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 2011-2024} published under the same MIT Licence**, see 

8U{https://www.Movable-Type.co.UK/scripts/latlong.html}, 

9U{https://www.Movable-Type.co.UK/scripts/latlong-vectors.html} and 

10U{https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html}. 

11''' 

12 

13from pygeodesy.basics import _isin, _xinstanceof, typename 

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

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

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

17 Transform, _WGS84 

18# from pygeodesy.ecef import EcefKarney # _MODS 

19from pygeodesy.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 

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

25from pygeodesy.interns import _COMMASPACE_, _datum_, _no_, _phi_ 

26from pygeodesy.interns import _ellipsoidal_, _spherical_ # PYCHOK used! 

27from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS 

28from pygeodesy.named import _name2__, _NamedLocal, _Pass 

29from pygeodesy.namedTuples import LatLon4Tuple, _NamedTupleTo , Vector3Tuple, \ 

30 Vector4Tuple, Bearing2Tuple # PYCHOK .sphericalBase 

31# from pygeodesy.nvectorBase import _N_vector # _MODS 

32from pygeodesy.props import deprecated_method, Property, Property_RO, property_doc_, \ 

33 property_RO, _update_all 

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

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, atan2, sincos2d, sincos2_, 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 degrees, fabs, radians, sqrt # from .fmath, .utily 

44 

45__all__ = _ALL_LAZY.cartesianBase 

46__version__ = '25.04.21' 

47 

48_r_ = 'r' 

49_resections = _MODS.into(resections=__name__) 

50_theta_ = 'theta' 

51 

52 

53class CartesianBase(Vector3d, _NamedLocal): 

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

55 ''' 

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

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

58 

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

60 '''New C{Cartesian...}. 

61 

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

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

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

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

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

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

68 or L{a_f2Tuple}). 

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

70 latlon C{B{ll}=None} (C{LatLon}). 

71 

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

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

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

75 not a L{Datum}. 

76 ''' 

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

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

79 if h is not None: 

80 self._height = Height(h) 

81 if d is not None: 

82 self.datum = d 

83 

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

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

86# ''' 

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

88# _NotImplemented(self, other) 

89 

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

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

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

93 

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

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

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

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

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

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

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

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

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

103 force C{z=INT0} (C{bool}). 

104 

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

106 

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

108 

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

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

111 

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

113 

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

115 ''' 

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

117 useZ=useZ, datum=self.datum) 

118 

119 @deprecated_method 

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

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

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

123 

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

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

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

127 

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

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

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

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

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

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

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

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

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

137 force C{z=INT0} (C{bool}). 

138 

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

140 

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

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

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

144 

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

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

147 

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

149 

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

151 ''' 

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

153 useZ=useZ, datum=self.datum) 

154 

155 @deprecated_method 

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

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

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

159 

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

161 def datum(self): 

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

163 ''' 

164 return self._datum 

165 

166 @datum.setter # PYCHOK setter! 

167 def datum(self, datum): 

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

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

170 

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

172 ''' 

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

174 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 optionally, 

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 _ecef9(self): 

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

218 ''' 

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

220 

221 @property_RO 

222 def ellipsoidalCartesian(self): 

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

224 ''' 

225 return False 

226 

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

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

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

230 

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

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

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

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

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

236 datum. 

237 

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

239 this C{pov}. 

240 

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

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

243 the ellipsoid. 

244 

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

246 

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

248 ''' 

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

250 

251 @Property 

252 def height(self): 

253 '''Get the height (C{meter}). 

254 ''' 

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

256 

257 @height.setter # PYCHOK setter! 

258 def height(self, height): 

259 '''Set the height (C{meter}). 

260 

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

262 

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

264 ''' 

265 h = Height(height) 

266 if self._height != h: 

267 _update_all(self) 

268 self._height = h 

269 

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

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

272 ''' 

273 if Cartesian is not None: 

274 r = Cartesian(r, **kwds) 

275 if datum is not None: 

276 r.datum = datum 

277 if height is not None: 

278 r.height = height # Height(height) 

279 return r 

280 

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

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

283 C{datum} ellipsoid surface. 

284 

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

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

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

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

289 cartesian's height. 

