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 2011-2024} 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 

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, property_doc_, \ 

32 property_RO, property_ROnce, _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__ = '24.11.06' 

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}), like B{C{y}}. 

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

67 or L{a_f2Tuple}). 

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

69 latlon C{B{ll}=None} (C{LatLon}). 

70 

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

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

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

74 not a L{Datum}. 

75 ''' 

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

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

78 if h is not None: 

79 self._height = Height(h) 

80 if d is not None: 

81 self.datum = d 

82 

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

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

85# ''' 

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

87# _NotImplemented(self, other) 

88 

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

90 '''3-Point resection between this and 2 other points using U{Cassini 

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

92 

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

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

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

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

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

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

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

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

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

102 force C{z=INT0} (C{bool}). 

103 

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

105 

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

107 

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

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

110 

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

112 

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

114 ''' 

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

116 useZ=useZ, datum=self.datum) 

117 

118 @deprecated_method 

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

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

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

122 

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

124 '''3-Point resection between this and 2 other points using U{Collins<https://Dokumen.tips/ 

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

126 

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

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

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

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

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

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

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

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

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

136 force C{z=INT0} (C{bool}). 

137 

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

139 

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

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

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

143 

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

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

146 

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

148 

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

150 ''' 

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

152 useZ=useZ, datum=self.datum) 

153 

154 @deprecated_method 

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

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

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

158 

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

160 def datum(self): 

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

162 ''' 

163 return self._datum 

164 

165 @datum.setter # PYCHOK setter! 

166 def datum(self, datum): 

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

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

169 

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

171 ''' 

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

173 if self._datum: # is not None 

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

175 raise _IsnotError(_ellipsoidal_, datum=datum) 

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

177 raise _IsnotError(_spherical_, datum=datum) 

178 if self._datum != d: 

179 _update_all(self) 

180 self._datum = d 

181 

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

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

184 

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

186 or L{Local9Tuple}). 

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

188 or C{None}. 

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

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

191 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 B{C{Cartesian_kwds}} 

198 item or C{datum} missing or incompatible. 

199 ''' 

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

201 if Cartesian is None: 

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

203 else: 

204 d = self.datum 

205 if not d: 

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

207 t = _xkwds_get(kwds, datum=d) 

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

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

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

211 r = Cartesian(*c, **kwds) 

212 return r.renamed(n) if n else r 

213 

214 @property_ROnce 

215 def Ecef(self): 

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

217 ''' 

218 return _MODS.ecef.EcefKarney 

219 

220 @Property_RO 

221 def _ecef9(self): 

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

223 ''' 

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

225 

226 @property_RO 

227 def ellipsoidalCartesian(self): 

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

229 ''' 

230 return False 

231 

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

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

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

235 

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

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

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

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

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

241 C{datum} ellipsoid. 

242 

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

244 this C{pov}. 

245 

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

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

248 the ellipsoid. 

249 

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

251 

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

253 ''' 

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

255 

256 @Property 

257 def height(self): 

258 '''Get the height (C{meter}). 

259 ''' 

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

261 

262 @height.setter # PYCHOK setter! 

263 def height(self, height): 

264 '''Set the height (C{meter}). 

265 

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

267 

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

269 ''' 

270 h = Height(height) 

271 if self._height != h: 

272 _update_all(self) 

273 self._height = h 

274 

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

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

277 ''' 

278 if Cartesian is not None: 

279 r = Cartesian(r, **kwds) 

280 if datum is not None: 

281 r.datum = datum 

282 if height is not None: 

283 r.height = height # Height(height) 

284 return r 

285 

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

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

288 

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

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

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

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

293 cartesian's height. 

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

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

296 keyword arguments. 

297 

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

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

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

301 

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

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

304 

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

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

307 

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

309 

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

311 ''' 

312 n = self.height3.__name__ 

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

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

315 if h and d: 

316 R, r = self.Roc2(earth=d) 

317 if R > EPS0: 

318 R = (R + h) / R 

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

320 c = c.times_(R, R, r) 

321 

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

323 if Cartesian_and_kwds: 

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

325 return r 

326 

327 @Property_RO 

328 def _height4(self): 

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

330 ''' 

331 try: 

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

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

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

335 return r 

336 

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

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

339 this datum's ellipsoid surface. 

340 

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

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

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

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

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

346 ellipsoid's surface, otherwise the intersection of the 

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

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

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

350 arguments. 

