Coverage for pygeodesy/geodsolve.py: 94%

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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.errors import _xkwds # from .karney 

14# from pygeodesy.geodesicx import GeodesicAreaExact # _MODS 

15# from pygeodesy.internals import printf # from .lazily 

16from pygeodesy.interns import NN, _a12_, _azi1_, _azi2_, \ 

17 _lat1_, _lat2_, _lon1_, _lon2_, _m12_, \ 

18 _M12_, _M21_, _s12_, _S12_, _UNDER_ 

19from pygeodesy.interns import _UNUSED_, _not_ # PYCHOK used! 

20from pygeodesy.karney import _Azi, Caps, _Deg, GeodesicError, _GTuple, \ 

21 _Pass, _Lat, _Lon, _M, _M2, _sincos2d, _xkwds 

22from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, \ 

23 _getenv, _PYGEODESY_GEODSOLVE_, printf 

24from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple 

25from pygeodesy.props import Property, Property_RO 

26from pygeodesy.solveBase import _SolveBase, _SolveLineBase 

27from pygeodesy.utily import _unrollon, _Wrap, wrap360 

28 

29__all__ = _ALL_LAZY.geodsolve 

30__version__ = '24.05.13' 

31 

32 

33class GeodSolve12Tuple(_GTuple): 

34 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with 

35 angles C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2} and C{azi2} and arc C{a12} all in 

36 C{degrees}, initial C{azi1} and final C{azi2} forward azimuths, distance C{s12} and 

37 reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and geodesic 

38 scale factors C{M12} and C{M21}, both C{scalar}, see U{GeodSolve 

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

40 ''' 

41 # from GeodSolve --help option -f ... lat1 lon1 azi1 lat2 lon2 azi2 s12 a12 m12 M12 M21 S12 

42 _Names_ = (_lat1_, _lon1_, _azi1_, _lat2_, _lon2_, _azi2_, _s12_, _a12_, _m12_, _M12_, _M21_, _S12_) 

43 _Units_ = (_Lat, _Lon, _Azi, _Lat, _Lon, _Azi, _M, _Deg, _Pass, _Pass, _Pass, _M2) 

44 

45 

46class _GeodesicSolveBase(_SolveBase): 

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

48 ''' 

49 _Error = GeodesicError 

50 _Names_Direct = \ 

51 _Names_Inverse = GeodSolve12Tuple._Names_ 

52 _Solve_name = 'GeodSolve' 

53 _Solve_path = _getenv(_PYGEODESY_GEODSOLVE_, _PYGEODESY_GEODSOLVE_) 

54 

55 @Property_RO 

56 def _b_option(self): 

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

58 

59 @Property_RO 

60 def _cmdBasic(self): 

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

62 ''' 

63 return (self.GeodSolve,) + self._b_option \ 

64 + self._e_option \ 

65 + self._E_option \ 

66 + self._p_option \ 

67 + self._u_option + ('-f',) 

68 

69 @Property_RO 

70 def _E_option(self): 

71 return ('-E',) if self.Exact else () 

72 

73 @Property 

74 def GeodSolve(self): 

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

76 executable (C{filename}). 

77 ''' 

78 return self._Solve_path 

79 

80 @GeodSolve.setter # PYCHOK setter! 

81 def GeodSolve(self, path): 

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

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

84 

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

86 isn't the C{GeodSolve} executable. 

87 ''' 

88 self._setSolve(path) 

89 

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

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

92 

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

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

95 (0..9) and the C{sep}arator string to join. Trailing 

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

97 1 and above, but kept for negative B{C{prec}} values. 

98 

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

100 ''' 

101 return _SolveBase._toStr(self, GeodSolve=self.GeodSolve, **prec_sep) 

102 

103 @Property_RO 

104 def _u_option(self): 

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

106 

107 

108class GeodesicSolve(_GeodesicSolveBase): 

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

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

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

112 

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

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

115 

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

117 executable for I{every} method call. 

118 ''' 

119 

120 def Area(self, polyline=False, name=NN): 

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

122 perimeter of a polygon. 

123 

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

125 area and perimeter (C{bool}). 

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

127 

128 @return: A L{GeodesicAreaExact} instance. 

129 

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

131 to the returned L{GeodesicAreaExact} instance. 

132 ''' 

133 gaX = _MODS.geodesicx.GeodesicAreaExact(self, polyline=polyline, 

134 name=name or self.name) 

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

136 gaX.verbose = True 

137 return gaX 

138 

139 Polygon = Area # for C{geographiclib} compatibility 

140 

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

142 '''Return the destination lat, lon and reverse azimuth 

143 (final bearing) in C{degrees}. 

144 

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

146 ''' 

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

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

149 iteration=r._iteration) 

150 

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

152 '''(INTERNAL) Short-cut version. 

153 ''' 

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

155 

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

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

158 on a single geodesic. 