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

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

292 keyword arguments. 

293 

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

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

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

297 

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

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

300 

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

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

303 

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

305 

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

307 ''' 

308 n = typename(self.height3) 

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

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

311 if h and d: 

312 R, r = self.Roc2(earth=d) 

313 if R > EPS0: 

314 R = (R + h) / R 

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

316 c = c.times_(R, R, r) 

317 

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

319 if Cartesian_and_kwds: 

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

321 return r 

322 

323 @Property_RO 

324 def _height4(self): 

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

326 ''' 

327 try: 

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

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

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

331 return r 

332 

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

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

335 this datum's ellipsoid surface. 

336 

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

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

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

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

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

342 ellipsoid's surface, otherwise the intersection of the 

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

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

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

346 arguments. 

347 

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

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

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

351 

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

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

354 

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

356 

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

358 

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

360 ''' 

361 n = typename(self.height4) 

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

363 if normal and d is self.datum: 

364 r = self._height4 

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

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

367 try: 

368 d = d.toEllipsoid(name=n) 

369 except (TypeError, ValueError): # TriaxialError 

370 d = None 

371 else: 

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

373 

374 if Cartesian_and_kwds: 

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

376 d = _spherical_datum(d, name=n) 

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

378 return r 

379 

380 @Property_RO 

381 def isEllipsoidal(self): 

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

383 ''' 

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

385 

386 @Property_RO 

387 def isSpherical(self): 

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

389 ''' 

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

391 

392 @Property_RO 

393 def latlon(self): 

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

395 ''' 

396 return self.toEcef().latlon 

397 

398 @Property_RO 

399 def latlonheight(self): 

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

401 ''' 

402 return self.toEcef().latlonheight 

403 

404 @Property_RO 

405 def latlonheightdatum(self): 

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

407 ''' 

408 return self.toEcef().latlonheightdatum 

409 

410 @Property_RO 

411 def _N_vector(self): 

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

413 ''' 

414 _N = _MODS.nvectorBase._N_vector_ 

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

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

417 

418 def _n_xyzh4(self, datum): 

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

420 ''' 

421 def _ErrorEPS0(x): 

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

423 

424 _xinstanceof(Datum, datum=datum) 

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

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

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

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

429 E = datum.ellipsoid 

430 x, y, z = self.xyz3 

431 

432 # Kenneth Gade eqn 23 

433 p = hypot2(x, y) * E.a2_ 

434 q = z**2 * E.e21 * E.a2_ 

435 r = fsumf_(p, q, -E.e4) / _6_0 

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

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

438 if isnear0(t): 

439 raise _ErrorEPS0(t) 

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

441 v = sqrt(u**2 + E.e4 * q) 

442 t = v * _2_0 

443 if t < EPS0: # isnear0 

444 raise _ErrorEPS0(t) 

445 w = fsumf_(u, v, -q) * E.e2 / t 

446 k = sqrt(fsumf_(u, v, w**2)) - w 

447 if isnear0(k): 

448 raise _ErrorEPS0(k) 

449 t = k + E.e2 

450 if isnear0(t): 

451 raise _ErrorEPS0(t) 

452 e = k / t 

453# d = e * hypot(x, y) 

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

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

456 if t < EPS0: # isnear0 

457 raise _ErrorEPS0(t) 

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

459 s = e / t # == e * tmp 

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

461 

462 @Property_RO 

463 def philam(self): 

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

465 ''' 

466 return self.toEcef().philam 

467 

468 @Property_RO 

469 def philamheight(self): 

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

471 ''' 

472 return self.toEcef().philamheight 

473 

474 @Property_RO 

475 def philamheightdatum(self): 

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

477 ''' 

478 return self.toEcef().philamheightdatum 

479 

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

481 '''3-Point resection between this and two other points using U{Pierlot 

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

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

484 

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

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

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

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

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

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

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

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

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

494 (C{bool}). 

