1

2# -*- coding: utf-8 -*-

3

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

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

6

7 After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see

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

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

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

11'''

12

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

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

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

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

17 Transform, _WGS84, _xinstanceof

18# from pygeodesy.ecef import EcefKarney # _MODS

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

20 _xdatum, _xkwds, _xkwds_get, _xkwds_pop2

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

22# from pygeodesy.formy import _hartzell # _MODS

23 from pygeodesy.fsums import fsumf_, Fmt

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

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

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

27 from pygeodesy.named import _name2__, _Pass

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

29 Vector4Tuple, Bearing2Tuple # PYCHOK .sphericalBase

30# from pygeodesy.nvectorBase import _N_vector # _MODS

31 from 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

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

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

39 from 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__ = '24.06.11'

47

48_r_ = 'r'

49_theta_ = 'theta'

50

51

52 class 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 optional,

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_RO

215 def Ecef(self):

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

217 '''

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

219 return E

220

221 @Property_RO

222 def _ecef9(self):

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

224 '''

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

226

227 @property_RO

228 def ellipsoidalCartesian(self):

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

230 '''

231 return False

232

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

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

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

236

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

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

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

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

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

242 C{datum} ellipsoid.

243

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

245 this C{pov}.

246

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

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

249 the ellipsoid.

250

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

252

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

254 '''

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

256

257 @Property

258 def height(self):

259 '''Get the height (C{meter}).

260 '''

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

262

263 @height.setter # PYCHOK setter!

264 def height(self, height):

265 '''Set the height (C{meter}).

266

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

268

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

270 '''

271 h = Height(height)

272 if self._height != h:

273 _update_all(self)

274 self._height = h

275

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

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

278 '''

279 if Cartesian is not None:

280 r = Cartesian(r, **kwds)

281 if datum is not None:

282 r.datum = datum

283 if height is not None:

284 r.height = height # Height(height)

285 return r

286

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

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

289

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

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

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

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

294 cartesian's height.

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

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

297 keyword arguments.

298

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

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

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

302

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

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

305

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

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

308

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

310

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

312 '''

313 n = self.height3.__name__

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

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

316 if h and d:

317 R, r = self.Roc2(earth=d)

318 if R > EPS0:

319 R = (R + h) / R

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

321 c = c.times_(R, R, r)

322

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

324 if Cartesian_and_kwds:

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

326 return r

327

328 @Property_RO

329 def _height4(self):

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

331 '''

332 try:

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

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

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

336 return r

337

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

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

340 this datum's ellipsoid surface.

341

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

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

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

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

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

347 ellipsoid's surface, otherwise the intersection of the

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

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

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

351 arguments.

352

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

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

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

356

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

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

359

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

361

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

363

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

365 '''

366 n = self.height4.__name__

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

368 if normal and d is self.datum:

369 r = self._height4

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

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

372 try:

373 d = d.toEllipsoid(name=n)

374 except (TypeError, ValueError): # TriaxialError

375 d = None

376 else:

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

378

379 if Cartesian_and_kwds:

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

381 d = _spherical_datum(d, name=n)

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

383 return r

384

385 @Property_RO

386 def isEllipsoidal(self):

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

388 '''

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

390

391 @Property_RO

392 def isSpherical(self):

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

394 '''

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

396

397 @Property_RO

398 def latlon(self):

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

400 '''

401 return self.toEcef().latlon

402

403 @Property_RO

404 def latlonheight(self):

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

406 '''

407 return self.toEcef().latlonheight

408

409 @Property_RO

410 def latlonheightdatum(self):

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

412 '''

413 return self.toEcef().latlonheightdatum

414

415 @Property_RO

416 def _Ltp(self):

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

418 '''

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

420

421 @Property_RO

422 def _N_vector(self):

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

424 '''

425 _N = _MODS.nvectorBase._N_vector_

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

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

428

429 def _n_xyzh4(self, datum):

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

431 '''

432 def _ErrorEPS0(x):

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

434

435 _xinstanceof(Datum, datum=datum)

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

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

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

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

440 E = datum.ellipsoid

441 x, y, z = self.xyz

442

443 # Kenneth Gade eqn 23

444 p = hypot2(x, y) * E.a2_

445 q = z**2 * E.e21 * E.a2_

446 r = fsumf_(p, q, -E.e4) / _6_0

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

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

449 if isnear0(t):

450 raise _ErrorEPS0(t)

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

452 v = sqrt(u**2 + E.e4 * q)

453 t = v * _2_0

454 if t < EPS0: # isnear0

455 raise _ErrorEPS0(t)

456 w = fsumf_(u, v, -q) * E.e2 / t

457 k = sqrt(fsumf_(u, v, w**2)) - w

458 if isnear0(k):

459 raise _ErrorEPS0(k)

460 t = k + E.e2

461 if isnear0(t):

462 raise _ErrorEPS0(t)

463 e = k / t

464# d = e * hypot(x, y)

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

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

467 if t < EPS0: # isnear0

468 raise _ErrorEPS0(t)

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

470 s = e / t # == e * tmp

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

472

473 @Property_RO

474 def philam(self):

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

476 '''

477 return self.toEcef().philam

478

479 @Property_RO

480 def philamheight(self):

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

482 '''

483 return self.toEcef().philamheight

484

485 @Property_RO

486 def philamheightdatum(self):

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

488 '''

489 return self.toEcef().philamheightdatum

490

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

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

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

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

495

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

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

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

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

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

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

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

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

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

505 (C{bool}).

