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

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

52 providing conversion to and from I{local} cartesian cordinates in a I{local tangent plane} as

53 opposed to I{geocentric} (ECEF) ones.

54'''

55

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

57 _xinstanceof, _xsubclassof

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

59 _0_0, _0_0001, _0_01, _0_5, _1_0, _1_0_1T, _2_0, _3_0, _4_0, \

60 _6_0, _60_0, _90_0, _100_0, isnon0, \

61 _N_2_0 # PYCHOK used!

62 from pygeodesy.datums import a_f2Tuple, _ellipsoidal_datum

63# from pygeodesy.ellipsoids import a_f2Tuple # from .datums

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

65 _xdatum, _xkwds

66 from pygeodesy.fmath import cbrt, fdot, hypot, hypot1, hypot2_

67 from pygeodesy.fsums import Fsum, fsum_

68 from pygeodesy.interns import NN, _a_, _C_, _datum_, _ellipsoid_, _f_, _h_, \

69 _height_, _lat_, _lon_, _M_, _name_, _singular_, \

70 _SPACE_, _x_, _xyz_, _y_, _z_

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

72 from pygeodesy.named import _NamedBase, _NamedTuple, notOverloaded, _Pass, _xnamed

73 from pygeodesy.namedTuples import LatLon2Tuple, LatLon3Tuple, \

74 PhiLam2Tuple, Vector3Tuple, Vector4Tuple

75 from pygeodesy.props import deprecated_method, Property_RO, property_RO, property_doc_

76 from pygeodesy.streprs import Fmt, unstr

77 from pygeodesy.units import Height, Int, Lam, Lat, Lon, Meter, Phi, Scalar, Scalar_

78 from pygeodesy.utily import atan2d, degrees90, degrees180, sincos2, sincos2_, \

79 sincos2d_

80

81 from math import asin, atan2, cos, degrees, fabs, radians, sqrt

82

83__all__ = _ALL_LAZY.ecef

84__version__ = '23.03.19'

85

86_Ecef_ = 'Ecef'

87_prolate_ = 'prolate'

88_TRIPS = 17 # 8..9 sufficient, EcefSudano.reverse

89_xyz_y_z = _xyz_, _y_, _z_ # _xargs_names(_xyzn4)[:3]

90

91

92 class EcefError(_ValueError):

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

94 '''

95 pass

96

97

98 def _llhn4(latlonh, lon, height, suffix=NN, Error=EcefError, name=NN): # in .ltp.LocalCartesian.forward and -.reset

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

100 '''

101 try:

102 lat, lon = latlonh.lat, latlonh.lon

103 h = getattr(latlonh, _height_,

104 getattr(latlonh, _h_, height))

105 n = getattr(latlonh, _name_, NN)

106 except AttributeError:

107 lat, h, n = latlonh, height, NN

108

109 try:

110 llhn = Lat(lat), Lon(lon), Height(h), (name or n)

111 except (TypeError, ValueError) as x:

112 t = _lat_, _lon_, _height_

113 if suffix:

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

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

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

117 return llhn

118

119

120 def _xyzn4(xyz, y, z, Types, Error=EcefError, name=NN, # in .ltp

121 _xyz_y_z_names=_xyz_y_z):

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

123 '''

124 try:

125 try:

126 t = xyz.x, xyz.y, xyz.z, getattr(xyz, _name_, name)

127 if not isinstance(xyz, Types):

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

129 except AttributeError:

130 t = map1(float, xyz, y, z) + (name,)

131

132 except (TypeError, ValueError) as x:

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

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

135 return t

136

137# assert _xyz_y_z == _xargs_names(_xyzn4)[:3]

138

139

140 class _EcefBase(_NamedBase):

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

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

143 '''

144 _datum = None

145 _E = None

146

147 def __init__(self, a_ellipsoid, f=None, name=NN):

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

149

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

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

152 equatorial radius (C{meter}).

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

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

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

156 @kwarg name: Optional name (C{str}).

157

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

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

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

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

162 '''

163 if name:

164 self.name = name

165 try:

166 E = a_ellipsoid

167 if f is None:

168 pass

169 elif isscalar(E) and isscalar(f):

170 E = a_f2Tuple(E, f)

171 else:

172 raise ValueError # _invalid_

173

174 d = _ellipsoidal_datum(E, name=name)

175 E = d.ellipsoid

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

177 raise ValueError # _invalid_

178

179 except (TypeError, ValueError) as x:

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

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

182

183 self._datum = d

184 self._E = E

185

186 def __eq__(self, other):

187 '''Compare this and an other Ecef.

