1

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

3

4 u'''I{Geocentric} Earth-Centered, Earth-Fixed (ECEF) coordinates.

5

6 Geocentric conversions transcoded from I{Charles Karney}'s C++ class U{Geocentric

7<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Geocentric.html>}

8 into pure Python class L{EcefKarney}, class L{EcefSudano} based on I{John Sudano}'s

9 U{paper<https://www.ResearchGate.net/publication/

10 3709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>},

11 class L{EcefVeness} transcoded from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal,

12 Cartesian<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}, class L{EcefYou}

13 implementing I{Rey-Jer You}'s U{transformations<https://www.ResearchGate.net/publication/240359424>} and

14 classes L{EcefFarrell22} and L{EcefFarrell22} from I{Jay A. Farrell}'s U{Table 2.1 and 2.2

15<https://Books.Google.com/books?id=fW4foWASY6wC>}, page 29-30.

16

17 Following is a copy of I{Karney}'s U{Detailed Description

18<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Geocentric.html>}.

19

20 Convert between geodetic coordinates C{lat}-, C{lon}gitude and height C{h} (measured vertically

21 from the surface of the ellipsoid) to geocentric C{x}, C{y} and C{z} coordinates, also known as

22 I{Earth-Centered, Earth-Fixed} (U{ECEF<https://WikiPedia.org/wiki/ECEF>}).

23

24 The origin of geocentric coordinates is at the center of the earth. The C{z} axis goes thru

25 the North pole, C{lat} = 90°. The C{x} axis goes thru C{lat} = 0°, C{lon} = 0°.

26

27 The I{local (cartesian) origin} is at (C{lat0}, C{lon0}, C{height0}). The I{local} C{x} axis points

28 East, the I{local} C{y} axis points North and the I{local} C{z} axis is normal to the ellipsoid. The

29 plane C{z = -height0} is tangent to the ellipsoid, hence the alternate name I{local tangent plane}.

30

31 Forward conversion from geodetic to geocentric (ECEF) coordinates is straightforward.

32

33 For the reverse transformation we use Hugues Vermeille's U{I{Direct transformation from geocentric

34 coordinates to geodetic coordinates}<https://DOI.org/10.1007/s00190-002-0273-6>}, J. Geodesy

35(2002) 76, page 451-454.

36

37 Several changes have been made to ensure that the method returns accurate results for all finite

38 inputs (even if h is infinite). The changes are described in Appendix B of C. F. F. Karney

39 U{I{Geodesics on an ellipsoid of revolution}<https://ArXiv.org/abs/1102.1215v1>}, Feb. 2011, 85,

40 105-117 (U{preprint<https://ArXiv.org/abs/1102.1215v1>}). Vermeille similarly updated his method

41 in U{I{An analytical method to transform geocentric into geodetic coordinates}

42<https://DOI.org/10.1007/s00190-010-0419-x>}, J. Geodesy (2011) 85, page 105-117. See U{Geocentric

43 coordinates<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>} for more information.

44

45 The errors in these routines are close to round-off. Specifically, for points within 5,000 Km of

46 the surface of the ellipsoid (either inside or outside the ellipsoid), the error is bounded by 7

47 nm (7 nanometers) for the WGS84 ellipsoid. See U{Geocentric coordinates

48<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>} for further information on the errors.

49

50@note: The C{reverse} methods of all C{Ecef...} classes return by default C{INT0} as the (geodetic)

51 longitude for I{polar} ECEF location C{x == y == 0}. Use keyword argument C{lon00} or property

52 C{lon00} to configure that value.

53

54@see: Module L{ltp} and class L{LocalCartesian}, a transcription of I{Charles Karney}'s C++ class

55 U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1LocalCartesian.html>},

56 for conversion between geodetic and I{local cartesian} coordinates in a I{local tangent

57 plane} as opposed to I{geocentric} (ECEF) ones.

58'''

59

60 from pygeodesy.basics import copysign0, isscalar, issubclassof, neg, map1, \

61 _xinstanceof, _xsubclassof # _args_kwds_names

62 from pygeodesy.constants import EPS, EPS0, EPS02, EPS1, EPS2, EPS_2, INT0, PI, PI_2, \

63 _0_0, _0_0001, _0_01, _0_5, _1_0, _1_0_1T, _N_1_0, \

64 _2_0, _N_2_0, _3_0, _4_0, _6_0, _60_0, _90_0, _N_90_0, \

65 _100_0, _copysign_1_0, isnon0 # PYCHOK used!

66 from pygeodesy.datums import a_f2Tuple, _ellipsoidal_datum, _WGS84, _EWGS84

67# from pygeodesy.ellipsoids import a_f2Tuple, _EWGS84 # from .datums

68 from pygeodesy.errors import _IndexError, LenError, _ValueError, _TypesError, \

69 _xattr, _xdatum, _xkwds, _xkwds_get

70 from pygeodesy.fmath import cbrt, fdot, Fpowers, hypot, hypot1, hypot2_, sqrt0

71 from pygeodesy.fsums import Fsum, fsumf_, Fmt, unstr

72 from pygeodesy.interns import NN, _a_, _C_, _datum_, _ellipsoid_, _f_, _height_, \

73 _lat_, _lon_, _M_, _name_, _singular_, _SPACE_, \

74 _x_, _xyz_, _y_, _z_

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

76 from pygeodesy.named import _name__, _name1__, _NamedBase, _NamedTuple, _Pass, _xnamed

77 from pygeodesy.namedTuples import LatLon2Tuple, LatLon3Tuple, \

78 PhiLam2Tuple, Vector3Tuple, Vector4Tuple

79 from pygeodesy.props import deprecated_method, Property_RO, property_ROver, property_doc_

80# from pygeodesy.streprs import Fmt, unstr # from .fsums

81 from pygeodesy.units import _isRadius, Degrees, Height, Int, Lam, Lat, Lon, Meter, \

82 Phi, Scalar, Scalar_

83 from pygeodesy.utily import atan1, atan1d, atan2d, degrees90, degrees180, \

84 sincos2, sincos2_, sincos2d, sincos2d_

85

86 from math import atan2, cos, degrees, fabs, radians, sqrt

87

88__all__ = _ALL_LAZY.ecef

89__version__ = '24.06.12'

90

91_Ecef_ = 'Ecef'

92_prolate_ = 'prolate'

93_TRIPS = 33 # 8..9 sufficient, EcefSudano.reverse

94_xyz_y_z = _xyz_, _y_, _z_ # _args_kwds_names(_xyzn4)[:3]

95

96

97 class EcefError(_ValueError):

98 '''An ECEF or C{Ecef*} related issue.

99 '''

100 pass

101

102

103 class _EcefBase(_NamedBase):

104 '''(INTERNAL) Base class for L{EcefFarrell21}, L{EcefFarrell22}, L{EcefKarney},

105 L{EcefSudano}, L{EcefVeness} and L{EcefYou}.

106 '''

107 _datum = _WGS84

108 _E = _EWGS84

109 _lon00 = INT0 # arbitrary, "polar" lon for LocalCartesian, Ltp

110

111 def __init__(self, a_ellipsoid=_EWGS84, f=None, lon00=INT0, **name):

112 '''New C{Ecef*} converter.

113

114 @arg a_ellipsoid: A (non-prolate) ellipsoid (L{Ellipsoid}, L{Ellipsoid2},

115 L{Datum} or L{a_f2Tuple}) or C{scalar} ellipsoid's

116 equatorial radius (C{meter}).

117 @kwarg f: C{None} or the ellipsoid flattening (C{scalar}), required

118 for C{scalar} B{C{a_ellipsoid}}, C{B{f}=0} represents a

119 sphere, negative B{C{f}} a prolate ellipsoid.

