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 

15from pygeodesy.interns import NN, _a12_, _azi1_, _azi2_, \ 

16 _lat1_, _lat2_, _lon1_, _lon2_, _m12_, \ 

17 _M12_, _M21_, _s12_, _S12_, _UNDER_ 

18from pygeodesy.interns import _UNUSED_, _not_ # PYCHOK used! 

19from pygeodesy.karney import _Azi, Caps, _Deg, GeodesicError, _GTuple, \ 

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

21from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, \ 

22 _PYGEODESY_GEODSOLVE_, _getenv, printf 

23from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple 

24from pygeodesy.props import Property, Property_RO 

25from pygeodesy.solveBase import _SolveBase, _SolveLineBase 

26from pygeodesy.utily import _unrollon, _Wrap, wrap360 

27 

28__all__ = _ALL_LAZY.geodsolve 

29__version__ = '24.04.07' 

30 

31 

32class GeodSolve12Tuple(_GTuple): 

33 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with 

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

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

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

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

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

39 ''' 

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

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

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

43 

44 

45class _GeodesicSolveBase(_SolveBase): 

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

47 ''' 

48 _Error = GeodesicError 

49 _Names_Direct = \ 

50 _Names_Inverse = GeodSolve12Tuple._Names_ 

51 _Solve_name = 'GeodSolve' 

52 _Solve_path = _getenv(_PYGEODESY_GEODSOLVE_, _PYGEODESY_GEODSOLVE_) 

53 

54 @Property_RO 

55 def _b_option(self): 

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

57 

58 @Property_RO 

59 def _cmdBasic(self): 

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

61 ''' 

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

63 + self._e_option \ 

64 + self._E_option \ 

65 + self._p_option \ 

66 + self._u_option + ('-f',) 

67 

68 @Property_RO 

69 def _E_option(self): 

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

71 

72 @Property 

73 def GeodSolve(self): 

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

75 executable (C{filename}). 

76 ''' 

77 return self._Solve_path 

78 

79 @GeodSolve.setter # PYCHOK setter! 

80 def GeodSolve(self, path): 

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

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

83 

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

85 isn't the C{GeodSolve} executable. 

86 ''' 

87 self._setSolve(path) 

88 

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

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

91 

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

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

94 (0..9) and the C{sep}arator string to join. Trailing 

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

96 1 and above, but kept for negative B{C{prec}} values. 

97 

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

99 ''' 

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

101 

102 @Property_RO 

103 def _u_option(self): 

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

105 

106 

107class GeodesicSolve(_GeodesicSolveBase): 

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

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

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

111 

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

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

114 

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

116 executable for I{every} method call. 

117 ''' 

118 

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

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

121 perimeter of a polygon. 

122 

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

124 area and perimeter (C{bool}). 

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

126 

127 @return: A L{GeodesicAreaExact} instance. 

128 

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

130 to the returned L{GeodesicAreaExact} instance. 

131 ''' 

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

133 name=name or self.name) 

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

135 gaX.verbose = True 

136 return gaX 

137 

138 Polygon = Area # for C{geographiclib} compatibility 

139 

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

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

142 (final bearing) in C{degrees}. 

143 

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

145 ''' 

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

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

148 iteration=r._iteration) 

149 

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

151 '''(INTERNAL) Short-cut version. 

152 ''' 

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

154 

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

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

157 on a single geodesic. 

158 

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

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

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

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

163 the capabilities the L{GeodesicLineSolve} instance should 

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

165 

166 @return: A L{GeodesicLineSolve} instance. 

167 

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

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

170 the limit C{ε → 0+}. 

171 

172 @see: C++ U{GeodesicExact.Line 

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

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

175 ''' 

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

177 

178 Line = DirectLine 

179 

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

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

182 ''' 

183 if wrap: 

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

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

186 

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

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

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

190 

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

192 ''' 

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

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

195 iteration=r._iteration) 

196 

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

198 '''(INTERNAL) Short-cut version. 

199 ''' 

200 if wrap: 

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

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

203 

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

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

206 on a single geodesic. 

207 

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

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

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

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

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

213 the capabilities the L{GeodesicLineSolve} instance should 

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

215 

216 @return: A L{GeodesicLineSolve} instance. 

217 

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

219 

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

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

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

223 ''' 

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

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

226 

227 

228class GeodesicLineSolve(_GeodesicSolveBase, _SolveLineBase): 

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

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

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

232 

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

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

235 

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

237 executable for I{every} method call. 

238 ''' 

239 

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

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

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

243 

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

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

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

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

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

249 the capabilities the L{GeodesicLineSolve} instance 

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

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

252 reflected in this L{GeodesicLineSolve} instance. 

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

254 

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

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

257 property C{geodesic.GeodSolve}. 

258 

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

260 ''' 

261 _xinstanceof(GeodesicSolve, geodesic=geodesic) 

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

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

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

265 try: 

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

267 except GeodesicError: 

268 pass 

269 

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

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

272 

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

274 second point (C{degrees}). 

275 

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

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

278 ''' 

279 return self._GDictInvoke(self._cmdArc, True, self._Names_Direct, a12) 

280 

281 @Property_RO 

282 def azi1(self): 

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

284 ''' 

285 return self._lla1.azi1 

286 

287 azi12 = azi1 # like RhumbLineSolve 

288 

289 @Property_RO 

290 def azi1_sincos2(self): 

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

292 ''' 

293 return _sincos2d(self.azi1) 

294 

295 azi12_sincos2 = azi1_sincos2 

296 

297 @Property_RO 

298 def _cmdArc(self): 

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

300 ''' 

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

302 

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

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

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

306 

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

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

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

310 

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

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

313 

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

315 

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

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

318 ''' 

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

320 

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

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

323 

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

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

326 (0..9) and the C{sep}arator string to join. Trailing 

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

328 1 and above, but kept for negative B{C{prec}} values. 

329 

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

331 ''' 

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

333 GeodSolve=self.GeodSolve, **prec_sep) 

334 

335 

336__all__ += _ALL_DOCS(_GeodesicSolveBase) 

337 

338if __name__ == '__main__': 

339 

340 from sys import argv 

341 

342 gS = GeodesicSolve(name='Test') 

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

344 

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

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

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

348 

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

350 printf('Direct: %r', r, nl=1) 

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

352 

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

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

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

356 

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

358 p = glS.Position(5.5e6) 

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

360 p = glS.ArcPosition(49.475527) 

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

362 

363# % python3 -m pygeodesy.geodsolve 

364 

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

366 

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

368 

369# 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) 

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

371 

372# 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) 

373# Inverse1: 49.94131021789904 

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

375 

376# 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) 

377# 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) 

378 

379 

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

381 

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

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

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

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

386# 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) 

387 

388# 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) 

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

390# 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) 

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

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

393# 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) 

394 

395# 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) 

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

397# 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) 

398# Inverse1: 49.94131021789904 

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

400# 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) 

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

402 

403# 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) 

404# 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) 

405 

406 

407# **) MIT License 

408# 

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

410# 

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

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

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

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

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

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

417# 

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

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

420# 

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

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

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

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

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

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

427# OTHER DEALINGS IN THE SOFTWARE.