188

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

190

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

192 '''

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

194 other.ellipsoid == self.ellipsoid)

195

196 @Property_RO

197 def equatoradius(self):

198 '''Get the I{equatorial} radius, semi-axis (C{meter}).

199 '''

200 return self.ellipsoid.a

201

202 a = equatorialRadius = equatoradius # Karney property

203

204 @Property_RO

205 def datum(self):

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

207 '''

208 return self._datum

209

210 @Property_RO

211 def ellipsoid(self):

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

213 '''

214 return self._E

215

216 @Property_RO

217 def flattening(self): # Karney property

218 '''Get the I{flattening} (C{float}), M{(a - b) / a}, positive for

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

220 '''

221 return self.ellipsoid.f

222

223 f = flattening

224

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

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

227 '''

228 E = self.ellipsoid

229

230 if _philam:

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

232 lat = Lat(degrees90( lat))

233 lon = Lon(degrees180(lon))

234 else:

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

236

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

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

239 x = (h + n) * ca

240

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

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

243 0, m, self.datum,

244 name=name or self.name)

245

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

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

248

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

250 latitude (C{degrees}).

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

252 (C{degrees}).

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

254 the surface of the ellipsoid.

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

256 @kwarg name: Optional name (C{str}).

257

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

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

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

261 and C{datum} if available.

262

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

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

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

266

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

268 and avoid double angle conversions.

269 '''

270 llhn = _llhn4(latlonh, lon, height, name=name)

271 return _EcefBase._forward(self, *llhn, M=M)

272

273 def forward_(self, phi, lam, height=0, M=False, name=NN):

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

275 in I{radians}.

276

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

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

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

280 the surface of the ellipsoid.

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

282 @kwarg name: Optional name (C{str}).

283

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

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

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

287

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

289 '''

290 try: # like function C{_llhn4} above

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

292 except (TypeError, ValueError) as x:

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

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

295

296 @property_RO

297 def _Geocentrics(self):

298 '''(INTERNAL) Valid geocentric classes.

299 '''

300 t = Ecef9Tuple, _MODS.cartesianBase.CartesianBase

301 _EcefBase._Geocentrics = t # overwrite the property

302 return t

303

304 @Property_RO

305 def _isYou(self):

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

307 '''

308 return isinstance(self, EcefYou)

309

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

311 '''Creation a rotation matrix.

312

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

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

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

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

317

318 @return: An L{EcefMatrix}.

319 '''

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

321

322 def reverse(self, xyz, y=None, z=None, M=False, name=NN): # PYCHOK no cover

323 '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}.

324 '''

325 notOverloaded(self, xyz, y=y, z=z, M=M, name=name)

326

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

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

329

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

331

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

333 '''

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

335

336

337 class EcefFarrell21(_EcefBase):

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

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

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

341 '''

342

343 def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M

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

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

346 page 29.

347

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

349 coordinate (C{meter}).

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

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

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

353 @kwarg name: Optional name (C{str}).

354

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

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

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

358 if available.

359

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

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

362 zero division error.

363

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

365 '''

366 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)

367

368 E = self.ellipsoid

369 a = E.a

370 a2 = E.a2

371 b2 = E.b2

372 e_ = E.a_b * E.e # 0.0820944... WGS84

373 e2 = E.e2

374 e4 = E.e4

375

376 try: # names as page 29

377 z2 = z**2

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

379

380 p = hypot(x, y)

381 p2 = p**2

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

383 F = b2 * z2 * 54

384 c = e4 * p2 * F / G**3

385 s = cbrt(_1_0 + c + sqrt(c**2 + c * 2))

386 P = F / (_3_0 * (fsum_(_1_0, s, _1_0 / s) * G)**2)

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

388 Q1 = Q + _1_0

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

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

391 -P * p2 * _0_5))

392 r = p + e2 * r0

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

394

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

396 t = atan2(z + e_**2 * v * z, p)

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

398

399 except (ValueError, ZeroDivisionError) as e:

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

401

402 return Ecef9Tuple(x, y, z, degrees90(t), atan2d(y, x), h,

403 1, None, self.datum,

404 name=name or self.name)

405

406

407 class EcefFarrell22(_EcefBase):

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

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

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

411 '''

412

413 def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M

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

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

416 page 30.

417

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

419 coordinate (C{meter}).

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

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

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

423 @kwarg name: Optional name (C{str}).

424

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

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

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

428 if available.

429

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

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

432 zero division error.