351 

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

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

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

355 

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

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

358 

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

360 

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

362 

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

364 ''' 

365 n = self.height4.__name__ 

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

367 if normal and d is self.datum: 

368 r = self._height4 

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

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

371 try: 

372 d = d.toEllipsoid(name=n) 

373 except (TypeError, ValueError): # TriaxialError 

374 d = None 

375 else: 

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

377 

378 if Cartesian_and_kwds: 

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

380 d = _spherical_datum(d, name=n) 

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

382 return r 

383 

384 @Property_RO 

385 def isEllipsoidal(self): 

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

387 ''' 

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

389 

390 @Property_RO 

391 def isSpherical(self): 

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

393 ''' 

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

395 

396 @Property_RO 

397 def latlon(self): 

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

399 ''' 

400 return self.toEcef().latlon 

401 

402 @Property_RO 

403 def latlonheight(self): 

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

405 ''' 

406 return self.toEcef().latlonheight 

407 

408 @Property_RO 

409 def latlonheightdatum(self): 

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

411 ''' 

412 return self.toEcef().latlonheightdatum 

413 

414 @Property_RO 

415 def _Ltp(self): 

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

417 ''' 

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

419 

420 @Property_RO 

421 def _N_vector(self): 

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

423 ''' 

424 _N = _MODS.nvectorBase._N_vector_ 

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

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

427 

428 def _n_xyzh4(self, datum): 

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

430 ''' 

431 def _ErrorEPS0(x): 

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

433 

434 _xinstanceof(Datum, datum=datum) 

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

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

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

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

439 E = datum.ellipsoid 

440 x, y, z = self.xyz3 

441 

442 # Kenneth Gade eqn 23 

443 p = hypot2(x, y) * E.a2_ 

444 q = z**2 * E.e21 * E.a2_ 

445 r = fsumf_(p, q, -E.e4) / _6_0 

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

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

448 if isnear0(t): 

449 raise _ErrorEPS0(t) 

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

451 v = sqrt(u**2 + E.e4 * q) 

452 t = v * _2_0 

453 if t < EPS0: # isnear0 

454 raise _ErrorEPS0(t) 

455 w = fsumf_(u, v, -q) * E.e2 / t 

456 k = sqrt(fsumf_(u, v, w**2)) - w 

457 if isnear0(k): 

458 raise _ErrorEPS0(k) 

459 t = k + E.e2 

460 if isnear0(t): 

461 raise _ErrorEPS0(t) 

462 e = k / t 

463# d = e * hypot(x, y) 

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

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

466 if t < EPS0: # isnear0 

467 raise _ErrorEPS0(t) 

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

469 s = e / t # == e * tmp 

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

471 

472 @Property_RO 

473 def philam(self): 

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

475 ''' 

476 return self.toEcef().philam 

477 

478 @Property_RO 

479 def philamheight(self): 

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

481 ''' 

482 return self.toEcef().philamheight 

483 

484 @Property_RO 

485 def philamheightdatum(self): 

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

487 ''' 

488 return self.toEcef().philamheightdatum 

489 

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

491 '''3-Point resection between this and two other points using U{Pierlot 

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

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

494 

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

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

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

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

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

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

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

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

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

504 (C{bool}). 

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

506 

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

508 

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

510 

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

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

513 

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

515 

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

517 ''' 

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

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

520 

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

522 '''3-Point resection between this and two other points using U{Pierlot 

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

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

525 

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

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

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

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

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

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

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

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

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

535 

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

537 

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

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

540 

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

542 

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

544 ''' 

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

546 useZ=useZ, datum=self.datum) 

547 

548 def Roc2(self, earth=None): 

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

550 

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

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

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

554 

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

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

557 

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

559 ''' 

560 r = z = fabs( self.z) 

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

562 if R < _0: # polar 

563 R = z 

564 elif z > _0: # non-equatorial 

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

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

567 M = e.M # EcefMatrix 

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

569 if ca < _0: # polar 

570 R = z 

571 else: # prime-vertical, normal roc R 

572 R = R / ca # /= chokes PyChecker 

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

574 return R, r 

575 

576 @property_RO 

577 def sphericalCartesian(self): 

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

579 ''' 

580 return False 

581 

582 @deprecated_method 

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

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

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

586 

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

588 '''3-Point resection between this and two other points using U{Tienstra 

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

590 

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

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

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

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

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

596 non-negative). 