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

496 

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

498 

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

500 

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

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

503 

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

505 

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

507 ''' 

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

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

510 

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

512 '''3-Point resection between this and two other points using U{Pierlot 

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

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

515 

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

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

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

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

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

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

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

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

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

525 

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

527 

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

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

530 

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

532 

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

534 ''' 

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

536 useZ=useZ, datum=self.datum) 

537 

538 def Roc2(self, earth=None): 

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

540 

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

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

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

544 

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

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

547 

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

549 ''' 

550 r = z = fabs( self.z) 

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

552 if R < _0: # polar 

553 R = z 

554 elif z > _0: # non-equatorial 

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

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

557 M = e.M # EcefMatrix 

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

559 if ca < _0: # polar 

560 R = z 

561 else: # prime-vertical, normal roc R 

562 R = R / ca # /= chokes PyChecker 

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

564 return R, r 

565 

566 @property_RO 

567 def sphericalCartesian(self): 

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

569 ''' 

570 return False 

571 

572 @deprecated_method 

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

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

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

576 

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

578 '''3-Point resection between this and two other points using U{Tienstra 

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

580 

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

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

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

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

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

586 non-negative). 

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

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

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

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

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

592 (C{bool}). 

593 

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

595 

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

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

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

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

600 

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

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

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

604 

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

606 

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

608 ''' 

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

610 useZ=useZ, datum=self.datum) 

611 

612 @deprecated_method 

613 def to2ab(self): # PYCHOK no cover 

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

615 

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

617 ''' 

618 return self.philam 

619 

620 @deprecated_method 

621 def to2ll(self): # PYCHOK no cover 

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

623 

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

625 ''' 

626 return self.latlon 

627 

628 @deprecated_method 

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

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

631 

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

633 

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

635 as its name may suggest. 

636 ''' 

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

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

639 

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

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

642# ''' 

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

644# if LL is not None: 

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

646# for n, v in pairs.items(): 

647# setattr(r, n, v) 

648# return r 

649 

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

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

652 

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

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

655 

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

657 

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

659 invalid. 

660 ''' 

661 _xinstanceof(Datum, datum2=datum2) 

662 

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

664 self.toDatum(datum) 

665 

666 i, d = False, c.datum 

667 if d == datum2: 

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

669 

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

671 datum2.transform.isunity): 

672 return c.dup(datum=datum2) 

673 

674 elif d == _WGS84: 

675 d = datum2 # convert from WGS84 to datum2 

676 

677 elif datum2 == _WGS84: 

678 i = True # convert to WGS84 by inverse transformation 

679 

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

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

682 d = datum2 

683 

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

685 

686 def toEcef(self): 

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

688 

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

690 with C{C} and C{M} if available. 

691 

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

693 ''' 

694 return self._ecef9 

695 

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

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

698 

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

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

701 C{B{LatLon} is not None}. 

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

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

704 C{B{LatLon} is None}. 

705 

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

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

708 and C{M} if available. 

709 

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

711 ''' 

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

713 if d == self.datum: 

714 r = self.toEcef() 

715 else: 

716 c = self.toDatum(d) 

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

718 

719 if LatLon: # class or .classof 

720 h = _heigHt(r, height) 

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

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

723 _xdatum(r.datum, d) 

724 return r 

725 

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

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

728 

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

730 (C{Nvector}) or C{None}. 

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

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

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

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

735 C{B{Nvector} is None}. 

736 

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

738 C{B{Nvector} is None}. 

739 

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

741 B{C{name_Nvector_kwds}} item. 

742 

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

744 ''' 

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

746 if datum is not None: 

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

748 if d != self.datum: 

749 r = self._n_xyzh4(d) 

750 

751 if Nvector is None: 

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

753 if n: 

754 r = r.dup(name=n) 

755 else: 

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

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

758 return r 

759 

760 def toRtp(self): 

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

762 

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

764 and C{phi}, both in L{Degrees}. 

