Coverage for pygeodesy/geodsolve.py: 84%
105 statements
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2# -*- coding: utf-8 -*-
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}.
8Set env variable C{PYGEODESY_GEODSOLVE} to the (fully qualified) path
9of the C{GeodSolve} executable.
10'''
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, _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, \
21 _0_0, NAN
22from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, \
23 _getenv, _PYGEODESY_GEODSOLVE_
24from pygeodesy.named import _name1__
25from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple
26from pygeodesy.props import Property, Property_RO, property_RO
27from pygeodesy.solveBase import _SolveBase, _SolveLineBase
28from pygeodesy.utily import _unrollon, _Wrap, wrap360
30__all__ = _ALL_LAZY.geodsolve
31__version__ = '24.06.26'
34class GeodSolve12Tuple(_GTuple):
35 '''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with
36 angles C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2} and C{azi2} and arc C{a12} all in
37 C{degrees}, initial C{azi1} and final C{azi2} forward azimuths, distance C{s12} and
38 reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and geodesic
39 scale factors C{M12} and C{M21}, both C{scalar}, see U{GeodSolve
40 <https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}.
41 '''
42 # from GeodSolve --help option -f ... lat1 lon1 azi1 lat2 lon2 azi2 s12 a12 m12 M12 M21 S12
43 _Names_ = (_lat1_, _lon1_, _azi1_, _lat2_, _lon2_, _azi2_, _s12_, _a12_, _m12_, _M12_, _M21_, _S12_)
44 _Units_ = (_Lat, _Lon, _Azi, _Lat, _Lon, _Azi, _M, _Deg, _Pass, _Pass, _Pass, _M2)
47class _GeodesicSolveBase(_SolveBase):
48 '''(INTERNAL) Base class for L{GeodesicSolve} and L{GeodesicLineSolve}.
49 '''
50 _Error = GeodesicError
51 _Names_Direct = \
52 _Names_Inverse = GeodSolve12Tuple._Names_
53 _Solve_name = 'GeodSolve'
54 _Solve_path = _getenv(_PYGEODESY_GEODSOLVE_, _PYGEODESY_GEODSOLVE_)
56 @Property_RO
57 def _b_option(self):
58 return ('-b',) if self.reverse2 else ()
60 @Property_RO
61 def _cmdBasic(self):
62 '''(INTERNAL) Get the basic C{GeodSolve} cmd (C{tuple}).
63 '''
64 return (self.GeodSolve, '-f') + (self._b_option +
65 self._e_option +
66 self._E_option +
67 self._p_option +
68 self._u_option)
70 @Property_RO
71 def _E_option(self):
72 return ('-E',) if self.Exact else ()
74 @Property
75 def GeodSolve(self):
76 '''Get the U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
77 executable (C{filename}).
78 '''
79 return self._Solve_path
81 @GeodSolve.setter # PYCHOK setter!
82 def GeodSolve(self, path):
83 '''Set the U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
84 executable (C{filename}), the (fully qualified) path to the C{GeodSolve} executable.
86 @raise GeodesicError: Invalid B{C{path}}, B{C{path}} doesn't exist or
87 isn't the C{GeodSolve} executable.
88 '''
89 self._setSolve(path)
91 def toStr(self, **prec_sep): # PYCHOK signature
92 '''Return this C{GeodesicSolve} as string.
94 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=', '}
95 for the C{float} C{prec}ision, number of decimal digits
96 (0..9) and the C{sep}arator string to join. Trailing
97 zero decimals are stripped for B{C{prec}} values of
98 1 and above, but kept for negative B{C{prec}} values.
100 @return: GeodesicSolve items (C{str}).
101 '''
102 return _SolveBase._toStr(self, GeodSolve=self.GeodSolve, **prec_sep)
104 @Property_RO
105 def _u_option(self):
106 return ('-u',) if self.unroll else ()
109class GeodesicSolve(_GeodesicSolveBase):
110 '''Wrapper to invoke I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
111 as an C{Exact} version of I{Karney}'s Python class U{Geodesic<https://GeographicLib.SourceForge.io/C++/doc/
112 python/code.html#geographiclib.geodesic.Geodesic>}.
114 @note: Use property C{GeodSolve} or env variable C{PYGEODESY_GEODSOLVE} to specify the (fully
115 qualified) path to the C{GeodSolve} executable.
117 @note: This C{geodesic} is intended I{for testing purposes only}, it invokes the C{GeodSolve}
118 executable for I{every} method call.
119 '''
121 def Area(self, polyline=False, **name):
122 '''Set up a L{GeodesicAreaExact} to compute area and
123 perimeter of a polygon.
125 @kwarg polyline: If C{True} perimeter only, otherwise
126 area and perimeter (C{bool}).
