1

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

3

4 u'''Wrapper to invoke I{Karney}'s U{GeodSolve

5<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} utility

6 as an (exact) geodesic, but intended I{for testing purposes only}.

7

8 Set env variable C{PYGEODESY_GEODSOLVE} to the (fully qualified) path

9 of the C{GeodSolve} executable.

10'''

11

12 from pygeodesy.basics import _xinstanceof

13# from pygeodesy.constants import NAN, _0_0 # from .karney

14# from pygeodesy.geodesicx import GeodesicAreaExact # _MODS

15 from pygeodesy.interns import NN, _UNDER_

16 from pygeodesy.karney import Caps, GeodesicError, GeodSolve12Tuple, \

17 _llz2line, _sincos2d, _0_0, NAN

18 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, \

19 _getenv, _PYGEODESY_GEODSOLVE_

20 from pygeodesy.named import _name1__

21 from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple

22 from pygeodesy.props import Property, Property_RO, property_RO

23 from pygeodesy.solveBase import _SolveGDictBase, _SolveGDictLineBase

24 from pygeodesy.utily import _unrollon, _Wrap, wrap360

25

26__all__ = _ALL_LAZY.geodsolve

27__version__ = '24.07.09'

28

29

30 class _GeodesicSolveBase(_SolveGDictBase):

31 '''(INTERNAL) Base class for L{GeodesicSolve} and L{GeodesicLineSolve}.

32 '''

33 _Error = GeodesicError

34 _Names_Direct = \

35 _Names_Inverse = GeodSolve12Tuple._Names_

36 _Xable_name = 'GeodSolve'

37 _Xable_path = _getenv(_PYGEODESY_GEODSOLVE_, _PYGEODESY_GEODSOLVE_)

38

39 @Property_RO

40 def _b_option(self):

41 return ('-b',) if self.reverse2 else ()

42

43 @Property_RO

44 def _cmdBasic(self):

45 '''(INTERNAL) Get the basic C{GeodSolve} cmd (C{tuple}).

46 '''

47 return (self.GeodSolve, '-f') + (self._b_option +

48 self._e_option +

49 self._E_option +

50 self._p_option +

51 self._u_option)

52

53 @Property

54 def GeodSolve(self):

55 '''Get the U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}

56 executable (C{filename}).

57 '''

58 return self._Xable_path

59

60 @GeodSolve.setter # PYCHOK setter!

61 def GeodSolve(self, path):

62 '''Set the U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}

63 executable (C{filename}), the (fully qualified) path to the C{GeodSolve} executable.

64

65 @raise GeodesicError: Invalid B{C{path}}, B{C{path}} doesn't exist or

66 isn't the C{GeodSolve} executable.

67 '''

68 self._setXable(path)

69

70 def toStr(self, **prec_sep): # PYCHOK signature

71 '''Return this C{GeodesicSolve} as string.

72

73 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}

74 for the C{float} C{prec}ision, number of decimal digits

75 (0..9) and the C{sep}arator string to join. Trailing

76 zero decimals are stripped for B{C{prec}} values of 1

77 and above, but kept for negative B{C{prec}} values.

78

79 @return: GeodesicSolve items (C{str}).

80 '''

81 return _SolveGDictBase._toStr(self, GeodSolve=self.GeodSolve, **prec_sep)

82

83 @Property_RO

84 def _u_option(self):

85 return ('-u',) if self.unroll else ()

86

87

88 class GeodesicSolve(_GeodesicSolveBase):

89 '''Wrapper to invoke I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}

90 as an C{Exact} version of I{Karney}'s Python class U{Geodesic<https://GeographicLib.SourceForge.io/C++/doc/

91 python/code.html#geographiclib.geodesic.Geodesic>}.

92

93 @note: Use property C{GeodSolve} or env variable C{PYGEODESY_GEODSOLVE} to specify the (fully

94 qualified) path to the C{GeodSolve} executable.

95

96 @note: This C{geodesic} is intended I{for testing purposes only}, it invokes the C{GeodSolve}

97 executable for I{every} method call.

98 '''

99

100 def Area(self, polyline=False, **name):

101 '''Set up a L{GeodesicAreaExact} to compute area and perimeter

102 of a polygon.

103

104 @kwarg polyline: If C{True} perimeter only, otherwise area

105 and perimeter (C{bool}).

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

107

108 @return: A L{GeodesicAreaExact} instance.

109

110 @note: The B{C{debug}} setting is passed as C{verbose}

111 to the returned L{GeodesicAreaExact} instance.

