian_and_kwds): 

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

873 

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

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

876 C{B{Cartesian}} keyword arguments. 

877 

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

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

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

881 

882 @see: Function L{rtp2xyz_}. 

883 ''' 

884 r, t, p = self 

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

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

887 

888 def toDegrees(self, **name): 

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

890 

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

892 

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

894 and C{phi} both in L{Degrees}. 

895 ''' 

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

897 

898 def toRadians(self, **name): 

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

900 

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

902 

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

904 and C{phi} both in L{Radians}. 

905 ''' 

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

907 

908 def _toU(self, U): 

909 M = RadiusThetaPhi3Tuple._Units_[0] # Meter 

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

911 

912 def _toX3U(self, _X3, U, name): 

913 r, t, p = self 

914 t, p, s = _X3(self, t, p) 

915 if s is None or name: 

916 n = self._name__(name) 

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

918 return s 

919 

920 

921def rtp2xyz(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds): 

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

923 

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

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

926 @arg phi: Azimuthal angle B{C{phi}} (C{degrees}), required if C{B{r_rtp}} is C{scalar}, 

927 ignored otherwise. 

928 

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

930 ''' 

931 if isinstance(r_rtp, RadiusThetaPhi3Tuple): 

932 c = r_rtp.toCartesian(**name_Cartesian_and_kwds) 

933 else: 

934 c = rtp2xyz_(r_rtp, radians(theta), radians(phi), **name_Cartesian_and_kwds) 

935 return c 

936 

937 

938def rtp2xyz_(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds): 

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

940 

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

942 L{RadiusThetaPhi3Tuple} instance. 

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

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

945 @arg phi: Azimuthal angle B{C{phi}} (C{radians}), required if C{B{r_rtp}} is C{scalar}, 

946 ignored otherwise. 

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

948 class to return the coordinates and optional, additional C{B{Cartesian}} 

949 keyword arguments. 

950 

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

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

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

954 

955 @raise TypeError: Invalid B{C{r_rtp}}, B{C{theta}}, B{C{phi}} or 

956 B{C{name_Cartesian_and_kwds}} item. 

957 

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

959 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and functions L{rtp2xyz} 

960 and L{xyz2rtp}. 

961 ''' 

962 if isinstance(r_rtp, RadiusThetaPhi3Tuple): 

963 c = r_rtp.toCartesian(**name_Cartesian_and_kwds) 

964 elif _isMeter(r_rtp): 

965 r = r_rtp 

966 if r and _isfinite(r): 

967 s, z, y, x = sincos2_(theta, phi) 

968 s *= r 

969 z *= r 

970 y *= s 

971 x *= s 

972 else: 

973 x = y = z = r 

974 

975 n, kwds = _name2__(**name_Cartesian_and_kwds) 

976 C, kwds = _xkwds_pop2(kwds, Cartesian=None) 

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

978 C(x, y, z, name=n, **kwds) 

979 else: 

980 raise _TypeError(r_rtp=r_rtp, theta=theta, phi=phi) 

981 return c 

982 

983 

984def _rtp3(where, U, *x_y_z, **name): 

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

986 ''' 

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

988 r = hypot_(x, y, z) 

989 if r > 0: 

990 t = acos1(z / r) 

991 p = atan2(y, x) 

992 while p < 0: 

993 p += PI2 

994 if U is Degrees: 

995 t = degrees(t) 

996 p = degrees(p) 

997 else: 

998 t = p = _0_0 

999 return RadiusThetaPhi3Tuple(r, t, p, **name)._toU(U) 

1000 

1001 

1002def xyz2rtp(x_xyz, y=0, z=0, **name): 

1003 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates. 

1004 

1005 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} and C{phi}, both 

1006 in L{Degrees}. 

1007 

1008 @see: Function L{xyz2rtp_} for further details. 

1009 ''' 

1010 return _rtp3(xyz2rtp, Degrees, x_xyz, y, z, **name) 

1011 

1012 

1013def xyz2rtp_(x_xyz, y=0, z=0, **name): 

1014 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates. 

1015 

1016 @arg x_xyz: X component (C{scalar}) or a cartesian (C{Cartesian}, L{Ecef9Tuple}, 

1017 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a C{tuple} or 

1018 C{list} of 3+ C{scalar} items) if no C{y_z} specified. 

1019 @arg y: Y component (C{scalar}), required if C{B{x_xyz}} is C{scalar}, ignored otherwise. 

1020 @arg z: Z component (C{scalar}), required if C{B{x_xyz}} is C{scalar}, ignored otherwise. 

1021 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1022 

1023 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with radial distance C{r} (C{meter}, 

1024 same units as C{x}, C{y} and C{z}), inclination C{theta} (with respect to the 

1025 positive z-axis) and azimuthal angle C{phi}, both in L{Radians}. 

1026 

1027 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>} 

1028 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and function L{xyz2rtp}. 

1029 ''' 

1030 return _rtp3(xyz2rtp_, Radians, x_xyz, y, z, **name) 

1031 

1032 

1033__all__ += _ALL_DOCS(CartesianBase) 

1034 

1035# **) MIT License 

1036# 

1037# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1038# 

1039# Permission is hereby granted, free of charge, to any person obtaining a 

1040# copy of this software and associated documentation files (the "Software"), 

1041# to deal in the Software without restriction, including without limitation 

1042# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1043# and/or sell copies of the Software, and to permit persons to whom the 

1044# Software is furnished to do so, subject to the following conditions: 

1045# 

1046# The above copyright notice and this permission notice shall be included 

1047# in all copies or substantial portions of the Software. 

1048# 

1049# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1050# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1051# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1052# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1053# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1054# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1055# OTHER DEALINGS IN THE SOFTWARE.