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__ = '24.06.10'

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}), ignored if B{C{x_xyz}}

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

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

68 or L{a_f2Tuple}).

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

70 latlon C{B{ll}=None} (C{LatLon}).

71

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

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

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

75 not a L{Datum}.

76 '''

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

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

79 if h is not None:

80 self._height = Height(h)

81 if d is not None:

82 self.datum = d

83

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

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

86# '''

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

88# _NotImplemented(self, other)

89

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

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

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

93

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

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

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

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

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

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

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

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

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

103 force C{z=INT0} (C{bool}).

104

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

106

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

108

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

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

111

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

113

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

115 '''

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

117 useZ=useZ, datum=self.datum)

118

119 @deprecated_method

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

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

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

123

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

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

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

127

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

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

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

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

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

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

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

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

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

137 force C{z=INT0} (C{bool}).

138

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

140

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

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

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

144

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

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

147

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

149

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

151 '''

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

153 useZ=useZ, datum=self.datum)

154

155 @deprecated_method

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

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

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

159

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

161 def datum(self):

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

163 '''

164 return self._datum

165

166 @datum.setter # PYCHOK setter!

167 def datum(self, datum):

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

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

170

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

172 '''

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

174 if self._datum: # is not None

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

176 raise _IsnotError(_ellipsoidal_, datum=datum)

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

178 raise _IsnotError(_spherical_, datum=datum)

179 if self._datum != d:

180 _update_all(self)

181 self._datum = d

182

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

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

185

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

187 or L{Local9Tuple}).

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

189 or C{None}.

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

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

192 C{B{Cartesian} is None}.

193

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

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

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

197

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

199 item or C{datum} missing or incompatible.

200 '''

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

202 if Cartesian is None:

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

204 else:

205 d = self.datum

206 if not d:

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

208 t = _xkwds_get(kwds, datum=d)

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

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

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

212 r = Cartesian(*c, **kwds)

213 return r.renamed(n) if n else r

214

215 @property_RO

216 def Ecef(self):

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

218 '''

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

220 return E

221

222 @Property_RO

223 def _ecef9(self):

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

225 '''

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

227

228 @property_RO

229 def ellipsoidalCartesian(self):

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

231 '''

232 return False

233

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

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

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

237

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

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

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

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

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

243 C{datum} ellipsoid.

244

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

246 this C{pov}.

247

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

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

250 the ellipsoid.

251

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

253

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

255 '''

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

257

258 @Property

259 def height(self):

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

261 '''

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

263

264 @height.setter # PYCHOK setter!

265 def height(self, height):

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

267

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

269

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

271 '''

272 h = Height(height)

273 if self._height != h:

274 _update_all(self)

275 self._height = h

276

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

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

279 '''

280 if Cartesian is not None:

281 r = Cartesian(r, **kwds)

282 if datum is not None:

283 r.datum = datum

284 if height is not None:

285 r.height = height # Height(height)

286 return r

287

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

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

290

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

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

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

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

295 cartesian's height.

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

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

298 keyword arguments.

299

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

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

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

303

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

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

306

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

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

309

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

311

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

313 '''

314 n = self.height3.__name__

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

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

317 if h and d:

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

319 if R > EPS0:

320 R = (R + h) / R

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

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

323

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

325 if Cartesian_and_kwds:

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

327 return r

328

329 @Property_RO

330 def _height4(self):

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

332 '''

333 try:

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

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

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

337 return r

338

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

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

341 this datum's ellipsoid surface.

342

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

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

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

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

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

348 ellipsoid's surface, otherwise the intersection of the

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

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

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

352 arguments.