120 @kwarg lon00: An arbitrary, I{"polar"} longitude (C{degrees}), see the

121 C{reverse} method.

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

123

124 @raise EcefError: If B{C{a_ellipsoid}} not L{Ellipsoid}, L{Ellipsoid2},

125 L{Datum} or L{a_f2Tuple} or C{scalar} or B{C{f}} not

126 C{scalar} or if C{scalar} B{C{a_ellipsoid}} not positive

127 or B{C{f}} not less than 1.0.

128 '''

129 try:

130 E = a_ellipsoid

131 if f is None:

132 pass

133 elif _isRadius(E) and isscalar(f):

134 E = a_f2Tuple(E, f)

135 else:

136 raise ValueError() # _invalid_

137

138 if E not in (_EWGS84, _WGS84):

139 d = _ellipsoidal_datum(E, **name)

140 E = d.ellipsoid

141 if E.a < EPS or E.f > EPS1:

142 raise ValueError() # _invalid_

143 self._datum = d

144 self._E = E

145

146 except (TypeError, ValueError) as x:

147 t = unstr(self.classname, a=a_ellipsoid, f=f)

148 raise EcefError(_SPACE_(t, _ellipsoid_), cause=x)

149

150 if name:

151 self.name = name

152 if lon00 is not INT0:

153 self.lon00 = lon00

154

155 def __eq__(self, other):

156 '''Compare this and an other Ecef.

157

158 @arg other: The other ecef (C{Ecef*}).

159

160 @return: C{True} if equal, C{False} otherwise.

161 '''

162 return other is self or (isinstance(other, self.__class__) and

163 other.ellipsoid == self.ellipsoid)

164

165 @Property_RO

166 def datum(self):

167 '''Get the datum (L{Datum}).

168 '''

169 return self._datum

170

171 @Property_RO

172 def ellipsoid(self):

173 '''Get the ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).

174 '''

175 return self._E

176

177 @Property_RO

178 def equatoradius(self):

179 '''Get the C{ellipsoid}'s equatorial radius, semi-axis (C{meter}).

180 '''

181 return self.ellipsoid.a

182

183 a = equatorialRadius = equatoradius # Karney property

184

185 @Property_RO

186 def flattening(self): # Karney property

187 '''Get the C{ellipsoid}'s flattening (C{scalar}), positive for

188 I{oblate}, negative for I{prolate} or C{0} for I{near-spherical}.

189 '''

190 return self.ellipsoid.f

191

192 f = flattening

193

194 def _forward(self, lat, lon, h, name, M=False, _philam=False): # in .ltp.LocalCartesian.forward and -.reset

195 '''(INTERNAL) Common for all C{Ecef*}.

196 '''

197 if _philam: # lat, lon in radians

198 sa, ca, sb, cb = sincos2_(lat, lon)

199 lat = Lat(degrees90( lat), Error=EcefError)

200 lon = Lon(degrees180(lon), Error=EcefError)

201 else:

202 sa, ca, sb, cb = sincos2d_(lat, lon)

203

204 E = self.ellipsoid

205 n = E.roc1_(sa, ca) if self._isYou else E.roc1_(sa)

206 z = (h + n * E.e21) * sa

207 x = (h + n) * ca

208

209 m = self._Matrix(sa, ca, sb, cb) if M else None

210 return Ecef9Tuple(x * cb, x * sb, z, lat, lon, h,

211 0, m, self.datum,

212 name=self._name__(name))

213

214 def forward(self, latlonh, lon=None, height=0, M=False, **name):

215 '''Convert from geodetic C{(lat, lon, height)} to geocentric C{(x, y, z)}.

216

217 @arg latlonh: Either a C{LatLon}, an L{Ecef9Tuple} or C{scalar}

218 latitude (C{degrees}).

219 @kwarg lon: Optional C{scalar} longitude for C{scalar} B{C{latlonh}}

220 (C{degrees}).

221 @kwarg height: Optional height (C{meter}), vertically above (or below)

222 the surface of the ellipsoid.

223 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).

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

225

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

227 geocentric C{(x, y, z)} coordinates for the given geodetic ones

228 C{(lat, lon, height)}, case C{C} 0, optional C{M} (L{EcefMatrix})

229 and C{datum} if available.

230

231 @raise EcefError: If B{C{latlonh}} not C{LatLon}, L{Ecef9Tuple} or

232 C{scalar} or B{C{lon}} not C{scalar} for C{scalar}

233 B{C{latlonh}} or C{abs(lat)} exceeds 90°.

234

235 @note: Use method C{.forward_} to specify C{lat} and C{lon} in C{radians}

236 and avoid double angle conversions.

237 '''

238 llhn = _llhn4(latlonh, lon, height, **name)

239 return self._forward(*llhn, M=M)

240

241 def forward_(self, phi, lam, height=0, M=False, **name):

242 '''Like method C{.forward} except with geodetic lat- and longitude given

243 in I{radians}.

244

245 @arg phi: Latitude in I{radians} (C{scalar}).

246 @arg lam: Longitude in I{radians} (C{scalar}).

247 @kwarg height: Optional height (C{meter}), vertically above (or below)

248 the surface of the ellipsoid.

249 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).

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

251

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

253 with C{lat} set to C{degrees90(B{phi})} and C{lon} to

254 C{degrees180(B{lam})}.

255

256 @raise EcefError: If B{C{phi}} or B{C{lam}} invalid or not C{scalar}.

257 '''

258 try: # like function C{_llhn4} below

259 plhn = Phi(phi), Lam(lam), Height(height), _name__(name)

260 except (TypeError, ValueError) as x:

261 raise EcefError(phi=phi, lam=lam, height=height, cause=x)

262 return self._forward(*plhn, M=M, _philam=True)

263

264 @property_ROver

265 def _Geocentrics(self):

266 '''(INTERNAL) Get the valid geocentric classes. I{once}.

267 '''

268 return (Ecef9Tuple, # overwrite property_ROver

269 _MODS.cartesianBase.CartesianBase)

270

271 @Property_RO

272 def _isYou(self):

273 '''(INTERNAL) Is this an C{EcefYou}?.

274 '''

275 return isinstance(self, EcefYou)

276

277 @property

278 def lon00(self):

279 '''Get the I{"polar"} longitude (C{degrees}), see method C{reverse}.

280 '''

281 return self._lon00

282

283 @lon00.setter # PYCHOK setter!

284 def lon00(self, lon00):

285 '''Set the I{"polar"} longitude (C{degrees}), see method C{reverse}.

286 '''

287 self._lon00 = Degrees(lon00=lon00)

288

289 def _Matrix(self, sa, ca, sb, cb):

290 '''Creation a rotation matrix.

291

292 @arg sa: C{sin(phi)} (C{float}).

293 @arg ca: C{cos(phi)} (C{float}).

294 @arg sb: C{sin(lambda)} (C{float}).

295 @arg cb: C{cos(lambda)} (C{float}).

296

297 @return: An L{EcefMatrix}.

298 '''

299 return self._xnamed(EcefMatrix(sa, ca, sb, cb))

300

301 def _polon(self, y, x, R, **lon00_name):

302 '''(INTERNAL) Handle I{"polar"} longitude.

303 '''

304 return atan2d(y, x) if R else _xkwds_get(lon00_name, lon00=self.lon00)

305

306 def reverse(self, xyz, y=None, z=None, M=False, **lon00_name): # PYCHOK no cover

307 '''I{Must be overloaded}.'''