433

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

435 '''

436 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)

437

438 E = self.ellipsoid

439 a = E.a

440 b = E.b

441

442 try: # see EcefVeness.reverse

443 p = hypot(x, y)

444 s, c = sincos2(atan2(z * a, p * b))

445

446 t = atan2(z + E.e22 * b * s**3,

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

448

449 s, c = sincos2(t)

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

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

452 else: # polar

453 h = fabs(z) - b

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

455

456 except (ValueError, ZeroDivisionError) as e:

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

458

459 return Ecef9Tuple(x, y, z, degrees90(t), atan2d(y, x), h,

460 1, None, self.datum,

461 name=name or self.name)

462

463

464 class EcefKarney(_EcefBase):

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

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

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

468

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

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

471 ways, C{v1} in east, north, up coordinates (where the components are

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

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

474 the rotation matrix.

475 '''

476

477 @Property_RO

478 def hmax(self):

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

480 '''

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

482

483 def reverse(self, xyz, y=None, z=None, M=False, name=NN):

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

485

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

487 coordinate (C{meter}).

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

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

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

491 @kwarg name: Optional name (C{str}).

492

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

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

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

496 C{datum} if available.

497

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

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

500

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

502 C{height} is returned, i.e., C{(lat, lon)} corresponds to the closest

503 point on the ellipsoid. If there are still multiple solutions with

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

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

506 different longitudes (applies only if C{x} = C{y} = 0) then C{lon} = 0

507 is returned. The returned C{height} value is not below M{−E.a * (1 −

508 E.e2) / sqrt(1 − E.e2 * sin(lat)**2)}. The returned C{lon} is in the

509 range [−180°, 180°]. Like C{forward} above, M{v1 = Transpose(M) ⋅ v0}.

510 '''

511 def norm3(y, x):

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

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

514

515 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)

516

517 E = self.ellipsoid

518

519 sb, cb, R = norm3(y, x)

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

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

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

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

524 # height. This avoids overflow, e.g., in the computation of disc

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

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

527 sb, cb, R = norm3(y * _0_5, x * _0_5)

528 sa, ca, _ = norm3(z * _0_5, R)

529 C = 1

530

531 elif E.e4: # E.isEllipsoidal

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

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

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

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

536 if E.isProlate:

537 p, q = q, p

538 r = p + q - E.e4

539 e = E.e4 * q

540 if e or r > 0:

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

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

543 s = e * p / _4_0 # s = r^3 * s

544 u = r = r / _6_0

545 r2 = r**2

546 r3 = r * r2

547 t3 = s + r3

548 disc = s * (r3 + t3)

549 if disc < 0:

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

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

552 # which avoids cancellation. Note, disc < 0 implies r < 0.

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

554 else:

555 # Pick the sign on the sqrt to maximize abs(T3). This

556 # minimizes loss of precision due to cancellation. The

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

558 # in definition of u.

559 if disc > 0:

560 t3 += copysign0(sqrt(disc), t3) # t3 = (r * t)^3

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

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

563 # t can be zero; but then r2 / t -> 0.

564 if t:

565 u = fsum_(u, t, r2 / t)

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

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

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

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

570 # Need to guard against w going negative due to roundoff in uv - q.

571 w = max(_0_0, E.e2abs * (uv - q) / (_2_0 * v))

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

573 # subtraction. Division by 0 not possible because uv > 0, w >= 0.

574 k1 = k2 = uv / (sqrt(uv + w**2) + w)

575 if E.isProlate:

576 k1 -= E.e2

577 else:

578 k2 += E.e2

579 sa, ca, h = norm3(z / k1, R / k2)

580 h *= k1 - E.e21

581 C = 2

582

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

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

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

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

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

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

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

590 q = E.e4 - p

591 if E.isProlate:

592 p, q = q, p

593 e = E.a

594 else:

595 e = E.b2_a

596 sa, ca, h = norm3(sqrt(q * E._1_e21), sqrt(p))

597 if z < 0:

598 sa = neg(sa) # for tiny negative z, not for prolate

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

600 C = 3

601

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

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

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

605 sa, ca, _ = norm3((z if h else _1_0), R)

606 h -= E.a

607 C = 4

608

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

610 return Ecef9Tuple(x, y, z, atan2d(sa, ca),

611 atan2d(sb, cb), h,

612 C, m, self.datum,

613 name=name or self.name)

614

615

616 class EcefSudano(_EcefBase):

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

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

619 3709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>}.

620 '''

621 _tol = EPS2

622

623 def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M

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

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

626 3709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>}.

627

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

629 coordinate (C{meter}).

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

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

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

633 @kwarg name: Optional name (C{str}).