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

507

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

509

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

511

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

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

514

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

516

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

518 '''

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

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

521

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

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

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

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

526

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

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

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

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

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

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

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

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

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

536

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

538

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

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

541

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

543

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

545 '''

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

547 useZ=useZ, datum=self.datum)

548

549 def Roc2(self, earth=None):

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

551

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

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

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

555

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

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

558

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

560 '''

561 r = z = fabs( self.z)

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

563 if R < _0: # polar

564 R = z

565 elif z > _0: # non-equatorial

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

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

568 M = e.M # EcefMatrix

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

570 if ca < _0: # polar

571 R = z

572 else: # prime-vertical, normal roc R

573 R = R / ca # /= chokes PyChecker

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

575 return R, r

576

577 @property_RO

578 def sphericalCartesian(self):

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

580 '''

581 return False

582

583 @deprecated_method

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

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

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

587

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

589 '''3-Point resection between this and two other points using U{Tienstra

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

591

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

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

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

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

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

597 non-negative).

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

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

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

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

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

603 (C{bool}).

604

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

606

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

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

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

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

611

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

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

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

615

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

617

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

619 '''

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

621 useZ=useZ, datum=self.datum)

622

623 @deprecated_method

624 def to2ab(self): # PYCHOK no cover

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

626

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

628 '''

629 return self.philam

630

631 @deprecated_method

632 def to2ll(self): # PYCHOK no cover

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

634

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

636 '''

637 return self.latlon

638

639 @deprecated_method

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

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

642

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

644

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

646 as its name may suggest.

647 '''

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

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

650

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

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

653# '''

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

655# if LL is not None:

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

657# for n, v in pairs.items():

658# setattr(r, n, v)

659# return r

660

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

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

663

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

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

666

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

668

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

670 invalid.

671 '''

672 _xinstanceof(Datum, datum2=datum2)

673

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

675 self.toDatum(datum)

676

677 i, d = False, c.datum

678 if d == datum2:

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

680

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

682 datum2.transform.isunity):

683 return c.dup(datum=datum2)

684

685 elif d == _WGS84:

686 d = datum2 # convert from WGS84 to datum2

687

688 elif datum2 == _WGS84:

689 i = True # convert to WGS84 by inverse transformation

690

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

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

693 d = datum2

694

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

696

697 def toEcef(self):

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

699

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

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

702

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

704 '''

705 return self._ecef9

706

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

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

709

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

711 or L{a_f2Tuple}).

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

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

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

715 (C{LatLon}) or C{None}.

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

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

718

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

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

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

722

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

724 '''

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

726 if d == self.datum:

727 r = self.toEcef()

728 else:

729 c = self.toDatum(d)

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

731

732 if LatLon: # class or .classof

733 h = _heigHt(r, height)

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

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

736 _xdatum(r.datum, d)

737 return r

738

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

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

741

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

743 L{Enu}, L{Ned}) or C{None}.

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

745 cartesian's LTP (L{Ltp}).

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

747 ignored if C{B{Xyz} is None}.

748

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

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

751

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

753 '''

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

755

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

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

758

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

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

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

762 '''

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

764

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

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

767

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

769 (C{Nvector}) or C{None}.

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

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

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

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

774 C{B{Nvector} is None}.

775

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

777 C{B{Nvector} is None}.

778

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

780 B{C{name_Nvector_kwds}} item.

781

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

783 '''

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

785 if datum is not None:

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

787 if d != self.datum:

788 r = self._n_xyzh4(d)

789

790 if Nvector is None:

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

792 if n:

793 r = r.dup(name=n)

794 else:

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

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

797 return r

798

799 def toRtp(self):

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

801

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

803 and C{phi}, both in L{Degrees}.

804

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

806 '''

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

808

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

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

811

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

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

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

815

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

817 '''

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

819

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

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

822

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

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

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

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

827

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

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

830

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

832 '''

833 _xinstanceof(Transform, transform=transform)

834 if transform.isunity:

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

836 else:

837 # if inverse and d != _WGS84:

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

839 # txt_not_=_WGS84.name)

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

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

842 return c

843

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

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

846

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

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

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

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

851

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

853 C{B{Vector} is None}.

854

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

856 '''

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

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

859

860

861 class RadiusThetaPhi3Tuple(_NamedTupleTo):

862 '''3-Tuple C{(r, theta, phi)} with radial distance C{r} in C{meter}, inclination

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

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

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

866 '''

867 _Names_ = (_r_, _theta_, _phi_)

868 _Units_ = ( Meter, _Pass, _Pass)

869

870 def toCartesian(self, **name_Cartesian_and_kwds):

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

872

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

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

875 C{B{Cartesian}} keyword arguments.

876

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

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

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

880

881 @see: Function L{rtp2xyz_}.