308 self._notOverloaded(xyz, y=y, z=z, M=M, **lon00_name)

309

310 def toStr(self, prec=9, **unused): # PYCHOK signature

311 '''Return this C{Ecef*} as a string.

312

313 @kwarg prec: Precision, number of decimal digits (0..9).

314

315 @return: This C{Ecef*} (C{str}).

316 '''

317 return self.attrs(_a_, _f_, _datum_, _name_, prec=prec) # _ellipsoid_

318

319

320 class EcefFarrell21(_EcefBase):

321 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)

322 coordinates based on I{Jay A. Farrell}'s U{Table 2.1<https://Books.Google.com/

323 books?id=fW4foWASY6wC>}, page 29.

324 '''

325

326 def reverse(self, xyz, y=None, z=None, M=None, **lon00_name): # PYCHOK unused M

327 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using

328 I{Farrell}'s U{Table 2.1<https://Books.Google.com/books?id=fW4foWASY6wC>},

329 page 29.

330

331 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}

332 coordinate (C{meter}).

333 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).

334 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).

335 @kwarg M: I{Ignored}, rotation matrix C{M} not available.

336 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument

337 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude

338 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.

339

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

341 geodetic coordinates C{(lat, lon, height)} for the given geocentric

342 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}

343 if available.

344

345 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}

346 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or

347 zero division error.

348

349 @see: L{EcefFarrell22} and L{EcefVeness}.

350 '''

351 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)

352

353 E = self.ellipsoid

354 a = E.a

355 a2 = E.a2

356 b2 = E.b2

357 e2 = E.e2

358 e2_ = E.e2abs * E.a2_b2 # (E.e * E.a_b)**2 = 0.0820944... WGS84

359 e4 = E.e4

360

361 try: # names as page 29

362 z2 = z**2

363 ez = z2 * (_1_0 - e2) # E.e2s2(z)

364

365 p = hypot(x, y)

366 p2 = p**2

367 G = p2 + ez - e2 * (a2 - b2) # p2 + ez - e4 * a2

368 F = b2 * z2 * 54

369 t = e4 * p2 * F / G**3

370 t = cbrt(sqrt(t * (t + _2_0)) + t + _1_0)

371 G *= fsumf_(t , _1_0, _1_0 / t)

372 P = F / (G**2 * _3_0)

373 Q = sqrt(_2_0 * e4 * P + _1_0)

374 Q1 = Q + _1_0

375 r0 = P * p * e2 / Q1 - sqrt(fsumf_(a2 * (Q1 / Q) * _0_5,

376 -P * ez / (Q * Q1),

377 -P * p2 * _0_5))

378 r = p + e2 * r0

379 v = b2 / (sqrt(r**2 + ez) * a)

380

381 h = hypot(r, z) * (_1_0 - v)

382 lat = atan1d((e2_ * v + _1_0) * z, p)

383 lon = self._polon(y, x, p, **lon00_name)

384 # note, phi and lam are swapped on page 29

385

386 except (ValueError, ZeroDivisionError) as e:

387 raise EcefError(x=x, y=y, z=z, cause=e)

388

389 return Ecef9Tuple(x, y, z, lat, lon, h,

390 1, None, self.datum,

391 name=self._name__(name))

392

393

394 class EcefFarrell22(_EcefBase):

395 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)

396 coordinates based on I{Jay A. Farrell}'s U{Table 2.2<https://Books.Google.com/

397 books?id=fW4foWASY6wC>}, page 30.

398 '''

399

400 def reverse(self, xyz, y=None, z=None, M=None, **lon00_name): # PYCHOK unused M

401 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using

402 I{Farrell}'s U{Table 2.2<https://Books.Google.com/books?id=fW4foWASY6wC>},

403 page 30.

404

405 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}

406 coordinate (C{meter}).

407 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).

408 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).

409 @kwarg M: I{Ignored}, rotation matrix C{M} not available.

410 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument

411 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude

412 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.

413

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

415 geodetic coordinates C{(lat, lon, height)} for the given geocentric

416 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum}

417 if available.

418

419 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}

420 not C{scalar} for C{scalar} B{C{xyz}} or C{sqrt} domain or

421 zero division error.

422

423 @see: L{EcefFarrell21} and L{EcefVeness}.

424 '''

425 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)

426

427 E = self.ellipsoid

428 a = E.a

429 b = E.b

430

431 try: # see EcefVeness.reverse

432 p = hypot(x, y)

433 lon = self._polon(y, x, p, **lon00_name)

434

435 s, c = sincos2(atan2(z * a, p * b)) # == _norm3

436 lat = atan1d(z + s**3 * b * E.e22,

437 p - c**3 * a * E.e2)

438

439 s, c = sincos2d(lat)

440 if c: # E.roc1_(s) = E.a / sqrt(1 - E.e2 * s**2)

441 h = p / c - (E.roc1_(s) if s else a)

442 else: # polar

443 h = fabs(z) - b

444 # note, phi and lam are swapped on page 30

445

446 except (ValueError, ZeroDivisionError) as e:

447 raise EcefError(x=x, y=y, z=z, cause=e)

448

449 return Ecef9Tuple(x, y, z, lat, lon, h,

450 1, None, self.datum,

451 name=self._name__(name))

452

453

454 class EcefKarney(_EcefBase):

455 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF)

456 coordinates transcoded from I{Karney}'s C++ U{Geocentric<https://GeographicLib.SourceForge.io/

457 C++/doc/classGeographicLib_1_1Geocentric.html>} methods.

458

459 @note: On methods C{.forward} and C{.forwar_}, let C{v} be a unit vector located

460 at C{(lat, lon, h)}. We can express C{v} as column vectors in one of two

461 ways, C{v1} in East, North, Up (ENU) coordinates (where the components are

462 relative to a local coordinate system at C{C(lat0, lon0, h0)}) or as C{v0}

463 in geocentric C{x, y, z} coordinates. Then, M{v0 = M ⋅ v1} where C{M} is

464 the rotation matrix.

465 '''

466

467 @Property_RO

468 def hmax(self):

469 '''Get the distance or height limit (C{meter}, conventionally).

470 '''

471 return self.equatoradius / EPS_2 # self.equatoradius * _2_EPS, 12M lighyears

472

473 def reverse(self, xyz, y=None, z=None, M=False, **lon00_name):

474 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}.

475

476 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}

477 coordinate (C{meter}).

478 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).

479 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).

480 @kwarg M: Optionally, return the rotation L{EcefMatrix} (C{bool}).

481 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument

482 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude

483 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.

484

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

486 geodetic coordinates C{(lat, lon, height)} for the given geocentric

487 ones C{(x, y, z)}, case C{C}, optional C{M} (L{EcefMatrix}) and

488 C{datum} if available.

489

490 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}

491 not C{scalar} for C{scalar} B{C{xyz}}.

492

493 @note: In general, there are multiple solutions and the result which minimizes

494 C{height} is returned, i.e., the C{(lat, lon)} corresponding to the

495 closest point on the ellipsoid. If there are still multiple solutions

496 with different latitudes (applies only if C{z} = 0), then the solution

497 with C{lat} > 0 is returned. If there are still multiple solutions with

498 different longitudes (applies only if C{x} = C{y} = 0), then C{lon00} is

499 returned. The returned C{lon} is in the range [−180°, 180°] and C{height}

500 is not below M{−E.a * (1 − E.e2) / sqrt(1 − E.e2 * sin(lat)**2)}. Like

501 C{forward} above, M{v1 = Transpose(M) ⋅ v0}.

502 '''

503 def _norm3(y, x):

504 h = hypot(y, x) # EPS0, EPS_2

505 return (y / h, x / h, h) if h > 0 else (_0_0, _1_0, h)

506

507 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)

508

509 E = self.ellipsoid

510 f = E.f

511

512 sb, cb, R = _norm3(y, x)

513 h = hypot(R, z) # distance to earth center

514 if h > self.hmax: # PYCHOK no cover

515 # We are really far away (> 12M light years). Treat the earth

516 # as a point and h above as an acceptable approximation to the

517 # height. This avoids overflow, e.g., in the computation of d

518 # below. It's possible that h has overflowed to INF, that's OK.

