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 _sincos2d, _Xables, _0_0, NAN

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

19 from pygeodesy.named import _name1__

20 from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple

21 from pygeodesy.props import Property, Property_RO, property_RO

22 from pygeodesy.solveBase import _SolveGDictBase, _SolveGDictLineBase

23 from pygeodesy.utily import _unrollon, _Wrap, wrap360

24

25__all__ = _ALL_LAZY.geodsolve

26__version__ = '24.11.02'

27

28

29 class _GeodesicSolveBase(_SolveGDictBase):

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

31 '''

32 _Error = GeodesicError

33 _Names_Direct = \

34 _Names_Inverse = GeodSolve12Tuple._Names_

35 _Xable_name = _Xables.GeodSolve.__name__

36 _Xable_path = _Xables.GeodSolve()

37

38 @Property_RO

39 def _b_option(self):

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

41

42 @Property_RO

43 def _cmdBasic(self):

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

45 '''

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

47 self._e_option +

48 self._E_option +

49 self._p_option +

50 self._u_option)

51

52 @Property

53 def GeodSolve(self):

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

55 executable (C{filename}).

56 '''

57 return self._Xable_path

58

59 @GeodSolve.setter # PYCHOK setter!

60 def GeodSolve(self, path):

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

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

63

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

65 isn't the C{GeodSolve} executable.

66 '''

67 self._setXable(path)

68

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

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

71

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

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

74 (0..9) and the C{sep}arator string to join. Trailing

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

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

77

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

79 '''

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

81

82 @Property_RO

83 def _u_option(self):

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

85

86

87 class GeodesicSolve(_GeodesicSolveBase):

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

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

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

91

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

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

94

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

96 executable for I{every} method call.

97 '''

98

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

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

101 of a polygon.

102

103 @kwarg polyline: If C{True}, compute the perimeter only, otherwise

104 perimeter and area (C{bool}).

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

106

107 @return: A L{GeodesicAreaExact} instance.

108

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

110 to the returned L{GeodesicAreaExact} instance.

111 '''

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

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

114 gaX.verbose = True

115 return gaX

116

117 Polygon = Area # for C{geographiclib} compatibility

118

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

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

121 in C{degrees}.

122

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

124 '''

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

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

127 iteration=r._iteration)

128

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

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

131 '''

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

133

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

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

136 on a single geodesic.

137

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

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

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

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

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

143 of L{Caps} values specifying the capabilities the

144 L{GeodesicLineSolve} instance should possess.

145

146 @return: A L{GeodesicLineSolve} instance.

147

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

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

150 the limit C{ε → 0+}.

151

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

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

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

155 '''

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

157

158 Line = DirectLine

159

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

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

162 '''

163 if wrap:

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

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

166

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

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

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

170

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

172 '''

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

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

175 iteration=r._iteration)

176

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

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

179 '''

180 if wrap:

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

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

183

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

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

186 on a single geodesic.

187

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

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

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

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

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

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

194 of L{Caps} values specifying the capabilities the

195 L{GeodesicLineSolve} instance should possess.

196

197 @return: A L{GeodesicLineSolve} instance.

198

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

200

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

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

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

204 '''

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

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

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

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

209 return gl

210

211

212 class GeodesicLineSolve(_GeodesicSolveBase, _SolveGDictLineBase):

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

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

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

216

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

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

219

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

221 executable for I{every} method call.

222 '''

223 _a13 = \

224 _s13 = NAN # see GeodesicSolve._InverseLine

225

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

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

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

229

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

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

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

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

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

235 capabilities the L{GeodesicLineSolve} instance should possess,

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

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

238 this L{GeodesicLineSolve} instance.

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

240

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

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

243 property C{geodesic.GeodSolve}.

244

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

246 '''

247 _xinstanceof(GeodesicSolve, geodesic=geodesic)

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

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

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

251 try:

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

253 except GeodesicError:

254 pass

255

256 @Property_RO

257 def a13(self):

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

259

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

261 '''

262 return self._a13

263

264 def Arc(self): # PYCHOK no cover

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

266

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

268 '''

269 return self.a13

270

271 def ArcPosition(self, a12, outmask=Caps.STANDARD): # PYCHOK no cover

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

273

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

275 second point (C{degrees}).

276

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

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

279 '''

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

281

282 @Property_RO

283 def azi1(self):

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

285 '''

286 return self._lla1.azi1

287

288 azi12 = azi1 # like RhumbLineSolve

289

290 @Property_RO

291 def azi1_sincos2(self):

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

293 '''

294 return _sincos2d(self.azi1)

295

296 azi12_sincos2 = azi1_sincos2

297

298 @Property_RO

299 def _cmdArc(self):

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

301 '''

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

303

304 def Distance(self):

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

306 '''

307 return self.s13

308

309 @property_RO

310 def geodesic(self):

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

312 '''

313 return self._solve # see .solveBase._SolveLineBase

314

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

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

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

318

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

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

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

322

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

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

325

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

327

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

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

330 '''

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

332

333 @Property_RO

334 def s13(self):

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

336

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

338 '''

339 return self._s13

340

341 def SetArc(self, a13): # PYCHOK no cover

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

343

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

345 point (C{degrees}).

346

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

348 the reference point or C{NAN}.

349 '''

350 if self._a13 != a13:

351 self._a13 = a13

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

353# _update_all(self)

354 return self._s13

355

356 def SetDistance(self, s13): # PYCHOK no cover

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

358

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

360

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

362 the reference point or C{NAN}.