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

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

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

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

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

602 (C{bool}). 

603 

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

605 

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

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

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

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

610 

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

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

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

614 

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

616 

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

618 ''' 

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

620 useZ=useZ, datum=self.datum) 

621 

622 @deprecated_method 

623 def to2ab(self): # PYCHOK no cover 

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

625 

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

627 ''' 

628 return self.philam 

629 

630 @deprecated_method 

631 def to2ll(self): # PYCHOK no cover 

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

633 

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

635 ''' 

636 return self.latlon 

637 

638 @deprecated_method 

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

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

641 

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

643 

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

645 as its name may suggest. 

646 ''' 

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

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

649 

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

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

652# ''' 

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

654# if LL is not None: 

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

656# for n, v in pairs.items(): 

657# setattr(r, n, v) 

658# return r 

659 

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

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

662 

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

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

665 

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

667 

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

669 invalid. 

670 ''' 

671 _xinstanceof(Datum, datum2=datum2) 

672 

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

674 self.toDatum(datum) 

675 

676 i, d = False, c.datum 

677 if d == datum2: 

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

679 

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

681 datum2.transform.isunity): 

682 return c.dup(datum=datum2) 

683 

684 elif d == _WGS84: 

685 d = datum2 # convert from WGS84 to datum2 

686 

687 elif datum2 == _WGS84: 

688 i = True # convert to WGS84 by inverse transformation 

689 

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

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

692 d = datum2 

693 

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

695 

696 def toEcef(self): 

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

698 

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

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

701 

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

703 ''' 

704 return self._ecef9 

705 

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

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

708 

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

710 or L{a_f2Tuple}). 

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

712 (C{meter}), only if C{B{LatLon} is not None}. 

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

714 (C{LatLon}) or C{None}. 

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

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

717 

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

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

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

721 

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

723 ''' 

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

725 if d == self.datum: 

726 r = self.toEcef() 

727 else: 

728 c = self.toDatum(d) 

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

730 

731 if LatLon: # class or .classof 

732 h = _heigHt(r, height) 

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

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

735 _xdatum(r.datum, d) 

736 return r 

737 

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

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

740 

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

742 L{Enu}, L{Ned}) or C{None}. 

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

744 cartesian's LTP (L{Ltp}). 

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

746 ignored if C{B{Xyz} is None}. 

747 

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

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

750 

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

752 ''' 

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

754 

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

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

757 

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

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

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

761 ''' 

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

763 

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

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

766 

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

768 (C{Nvector}) or C{None}. 

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

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

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

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

773 C{B{Nvector} is None}. 

774 

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

776 C{B{Nvector} is None}. 

777 

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

779 B{C{name_Nvector_kwds}} item. 

780 

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

782 ''' 

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

784 if datum is not None: 

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

786 if d != self.datum: 

787 r = self._n_xyzh4(d) 

788 

789 if Nvector is None: 

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

791 if n: 

792 r = r.dup(name=n) 

793 else: 

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

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

796 return r 

797 

798 def toRtp(self): 

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

800 

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

802 and C{phi}, both in L{Degrees}. 

803 

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

805 ''' 

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

807 

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

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

810 

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

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

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

814 

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

816 ''' 

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

818 

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

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

821 

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

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

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

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

826 

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

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

829 

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

831 ''' 

832 _xinstanceof(Transform, transform=transform) 

833 if transform.isunity: 

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

835 else: 

836 # if inverse and d != _WGS84: 

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

838 # txt_not_=_WGS84.name) 

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

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

841 return c 

842 

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

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

845 

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

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

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

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

850 

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

852 C{B{Vector} is None}. 

853 

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

855 ''' 

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

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

858 

859 

860class RadiusThetaPhi3Tuple(_NamedTupleTo): 

861 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination 

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

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

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

865 ''' 

866 _Names_ = (_r_, _theta_, _phi_) 

867 _Units_ = ( Meter, _Pass, _Pass) 

868 

869 def toCartesian(self, **name_Cartesian_and_kwds): 

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

871 

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

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

874 C{B{Cartesian}} keyword arguments. 

875 

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

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

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

879 

880 @see: Function L{rtp2xyz_}. 

881 ''' 

882 r, t, p = self 

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

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

885 

886 def toDegrees(self, **name): 

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

888 

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

890 

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

892 and C{phi} both in L{Degrees}. 