519 # Treat finite x, y, but R overflows to +INF by scaling by 2.

520 sb, cb, R = _norm3(y * _0_5, x * _0_5)

521 sa, ca, _ = _norm3(z * _0_5, R)

522 C = 1

523

524 elif E.e4: # E.isEllipsoidal

525 # Treat prolate spheroids by swapping R and Z here and by

526 # switching the arguments to phi = atan2(...) at the end.

527 p = (R / E.a)**2

528 q = (z / E.a)**2 * E.e21

529 if f < 0:

530 p, q = q, p

531 r = fsumf_(p, q, -E.e4)

532 e = E.e4 * q

533 if e or r > 0:

534 # Avoid possible division by zero when r = 0 by multiplying

535 # equations for s and t by r^3 and r, respectively.

536 s = d = e * p / _4_0 # s = r^3 * s

537 u = r = r / _6_0

538 r2 = r**2

539 r3 = r2 * r

540 t3 = r3 + s

541 d *= t3 + r3

542 if d < 0:

543 # t is complex, but the way u is defined, the result is real.

544 # There are three possible cube roots. We choose the root

545 # which avoids cancellation. Note, d < 0 implies r < 0.

546 u += cos(atan2(sqrt(-d), -t3) / _3_0) * r * _2_0

547 else:

548 # Pick the sign on the sqrt to maximize abs(t3). This

549 # minimizes loss of precision due to cancellation. The

550 # result is unchanged because of the way the t is used

551 # in definition of u.

552 if d > 0:

553 t3 += copysign0(sqrt(d), t3) # t3 = (r * t)^3

554 # N.B. cbrt always returns the real root, cbrt(-8) = -2.

555 t = cbrt(t3) # t = r * t

556 if t: # t can be zero; but then r2 / t -> 0.

557 u = fsumf_(u, t, r2 / t)

558 v = sqrt(e + u**2) # guaranteed positive

559 # Avoid loss of accuracy when u < 0. Underflow doesn't occur in

560 # E.e4 * q / (v - u) because u ~ e^4 when q is small and u < 0.

561 u = (e / (v - u)) if u < 0 else (u + v) # u+v, guaranteed positive

562 # Need to guard against w going negative due to roundoff in u - q.

563 w = E.e2abs * (u - q) / (_2_0 * v)

564 # Rearrange expression for k to avoid loss of accuracy due to

565 # subtraction. Division by 0 not possible because u > 0, w >= 0.

566 k1 = k2 = (u / (sqrt(u + w**2) + w)) if w > 0 else sqrt(u)

567 if f < 0:

568 k1 -= E.e2

569 else:

570 k2 += E.e2

571 sa, ca, h = _norm3(z / k1, R / k2)

572 h *= k1 - E.e21

573 C = 2

574

575 else: # e = E.e4 * q == 0 and r <= 0

576 # This leads to k = 0 (oblate, equatorial plane) and k + E.e^2 = 0

577 # (prolate, rotation axis) and the generation of 0/0 in the general

578 # formulas for phi and h, using the general formula and division

579 # by 0 in formula for h. Handle this case by taking the limits:

580 # f > 0: z -> 0, k -> E.e2 * sqrt(q) / sqrt(E.e4 - p)

581 # f < 0: r -> 0, k + E.e2 -> -E.e2 * sqrt(q) / sqrt(E.e4 - p)

582 q = E.e4 - p

583 if f < 0:

584 p, q = q, p

585 e = E.a

586 else:

587 e = E.b2_a

588 sa, ca, h = _norm3(sqrt(q * E._1_e21), sqrt(p))

589 if z < 0: # for tiny negative z, not for prolate

590 sa = neg(sa)

591 h *= neg(e / E.e2abs)

592 C = 3

593

594 else: # E.e4 == 0, spherical case

595 # Dealing with underflow in the general case with E.e2 = 0 is

596 # difficult. Origin maps to North pole, same as with ellipsoid.

597 sa, ca, _ = _norm3((z if h else _1_0), R)

598 h -= E.a

599 C = 4

600

601 # lon00 <https://GitHub.com/mrJean1/PyGeodesy/issues/77>

602 lon = self._polon(sb, cb, R, **lon00_name)

603 m = self._Matrix(sa, ca, sb, cb) if M else None

604 return Ecef9Tuple(x, y, z, atan1d(sa, ca), lon, h,

605 C, m, self.datum, name=self._name__(name))

606

607

608 class EcefSudano(_EcefBase):

609 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates

610 based on I{John J. Sudano}'s U{paper<https://www.ResearchGate.net/publication/3709199>}.

611 '''

612 _tol = EPS2

613

614 def reverse(self, xyz, y=None, z=None, M=None, **lon00_name): # PYCHOK unused M

615 '''Convert from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)} using

616 I{Sudano}'s U{iterative method<https://www.ResearchGate.net/publication/3709199>}.

617

618 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}

619 coordinate (C{meter}).

620 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).

621 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).

622 @kwarg M: I{Ignored}, rotation matrix C{M} not available.

623 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument

624 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude

625 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.

626

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

628 coordinates C{(lat, lon, height)} for the given geocentric ones C{(x, y, z)},

629 iteration C{C}, C{M=None} always and C{datum} if available.

630

631 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}

632 not C{scalar} for C{scalar} B{C{xyz}} or no convergence.

633 '''

634 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)

635

636 E = self.ellipsoid

637 e = E.e2 * E.a

638 R = hypot(x, y) # Rh

639 d = e - R

640

641 _a = fabs

642 lat = atan1d(z, R * E.e21)

643 sa, ca = sincos2d(_a(lat))

644 # Sudano's Eq (A-6) and (A-7) refactored/reduced,

645 # replacing Rn from Eq (A-4) with n = E.a / ca:

646 # N = ca**2 * ((z + E.e2 * n * sa) * ca - R * sa)

647 # = ca**2 * (z * ca + E.e2 * E.a * sa - R * sa)

648 # = ca**2 * (z * ca + (E.e2 * E.a - R) * sa)

649 # D = ca**3 * (E.e2 * n / E.e2s2(sa)) - R

650 # = ca**2 * (E.e2 * E.a / E.e2s2(sa) - R / ca**2)

651 # N / D = (z * ca + (E.e2 * E.a - R) * sa) /

652 # (E.e2 * E.a / E.e2s2(sa) - R / ca**2)

653 _E = EPS_2

654 tol = self.tolerance

655 _S2 = Fsum(sa).fsum2f_

656 _rt = sqrt

657 for i in range(1, _TRIPS):

658 ca2 = _1_0 - sa**2

659 if ca2 < _E: # PYCHOK no cover

660 ca = _0_0

661 break

662 ca = _rt(ca2)

663 r = e / E.e2s2(sa) - R / ca2

664 if _a(r) < _E:

665 break

666 lat = None

667 sa, r = _S2(-z * ca / r, -d * sa / r)

668 if _a(r) < tol:

669 break

670 else:

671 t = unstr(self.reverse, x=x, y=y, z=z)

672 raise EcefError(t, txt=Fmt.no_convergence(r, tol))

673

674 if lat is None:

675 lat = copysign0(atan1d(_a(sa), ca), z)

676 lon = self._polon(y, x, R, **lon00_name)

677

678 h = fsumf_(R * ca, _a(z * sa), -E.a * E.e2s(sa)) # use Veness'

679 # because Sudano's Eq (7) doesn't produce the correct height

680 # h = (fabs(z) + R - E.a * cos(a + E.e21) * sa / ca) / (ca + sa)

681 return Ecef9Tuple(x, y, z, lat, lon, h,

682 i, None, self.datum, # C=i, M=None

683 iteration=i, name=self._name__(name))

684

685 @property_doc_(''' the convergence tolerance (C{float}).''')