353

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

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

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

357

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

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

360

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

362

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

364

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

366 '''

367 n = self.height4.__name__

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

369 if normal and d is self.datum:

370 r = self._height4

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

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

373 try:

374 d = d.toEllipsoid(name=n)

375 except (TypeError, ValueError): # TriaxialError

376 d = None

377 else:

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

379

380 if Cartesian_and_kwds:

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

382 d = _spherical_datum(d, name=n)

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

384 return r

385

386 @Property_RO

387 def isEllipsoidal(self):

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

389 '''

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

391

392 @Property_RO

393 def isSpherical(self):

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

395 '''

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

397

398 @Property_RO

399 def latlon(self):

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

401 '''

402 return self.toEcef().latlon

403

404 @Property_RO

405 def latlonheight(self):

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

407 '''

408 return self.toEcef().latlonheight

409

410 @Property_RO

411 def latlonheightdatum(self):

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

413 '''

414 return self.toEcef().latlonheightdatum

415

416 @Property_RO

417 def _Ltp(self):

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

419 '''

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

421

422 @Property_RO

423 def _N_vector(self):

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

425 '''

426 _N = _MODS.nvectorBase._N_vector_

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

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

429

430 def _n_xyzh4(self, datum):

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

432 '''

433 def _ErrorEPS0(x):

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

435

436 _xinstanceof(Datum, datum=datum)

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

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

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

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

441 E = datum.ellipsoid

442 x, y, z = self.xyz

443

444 # Kenneth Gade eqn 23

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

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

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

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

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

450 if isnear0(t):

451 raise _ErrorEPS0(t)

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

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

454 t = v * _2_0

455 if t < EPS0: # isnear0

456 raise _ErrorEPS0(t)

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

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

459 if isnear0(k):

460 raise _ErrorEPS0(k)

461 t = k + E.e2

462 if isnear0(t):

463 raise _ErrorEPS0(t)

464 e = k / t

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

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

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

468 if t < EPS0: # isnear0

469 raise _ErrorEPS0(t)

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

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

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

473

474 @Property_RO

475 def philam(self):

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

477 '''

478 return self.toEcef().philam

479

480 @Property_RO

481 def philamheight(self):

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

483 '''

484 return self.toEcef().philamheight

485

486 @Property_RO

487 def philamheightdatum(self):

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

489 '''

490 return self.toEcef().philamheightdatum

491

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

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

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

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

496

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

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

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

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

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

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

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

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

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

506 (C{bool}).

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

508

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

510

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

512

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

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

515

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

517

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

519 '''

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

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

522

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

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

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

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

527

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

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

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

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

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

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

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

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

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

537

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

539

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

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

542

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

544

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

546 '''

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

548 useZ=useZ, datum=self.datum)

549

550 def Roc2(self, earth=None):

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

552

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

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

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

556

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

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

559

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

561 '''

562 r = z = fabs( self.z)

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

564 if R < _0: # polar

565 R = z

566 elif z > _0: # non-equatorial

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

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

569 M = e.M # EcefMatrix

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

571 if ca < _0: # polar

572 R = z

573 else: # prime-vertical, normal roc R

574 R = R / ca # /= chokes PyChecker

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

576 return R, r

577

578 @property_RO

579 def sphericalCartesian(self):

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

581 '''

582 return False

583

584 @deprecated_method

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

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

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

588

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

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

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

592

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

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

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

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

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

598 non-negative).

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

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

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

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

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

604 (C{bool}).

605

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

607

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

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

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

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

612

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

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

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

616

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

618

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

620 '''

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

622 useZ=useZ, datum=self.datum)

623

624 @deprecated_method

625 def to2ab(self): # PYCHOK no cover

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

627

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

629 '''

630 return self.philam

631

632 @deprecated_method

633 def to2ll(self): # PYCHOK no cover

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

635

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

637 '''

638 return self.latlon

639

640 @deprecated_method

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

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

643

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

645

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

647 as its name may suggest.

648 '''

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

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

651

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

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

654# '''

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

656# if LL is not None:

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

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

659# setattr(r, n, v)

660# return r

661

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

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

664

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

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

667

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

669

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

671 invalid.

672 '''

673 _xinstanceof(Datum, datum2=datum2)

674

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

676 self.toDatum(datum)

677

678 i, d = False, c.datum

679 if d == datum2:

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

681

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

683 datum2.transform.isunity):

684 return c.dup(datum=datum2)

685

686 elif d == _WGS84:

687 d = datum2 # convert from WGS84 to datum2

688

689 elif datum2 == _WGS84:

690 i = True # convert to WGS84 by inverse transformation

691

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

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

694 d = datum2

695

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

697

698 def toEcef(self):

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

700

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

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

703

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

705 '''

706 return self._ecef9

707

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

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

710

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

712 or L{a_f2Tuple}).