634

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

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

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

638

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

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

641 '''

642 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)

643

644 E = self.ellipsoid

645 e = E.e2 * E.a

646 h = hypot(x, y) # Rh

647 d = e - h

648

649 a = atan2(z, h * E.e21)

650 sa, ca = sincos2(fabs(a))

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

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

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

654 # = ca**2 * (z * ca + E.e2 * E.a * sa - h * sa)

655 # = ca**2 * (z * ca + (E.e2 * E.a - h) * sa)

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

657 # = ca**2 * (E.e2 * E.a / E.e2s2(sa) - h / ca**2)

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

659 # (E.e2 * E.a / E.e2s2(sa) - h / ca**2)

660 tol = self.tolerance

661 _S2_ = Fsum(sa).fsum2_

662 for C in range(1, _TRIPS):

663 ca2 = _1_0 - sa**2

664 if ca2 < EPS_2: # PYCHOK no cover

665 ca = _0_0

666 break

667 ca = sqrt(ca2)

668 r = e / E.e2s2(sa) - h / ca2

669 if fabs(r) < EPS_2:

670 break

671 a = None

672 sa, r = _S2_(-z * ca / r, -d * sa / r)

673 if fabs(r) < tol:

674 break

675 else:

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

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

678

679 if a is None:

680 a = copysign0(asin(sa), z)

681 h = fsum_(h * ca, fabs(z * sa), -E.a * E.e2s(sa)) # use Veness',

682 # since Sudano's Eq (7) doesn't provide the correct height

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

684

685 r = Ecef9Tuple(x, y, z, degrees90(a), atan2d(y, x), h,

686 C, None, self.datum,

687 name=name or self.name)

688 r._iteration = C

689 return r

690

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

692 def tolerance(self):

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

694 '''

695 return self._tol

696

697 @tolerance.setter # PYCHOK setter!

698 def tolerance(self, tol):

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

700

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

702 '''

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

704

705

706 class EcefVeness(_EcefBase):

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

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

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

710

711 @see: U{I{A Guide to Coordinate Systems in Great Britain}<https://

712 www.OrdnanceSurvey.co.UK/documents/resources/guide-coordinate-systems-great-britain.pdf>},

713 section I{B) Converting between 3D Cartesian and ellipsoidal

714 latitude, longitude and height coordinates}.

715 '''

716

717 def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M

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

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

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

721

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

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

724 233668213_The_Accuracy_of_Geodetic_Latitude_and_Height_Equations>}, Survey Review,

725 Vol 28, 218, Oct 1985.

726

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

728 coordinate (C{meter}).

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

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

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

732 @kwarg name: Optional name (C{str}).

733

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

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

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

737

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

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

740

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

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

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

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

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

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

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

748 publication/3709199_An_exact_conversion_from_an_Earth-centered_coordinate_system_to_latitude_longitude_and_altitude>}.

749 '''

750 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)

751

752 E = self.ellipsoid

753

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

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

756 if min(p, r) > EPS0:

757 # parametric latitude (Bowring eqn 17, replaced)

758 t = (E.b * z) / (E.a * p) * (_1_0 + E.e22 * E.b / r)

759 c = _1_0 / hypot1(t)

760 s = t * c

761

762 # geodetic latitude (Bowring eqn 18)

763 a = atan2(z + E.e22 * E.b * s**3,

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

765

766 # height above ellipsoid (Bowring eqn 7)

767 sa, ca = sincos2(a)

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

769# h = p * ca + z * sa - (E.a * E.a / r)

770 h = fsum_(p * ca, z * sa, -E.a * E.e2s(sa))

771

772 C, lat, lon = 1, degrees90(a), atan2d(y, x)

773

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

775 elif p > EPS: # lat arbitrarily zero

776 C, lat, lon, h = 2, _0_0, atan2d(y, x), p - E.a

777

778 else: # polar lat, lon arbitrarily zero

779 C, lat, lon, h = 3, copysign0(_90_0, z), _0_0, fabs(z) - E.b

780

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

782 C, None, # M=None

783 self.datum, name=name or self.name)

784

785

786 class EcefYou(_EcefBase):

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

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

789

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

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

792 11589/115114_9021_geod2ellip_final.pdf>} Studia Geophysica et Geodaetica, 2008, 52,

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

794 '''

795

796 def __init__(self, a_ellipsoid, f=None, name=NN):

797 _EcefBase.__init__(self, a_ellipsoid, f=f, name=name) # inherited documentation

798 E = self.ellipsoid

799 if E.isProlate or (E.a2 - E.b2) < 0:

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

801

802 def reverse(self, xyz, y=None, z=None, M=None, name=NN): # PYCHOK unused M

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

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

805

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

807 coordinate (C{meter}).

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

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

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

811 @kwarg name: Optional name (C{str}).

812

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

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

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

816 available.