363 '''

364 if self._s13 != s13:

365 self._s13 = s13

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

367# _update_all(self)

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

369

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

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

372

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

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

375 (0..9) and the C{sep}arator string to join. Trailing

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

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

378

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

380 '''

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

382 GeodSolve=self.GeodSolve, **prec_sep)

383

384

385__all__ += _ALL_DOCS(_GeodesicSolveBase)

386

387 if __name__ == '__main__':

388

389 def _main():

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 not _Xables.X_OK(gS.GeodSolve): # not set

397 gS.GeodSolve = _Xables.GeodSolve(_Xables.bin_)

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: %5s %r', p == r, p, nl=1)

411 p = glS.ArcPosition(49.475527)

412 printf('ArcPosition: %5s %r', p == r, p)

413

414 _main()

415

416# % python3 -m pygeodesy.geodsolve

417

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

419

420# 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)

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

422

423# 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)

424# Inverse1: 49.94131021789904

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

426

427# 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)

428# 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)

429

430

431# % python3 -m pygeodesy.geodsolve

432

433# version: /opt/local/bin/GeodSolve: GeographicLib version 2.3

434

435# 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=39735075134877.078125)

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

437

438# 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)

439# Inverse1: 49.94131021789904

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

441

442# Position: False GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141173, s12=5500000.0)

443# ArcPosition: False GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141174, s12=5499999.948497)

444

445

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

447

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

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

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

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

452# 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)

453

454# 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)

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

456# 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)

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

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

459# 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)

460

461# 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)

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

463# 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)

464# Inverse1: 49.94131021789904

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

466# 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)

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

468

469# 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)

470# 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)

471

472

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

474

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

476# GeodesicSolve 'Test'@1: '/opt/local/bin/GeodSolve: GeographicLib version 2.3' (0, stdout/-err)

477# GeodesicSolve 'Test'@1: /opt/local/bin/GeodSolve: GeographicLib version 2.3 (0)

478# version: /opt/local/bin/GeodSolve: GeographicLib version 2.3

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

480# GeodesicSolve 'Test'@2: '40.600000000000001 -73.799999999999997 51.000000000000000 51.884564505606761 -1.141172861200843 107.189397162605871 5500000.0000000000 49.475527463251460 4844148.7031014860 0.65091056699808614 0.65122865892196569 39735075134877.078' (0, stdout/-err)

481# GeodesicSolve 'Test'@2: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.0, lat2=51.884564505606761, lon2=-1.141172861200843, azi2=107.189397162605871, s12=5500000.0, a12=49.47552746325146, m12=4844148.703101486, M12=0.65091056699808614, M21=0.65122865892196569, S12=39735075134877.078 (0)

482

483# 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=39735075134877.078125)

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

485# GeodesicSolve 'Test'@3: '40.600000000000001 -73.799999999999997 51.000000000000000 51.884564505606761 -1.141172861200843 107.189397162605871 5500000.0000000000 49.475527463251460 4844148.7031014860 0.65091056699808614 0.65122865892196569 39735075134877.078' (0, stdout/-err)

486# GeodesicSolve 'Test'@3: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.0, lat2=51.884564505606761, lon2=-1.141172861200843, azi2=107.189397162605871, s12=5500000.0, a12=49.47552746325146, m12=4844148.703101486, M12=0.65091056699808614, M21=0.65122865892196569, S12=39735075134877.078 (0)

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

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

489# GeodesicSolve 'Test'@4: '40.600000000000001 -73.799999999999997 51.198882845579824 51.600000000000001 -0.500000000000000 107.821776735514248 5551759.4003186813 49.941310217899037 4877684.6027061967 0.64472969205948238 0.64504567852134398 40041368848742.531' (0, stdout/-err)

490# GeodesicSolve 'Test'@4: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.198882845579824, lat2=51.600000000000001, lon2=-0.5, azi2=107.821776735514248, s12=5551759.4003186813, a12=49.941310217899037, m12=4877684.6027061967, M12=0.64472969205948238, M21=0.64504567852134398, S12=40041368848742.531 (0)

491

492# 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)

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

494# GeodesicSolve 'Test'@5: '40.600000000000001 -73.799999999999997 51.198882845579824 51.600000000000001 -0.500000000000000 107.821776735514248 5551759.4003186813 49.941310217899037 4877684.6027061967 0.64472969205948238 0.64504567852134398 40041368848742.531' (0, stdout/-err)

495# GeodesicSolve 'Test'@5: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.198882845579824, lat2=51.600000000000001, lon2=-0.5, azi2=107.821776735514248, s12=5551759.4003186813, a12=49.941310217899037, m12=4877684.6027061967, M12=0.64472969205948238, M21=0.64504567852134398, S12=40041368848742.531 (0)

496# Inverse1: 49.94131021789904

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

498# GeodesicSolve 'Test'@6: '40.600000000000001 -73.799999999999997 51.198882845579824 51.600000000000001 -0.500000000000000 107.821776735514248 5551759.4003186813 49.941310217899037 4877684.6027061967 0.64472969205948238 0.64504567852134398 40041368848742.531' (0, stdout/-err)

499# GeodesicSolve 'Test'@6: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.198882845579824, lat2=51.600000000000001, lon2=-0.5, azi2=107.821776735514248, s12=5551759.4003186813, a12=49.941310217899037, m12=4877684.6027061967, M12=0.64472969205948238, M21=0.64504567852134398, S12=40041368848742.531 (0)

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

501

502# Position: False GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141173, s12=5500000.0)

503# ArcPosition: False GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141174, s12=5499999.948497)

504

505# **) MIT License

506#

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

508#

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

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

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

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

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

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

515#

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

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

518#

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

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

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

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

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

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

525# OTHER DEALINGS IN THE SOFTWARE.