686 def tolerance(self):

687 '''Get the convergence tolerance (C{scalar}).

688 '''

689 return self._tol

690

691 @tolerance.setter # PYCHOK setter!

692 def tolerance(self, tol):

693 '''Set the convergence tolerance (C{scalar}).

694

695 @raise EcefError: Non-scalar or invalid B{C{tol}}.

696 '''

697 self._tol = Scalar_(tolerance=tol, low=EPS, Error=EcefError)

698

699

700 class EcefVeness(_EcefBase):

701 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates

702 transcoded from I{Chris Veness}' JavaScript classes U{LatLonEllipsoidal, Cartesian<https://

703 www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.

704

705 @see: U{I{A Guide to Coordinate Systems in Great Britain}<https://www.OrdnanceSurvey.co.UK/

706 documents/resources/guide-coordinate-systems-great-britain.pdf>}, section I{B) Converting

707 between 3D Cartesian and ellipsoidal latitude, longitude and height coordinates}.

708 '''

709

710 def reverse(self, xyz, y=None, z=None, M=None, **lon00_name): # PYCHOK unused M

711 '''Conversion from geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}

712 transcoded from I{Chris Veness}' U{JavaScript<https://www.Movable-Type.co.UK/

713 scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.

714

715 Uses B. R. Bowring’s formulation for μm precision in concise form U{I{The accuracy

716 of geodetic latitude and height equations}<https://www.ResearchGate.net/publication/

717 233668213>}, Survey Review, Vol 28, 218, Oct 1985.

718

719 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}

720 coordinate (C{meter}).

721 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).

722 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).

723 @kwarg M: I{Ignored}, rotation matrix C{M} not available.

724 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument

725 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude

726 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.

727

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

729 geodetic coordinates C{(lat, lon, height)} for the given geocentric

730 ones C{(x, y, z)}, case C{C}, C{M=None} always and C{datum} if available.

731

732 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}

733 not C{scalar} for C{scalar} B{C{xyz}}.

734

735 @see: Toms, Ralph M. U{I{An Efficient Algorithm for Geocentric to Geodetic

736 Coordinate Conversion}<https://www.OSTI.gov/scitech/biblio/110235>},

737 Sept 1995 and U{I{An Improved Algorithm for Geocentric to Geodetic

738 Coordinate Conversion}<https://www.OSTI.gov/scitech/servlets/purl/231228>},

739 Apr 1996, both from Lawrence Livermore National Laboratory (LLNL) and

740 Sudano, John J, U{I{An exact conversion from an Earth-centered coordinate

741 system to latitude longitude and altitude}<https://www.ResearchGate.net/

742 publication/3709199>}.

743 '''

744 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)

745

746 E = self.ellipsoid

747 a = E.a

748

749 p = hypot(x, y) # distance from minor axis

750 r = hypot(p, z) # polar radius

751 if min(p, r) > EPS0:

752 b = E.b * E.e22

753 # parametric latitude (Bowring eqn 17, replaced)

754 t = (E.b * z) / (a * p) * (_1_0 + b / r)

755 c = _1_0 / hypot1(t)

756 s = c * t

757 # geodetic latitude (Bowring eqn 18)

758 lat = atan1d(z + s**3 * b,

759 p - c**3 * a * E.e2)

760

761 # height above ellipsoid (Bowring eqn 7)

762 sa, ca = sincos2d(lat)

763# r = a / E.e2s(sa) # length of normal terminated by minor axis

764# h = p * ca + z * sa - (a * a / r)

765 h = fsumf_(p * ca, z * sa, -a * E.e2s(sa))

766 C = 1

767

768 # see <https://GIS.StackExchange.com/questions/28446>

769 elif p > EPS: # lat arbitrarily zero, equatorial lon

770 C, lat, h = 2, _0_0, (p - a)

771

772 else: # polar lat, lon arbitrarily lon00

773 C, lat, h = 3, (_N_90_0 if z < 0 else _90_0), (fabs(z) - E.b)

774

775 lon = self._polon(y, x, p, **lon00_name)

776 return Ecef9Tuple(x, y, z, lat, lon, h,

777 C, None, self.datum, # M=None

778 name=self._name__(name))

779

780

781 class EcefYou(_EcefBase):

782 '''Conversion between geodetic and geocentric, I{Earth-Centered, Earth-Fixed} (ECEF) coordinates

783 using I{Rey-Jer You}'s U{transformation<https://www.ResearchGate.net/publication/240359424>}

784 for I{non-prolate} ellipsoids.

785

786 @see: Featherstone, W.E., Claessens, S.J. U{I{Closed-form transformation between geodetic and

787 ellipsoidal coordinates}<https://Espace.Curtin.edu.AU/bitstream/handle/20.500.11937/

788 11589/115114_9021_geod2ellip_final.pdf>} Studia Geophysica et Geodaetica, 2008, 52,

789 pages 1-18 and U{PyMap3D <https://PyPI.org/project/pymap3d>}.

790 '''

791

792 def __init__(self, a_ellipsoid=_EWGS84, f=None, **lon00_name): # PYCHOK signature

793 _EcefBase.__init__(self, a_ellipsoid, f=f, **lon00_name) # inherited documentation

794 self._ee2 = EcefYou._ee2(self.ellipsoid)

795

796 @staticmethod

797 def _ee2(E):

798 e2 = E.a2 - E.b2

799 if e2 < 0 or E.f < 0:

800 raise EcefError(ellipsoid=E, txt=_prolate_)

801 return sqrt0(e2), e2

802

803 def reverse(self, xyz, y=None, z=None, M=None, **lon00_name): # PYCHOK unused M

804 '''Convert geocentric C{(x, y, z)} to geodetic C{(lat, lon, height)}

805 using I{Rey-Jer You}'s transformation.

806

807 @arg xyz: A geocentric (C{Cartesian}, L{Ecef9Tuple}) or C{scalar} ECEF C{x}

808 coordinate (C{meter}).

809 @kwarg y: ECEF C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).

810 @kwarg z: ECEF C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).

811 @kwarg M: I{Ignored}, rotation matrix C{M} not available.

812 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and optional keyword argument

813 C{B{lon00}=INT0} (C{degrees}), an arbitrary I{"polar"} longitude

814 returned if C{B{x}=0} and C{B{y}=0}, see property C{lon00}.

815

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

817 geodetic coordinates C{(lat, lon, height)} for the given geocentric

818 ones C{(x, y, z)}, case C{C=1}, C{M=None} always and C{datum} if

819 available.

820

821 @raise EcefError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or

822 B{C{z}} not C{scalar} for C{scalar} B{C{xyz}} or the

823 ellipsoid is I{prolate}.