817

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

819 B{C{z}} not C{scalar} for C{scalar} B{C{xyz}}.

820 '''

821 x, y, z, name = _xyzn4(xyz, y, z, self._Geocentrics, name=name)

822

823 r2 = hypot2_(x, y, z)

824

825 E = self.ellipsoid

826 e2 = E.a2 - E.b2 # == E.e2 * E.a2

827 if e2 < 0:

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

829 e = sqrt(e2) # XXX sqrt0(e2)?

830

831 q = hypot(x, y)

832 u = fsum_(r2, -e2, hypot(r2 - e2, 2 * e * z)) * _0_5

833 if u > EPS02:

834 u = sqrt(u)

835 p = hypot(u, e)

836 B = atan2(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 += fsum_(u * E.b, -p, e2) / d

843 sB, cB = sincos2(B)

844 elif u < 0:

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

846 else:

847 sB, cB = copysign0(_1_0, z), _0_0

848

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

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

851 h = neg(h) # inside ellipsoid

852

853 return Ecef9Tuple(x, y, z, atan2d(E.a * sB, E.b * cB), # atan(E.a_b * tan(B))

854 atan2d(y, x), h,

855 1, None, # C=1, M=None

856 self.datum, name=name or self.name)

857

858

859 class EcefMatrix(_NamedTuple):

860 '''A rotation matrix.

861 '''

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

863 '_1_0_', '_1_1_', '_1_2_',

864 '_2_0_', '_2_1_', '_2_2_')

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

866

867 def _validate(self, **_OK): # PYCHOK unused

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

869 '''

870 _NamedTuple._validate(self, _OK=True)

871

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

873 '''New L{EcefMatrix} matrix.

874

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

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

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

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

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

880

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

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

883 '''

884 t = sa, ca, sb, cb

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

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

887

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

889 raise EcefError(unstr(EcefMatrix.__name__, *t))

890

891 else: # build matrix from the following quaternion operations

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

893 # or

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

895 # where

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

897

898 # Local X axis (east) in geocentric coords

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

900 # Local Y axis (north) in geocentric coords

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

902 # Local Z axis (up) in geocentric coords

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

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

905 cb, -sb * sa, sb * ca,

906 _0_0, ca, sa)

907

908 return _NamedTuple.__new__(cls, *t)

909

910 def column(self, column):

911 '''Get matrix B{C{column}} as 3-tuple.

912 '''

913 if 0 <= column < 3:

914 return self[column::3]

915 raise _IndexError(column=column)

916

917 @Property_RO

918 def _column_0(self):

919 return self.column(0)

920

921 @Property_RO

922 def _column_1(self):

923 return self.column(1)

924

925 @Property_RO

926 def _column_2(self):

927 return self.column(2)

928

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

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

931

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

933 '''

934 return self.classof(*self)

935

936 __copy__ = __deepcopy__ = copy

937

938 def multiply(self, other):

939 '''Matrix multiply M{M0' ⋅ M} this matrix transposed with

940 an other matrix.

941

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

943

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

945

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

947 '''

948 _xinstanceof(EcefMatrix, other=other)

949

950 # like LocalCartesian.MatrixMultiply, transposed(self) X other

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

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

953 return _xnamed(EcefMatrix(*M), EcefMatrix.multiply.__name__)

954

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

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

957

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

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

960

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

962

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

964 '''

965 if xyz0:

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

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

968

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

970

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

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

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

974 return (fdot(xyz, *self._column_0),

975 fdot(xyz, *self._column_1),

976 fdot(xyz, *self._column_2))

977

978 def row(self, row):

979 '''Get matrix B{C{row}} as 3-tuple.

980 '''

981 if 0 <= row < 3:

982 r = row * 3

983 return self[r:r+3]

984 raise _IndexError(row=row)

985

986 @Property_RO

987 def _row_0(self):

988 return self.row(0)

989

990 @Property_RO

991 def _row_1(self):

992 return self.row(1)

993

994 @Property_RO

995 def _row_2(self):

996 return self.row(2)

997

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

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

1000

1001 @arg xyz: Local C{(x, y, z)} coordinates (C{3-tuple}).

1002 @arg xyz0: Optional, local C{(x0, y0, z0)} origin (C{3-tuple}).

1003

1004 @return: Unrotated C{(x, y, z)} location (C{3-tuple}).

1005

1006 @raise LenError: Unequal C{len(B{xyz})} and C{len(B{xyz0})}.

