Coverage for pygeodesy/geodsolve.py: 88%

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1 

2# -*- coding: utf-8 -*- 

3 

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

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

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

7 

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

9of the C{GeodSolve} executable. 

10''' 

11 

12from pygeodesy.basics import _xinstanceof 

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

14# from pygeodesy.geodesicx import GeodesicAreaExact # _MODS 

15from pygeodesy.interns import NN, _UNDER_ 

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

17 _sincos2d, _0_0, NAN 

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

19 _getenv, _PYGEODESY_GEODSOLVE_ 

20from pygeodesy.named import _name1__ 

21from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple 

22from pygeodesy.props import Property, Property_RO, property_RO 

23from pygeodesy.solveBase import _SolveGDictBase, _SolveGDictLineBase 

24from pygeodesy.utily import _unrollon, _Wrap, wrap360 

25 

26__all__ = _ALL_LAZY.geodsolve 

27__version__ = '24.07.11' 

28 

29 

30class _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 

88class 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 _InverseLine2(self, lat1, lon1, lat2, lon2, **caps_name): # in .geodesici 

186# '''(INTERNAL) Helper for L{InverseLine} and L{_InverseLine}. 

187# ''' 

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

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

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

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

192# return gl, r 

193 

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

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

196 on a single geodesic. 

197 

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

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

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

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

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

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

204 of L{Caps} values specifying the capabilities the 

205 L{GeodesicLineSolve} instance should possess. 

206 

207 @return: A L{GeodesicLineSolve} instance. 

208 

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

210 

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

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

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

214 ''' 

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

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

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

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

219 return gl 

220 

221 

222class GeodesicLineSolve(_GeodesicSolveBase, _SolveGDictLineBase): 

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

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

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

226 

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

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

229 

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

231 executable for I{every} method call. 

232 ''' 

233 _a13 = \ 

234 _s13 = NAN # see GeodesicSolve._InverseLine 

235 

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

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

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

239 

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

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

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

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

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

245 capabilities the L{GeodesicLineSolve} instance should possess, 

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

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

248 this L{GeodesicLineSolve} instance. 

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

250 

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

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

253 property C{geodesic.GeodSolve}. 

254 

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

256 ''' 

257 _xinstanceof(GeodesicSolve, geodesic=geodesic) 

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

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

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

261 try: 

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

263 except GeodesicError: 

264 pass 

265 

266 @Property_RO 

267 def a13(self): 

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

269 

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

271 ''' 

272 return self._a13 

273 

274 def Arc(self): 

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

276 

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

278 ''' 

279 return self.a13 

280 

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

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

283 

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

285 second point (C{degrees}). 

286 

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

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

289 ''' 

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

291 

292 @Property_RO 

293 def azi1(self): 

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

295 ''' 

296 return self._lla1.azi1 

297 

298 azi12 = azi1 # like RhumbLineSolve 

299 

300 @Property_RO 

301 def azi1_sincos2(self): 

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

303 ''' 

304 return _sincos2d(self.azi1) 

305 

306 azi12_sincos2 = azi1_sincos2 

307 

308 @Property_RO 

309 def _cmdArc(self): 

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

311 ''' 

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

313 

314 def Distance(self): 

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

316 ''' 

317 return self.s13 

318 

319 @property_RO 

320 def geodesic(self): 

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

322 ''' 

323 return self._solve # see .solveBase._SolveLineBase 

324 

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

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

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

328 

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

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

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

332 

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

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

335 

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

337 

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

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

340 ''' 

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

342 

343 @Property_RO 

344 def s13(self): 

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

346 

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

348 ''' 

349 return self._s13 

350 

351 def SetArc(self, a13): 

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

353 

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

355 point (C{degrees}). 

356 

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

358 the reference point or C{NAN}. 

359 ''' 

360 if self._a13 != a13: 

361 self._a13 = a13 

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

363# _update_all(self) 

364 return self._s13 

365 

366 def SetDistance(self, s13): 

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

368 

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

370 

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

372 and the reference point or C{NAN}. 

373 ''' 

374 if self._s13 != s13: 

375 self._s13 = s13 

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

377# _update_all(self) 

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

379 

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

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

382 

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

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

385 (0..9) and the C{sep}arator string to join. Trailing 

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

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

388 

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

390 ''' 

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

392 GeodSolve=self.GeodSolve, **prec_sep) 

393 

394 

395__all__ += _ALL_DOCS(_GeodesicSolveBase) 

396 

397if __name__ == '__main__': 

398 

399 from pygeodesy import printf 

400 from sys import argv 

401 

402 gS = GeodesicSolve(name='Test') 

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

404 

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

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

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

408 

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

410 printf('Direct: %r', r, nl=1) 

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

412 

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

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

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

416 

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

418 p = glS.Position(5.5e6) 

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

420 p = glS.ArcPosition(49.475527) 

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

422 

423 

424# % python3 -m pygeodesy.geodsolve 

425 

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

427 

428# 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) 

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

430 

431# 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) 

432# Inverse1: 49.94131021789904 

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

434 

435# 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) 

436# 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) 

437 

438 

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

440 

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

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

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

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

445# 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) 

446 

447# 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) 

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

449# 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) 

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

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

452# 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) 

453 

454# 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) 

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

456# 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) 

457# Inverse1: 49.94131021789904 

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

459# 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) 

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

461 

462# 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) 

463# 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) 

464 

465# **) MIT License 

466# 

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

468# 

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

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

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

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

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

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

475# 

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

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

478# 

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

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

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

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

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

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

485# OTHER DEALINGS IN THE SOFTWARE.