824 '''

825 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, **lon00_name)

826

827 E = self.ellipsoid

828 e, e2 = self._ee2

829

830 q = hypot(x, y) # R

831 u = Fpowers(2, x, y, z) - e2

832 u = u.fadd_(hypot(u, e * z * _2_0)).fover(_2_0)

833 if u > EPS02:

834 u = sqrt(u)

835 p = hypot(u, e)

836 B = atan1(p * z, u * q) # beta0 = atan(p / u * z / q)

837 sB, cB = sincos2(B)

838 if cB and sB:

839 p *= E.a

840 d = (p / cB - e2 * cB) / sB

841 if isnon0(d):

842 B += fsumf_(u * E.b, -p, e2) / d

843 sB, cB = sincos2(B)

844 elif u < (-EPS2):

845 raise EcefError(x=x, y=y, z=z, u=u, txt=_singular_)

846 else:

847 sB, cB = _copysign_1_0(z), _0_0

848

849 lat = atan1d(E.a * sB, E.b * cB) # atan(E.a_b * tan(B))

850 lon = self._polon(y, x, q, **lon00_name)

851

852 h = hypot(z - E.b * sB, q - E.a * cB)

853 if hypot2_(x, y, z * E.a_b) < E.a2:

854 h = neg(h) # inside ellipsoid

855 return Ecef9Tuple(x, y, z, lat, lon, h,

856 1, None, self.datum, # C=1, M=None

857 name=self._name__(name))

858

859

860 class EcefMatrix(_NamedTuple):

861 '''A rotation matrix known as I{East-North-Up (ENU) to ECEF}.

862

863 @see: U{From ENU to ECEF<https://WikiPedia.org/wiki/

864 Geographic_coordinate_conversion#From_ECEF_to_ENU>} and

865 U{Issue #74<https://Github.com/mrJean1/PyGeodesy/issues/74>}.

866 '''

867 _Names_ = ('_0_0_', '_0_1_', '_0_2_', # row-order

868 '_1_0_', '_1_1_', '_1_2_',

869 '_2_0_', '_2_1_', '_2_2_')

870 _Units_ = (Scalar,) * len(_Names_)

871

872 def _validate(self, **unused): # PYCHOK unused

873 '''(INTERNAL) Allow C{_Names_} with leading underscore.

874 '''

875 _NamedTuple._validate(self, underOK=True)

876

877 def __new__(cls, sa, ca, sb, cb, *_more):

878 '''New L{EcefMatrix} matrix.

879

880 @arg sa: C{sin(phi)} (C{float}).

881 @arg ca: C{cos(phi)} (C{float}).

882 @arg sb: C{sin(lambda)} (C{float}).

883 @arg cb: C{cos(lambda)} (C{float}).

884 @arg _more: (INTERNAL) from C{.multiply}.

885

886 @raise EcefError: If B{C{sa}}, B{C{ca}}, B{C{sb}} or

887 B{C{cb}} outside M{[-1.0, +1.0]}.

888 '''

889 t = sa, ca, sb, cb

890 if _more: # all 9 matrix elements ...

891 t += _more # ... from .multiply

892

893 elif max(map(fabs, t)) > _1_0:

894 raise EcefError(unstr(EcefMatrix, *t))

895

896 else: # build matrix from the following quaternion operations

897 # qrot(lam, [0,0,1]) * qrot(phi, [0,-1,0]) * [1,1,1,1]/2

898 # or

899 # qrot(pi/2 + lam, [0,0,1]) * qrot(-pi/2 + phi, [-1,0,0])

900 # where

901 # qrot(t,v) = [cos(t/2), sin(t/2)*v[1], sin(t/2)*v[2], sin(t/2)*v[3]]

902

903 # Local X axis (East) in geocentric coords

904 # M[0] = -slam; M[3] = clam; M[6] = 0;

905 # Local Y axis (North) in geocentric coords

906 # M[1] = -clam * sphi; M[4] = -slam * sphi; M[7] = cphi;

907 # Local Z axis (Up) in geocentric coords

908 # M[2] = clam * cphi; M[5] = slam * cphi; M[8] = sphi;

909 t = (-sb, -cb * sa, cb * ca,

910 cb, -sb * sa, sb * ca,

911 _0_0, ca, sa)

912

913 return _NamedTuple.__new__(cls, *t)

914

915 def column(self, column):

916 '''Get this matrix' B{C{column}} 0, 1 or 2 as C{3-tuple}.

917 '''

918 if 0 <= column < 3:

919 return self[column::3]

920 raise _IndexError(column=column)

921

922 def copy(self, **unused): # PYCHOK signature

923 '''Make a shallow or deep copy of this instance.

924

925 @return: The copy (C{This class} or subclass thereof).

926 '''

927 return self.classof(*self)

928

929 __copy__ = __deepcopy__ = copy

930

931 @Property_RO

932 def matrix3(self):

933 '''Get this matrix' rows (C{3-tuple} of 3 C{3-tuple}s).

934 '''

935 return tuple(map(self.row, range(3)))

936

937 @Property_RO

938 def matrixTransposed3(self):

939 '''Get this matrix' I{Transposed} rows (C{3-tuple} of 3 C{3-tuple}s).

940 '''

941 return tuple(map(self.column, range(3)))

942

943 def multiply(self, other):

944 '''Matrix multiply M{M0' ⋅ M} this matrix I{Transposed}

945 with an other matrix.

946

947 @arg other: The other matrix (L{EcefMatrix}).

948

949 @return: The matrix product (L{EcefMatrix}).

950

951 @raise TypeError: If B{C{other}} is not an L{EcefMatrix}.

952 '''

953 _xinstanceof(EcefMatrix, other=other)

954 # like LocalCartesian.MatrixMultiply, C{self.matrixTransposed3 X other.matrix3}

955 # <https://GeographicLib.SourceForge.io/C++/doc/LocalCartesian_8cpp_source.html>

956 # X = (fdot(self.column(r), *other.column(c)) for r in (0,1,2) for c in (0,1,2))

957 X = (fdot(self[r::3], *other[c::3]) for r in range(3) for c in range(3))

958 return _xnamed(EcefMatrix(*X), EcefMatrix.multiply.__name__)

959

960 def rotate(self, xyz, *xyz0):

961 '''Forward rotation M{M0' ⋅ ([x, y, z] - [x0, y0, z0])'}.

962

963 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).

964 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).

965

966 @return: Rotated C{(x, y, z)} location (C{3-tuple}).

967

968 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.

969 '''

970 if xyz0:

971 if len(xyz0) != len(xyz):

972 raise LenError(self.rotate, xyz0=len(xyz0), xyz=len(xyz))

973 xyz = tuple(c - c0 for c, c0 in zip(xyz, xyz0))

974

975 # x' = M[0] * x + M[3] * y + M[6] * z

976 # y' = M[1] * x + M[4] * y + M[7] * z

977 # z' = M[2] * x + M[5] * y + M[8] * z

978 return (fdot(xyz, *self[0::3]), # .column(0)

979 fdot(xyz, *self[1::3]), # .column(1)

980 fdot(xyz, *self[2::3])) # .column(2)

981

982 def row(self, row):

983 '''Get this matrix' B{C{row}} 0, 1 or 2 as C{3-tuple}.

984 '''

985 if 0 <= row < 3:

986 r = row * 3

987 return self[r:r+3]

988 raise _IndexError(row=row)

989

990 def unrotate(self, xyz, *xyz0):

991 '''Inverse rotation M{[x0, y0, z0] + M0 ⋅ [x,y,z]'}.

992

993 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).

994 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).

995

996 @return: Unrotated C{(x, y, z)} location (C{3-tuple}).

997

998 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.