112 '''

113 gaX = _MODS.geodesicx.GeodesicAreaExact(self, polyline=polyline, **name)

114 if self.verbose or self.debug: # PYCHOK no cover

115 gaX.verbose = True

116 return gaX

117

118 Polygon = Area # for C{geographiclib} compatibility

119

120 def Direct3(self, lat1, lon1, azi1, s12): # PYCHOK outmask

121 '''Return the destination lat, lon and reverse azimuth (final bearing)

122 in C{degrees}.

123

124 @return: L{Destination3Tuple}C{(lat, lon, final)}.

125 '''

126 r = self._GDictDirect(lat1, lon1, azi1, False, s12, floats=False)

127 return Destination3Tuple(float(r.lat2), float(r.lon2), wrap360(r.azi2),

128 iteration=r._iteration)

129

130 def _DirectLine(self, ll1, azi12, **caps_name): # PYCHOK no cover

131 '''(INTERNAL) Short-cut version.

132 '''

133 return self.DirectLine(ll1.lat, ll1.lon, azi12, **caps_name)

134

135 def DirectLine(self, lat1, lon1, azi1, **caps_name):

136 '''Set up a L{GeodesicLineSolve} to compute several points

137 on a single geodesic.

138

139 @arg lat1: Latitude of the first point (C{degrees}).

140 @arg lon1: Longitude of the first point (C{degrees}).

141 @arg azi1: Azimuth at the first point (compass C{degrees}).

142 @kwarg caps_name: Optional C{B{name}=NN} (C{str}) and keyword

143 argument C{B{caps}=Caps.ALL}, bit-or'ed combination

144 of L{Caps} values specifying the capabilities the

145 L{GeodesicLineSolve} instance should possess.

146

147 @return: A L{GeodesicLineSolve} instance.

148

149 @note: If the point is at a pole, the azimuth is defined by keeping

150 B{C{lon1}} fixed, writing C{B{lat1} = ±(90 − ε)}, and taking

151 the limit C{ε → 0+}.

152

153 @see: C++ U{GeodesicExact.Line

154 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicExact.html>}

155 and Python U{Geodesic.Line<https://GeographicLib.SourceForge.io/Python/doc/code.html>}.

156 '''

157 return GeodesicLineSolve(self, lat1, lon1, azi1, **_name1__(caps_name, _or_nameof=self))

158

159 Line = DirectLine

160

161 def _Inverse(self, ll1, ll2, wrap, **outmask): # PYCHOK no cover

162 '''(INTERNAL) Short-cut version, see .ellipsoidalBaseDI.intersecant2.

163 '''

164 if wrap:

165 ll2 = _unrollon(ll1, _Wrap.point(ll2))

166 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask)

167

168 def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask

169 '''Return the distance in C{meter} and the forward and

170 reverse azimuths (initial and final bearing) in C{degrees}.

171

172 @return: L{Distance3Tuple}C{(distance, initial, final)}.

173 '''

174 r = self._GDictInverse(lat1, lon1, lat2, lon2, floats=False)

175 return Distance3Tuple(float(r.s12), wrap360(r.azi1), wrap360(r.azi2),

176 iteration=r._iteration)

177

178 def _InverseLine(self, ll1, ll2, wrap, **caps_name): # PYCHOK no cover

179 '''(INTERNAL) Short-cut version.

180 '''

181 if wrap:

182 ll2 = _unrollon(ll1, _Wrap.point(ll2))

183 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name)

184

185 def InverseLine(self, lat1, lon1, lat2, lon2, **caps_name): # PYCHOK no cover

186 '''Set up a L{GeodesicLineSolve} to compute several points

187 on a single geodesic.

188

189 @arg lat1: Latitude of the first point (C{degrees}).

190 @arg lon1: Longitude of the first point (C{degrees}).

191 @arg lat2: Latitude of the second point (C{degrees}).

192 @arg lon2: Longitude of the second point (C{degrees}).

193 @kwarg caps_name: Optional C{B{name}=NN} (C{str}) and keyword

194 argument C{B{caps}=Caps.ALL}, bit-or'ed combination

195 of L{Caps} values specifying the capabilities the

196 L{GeodesicLineSolve} instance should possess.

197

198 @return: A L{GeodesicLineSolve} instance.

199

200 @note: Both B{C{lat1}} and B{C{lat2}} should in the range C{[-90, +90]}.