127 @kwarg name: Optional C{B{name}=NN} (C{str}).
129 @return: A L{GeodesicAreaExact} instance.
131 @note: The B{C{debug}} setting is passed as C{verbose}
132 to the returned L{GeodesicAreaExact} instance.
133 '''
134 gaX = _MODS.geodesicx.GeodesicAreaExact(self, polyline=polyline, **name)
135 if self.verbose or self.debug: # PYCHOK no cover
136 gaX.verbose = True
137 return gaX
139 Polygon = Area # for C{geographiclib} compatibility
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}.
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)
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)
156 def DirectLine(self, lat1, lon1, azi1, **caps_name):
157 '''Set up a L{GeodesicLineSolve} to compute several points
158 on a single geodesic.
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: Optional C{B{name}=NN} (C{str}) and keyword
164 argument C{B{caps}=Caps.ALL}, bit-or'ed combination
165 of L{Caps} values specifying the capabilities the
166 L{GeodesicLineSolve} instance should possess.
168 @return: A L{GeodesicLineSolve} instance.
170 @note: If the point is at a pole, the azimuth is defined by keeping
171 B{C{lon1}} fixed, writing C{B{lat1} = ±(90 − ε)}, and taking
172 the limit C{ε → 0+}.
174 @see: C++ U{GeodesicExact.Line
175 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicExact.html>}
176 and Python U{Geodesic.Line<https://GeographicLib.SourceForge.io/Python/doc/code.html>}.
177 '''
178 return GeodesicLineSolve(self, lat1, lon1, azi1, **_name1__(caps_name, _or_nameof=self))
180 Line = DirectLine
182 def _Inverse(self, ll1, ll2, wrap, **outmask): # PYCHOK no cover
183 '''(INTERNAL) Short-cut version, see .ellipsoidalBaseDI.intersecant2.
184 '''
185 if wrap:
186 ll2 = _unrollon(ll1, _Wrap.point(ll2))
187 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask)
189 def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask
190 '''Return the distance in C{meter} and the forward and
191 reverse azimuths (initial and final bearing) in C{degrees}.
193 @return: L{Distance3Tuple}C{(distance, initial, final)}.
194 '''
195 r = self._GDictInverse(lat1, lon1, lat2, lon2, floats=False)
196 return Distance3Tuple(float(r.s12), wrap360(r.azi1), wrap360(r.azi2),
197 iteration=r._iteration)
199 def _InverseLine(self, ll1, ll2, wrap, **caps_name): # PYCHOK no cover
200 '''(INTERNAL) Short-cut version.
201 '''
202 if wrap:
203 ll2 = _unrollon(ll1, _Wrap.point(ll2))
204 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name)
206 def InverseLine(self, lat1, lon1, lat2, lon2, **caps_name): # PYCHOK no cover
207 '''Set up a L{GeodesicLineSolve} to compute several points
208 on a single geodesic.
210 @arg lat1: Latitude of the first point (C{degrees}).
211 @arg lon1: Longitude of the first point (C{degrees}).
212 @arg lat2: Latitude of the second point (C{degrees}).
213 @arg lon2: Longitude of the second point (C{degrees}).
214 @kwarg caps_name: Optional C{B{name}=NN} (C{str}) and keyword
215 argument C{B{caps}=Caps.ALL}, bit-or'ed combination
216 of L{Caps} values specifying the capabilities the
217 L{GeodesicLineSolve} instance should possess.
219 @return: A L{GeodesicLineSolve} instance.
221 @note: Both B{C{lat1}} and B{C{lat2}} should in the range C{[-90, +90]}.
223 @see: C++ U{GeodesicExact.InverseLine
224 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicExact.html>} and
225 Python U{Geodesic.InverseLine<https://GeographicLib.SourceForge.io/Python/doc/code.html>}.
226 '''
227 r = self.Inverse(lat1, lon1, lat2, lon2)
228 gl = GeodesicLineSolve(self, lat1, lon1, r.azi1, **_name1__(caps_name, _or_nameof=self))
229 gl._a13 = r.a12 # gl.SetArc(r.a12)
230 gl._s13 = r.s12 # gl.SetDistance(r.s12)
231 return gl
234class GeodesicLineSolve(_GeodesicSolveBase, _SolveLineBase):
235 '''Wrapper to invoke I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
236 as an C{Exact} version of I{Karney}'s Python class U{GeodesicLine<https://GeographicLib.SourceForge.io/C++/doc/
237 python/code.html#geographiclib.geodesicline.GeodesicLine>}.
239 @note: Use property C{GeodSolve} or env variable C{PYGEODESY_GEODSOLVE} to specify the (fully
240 qualified) path to the C{GeodSolve} executable.
