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

13# from pygeodesy.geodesicx import GeodesicAreaExact # _MODS

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

15 _lat1_, _lat2_, _lon1_, _lon2_, _m12_, \

16 _M12_, _M21_, _s12_, _S12_, _UNDER_

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

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

19 _Pass, _Lat, _Lon, _M, _M2, _sincos2d

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

21 _getenv, _PYGEODESY_GEODSOLVE_

22 from pygeodesy.named import _name1__

23 from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple

24 from pygeodesy.props import Property, Property_RO

25 from pygeodesy.solveBase import _SolveBase, _SolveLineBase

26 from pygeodesy.utily import _unrollon, _Wrap, wrap360

27

28__all__ = _ALL_LAZY.geodsolve

29__version__ = '24.05.31'

30

31

32 class 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

45 class _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

107 class 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):

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 C{B{name}=NN} (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, **name)

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

134 gaX.verbose = True

135 return gaX

136

137 Polygon = Area # for C{geographiclib} compatibility

138

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

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

141 (final bearing) in C{degrees}.

142

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

144 '''

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

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

147 iteration=r._iteration)

148

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

150 '''(INTERNAL) Short-cut version.

151 '''

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

153

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

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

156 on a single geodesic.

157

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

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

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

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

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

163 of L{Caps} values specifying the capabilities the

164 L{GeodesicLineSolve} instance should possess.

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, **_name1__(caps_name, _or_nameof=self))

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: Optional C{B{name}=NN} (C{str}) and keyword

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

214 of L{Caps} values specifying the capabilities the

215 L{GeodesicLineSolve} instance should possess.

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, **_name1__(caps_name, _or_nameof=self))

227

228

229 class 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):

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 the

250 capabilities the L{GeodesicLineSolve} instance should possess,

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

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

253 this L{GeodesicLineSolve} instance.

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

255

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

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=_UNDER_(NN, geodesic.name)) # NOT _under!

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

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

339 if __name__ == '__main__':

340

341 from pygeodesy import printf

342 from sys import argv

343

344 gS = GeodesicSolve(name='Test')

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

346

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

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

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

350

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

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

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

354

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

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

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

358

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

360 p = glS.Position(5.5e6)

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

362 p = glS.ArcPosition(49.475527)

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

364

365# % python3 -m pygeodesy.geodsolve

366

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

368

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

370

371# 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)

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

373

374# 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)

375# Inverse1: 49.94131021789904

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

377

378# 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)

379# 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)

380

381

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

383

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

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

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

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

388# 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)

389

390# 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)

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

392# 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)

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

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

395# 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)

396

397# 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)

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

399# 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)

400# Inverse1: 49.94131021789904

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

402# 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)

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

404

405# 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)

406# 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)

407

408

409# **) MIT License

410#

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

412#

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

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

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

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

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

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

419#

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

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

422#

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

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

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

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

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

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

429# OTHER DEALINGS IN THE SOFTWARE.