201

202 @see: C++ U{GeodesicExact.InverseLine

203 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicExact.html>} and

204 Python U{Geodesic.InverseLine<https://GeographicLib.SourceForge.io/Python/doc/code.html>}.

205 '''

206 r = self.Inverse(lat1, lon1, lat2, lon2)

207 gl = GeodesicLineSolve(self, lat1, lon1, r.azi1, **_name1__(caps_name, _or_nameof=self))

208 gl._a13 = r.a12 # gl.SetArc(r.a12)

209 gl._s13 = r.s12 # gl.SetDistance(r.s12)

210 return _llz2line(gl, lat2=lat2, lon2=lon2, azi2=r.azi2)

211

212

213 class GeodesicLineSolve(_GeodesicSolveBase, _SolveGDictLineBase):

214 '''Wrapper to invoke I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}

215 as an C{Exact} version of I{Karney}'s Python class U{GeodesicLine<https://GeographicLib.SourceForge.io/C++/doc/

216 python/code.html#geographiclib.geodesicline.GeodesicLine>}.

217

218 @note: Use property C{GeodSolve} or env variable C{PYGEODESY_GEODSOLVE} to specify the (fully

219 qualified) path to the C{GeodSolve} executable.

220

221 @note: This C{geodesic} is intended I{for testing purposes only}, it invokes the C{GeodSolve}

222 executable for I{every} method call.

223 '''

224 _a13 = \

225 _s13 = NAN # see GeodesicSolve._InverseLine

226

227 def __init__(self, geodesic, lat1, lon1, azi1, caps=Caps.ALL, **name):

228 '''New L{GeodesicLineSolve} instance, allowing points to be found along

229 a geodesic starting at C{(B{lat1}, B{lon1})} with azimuth B{C{azi1}}.

230

231 @arg geodesic: The geodesic to use (L{GeodesicSolve}).

232 @arg lat1: Latitude of the first point (C{degrees}).

233 @arg lon1: Longitude of the first point (C{degrees}).

234 @arg azi1: Azimuth at the first points (compass C{degrees}).

235 @kwarg caps: Bit-or'ed combination of L{Caps} values specifying the

236 capabilities the L{GeodesicLineSolve} instance should possess,

237 C{B{caps}=Caps.ALL} always. Include C{Caps.LINE_OFF} if

238 updates to the B{C{geodesic}} should I{not} be reflected in

239 this L{GeodesicLineSolve} instance.

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

241

242 @raise GeodesicError: Invalid path for the C{GeodSolve} executable

243 or isn't the C{GeodSolve} executable, see

244 property C{geodesic.GeodSolve}.

245

246 @raise TypeError: Invalid B{C{geodesic}}.

247 '''

248 _xinstanceof(GeodesicSolve, geodesic=geodesic)

249 if (caps & Caps.LINE_OFF): # copy to avoid updates

250 geodesic = geodesic.copy(deep=False, name=_UNDER_(NN, geodesic.name)) # NOT _under!

251 _SolveGDictLineBase.__init__(self, geodesic, lat1, lon1, caps, azi1=azi1, **name)

252 try:

253 self.GeodSolve = geodesic.GeodSolve # geodesic or copy of geodesic

254 except GeodesicError:

255 pass

256

257 @Property_RO

258 def a13(self):

259 '''Get the arc length to reference point 3 (C{degrees}).

260

261 @see: Methods L{Arc} and L{SetArc}.

262 '''

263 return self._a13

264

265 def Arc(self):

266 '''Return the arc length to reference point 3 (C{degrees} or C{NAN}).

267

268 @see: Method L{SetArc} and property L{a13}.

269 '''

270 return self.a13

271

272 def ArcPosition(self, a12, outmask=Caps.STANDARD): # PYCHOK unused

273 '''Find the position on the line given B{C{a12}}.

274

275 @arg a12: Spherical arc length from the first point to the

276 second point (C{degrees}).

277

278 @return: A C{GDict} with 12 items C{lat1, lon1, azi1, lat2, lon2,

279 azi2, m12, a12, s12, M12, M21, S12}.

280 '''

281 return self._GDictInvoke(self._cmdArc, self._Names_Direct, a12)._unCaps(outmask)

282

283 @Property_RO

284 def azi1(self):

285 '''Get the azimuth at the first point (compass C{degrees}).

286 '''

287 return self._lla1.azi1

288

289 azi12 = azi1 # like RhumbLineSolve

290

291 @Property_RO

292 def azi1_sincos2(self):

293 '''Get the sine and cosine of the first point's azimuth (2-tuple C{(sin, cos)}).

294 '''

295 return _sincos2d(self.azi1)

296

297 azi12_sincos2 = azi1_sincos2

298

299 @Property_RO

300 def _cmdArc(self):

301 '''(INTERNAL) Get the C{GeodSolve} I{-a -L} cmd (C{tuple}).