765 

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

767 ''' 

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

769 

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

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

772 

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

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

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

776 

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

778 ''' 

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

780 

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

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

783 

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

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

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

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

788 

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

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

791 

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

793 ''' 

794 _xinstanceof(Transform, transform=transform) 

795 if transform.isunity: 

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

797 else: 

798 # if inverse and d != _WGS84: 

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

800 # txt_not_=_WGS84.name) 

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

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

803 return c 

804 

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

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

807 

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

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

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

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

812 

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

814 C{B{Vector} is None}. 

815 

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

817 ''' 

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

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

820 

821 

822class RadiusThetaPhi3Tuple(_NamedTupleTo): 

823 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination 

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

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

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

827 ''' 

828 _Names_ = (_r_, _theta_, _phi_) 

829 _Units_ = ( Meter, _Pass, _Pass) 

830 

831 def toCartesian(self, **name_Cartesian_and_kwds): 

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

833 

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

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

836 C{B{Cartesian}} keyword arguments. 

837 

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

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

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

841 

842 @see: Function L{rtp2xyz_}. 

843 ''' 

844 r, t, p = self 

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

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

847 

848 def toDegrees(self, **name): 

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

850 

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

852 

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

854 and C{phi} both in L{Degrees}. 

855 ''' 

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

857 

858 def toRadians(self, **name): 

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

860 

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

862 

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

864 and C{phi} both in L{Radians}. 

865 ''' 

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

867 

868 def _toU(self, U): 

869 M = RadiusThetaPhi3Tuple._Units_[0] # Meter 

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

871 

872 def _toX3U(self, _X3, U, name): 

873 r, t, p = self 

874 t, p, s = _X3(self, t, p) 

875 if s is None or name: 

876 n = self._name__(name) 

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

878 return s 

879 

880 

881def rtp2xyz(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds): 

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

883 

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

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

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

887 

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

889 ''' 

890 if isinstance(r_rtp, RadiusThetaPhi3Tuple): 

891 c = r_rtp.toCartesian(**name_Cartesian_and_kwds) 

892 else: 

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

894 return c 

895 

896 

897def rtp2xyz_(r_rtp, theta=0, phi=0, **name_Cartesian_and_kwds): 

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

899 

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

901 L{RadiusThetaPhi3Tuple} instance. 

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

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

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

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

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

907 keyword arguments. 

908 

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

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

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

912 

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

914 B{C{name_Cartesian_and_kwds}} item. 

915 

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

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

918 and L{xyz2rtp}. 

919 ''' 

920 if isinstance(r_rtp, RadiusThetaPhi3Tuple): 

921 c = r_rtp.toCartesian(**name_Cartesian_and_kwds) 

922 elif _isMeter(r_rtp): 

923 r = r_rtp 

924 if r and _isfinite(r): 

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

926 s *= r 

927 z *= r 

928 y *= s 

929 x *= s 

930 else: 

931 x = y = z = r 

932 

933 n, kwds = _name2__(**name_Cartesian_and_kwds) 

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

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

936 C(x, y, z, name=n, **kwds) 

937 else: 

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

939 return c 

940 

941 

942def _rtp3(where, U, *x_y_z, **name): 

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

944 ''' 

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

946 r = hypot_(x, y, z) 

947 if r > 0: 

948 t = acos1(z / r) 

949 p = atan2(y, x) 

950 while p < 0: 

951 p += PI2 

952 if U is Degrees: 

953 t = degrees(t) 

954 p = degrees(p) 

955 else: 

956 t = p = _0_0 

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

958 

959 

960def xyz2rtp(x_xyz, y=0, z=0, **name): 

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

962 

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

964 in L{Degrees}. 

965 

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

967 ''' 

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

969 

970 

971def xyz2rtp_(x_xyz, y=0, z=0, **name): 

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

973 

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

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

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

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

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

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

980 

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

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

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

984 

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

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

987 ''' 

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

989 

990 

991__all__ += _ALL_DOCS(CartesianBase) 

992 

993# **) MIT License 

994# 

995# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

996# 

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

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

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

1000# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

1001# and/or sell copies of the Software, and to permit persons to whom the 

1002# Software is furnished to do so, subject to the following conditions: 

1003# 

1004# The above copyright notice and this permission notice shall be included 

1005# in all copies or substantial portions of the Software. 

1006# 

1007# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

1008# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

1009# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

1010# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

1011# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

1012# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

1013# OTHER DEALINGS IN THE SOFTWARE.