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 _llz2line, _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__ = '24.07.09' 

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 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} values specifying the capabilities the 

196 L{GeodesicLineSolve} instance should possess. 

197 

198 @return: A L{GeodesicLineSolve} instance. 

199 

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

201 

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

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

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

205 ''' 

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

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

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

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

210 return _llz2line(gl, lat2=lat2, lon2=lon2, azi2=r.azi2) 

211 

212 

213class GeodesicLineSolve(_GeodesicSolveBase, _SolveGDictLineBase): 

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

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

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

217 

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

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

220 

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

222 executable for I{every} method call. 

223 ''' 

224 _a13 = \ 

225 _s13 = NAN # see GeodesicSolve._InverseLine 

226 

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

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

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

230 

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

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

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

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

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

236 capabilities the L{GeodesicLineSolve} instance should possess, 

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

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

239 this L{GeodesicLineSolve} instance. 

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

241 

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

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

244 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): 

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 unused 

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): 

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): 

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 

363 and 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 

388if __name__ == '__main__': 

389 

390 from pygeodesy import printf 

391 from sys import argv 

392 

393 gS = GeodesicSolve(name='Test') 

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

395 

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

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

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

399 

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

401 printf('Direct: %r', r, nl=1) 

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

403 

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

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

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

407 

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

409 p = glS.Position(5.5e6) 

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

411 p = glS.ArcPosition(49.475527) 

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

413 

414 

415# % python3 -m pygeodesy.geodsolve 

416 

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

418 

419# 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) 

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

421 

422# 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) 

423# Inverse1: 49.94131021789904 

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

425 

426# 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) 

427# 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) 

428 

429 

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

431 

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

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

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

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

436# 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) 

437 

438# 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) 

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

440# 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) 

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

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

443# 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) 

444 

445# 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) 

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

447# 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) 

448# Inverse1: 49.94131021789904 

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

450# 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) 

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

452 

453# 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) 

454# 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) 

455 

456# **) MIT License 

457# 

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

459# 

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

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

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

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

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

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

466# 

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

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

469# 

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

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

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

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

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

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

476# OTHER DEALINGS IN THE SOFTWARE.