302 '''

303 return self._cmdDistance + ('-a',)

304

305 def Distance(self):

306 '''Return the distance to reference point 3 (C{meter} or C{NAN}).

307 '''

308 return self.s13

309

310 @property_RO

311 def geodesic(self):

312 '''Get the geodesic (L{GeodesicSolve}).

313 '''

314 return self._solve # see .solveBase._SolveLineBase

315

316 def Intersecant2(self, lat0, lon0, radius, **kwds): # PYCHOK no cover

317 '''B{Not implemented}, throws a C{NotImplementedError} always.'''

318 self._notImplemented(lat0, lon0, radius, **kwds)

319

320 def PlumbTo(self, lat0, lon0, **kwds): # PYCHOK no cover

321 '''B{Not implemented}, throws a C{NotImplementedError} always.'''

322 self._notImplemented(lat0, lon0, **kwds)

323

324 def Position(self, s12, outmask=Caps.STANDARD):

325 '''Find the position on the line given B{C{s12}}.

326

327 @arg s12: Distance from the first point to the second (C{meter}).

328

329 @return: A C{GDict} with 12 items C{lat1, lon1, azi1, lat2, lon2,

330 azi2, m12, a12, s12, M12, M21, S12}, possibly C{a12=NAN}.

331 '''

332 return self._GDictInvoke(self._cmdDistance, self._Names_Direct, s12)._unCaps(outmask)

333

334 @Property_RO

335 def s13(self):

336 '''Get the distance to reference point 3 (C{meter} or C{NAN}).

337

338 @see: Methods L{Distance} and L{SetDistance}.

339 '''

340 return self._s13

341

342 def SetArc(self, a13):

343 '''Set reference point 3 in terms relative to the first point.

344

345 @arg a13: Spherical arc length from the first to the reference

346 point (C{degrees}).

347

348 @return: The distance C{s13} (C{meter}) between the first and

349 the reference point or C{NAN}.

350 '''

351 if self._a13 != a13:

352 self._a13 = a13

353 self._s13 = self.ArcPosition(a13, outmask=Caps.DISTANCE).s12 # if a13 else _0_0

354# _update_all(self)

355 return self._s13

356

357 def SetDistance(self, s13):

358 '''Set reference point 3 in terms relative to the first point.

359

360 @arg s13: Distance from the first to the reference point (C{meter}).

361

362 @return: The arc length C{a13} (C{degrees}) between the first

363 and the reference point or C{NAN}.

364 '''

365 if self._s13 != s13:

366 self._s13 = s13

367 self._a13 = self.Position(s13, outmask=Caps.DISTANCE).a12 if s13 else _0_0

368# _update_all(self)

369 return self._a13 # NAN for GeodesicLineExact without Cap.DISTANCE_IN

370

371 def toStr(self, **prec_sep): # PYCHOK signature

372 '''Return this C{GeodesicLineSolve} as string.

373

374 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}

375 for the C{float} C{prec}ision, number of decimal digits

376 (0..9) and the C{sep}arator string to join. Trailing

377 zero decimals are stripped for B{C{prec}} values of 1

378 and above, but kept for negative B{C{prec}} values.

379

380 @return: GeodesicLineSolve items (C{str}).

381 '''

382 return _SolveGDictLineBase._toStr(self, azi1=self.azi1, geodesic=self._solve,

383 GeodSolve=self.GeodSolve, **prec_sep)

384

385

386__all__ += _ALL_DOCS(_GeodesicSolveBase)

387

388 if __name__ == '__main__':

389

390 from pygeodesy import printf

391 from sys import argv

392

393 gS = GeodesicSolve(name='Test')

394 gS.verbose = '--verbose' in argv # or '-v' in argv

395

396 if gS.GeodSolve in (_PYGEODESY_GEODSOLVE_, None): # not set

397 gS.GeodSolve = '/opt/local/bin/GeodSolve' # '/opt/local/Cellar/geographiclib/2.3/bin/GeodSolve' # HomeBrew

398 printf('version: %s', gS.version)

399

400 r = gS.Direct(40.6, -73.8, 51, 5.5e6)

401 printf('Direct: %r', r, nl=1)

402 printf('Direct3: %r', gS.Direct3(40.6, -73.8, 51, 5.5e6))

403

404 printf('Inverse: %r', gS.Inverse( 40.6, -73.8, 51.6, -0.5), nl=1)

405 printf('Inverse1: %r', gS.Inverse1(40.6, -73.8, 51.6, -0.5))

406 printf('Inverse3: %r', gS.Inverse3(40.6, -73.8, 51.6, -0.5))