999 '''

1000 if xyz0:

1001 if len(xyz0) != len(xyz):

1002 raise LenError(self.unrotate, xyz0=len(xyz0), xyz=len(xyz))

1003 _xyz = _1_0_1T + xyz

1004 # x' = x0 + M[0] * x + M[1] * y + M[2] * z

1005 # y' = y0 + M[3] * x + M[4] * y + M[5] * z

1006 # z' = z0 + M[6] * x + M[7] * y + M[8] * z

1007 xyz_ = (fdot(_xyz, xyz0[0], *self[0:3]), # .row(0)

1008 fdot(_xyz, xyz0[1], *self[3:6]), # .row(1)

1009 fdot(_xyz, xyz0[2], *self[6:9])) # .row(2)

1010 else:

1011 # x' = M[0] * x + M[1] * y + M[2] * z

1012 # y' = M[3] * x + M[4] * y + M[5] * z

1013 # z' = M[6] * x + M[7] * y + M[8] * z

1014 xyz_ = (fdot(xyz, *self[0:3]), # .row(0)

1015 fdot(xyz, *self[3:6]), # .row(1)

1016 fdot(xyz, *self[6:9])) # .row(2)

1017 return xyz_

1018

1019

1020 class Ecef9Tuple(_NamedTuple):

1021 '''9-Tuple C{(x, y, z, lat, lon, height, C, M, datum)} with I{geocentric}

1022 C{x}, C{y} and C{z} plus I{geodetic} C{lat}, C{lon} and C{height}, case

1023 C{C} (see the C{Ecef*.reverse} methods) and optionally, the rotation

1024 matrix C{M} (L{EcefMatrix}) and C{datum}, with C{lat} and C{lon} in

1025 C{degrees} and C{x}, C{y}, C{z} and C{height} in C{meter}, conventionally.

1026 '''

1027 _Names_ = (_x_, _y_, _z_, _lat_, _lon_, _height_, _C_, _M_, _datum_)

1028 _Units_ = ( Meter, Meter, Meter, Lat, Lon, Height, Int, _Pass, _Pass)

1029

1030 @property_ROver

1031 def _CartesianBase(self):

1032 '''(INTERNAL) Get class C{CartesianBase}, I{once}.

1033 '''

1034 return _MODS.cartesianBase.CartesianBase # overwrite property_ROver

1035

1036 @deprecated_method

1037 def convertDatum(self, datum2): # for backward compatibility

1038 '''DEPRECATED, use method L{toDatum}.'''

1039 return self.toDatum(datum2)

1040

1041 @Property_RO

1042 def lam(self):

1043 '''Get the longitude in C{radians} (C{float}).

1044 '''

1045 return self.philam.lam

1046

1047 @Property_RO

1048 def lamVermeille(self):

1049 '''Get the longitude in C{radians} M{[-PI*3/2..+PI*3/2]} after U{Vermeille

1050 <https://Search.ProQuest.com/docview/639493848>} (2004), page 95.

1051

1052 @see: U{Karney<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>},

1053 U{Vermeille<https://Search.ProQuest.com/docview/847292978>} 2011, pp 112-113, 116

1054 and U{Featherstone, et.al.<https://Search.ProQuest.com/docview/872827242>}, page 7.

1055 '''

1056 x, y = self.x, self.y

1057 if y > EPS0:

1058 r = atan2(x, hypot(y, x) + y) * _N_2_0 + PI_2

1059 elif y < -EPS0:

1060 r = atan2(x, hypot(y, x) - y) * _2_0 - PI_2

1061 else: # y == 0

1062 r = PI if x < 0 else _0_0

1063 return Lam(Vermeille=r)

1064

1065 @Property_RO

1066 def latlon(self):

1067 '''Get the lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).

1068 '''

1069 return LatLon2Tuple(self.lat, self.lon, name=self.name)

1070

1071 @Property_RO

1072 def latlonheight(self):

1073 '''Get the lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).

1074 '''

1075 return self.latlon.to3Tuple(self.height)

1076

1077 @Property_RO

1078 def latlonheightdatum(self):

1079 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).

1080 '''

1081 return self.latlonheight.to4Tuple(self.datum)

1082

1083 @Property_RO

1084 def latlonVermeille(self):

1085 '''Get the latitude and I{Vermeille} longitude in C{degrees [-225..+225]} (L{LatLon2Tuple}C{(lat, lon)}).

1086

1087 @see: Property C{lonVermeille}.

1088 '''

1089 return LatLon2Tuple(self.lat, self.lonVermeille, name=self.name)

1090

1091 @Property_RO

1092 def lonVermeille(self):

1093 '''Get the longitude in C{degrees [-225..+225]} after U{Vermeille

1094 <https://Search.ProQuest.com/docview/639493848>} (2004), p 95.

1095

1096 @see: Property C{lamVermeille}.

1097 '''

1098 return Lon(Vermeille=degrees(self.lamVermeille))

1099

1100 @Property_RO

1101 def phi(self):

1102 '''Get the latitude in C{radians} (C{float}).

1103 '''

1104 return self.philam.phi

1105

1106 @Property_RO

1107 def philam(self):

1108 '''Get the lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).

1109 '''

1110 return PhiLam2Tuple(radians(self.lat), radians(self.lon), name=self.name)

1111

1112 @Property_RO

1113 def philamheight(self):

1114 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).

1115 '''

1116 return self.philam.to3Tuple(self.height)

1117

1118 @Property_RO

1119 def philamheightdatum(self):

1120 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).

1121 '''

1122 return self.philamheight.to4Tuple(self.datum)

1123

1124 @Property_RO

1125 def philamVermeille(self):

1126 '''Get the latitude and I{Vermeille} longitude in C{radians [-PI*3/2..+PI*3/2]} (L{PhiLam2Tuple}C{(phi, lam)}).

1127

1128 @see: Property C{lamVermeille}.

1129 '''

1130 return PhiLam2Tuple(radians(self.lat), self.lamVermeille, name=self.name)

1131

1132 def toCartesian(self, Cartesian=None, **Cartesian_kwds):

1133 '''Return the geocentric C{(x, y, z)} coordinates as an ellipsoidal or spherical

1134 C{Cartesian}.

1135

1136 @kwarg Cartesian: Optional class to return C{(x, y, z)} (L{ellipsoidalKarney.Cartesian},

1137 L{ellipsoidalNvector.Cartesian}, L{ellipsoidalVincenty.Cartesian},

1138 L{sphericalNvector.Cartesian} or L{sphericalTrigonometry.Cartesian})

1139 or C{None}.

1140 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored

1141 if C{B{Cartesian} is None}.

1142

1143 @return: A C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} instance or

1144 a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Cartesian} is None}.

1145

1146 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.

1147 '''

1148 if Cartesian in (None, Vector4Tuple):

1149 r = self.xyzh

1150 elif Cartesian is Vector3Tuple:

1151 r = self.xyz

1152 else:

1153 _xsubclassof(self._CartesianBase, Cartesian=Cartesian)

1154 r = Cartesian(self, **_name1__(Cartesian_kwds, _or_nameof=self))

1155 return r

1156

1157 def toDatum(self, datum2, **name):

1158 '''Convert this C{Ecef9Tuple} to an other datum.

1159

1160 @arg datum2: Datum to convert I{to} (L{Datum}).

1161 @kwarg name: Optional C{B{name}=NN} (C{str}).

1162

1163 @return: The converted 9-Tuple (C{Ecef9Tuple}).

1164

1165 @raise TypeError: The B{C{datum2}} is not a L{Datum}.

1166 '''

1167 n = _name__(name, _or_nameof=self)

1168 if self.datum in (None, datum2): # PYCHOK _Names_

1169 r = self.copy(name=n)

1170 else:

1171 c = self._CartesianBase(self, datum=self.datum, name=n) # PYCHOK _Names_

1172 # c.toLatLon converts datum, x, y, z, lat, lon, etc.