1007 '''

1008 if xyz0:

1009 if len(xyz0) != len(xyz):

1010 raise LenError(self.unrotate, xyz0=len(xyz0), xyz=len(xyz))

1011

1012 _xyz = _1_0_1T + xyz

1013 # x' = x0 + M[0] * x + M[1] * y + M[2] * z

1014 # y' = y0 + M[3] * x + M[4] * y + M[5] * z

1015 # z' = z0 + M[6] * x + M[7] * y + M[8] * z

1016 xyz_ = (fdot(_xyz, xyz0[0], *self._row_0),

1017 fdot(_xyz, xyz0[1], *self._row_1),

1018 fdot(_xyz, xyz0[2], *self._row_2))

1019 else:

1020 # x' = M[0] * x + M[1] * y + M[2] * z

1021 # y' = M[3] * x + M[4] * y + M[5] * z

1022 # z' = M[6] * x + M[7] * y + M[8] * z

1023 xyz_ = (fdot(xyz, *self._row_0),

1024 fdot(xyz, *self._row_1),

1025 fdot(xyz, *self._row_2))

1026 return xyz_

1027

1028

1029 class Ecef9Tuple(_NamedTuple):

1030 '''9-Tuple C{(x, y, z, lat, lon, height, C, M, datum)} with I{geocentric}

1031 C{x}, C{y} and C{z} plus I{geodetic} C{lat}, C{lon} and C{height}, case

1032 C{C} (see the C{Ecef*.reverse} methods) and optionally, the rotation

1033 matrix C{M} (L{EcefMatrix}) and C{datum}, with C{lat} and C{lon} in

1034 C{degrees} and C{x}, C{y}, C{z} and C{height} in C{meter}, conventionally.

1035 '''

1036 _Names_ = (_x_, _y_, _z_, _lat_, _lon_, _height_, _C_, _M_, _datum_)

1037 _Units_ = ( Meter, Meter, Meter, Lat, Lon, Height, Int, _Pass, _Pass)

1038

1039 _IndexM = _Names_.index(_M_) # for ._M_x_M

1040

1041 @property_RO

1042 def _CartesianBase(self):

1043 '''(INTERNAL) Get/cache class C{CartesianBase}.

1044 '''

1045 Ecef9Tuple._CartesianBase = C = _MODS.cartesianBase.CartesianBase # overwrite property

1046 return C

1047

1048 @deprecated_method

1049 def convertDatum(self, datum2): # for backward compatibility

1050 '''DEPRECATED, use method L{toDatum}.'''

1051 return self.toDatum(datum2)

1052

1053 @Property_RO

1054 def lam(self):

1055 '''Get the longitude in C{radians} (C{float}).

1056 '''

1057 return self.philam.lam

1058

1059 @Property_RO

1060 def lamVermeille(self):

1061 '''Get the longitude in C{radians [-PI*3/2..+PI*3/2]} after U{Vermeille

1062 <https://Search.ProQuest.com/docview/639493848>} (2004), page 95.

1063

1064 @see: U{Karney<https://GeographicLib.SourceForge.io/C++/doc/geocentric.html>},

1065 U{Vermeille<https://Search.ProQuest.com/docview/847292978>} 2011, pp 112-113, 116

1066 and U{Featherstone, et.al.<https://Search.ProQuest.com/docview/872827242>}, page 7.

1067 '''

1068 x, y = self.x, self.y

1069 if y > EPS0:

1070 r = _N_2_0 * atan2(x, hypot(y, x) + y) + PI_2

1071 elif y < -EPS0:

1072 r = _2_0 * atan2(x, hypot(y, x) - y) - PI_2

1073 else: # y == 0

1074 r = PI if x < 0 else _0_0

1075 return Lam(Vermeille=r)

1076

1077 @Property_RO

1078 def latlon(self):

1079 '''Get the lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).

1080 '''

1081 return LatLon2Tuple(self.lat, self.lon, name=self.name)

1082

1083 @Property_RO

1084 def latlonheight(self):

1085 '''Get the lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).

1086 '''

1087 return self.latlon.to3Tuple(self.height)

1088

1089 @Property_RO

1090 def latlonheightdatum(self):

1091 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).

1092 '''

1093 return self.latlonheight.to4Tuple(self.datum)

1094

1095 @Property_RO

1096 def latlonVermeille(self):

1097 '''Get the latitude and I{Vermeille} longitude in C{degrees [-225..+225]} (L{LatLon2Tuple}C{(lat, lon)}).

1098

1099 @see: Property C{lonVermeille}.

1100 '''

1101 return LatLon2Tuple(self.lat, self.lonVermeille, name=self.name)

1102

1103 @Property_RO

1104 def lonVermeille(self):

1105 '''Get the longitude in C{degrees [-225..+225]} after U{Vermeille

1106 <https://Search.ProQuest.com/docview/639493848>} (2004), p 95.