882 '''

883 r, t, p = self

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

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

886

887 def toDegrees(self, **name):

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

889

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

891

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

893 and C{phi} both in L{Degrees}.

894 '''

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

896

897 def toRadians(self, **name):

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

899

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

901

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

903 and C{phi} both in L{Radians}.

904 '''

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

906

907 def _toU(self, U):

908 M = RadiusThetaPhi3Tuple._Units_[0] # Meter

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

910

911 def _toX3U(self, _X3, U, name):

912 r, t, p = self

913 t, p, s = _X3(self, t, p)

914 if s is None or name:

915 n = self._name__(name)

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

917 return s

918

919

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

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

922

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

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

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

926

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

928 '''

929 if isinstance(r_rtp, RadiusThetaPhi3Tuple):

930 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)

931 else:

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

933 return c

934

935

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

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

938

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

940 L{RadiusThetaPhi3Tuple} instance.

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

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

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

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

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

946 keyword arguments.

947

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

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

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

951

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

953 B{C{name_Cartesian_and_kwds}} item.

954

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

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

957 and L{xyz2rtp}.

958 '''

959 if isinstance(r_rtp, RadiusThetaPhi3Tuple):

960 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)

961 elif _isMeter(r_rtp):

962 r = r_rtp

963 if r and _isfinite(r):

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

965 s *= r

966 z *= r

967 y *= s

968 x *= s

969 else:

970 x = y = z = r

971

972 n, kwds = _name2__(**name_Cartesian_and_kwds)

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

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

975 C(x, y, z, name=n, **kwds)

976 else:

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

978 return c

979

980

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

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

983 '''

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

985 r = hypot_(x, y, z)

986 if r > 0:

987 t = acos1(z / r)

988 p = atan2(y, x)

989 while p < 0:

990 p += PI2

991 if U is Degrees:

992 t = degrees(t)

993 p = degrees(p)

994 else:

995 t = p = _0_0

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

997

998

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

1000 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.

1001

1002 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with C{theta} and C{phi}, both

1003 in L{Degrees}.

1004

1005 @see: Function L{xyz2rtp_} for further details.

1006 '''

1007 return _rtp3(xyz2rtp, Degrees, x_xyz, y, z, **name)

1008

1009

1010 def xyz2rtp_(x_xyz, y=0, z=0, **name):

1011 '''Convert cartesian C{(x, y, z)} to I{spherical, polar} C{(r, theta, phi)} coordinates.

1012

1013 @arg x_xyz: X component (C{scalar}) or a cartesian (C{Cartesian}, L{Ecef9Tuple},

1014 C{Nvector}, L{Vector3d}, L{Vector3Tuple}, L{Vector4Tuple} or a C{tuple} or

1015 C{list} of 3+ C{scalar} items) if no C{y_z} specified.

1016 @arg y: Y component (C{scalar}), required if C{B{x_xyz}} is C{scalar}, ignored otherwise.

1017 @arg z: Z component (C{scalar}), like B{C{y}}.

1018 @kwarg name: Optional C{B{name}=NN} (C{str}).

1019

1020 @return: L{RadiusThetaPhi3Tuple}C{(r, theta, phi)} with radial distance C{r} (C{meter},

1021 same units as C{x}, C{y} and C{z}), inclination C{theta} (with respect to the

1022 positive z-axis) and azimuthal angle C{phi}, both in L{Radians}.

1023

1024 @see: U{Physics convention<https://WikiPedia.org/wiki/Spherical_coordinate_system>}

1025 (ISO 80000-2:2019), class L{RadiusThetaPhi3Tuple} and function L{xyz2rtp}.

1026 '''

1027 return _rtp3(xyz2rtp_, Radians, x_xyz, y, z, **name)

1028

1029

1030__all__ += _ALL_DOCS(CartesianBase)

1031

1032# **) MIT License

1033#

1034# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1035#

1036# Permission is hereby granted, free of charge, to any person obtaining a

1037# copy of this software and associated documentation files (the "Software"),

1038# to deal in the Software without restriction, including without limitation

1039# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1040# and/or sell copies of the Software, and to permit persons to whom the

1041# Software is furnished to do so, subject to the following conditions:

1042#

1043# The above copyright notice and this permission notice shall be included

1044# in all copies or substantial portions of the Software.

1045#

1046# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1047# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1048# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1049# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1050# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1051# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

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