159 

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

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

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

163 @kwarg caps_name: Bit-or'ed combination of L{Caps} values specifying 

164 the capabilities the L{GeodesicLineSolve} instance should 

165 possess, C{caps=Caps.ALL} always. 

166 

167 @return: A L{GeodesicLineSolve} instance. 

168 

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

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

171 the limit C{ε → 0+}. 

172 

173 @see: C++ U{GeodesicExact.Line 

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

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

176 ''' 

177 return GeodesicLineSolve(self, lat1, lon1, azi1, **_xkwds(caps_name, name=self.name)) 

178 

179 Line = DirectLine 

180 

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

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

183 ''' 

184 if wrap: 

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

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

187 

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

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

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

191 

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

193 ''' 

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

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

196 iteration=r._iteration) 

197 

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

199 '''(INTERNAL) Short-cut version. 

200 ''' 

201 if wrap: 

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

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

204 

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

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

207 on a single geodesic. 

208 

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

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

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

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

213 @kwarg caps_name: Bit-or'ed combination of L{Caps} values specifying 

214 the capabilities the L{GeodesicLineSolve} instance should 

215 possess, C{caps=Caps.ALL} always. 

216 

217 @return: A L{GeodesicLineSolve} instance. 

218 

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

220 

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

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

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

224 ''' 

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

226 return GeodesicLineSolve(self, lat1, lon1, r.azi1, **_xkwds(caps_name, name=self.name)) 

227 

228 

229class GeodesicLineSolve(_GeodesicSolveBase, _SolveLineBase): 

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

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

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

233 

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

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

236 

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

238 executable for I{every} method call. 

239 ''' 

240 

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

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

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

244 

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

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

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

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

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

250 the capabilities the L{GeodesicLineSolve} instance 

251 should possess, always C{Caps.ALL}. Use C{Caps.LINE_OFF} 

252 if updates to the B{C{geodesic}} should I{not} be 

253 reflected in this L{GeodesicLineSolve} instance. 

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

255 

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

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

258 property C{geodesic.GeodSolve}. 

259 

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

261 ''' 

262 _xinstanceof(GeodesicSolve, geodesic=geodesic) 

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

264 geodesic = geodesic.copy(deep=False, name=NN(_UNDER_, geodesic.name)) 

265 _SolveLineBase.__init__(self, geodesic, lat1, lon1, caps, name, azi1=azi1) 

266 try: 

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

268 except GeodesicError: 

269 pass 

270 

271 def ArcPosition(self, a12, outmask=_UNUSED_): # PYCHOK unused 

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, True, self._Names_Direct, a12) 

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

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

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

307 

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

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

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

311 

312 def Position(self, s12, outmask=_UNUSED_): # PYCHOK unused 

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

314 

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

316 

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

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

319 ''' 

320 return self._GDictInvoke(self._cmdDistance, True, self._Names_Direct, s12) 

321 

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

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

324 

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

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

327 (0..9) and the C{sep}arator string to join. Trailing 

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

329 1 and above, but kept for negative B{C{prec}} values. 

330 

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

332 ''' 

333 return _SolveLineBase._toStr(self, azi1=self.azi1, geodesic=self._solve, 

334 GeodSolve=self.GeodSolve, **prec_sep) 

335 

336 

337__all__ += _ALL_DOCS(_GeodesicSolveBase) 

338 

339if __name__ == '__main__': 

340 

341 from sys import argv 

342 

343 gS = GeodesicSolve(name='Test') 

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

345 

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

347 gS.GeodSolve = '/opt/local/bin/GeodSolve' # '/opt/local/Cellar/geographiclib/1.51/bin/GeodSolve' # HomeBrew 

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

349 

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

351 printf('Direct: %r', r, nl=1) 

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

353 

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

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

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

357 

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

359 p = glS.Position(5.5e6) 

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

361 p = glS.ArcPosition(49.475527) 

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

363 

364# % python3 -m pygeodesy.geodsolve 

365 

366# version: /opt/local/bin/GeodSolve: GeographicLib version 1.51 

367 

368# version: /opt/local/bin/GeodSolve: GeographicLib version 1.51 

369 

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

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

372 

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

374# Inverse1: 49.94131021789904 

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

376 

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

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

379 

380 

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

382 

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

384# GeodesicSolve 'Test' 1: /opt/local/bin/GeodSolve: GeographicLib version 1.51 (0) 

385# version: /opt/local/bin/GeodSolve: GeographicLib version 1.51 

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

387# 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) 

388 

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

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

391# 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) 

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

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

394# 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) 

395 

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

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

398# 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) 

399# Inverse1: 49.94131021789904 

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

401# 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) 

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

403 

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

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

406 

407 

408# **) MIT License 

409# 

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

411# 

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

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

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

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

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

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

418# 

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

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

421# 

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

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

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

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

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

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

428# OTHER DEALINGS IN THE SOFTWARE.