1107

1108 @see: Property C{lamVermeille}.

1109 '''

1110 return Lon(Vermeille=degrees(self.lamVermeille))

1111

1112 def _T_x_M(self, T):

1113 '''(INTERNAL) Update M{self.M = T.multiply(self.M)}.

1114 '''

1115 t = list(self)

1116 M = self._IndexM

1117 t[M] = T.multiply(t[M])

1118 return self.classof(*t)

1119

1120 @Property_RO

1121 def phi(self):

1122 '''Get the latitude in C{radians} (C{float}).

1123 '''

1124 return self.philam.phi

1125

1126 @Property_RO

1127 def philam(self):

1128 '''Get the lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).

1129 '''

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

1131

1132 @Property_RO

1133 def philamheight(self):

1134 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).

1135 '''

1136 return self.philam.to3Tuple(self.height)

1137

1138 @Property_RO

1139 def philamheightdatum(self):

1140 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).

1141 '''

1142 return self.philamheight.to4Tuple(self.datum)

1143

1144 @Property_RO

1145 def philamVermeille(self):

1146 '''Get the latitude and I{Vermeille} longitude in C{radians [-PI*3/2..+PI*3/2]} (L{PhiLam2Tuple}C{(phi, lam)}).

1147

1148 @see: Property C{lamVermeille}.

1149 '''

1150 return PhiLam2Tuple(radians(self.lat), self.lamVermeille, name=self.name)

1151

1152 def toCartesian(self, Cartesian=None, **Cartesian_kwds):

1153 '''Return the geocentric C{(x, y, z)} coordinates as an ellipsoidal or spherical

1154 C{Cartesian}.

1155

1156 @kwarg Cartesian: Optional class to return C{(x, y, z)} (L{ellipsoidalKarney.Cartesian},

1157 L{ellipsoidalNvector.Cartesian}, L{ellipsoidalVincenty.Cartesian},

1158 L{sphericalNvector.Cartesian} or L{sphericalTrigonometry.Cartesian})

1159 or C{None}.

1160 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored

1161 if C{B{Cartesian} is None}.

1162

1163 @return: A C{B{Cartesian}(x, y, z, **B{Cartesian_kwds})} instance or

1164 a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Cartesian} is None}.

1165

1166 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}.

1167 '''

1168 if Cartesian in (None, Vector4Tuple):

1169 r = self.xyzh

1170 elif Cartesian is Vector3Tuple:

1171 r = self.xyz

1172 else:

1173 _xsubclassof(self._CartesianBase, Cartesian=Cartesian)

1174 r = Cartesian(self, **_xkwds(Cartesian_kwds, name=self.name))

1175 return r

1176

1177 def toDatum(self, datum2):

1178 '''Convert this C{Ecef9Tuple} to an other datum.

1179

1180 @arg datum2: Datum to convert I{to} (L{Datum}).

1181

1182 @return: The converted 9-Tuple (C{Ecef9Tuple}).

1183

1184 @raise TypeError: The B{C{datum2}} is not a L{Datum}.

1185 '''

1186 if self.datum in (None, datum2): # PYCHOK _Names_

1187 r = self.copy()

1188 else:

1189 c = self._CartesianBase(self, datum=self.datum, name=self.name) # PYCHOK _Names_

1190 # c.toLatLon converts datum, x, y, z, lat, lon, etc.

1191 # and returns another Ecef9Tuple iff LatLon is None

1192 r = c.toLatLon(datum=datum2, LatLon=None)

1193 return r

1194

1195 def toLatLon(self, LatLon=None, **LatLon_kwds):

1196 '''Return the geodetic C{(lat, lon, height[, datum])} coordinates.

1197

1198 @kwarg LatLon: Optional class to return C{(lat, lon, height[, datum])}

1199 or C{None}.

1200 @kwarg LatLon_kwds: Optional B{C{height}}, B{C{datum}} and other

1201 B{C{LatLon}} keyword arguments.

1202

1203 @return: An instance of C{B{LatLon}(lat, lon, **B{LatLon_kwds})}

1204 or if B{C{LatLon}} is C{None}, a L{LatLon3Tuple}C{(lat, lon,

1205 height)} respectively L{LatLon4Tuple}C{(lat, lon, height,

1206 datum)} depending on whether C{datum} is un-/specified.

1207

1208 @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}.

