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 # typename

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

14# from pygeodesy.geodesicx import GeodesicAreaExact # _MODS

15 from pygeodesy.interns import _DMAIN_, 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__ = '25.04.14'

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__ # typename

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<pygeodesy.karney.Caps>} values specifying

144 the capabilities the L{GeodesicLineSolve} instance

145 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<pygeodesy.karney.Caps>} values specifying

196 the capabilities the L{GeodesicLineSolve} instance

197 should possess.

198

199 @return: A L{GeodesicLineSolve} instance.

200

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

202

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

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

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

206 '''

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

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

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

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

211 return gl

212

213

214 class GeodesicLineSolve(_GeodesicSolveBase, _SolveGDictLineBase):

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

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

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

218

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

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

221

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

223 executable for I{every} method call.

224 '''

225 _a13 = \

226 _s13 = NAN # see GeodesicSolve._InverseLine

227

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

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

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

231

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

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

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

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

236 @kwarg caps: Bit-or'ed combination of L{Caps<pygeodesy.karney.Caps>} values

237 specifying the capabilities the L{GeodesicLineSolve} instance

238 should possess, C{B{caps}=Caps.ALL} always. Include C{Caps.LINE_OFF}

239 if updates to the B{C{geodesic}} should I{not be reflected} in this

240 L{GeodesicLineSolve} instance.

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

242

243 @raise GeodesicError: Invalid path for the C{GeodSolve} executable or isn't the

244 C{GeodSolve} executable, see 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): # PYCHOK no cover

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 no cover

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): # PYCHOK no cover

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): # PYCHOK no cover

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 and

363 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__ == _DMAIN_:

389

390 def _main():

391 from pygeodesy import printf

392 from sys import argv

393

394 gS = GeodesicSolve(name='Test')

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

396

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

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

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

400

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

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

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

404

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

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

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

408

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

410 p = glS.Position(5.5e6)

411 printf('Position: %5s %r', p == r, p, nl=1)

412 p = glS.ArcPosition(49.475527)

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

414

415 _main()

416

417# % python3 -m pygeodesy.geodsolve

418

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

420

421# 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)

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

423

424# 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)

425# Inverse1: 49.94131021789904

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

427

428# 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)

429# 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)

430

431

432# % python3 -m pygeodesy.geodsolve

433

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

435

436# 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)

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

438

439# 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)

440# Inverse1: 49.94131021789904

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

442

443# 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)

444# 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)

445

446

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

448

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

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

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

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

453# 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)

454

455# 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)

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

457# 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)

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

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

460# 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)

461

462# 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)

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

464# 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)

465# Inverse1: 49.94131021789904

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

467# 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)

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

469

470# 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)

471# 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)

472

473

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

475

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

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

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

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

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

481# 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)

482# 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)

483

484# 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)

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

486# 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)

487# 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)

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

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

490# 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)

491# 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)

492

493# 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)

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

495# 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)

496# 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)

497# Inverse1: 49.94131021789904

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

499# 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)

500# 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)

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

502

503# 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)

504# 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)

505

506# **) MIT License

507#

508# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.

509#

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

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

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

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

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

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

516#

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

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

519#

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

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

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

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

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

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

526# OTHER DEALINGS IN THE SOFTWARE.