893 ''' 

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

895 

896 def toRadians(self, **name): 

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

898 

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

900 

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

902 and C{phi} both in L{Radians}. 

903 ''' 

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

905 

906 def _toU(self, U): 

907 M = RadiusThetaPhi3Tuple._Units_[0] # Meter 

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

909 

910 def _toX3U(self, _X3, U, name): 

911 r, t, p = self 

912 t, p, s = _X3(self, t, p) 

913 if s is None or name: 

914 n = self._name__(name) 

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

916 return s 

917 

918 

919def rtp2xyz(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds): 

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

921 

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

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

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

925 

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

927 ''' 

928 if isinstance(r_rtp, RadiusThetaPhi3Tuple): 

929 c = r_rtp.toCartesian(**name_Cartesian_and_kwds) 

930 else: 

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

932 return c 

933 

934 

935def rtp2xyz_(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds): 

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

937 

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

939 L{RadiusThetaPhi3Tuple} instance. 

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

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

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

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

944 class to return the coordinates and optionally, additional C{B{Cartesian}} 

945 keyword arguments. 

946 

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

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

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

950 

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

952 B{C{name_Cartesian_and_kwds}} item. 

953 

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

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

956 and L{xyz2rtp}. 

957 ''' 

958 if isinstance(r_rtp, RadiusThetaPhi3Tuple): 

959 c = r_rtp.toCartesian(**name_Cartesian_and_kwds) 

960 elif _isMeter(r_rtp): 

961 r = r_rtp 

962 if r and _isfinite(r): 

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

964 s *= r 

965 z *= r 

966 y *= s 

967 x *= s 

968 else: 

969 x = y = z = r 

970 

971 n, kwds = _name2__(**name_Cartesian_and_kwds) 

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

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

974 C(x, y, z, name=n, **kwds) 

975 else: 

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

977 return c 

978 

979 

980def _rtp3(where, U, *x_y_z, **name): 

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

982 ''' 

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

984 r = hypot_(x, y, z) 

985 if r > 0: 

986 t = acos1(z / r) 

987 p = atan2(y, x) 

988 while p < 0: 

989 p += PI2 

990 if U is Degrees: 

991 t = degrees(t) 

992 p = degrees(p) 

993 else: 

994 t = p = _0_0 

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

996 

997 

998def xyz2rtp(x_xyz, y=0, z=0, **name): 

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

1000 

1001 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} and C{phi}, both 

1002 in L{Degrees}. 

1003 

1004 @see: Function L{xyz2rtp_} for further details. 

1005 ''' 

1006 return _rtp3(xyz2rtp, Degrees, x_xyz, y, z, **name) 

1007 

1008 

1009def xyz2rtp_(x_xyz, y=0, z=0, **name): 

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

1011 

1012 @arg x_xyz: X component (C{scalar}) or a cartesian (C{Cartesian}, L{Ecef9Tuple}, 

1013 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a C{tuple} or 

1014 C{list} of 3+ C{scalar} items) if no C{y_z} specified. 

1015 @arg y: Y component (C{scalar}), required if C{B{x_xyz}} is C{scalar}, ignored otherwise. 

1016 @arg z: Z component (C{scalar}), like B{C{y}}. 

1017 @kwarg name: Optional C{B{name}=NN} (C{str}). 

1018 

1019 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with radial distance C{r} (C{meter}, 

1020 same units as C{x}, C{y} and C{z}), inclination C{theta} (with respect to the 

1021 positive z-axis) and azimuthal angle C{phi}, both in L{Radians}. 

1022 

1023 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>} 

1024 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and function L{xyz2rtp}. 

1025 ''' 

1026 return _rtp3(xyz2rtp_, Radians, x_xyz, y, z, **name) 

1027 

1028 

1029__all__ += _ALL_DOCS(CartesianBase) 

1030 

1031# **) MIT License 

1032# 

1033# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

1034# 

1035# Permission is hereby granted, free of charge, to any person obtaining a 

1036# copy of this software and associated documentation files (the "Software"), 

1037# to deal in the Software without restriction, including without limitation 

1038# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1039# and/or sell copies of the Software, and to permit persons to whom the 

1040# Software is furnished to do so, subject to the following conditions: 

1041# 

1042# The above copyright notice and this permission notice shall be included 

1043# in all copies or substantial portions of the Software. 

1044# 

1045# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1046# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1047# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1048# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1049# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1050# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1051# OTHER DEALINGS IN THE SOFTWARE.