1209 '''

1210 kwds = _xkwds(LatLon_kwds, height=self.height, datum=self.datum, name=self.name) # PYCHOK Ecef9Tuple

1211 d = kwds[_datum_]

1212 if LatLon is None:

1213 r = LatLon3Tuple(self.lat, self.lon, kwds[_height_], name=kwds[_name_]) # PYCHOK Ecef9Tuple

1214 if d:

1215 r = r.to4Tuple(d) # checks type(d)

1216 else:

1217 if d is None: # remove None datum

1218 _ = kwds.pop[_datum_]

1219 r = LatLon(self.lat, self.lon, **kwds) # PYCHOK Ecef9Tuple

1220 _xdatum(getattr(r, _datum_, self.datum), self.datum) # PYCHOK Ecef9Tuple

1221 return r

1222

1223 def toLocal(self, ltp, Xyz=None, **Xyz_kwds):

1224 '''Convert this geocentric to I{local} C{x}, C{y} and C{z}.

1225

1226 @kwarg ltp: The I{local tangent plane} (LTP) to use (L{Ltp}).

1227 @kwarg Xyz: Optional class to return C{x}, C{y} and C{z}

1228 (L{XyzLocal}, L{Enu}, L{Ned}) or C{None}.

1229 @kwarg Xyz_kwds: Optional, additional B{C{Xyz}} keyword

1230 arguments, ignored if C{B{Xyz} is None}.

1231

1232 @return: An B{C{Xyz}} instance or if C{B{Xyz} is None},

1233 a L{Local9Tuple}C{(x, y, z, lat, lon, height,

1234 ltp, ecef, M)} with C{M=None}, always.

1235

1236 @raise TypeError: Invalid B{C{ltp}}.

1237 '''

1238 return _MODS.ltp._xLtp(ltp)._ecef2local(self, Xyz, Xyz_kwds)

1239

1240 def toVector(self, Vector=None, **Vector_kwds):

1241 '''Return the geocentric C{(x, y, z)} coordinates as vector.

1242

1243 @kwarg Vector: Optional vector class to return C{(x, y, z)} or

1244 C{None}.

1245 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword

1246 arguments, ignored if C{B{Vector} is None}.

1247

1248 @return: A C{Vector}C{(x, y, z, **Vector_kwds)} instance or a

1249 L{Vector3Tuple}C{(x, y, z)} if B{C{Vector}} is C{None}.

1250

1251 @see: Propertes C{xyz} and C{xyzh}

1252 '''

1253 return self.xyz if Vector is None else self._xnamed(

1254 Vector(self.x, self.y, self.z, **Vector_kwds)) # PYCHOK Ecef9Tuple

1255

1256 @Property_RO

1257 def xyz(self):

1258 '''Get the geocentric C{(x, y, z)} coordinates (L{Vector3Tuple}C{(x, y, z)}).

1259 '''

1260 return Vector3Tuple(self.x, self.y, self.z, name=self.name)

1261

1262 @Property_RO

1263 def xyzh(self):

1264 '''Get the geocentric C{(x, y, z)} coordinates and C{height} (L{Vector4Tuple}C{(x, y, z, h)})

1265 '''

1266 return self.xyz.to4Tuple(self.height)

1267

1268

1269 def _4Ecef(this, Ecef): # in .datums.Datum.ecef, .ellipsoids.Ellipsoid.ecef

1270 '''Return an ECEF converter for C{this} L{Datum} or L{Ellipsoid}.

1271 '''

1272 if Ecef is None:

1273 Ecef = EcefKarney

1274 else:

1275 _xinstanceof(*_Ecefs, Ecef=Ecef)

1276 return Ecef(this, name=this.name)

1277

1278

1279 def _xEcef(Ecef): # PYCHOK .latlonBase.py

1280 '''(INTERNAL) Validate B{C{Ecef}} I{class}.

1281 '''

1282 if issubclassof(Ecef, _EcefBase):

1283 return Ecef

1284 raise _TypesError(_Ecef_, Ecef, *_Ecefs)

1285

1286

1287_Ecefs = (EcefKarney, EcefSudano, EcefVeness, EcefYou,

1288 EcefFarrell21, EcefFarrell22)

1289

1290__all__ += _ALL_DOCS(_EcefBase)

1291

1292# **) MIT License

1293#

1294# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

1295#

1296# Permission is hereby granted, free of charge, to any person obtaining a

1297# copy of this software and associated documentation files (the "Software"),

1298# to deal in the Software without restriction, including without limitation

1299# the rights to use, copy, modify, merge, publish, distribute, sublicense,

1300# and/or sell copies of the Software, and to permit persons to whom the

1301# Software is furnished to do so, subject to the following conditions:

1302#

1303# The above copyright notice and this permission notice shall be included

1304# in all copies or substantial portions of the Software.

1305#

1306# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS

1307# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

1308# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL

1309# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR

1310# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,

1311# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

1312# OTHER DEALINGS IN THE SOFTWARE.