1173 # and returns another Ecef9Tuple iff LatLon is None

1174 r = c.toLatLon(datum=datum2, LatLon=None)

1175 return r

1176

1177 def toLatLon(self, LatLon=None, **LatLon_kwds):

1178 '''Return the geodetic C{(lat, lon, height[, datum])} coordinates.

1179

1180 @kwarg LatLon: Optional class to return C{(lat, lon, height[, datum])}

1181 or C{None}.

1182 @kwarg LatLon_kwds: Optional B{C{height}}, B{C{datum}} and other

1183 B{C{LatLon}} keyword arguments.

1184

1185 @return: An instance of C{B{LatLon}(lat, lon, **B{LatLon_kwds})}

1186 or if C{B{LatLon} is None}, a L{LatLon3Tuple}C{(lat, lon,

1187 height)} respectively L{LatLon4Tuple}C{(lat, lon, height,

1188 datum)} depending on whether C{datum} is un-/specified.

1189

1190 @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}.

1191 '''

1192 lat, lon, D = self.lat, self.lon, self.datum # PYCHOK Ecef9Tuple

1193 kwds = _name1__(LatLon_kwds, _or_nameof=self)

1194 kwds = _xkwds(kwds, height=self.height, datum=D) # PYCHOK Ecef9Tuple

1195 d = kwds.get(_datum_, LatLon)

1196 if LatLon is None:

1197 r = LatLon3Tuple(lat, lon, kwds[_height_], name=kwds[_name_])

1198 if d is not None:

1199 # assert d is not LatLon

1200 r = r.to4Tuple(d) # checks type(d)

1201 else:

1202 if d is None:

1203 _ = kwds.pop(_datum_) # remove None datum

1204 r = LatLon(lat, lon, **kwds)

1205 _xdatum(_xattr(r, datum=D), D)

1206 return r

1207

1208 def toLocal(self, ltp, Xyz=None, **Xyz_kwds):

1209 '''Convert this geocentric to I{local} C{x}, C{y} and C{z}.

1210

1211 @kwarg ltp: The I{local tangent plane} (LTP) to use (L{Ltp}).

1212 @kwarg Xyz: Optional class to return C{x}, C{y} and C{z}

1213 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.

1214 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword

1215 arguments, ignored if C{B{Xyz} is None}.

1216

1217 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},

1218 a L{Local9Tuple}C{(x, y, z, lat, lon, height,

1219 ltp, ecef, M)} with C{M=None}, always.

1220

1221 @raise TypeError: Invalid B{C{ltp}}.

1222 '''

1223 return _MODS.ltp._xLtp(ltp)._ecef2local(self, Xyz, Xyz_kwds)

1224

1225 def toVector(self, Vector=None, **Vector_kwds):

1226 '''Return the geocentric C{(x, y, z)} coordinates as vector.

1227

1228 @kwarg Vector: Optional vector class to return C{(x, y, z)} or

1229 C{None}.

1230 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword

1231 arguments, ignored if C{B{Vector} is None}.

1232

1233 @return: A C{Vector}C{(x, y, z, **Vector_kwds)} instance or a

1234 L{Vector3Tuple}C{(x, y, z)} if C{B{Vector} is None}.

1235

1236 @see: Propertes C{xyz} and C{xyzh}

1237 '''

1238 return self.xyz if Vector is None else Vector(

1239 *self.xyz, **_name1__(Vector_kwds, _or_nameof=self)) # PYCHOK Ecef9Tuple

1240

1241# def _T_x_M(self, T):

1242# '''(INTERNAL) Update M{self.M = T.multiply(self.M)}.

1243# '''

1244# return self.dup(M=T.multiply(self.M))

1245

1246 @Property_RO

1247 def xyz(self):

1248 '''Get the geocentric C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}).

1249 '''

1250 return Vector3Tuple(self.x, self.y, self.z, name=self.name)

1251

1252 @Property_RO

1253 def xyzh(self):

1254 '''Get the geocentric C{(x, y, z)} coordinates and C{height} (L{Vector4Tuple}C{(x, y, z, h)})

1255 '''

1256 return self.xyz.to4Tuple(self.height)

1257

1258

1259 def _4Ecef(this, Ecef): # in .datums.Datum.ecef, .ellipsoids.Ellipsoid.ecef

1260 '''Return an ECEF converter for C{this} L{Datum} or L{Ellipsoid}.

1261 '''

1262 if Ecef is None:

1263 Ecef = EcefKarney

1264 else:

1265 _xinstanceof(*_Ecefs, Ecef=Ecef)

1266 return Ecef(this, name=this.name)

1267

1268

1269 def _llhn4(latlonh, lon, height, suffix=NN, Error=EcefError, **name): # in .ltp

1270 '''(INTERNAL) Get a C{(lat, lon, h, name)} 4-tuple.

1271 '''

1272 try:

1273 lat, lon = latlonh.lat, latlonh.lon

1274 h = _xattr(latlonh, height=_xattr(latlonh, h=height))

1275 n = _name__(name, _or_nameof=latlonh) # == latlonh._name__(name)

1276 except AttributeError:

1277 lat, h, n = latlonh, height, _name__(**name)

1278 try:

1279 return Lat(lat), Lon(lon), Height(h), n

1280 except (TypeError, ValueError) as x:

1281 t = _lat_, _lon_, _height_

1282 if suffix:

1283 t = (_ + suffix for _ in t)

1284 d = dict(zip(t, (lat, lon, h)))

1285 raise Error(cause=x, **d)

1286

1287

1288 def _xEcef(Ecef): # PYCHOK .latlonBase

1289 '''(INTERNAL) Validate B{C{Ecef}} I{class}.

1290 '''

1291 if issubclassof(Ecef, _EcefBase):

1292 return Ecef

1293 raise _TypesError(_Ecef_, Ecef, *_Ecefs)

1294

1295

1296# kwd lon00 unused but will throw a TypeError if misspelled, etc.

1297 def _xyzn4(xyz, y, z, Types, Error=EcefError, lon00=0, # PYCHOK unused

1298 _xyz_y_z_names=_xyz_y_z, **name): # in .ltp

1299 '''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple.

1300 '''

1301 try:

1302 n = _name__(name, _or_nameof=xyz) # == xyz._name__(name)

1303 try:

1304 t = xyz.x, xyz.y, xyz.z, n

1305 if not isinstance(xyz, Types):

1306 raise _TypesError(_xyz_y_z_names[0], xyz, *Types)

1307 except AttributeError:

1308 t = map1(float, xyz, y, z) + (n,)

1309 except (TypeError, ValueError) as x:

1310 d = dict(zip(_xyz_y_z_names, (xyz, y, z)))

1311 raise Error(cause=x, **d)

1312 return t

1313# assert _xyz_y_z == _args_kwds_names(_xyzn4)[:3]

1314

1315

1316_Ecefs = (EcefKarney, EcefSudano, EcefVeness, EcefYou,

1317 EcefFarrell21, EcefFarrell22)

1318__all__ += _ALL_DOCS(_EcefBase)

1319

1320# **) MIT License

1321#

1322# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

1323#

1324# Permission is hereby granted, free of charge, to any person obtaining a

1325# copy of this software and associated documentation files (the "Software"),

1326# to deal in the Software without restriction, including without limitation

1327# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1328# and/or sell copies of the Software, and to permit persons to whom the

1329# Software is furnished to do so, subject to the following conditions:

1330#

1331# The above copyright notice and this permission notice shall be included

1332# in all copies or substantial portions of the Software.

1333#

1334# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1335# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1336# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1337# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1338# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1339# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1340# OTHER DEALINGS IN THE SOFTWARE.