407

408 glS = GeodesicLineSolve(gS, 40.6, -73.8, 51, name='LineTest')

409 p = glS.Position(5.5e6)

410 printf('Position: %s %r', p == r, p, nl=1)

411 p = glS.ArcPosition(49.475527)

412 printf('ArcPosition: %s %r', p == r, p)

413

414

415# % python3 -m pygeodesy.geodsolve

416

417# version: /opt/local/bin/GeodSolve: GeographicLib version 2.2

418

419# Direct: GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141173, m12=4844148.703101, M12=0.650911, M21=0.651229, s12=5500000.0, S12=39735075134877.09375)

420# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)

421

422# Inverse: GDict(a12=49.94131, azi1=51.198883, azi2=107.821777, lat1=40.6, lat2=51.6, lon1=-73.8, lon2=-0.5, m12=4877684.602706, M12=0.64473, M21=0.645046, s12=5551759.400319, S12=40041368848742.53125)

423# Inverse1: 49.94131021789904

424# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)

425

426# Position: True GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141173, m12=4844148.703101, M12=0.650911, M21=0.651229, s12=5500000.0, S12=39735075134877.09375)

427# ArcPosition: False GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141174, m12=4844148.669561, M12=0.650911, M21=0.651229, s12=5499999.948497, S12=39735074737272.734375)

428

429

430# % python3 -m pygeodesy.geodsolve --verbose

431

432# GeodesicSolve 'Test' 1: /opt/local/bin/GeodSolve --version (invoke)

433# GeodesicSolve 'Test' 1: /opt/local/bin/GeodSolve: GeographicLib version 2.2 (0)

434# version: /opt/local/bin/GeodSolve: GeographicLib version 2.2

435# GeodesicSolve 'Test' 2: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct)

436# GeodesicSolve 'Test' 2: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.0, lat2=51.884564505606761, lon2=-1.141172861200829, azi2=107.189397162605886, s12=5500000.0, a12=49.475527463251467, m12=4844148.703101486, M12=0.65091056699808603, M21=0.65122865892196558, S12=39735075134877.094 (0)

437

438# Direct: GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141173, m12=4844148.703101, M12=0.650911, M21=0.651229, s12=5500000.0, S12=39735075134877.09375)

439# GeodesicSolve 'Test' 3: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct3)

440# GeodesicSolve 'Test' 3: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.0, lat2=51.884564505606761, lon2=-1.141172861200829, azi2=107.189397162605886, s12=5500000.0, a12=49.475527463251467, m12=4844148.703101486, M12=0.65091056699808603, M21=0.65122865892196558, S12=39735075134877.094 (0)

441# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)

442# GeodesicSolve 'Test' 4: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse)

443# GeodesicSolve 'Test' 4: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.198882845579824, lat2=51.600000000000001, lon2=-0.5, azi2=107.821776735514248, s12=5551759.4003186841, a12=49.941310217899037, m12=4877684.6027061976, M12=0.64472969205948238, M21=0.64504567852134398, S12=40041368848742.531 (0)

444

445# Inverse: GDict(a12=49.94131, azi1=51.198883, azi2=107.821777, lat1=40.6, lat2=51.6, lon1=-73.8, lon2=-0.5, m12=4877684.602706, M12=0.64473, M21=0.645046, s12=5551759.400319, S12=40041368848742.53125)

446# GeodesicSolve 'Test' 5: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse1)

447# GeodesicSolve 'Test' 5: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.198882845579824, lat2=51.600000000000001, lon2=-0.5, azi2=107.821776735514248, s12=5551759.4003186841, a12=49.941310217899037, m12=4877684.6027061976, M12=0.64472969205948238, M21=0.64504567852134398, S12=40041368848742.531 (0)

448# Inverse1: 49.94131021789904

449# GeodesicSolve 'Test' 6: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse3)

450# GeodesicSolve 'Test' 6: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.198882845579824, lat2=51.600000000000001, lon2=-0.5, azi2=107.821776735514248, s12=5551759.4003186841, a12=49.941310217899037, m12=4877684.6027061976, M12=0.64472969205948238, M21=0.64504567852134398, S12=40041368848742.531 (0)

451# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)

452

453# Position: True GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141173, m12=4844148.703101, M12=0.650911, M21=0.651229, s12=5500000.0, S12=39735075134877.09375)

454# ArcPosition: False GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141174, m12=4844148.669561, M12=0.650911, M21=0.651229, s12=5499999.948497, S12=39735074737272.734375)

455

456# **) MIT License

457#

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

459#

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

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

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

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

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

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

466#

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

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

469#

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

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

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

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

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