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

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

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

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

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

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

719

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

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

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

723

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

725 '''

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

727 if d == self.datum:

728 r = self.toEcef()

729 else:

730 c = self.toDatum(d)

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

732

733 if LatLon: # class or .classof

734 h = _heigHt(r, height)

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

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

737 _xdatum(r.datum, d)

738 return r

739

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

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

742

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

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

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

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

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

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

749

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

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

752

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

754 '''

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

756

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

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

759

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

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

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

763 '''

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

765

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

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

768

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

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

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

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

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

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

775 C{B{Nvector} is None}.

776

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

778 B{C{Nvector}} is C{None}.

779

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

781 B{C{name_Nvector_kwds}} item.

782

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

784 '''

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

786 if datum is not None:

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

788 if d != self.datum:

789 r = self._n_xyzh4(d)

790

791 if Nvector is None:

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

793 if n:

794 r = r.dup(name=n)

795 else:

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

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

798 return r

799

800 def toRtp(self):

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

802

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

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

805

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

807 '''

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

809

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

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

812

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

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

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

816

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

818 '''

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

820

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

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

823

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

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

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

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

828

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

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

831

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

833 '''

834 _xinstanceof(Transform, transform=transform)

835 if transform.isunity:

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

837 else:

838 # if inverse and d != _WGS84:

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

840 # txt_not_=_WGS84.name)

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

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

843 return c

844

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

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

847

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

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

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

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

852

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

854 B{C{Vector}} is C{None}.

855

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

857 '''

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

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

860

861

862 class RadiusThetaPhi3Tuple(_NamedTupleTo):

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

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

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

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

867 '''

868 _Names_ = (_r_, _theta_, _phi_)

869 _Units_ = ( Meter, _Pass, _Pass)

870

871 def toCartesian(self, **name_Cartesian_and_kwds):

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

873

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

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

876 C{B{Cartesian}} keyword arguments.

877

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

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

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

881

882 @see: Function L{rtp2xyz_}.

883 '''

884 r, t, p = self

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

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

887

888 def toDegrees(self, **name):

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

890

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

892

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

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

895 '''

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

897

898 def toRadians(self, **name):

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

900

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

902

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

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

905 '''

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

907

908 def _toU(self, U):

909 M = RadiusThetaPhi3Tuple._Units_[0] # Meter

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

911

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

913 r, t, p = self

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

915 if s is None or name:

916 n = self._name__(name)

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

918 return s

919

920

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

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

923

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

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

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

927 ignored otherwise.

928

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

930 '''

931 if isinstance(r_rtp, RadiusThetaPhi3Tuple):

932 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)

933 else:

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

935 return c

936

937

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

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

940

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

942 L{RadiusThetaPhi3Tuple} instance.

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

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

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

946 ignored otherwise.

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

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

949 keyword arguments.

950

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

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

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

954

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

956 B{C{name_Cartesian_and_kwds}} item.

957

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

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

960 and L{xyz2rtp}.

961 '''

962 if isinstance(r_rtp, RadiusThetaPhi3Tuple):

963 c = r_rtp.toCartesian(**name_Cartesian_and_kwds)

964 elif _isMeter(r_rtp):

965 r = r_rtp

966 if r and _isfinite(r):

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

968 s *= r

969 z *= r

970 y *= s

971 x *= s

972 else:

973 x = y = z = r

974

975 n, kwds = _name2__(**name_Cartesian_and_kwds)

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

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

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

979 else:

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

981 return c

982

983

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

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

986 '''

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

988 r = hypot_(x, y, z)

989 if r > 0:

990 t = acos1(z / r)

991 p = atan2(y, x)

992 while p < 0:

993 p += PI2

994 if U is Degrees:

995 t = degrees(t)

996 p = degrees(p)

997 else:

998 t = p = _0_0

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

1000

1001

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

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

1004

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

1006 in L{Degrees}.

1007

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

1009 '''

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

1011

1012

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

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

1015

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

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

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

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

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

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

1022

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

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

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

1026

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

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

1029 '''

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

1031

1032

1033__all__ += _ALL_DOCS(CartesianBase)

1034

1035# **) MIT License

1036#

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

1038#

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

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

1045#

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

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