242 @note: This C{geodesic} is intended I{for testing purposes only}, it invokes the C{GeodSolve}
243 executable for I{every} method call.
244 '''
245 _a13 = \
246 _s13 = NAN # see GeodesicSolve._InverseLine
248 def __init__(self, geodesic, lat1, lon1, azi1, caps=Caps.ALL, **name):
249 '''New L{GeodesicLineSolve} instance, allowing points to be found along
250 a geodesic starting at C{(B{lat1}, B{lon1})} with azimuth B{C{azi1}}.
252 @arg geodesic: The geodesic to use (L{GeodesicSolve}).
253 @arg lat1: Latitude of the first point (C{degrees}).
254 @arg lon1: Longitude of the first point (C{degrees}).
255 @arg azi1: Azimuth at the first points (compass C{degrees}).
256 @kwarg caps: Bit-or'ed combination of L{Caps} values specifying the
257 capabilities the L{GeodesicLineSolve} instance should possess,
258 C{B{caps}=Caps.ALL} always. Include C{Caps.LINE_OFF} if
259 updates to the B{C{geodesic}} should I{not} be reflected in
260 this L{GeodesicLineSolve} instance.
261 @kwarg name: Optional C{B{name}=NN} (C{str}).
263 @raise GeodesicError: Invalid path for the C{GeodSolve} executable
264 or isn't the C{GeodSolve} executable, see
265 property C{geodesic.GeodSolve}.
267 @raise TypeError: Invalid B{C{geodesic}}.
268 '''
269 _xinstanceof(GeodesicSolve, geodesic=geodesic)
270 if (caps & Caps.LINE_OFF): # copy to avoid updates
271 geodesic = geodesic.copy(deep=False, name=_UNDER_(NN, geodesic.name)) # NOT _under!
272 _SolveLineBase.__init__(self, geodesic, lat1, lon1, caps, azi1=azi1, **name)
273 try:
274 self.GeodSolve = geodesic.GeodSolve # geodesic or copy of geodesic
275 except GeodesicError:
276 pass
278 @Property_RO
279 def a13(self):
280 '''Get the arc length to reference point 3 (C{degrees}).
282 @see: Methods L{Arc} and L{SetArc}.
283 '''
284 return self._a13
286 def Arc(self):
287 '''Return the arc length to reference point 3 (C{degrees} or C{NAN}).
289 @see: Method L{SetArc} and property L{a13}.
290 '''
291 return self.a13
293 def ArcPosition(self, a12, outmask=Caps.STANDARD): # PYCHOK unused
294 '''Find the position on the line given B{C{a12}}.
296 @arg a12: Spherical arc length from the first point to the
297 second point (C{degrees}).
299 @return: A C{GDict} with 12 items C{lat1, lon1, azi1, lat2, lon2,
300 azi2, m12, a12, s12, M12, M21, S12}.
301 '''
302 return self._GDictInvoke(self._cmdArc, True, self._Names_Direct, a12)._unCaps(outmask)
304 @Property_RO
305 def azi1(self):
306 '''Get the azimuth at the first point (compass C{degrees}).
307 '''
308 return self._lla1.azi1
310 azi12 = azi1 # like RhumbLineSolve
312 @Property_RO
313 def azi1_sincos2(self):
314 '''Get the sine and cosine of the first point's azimuth (2-tuple C{(sin, cos)}).
315 '''
316 return _sincos2d(self.azi1)
318 azi12_sincos2 = azi1_sincos2
320 @Property_RO
321 def _cmdArc(self):
322 '''(INTERNAL) Get the C{GeodSolve} I{-a -L} cmd (C{tuple}).
323 '''
324 return self._cmdDistance + ('-a',)
326 def Distance(self):
327 '''Return the distance to reference point 3 (C{meter} or C{NAN}).
328 '''
329 return self.s13
331 @property_RO
332 def geodesic(self):
333 '''Get the geodesic (L{GeodesicSolve}).
334 '''
335 return self._solve # see .solveBase._SolveLineBase
337 def Intersecant2(self, lat0, lon0, radius, **kwds): # PYCHOK no cover
338 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
339 self._notImplemented(lat0, lon0, radius, **kwds)
341 def PlumbTo(self, lat0, lon0, **kwds): # PYCHOK no cover
342 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
343 self._notImplemented(lat0, lon0, **kwds)
345 def Position(self, s12, outmask=Caps.STANDARD):
346 '''Find the position on the line given B{C{s12}}.
348 @arg s12: Distance from the first point to the second (C{meter}).
350 @return: A C{GDict} with 12 items C{lat1, lon1, azi1, lat2, lon2,
351 azi2, m12, a12, s12, M12, M21, S12}, possibly C{a12=NAN}.
352 '''
353 return self._GDictInvoke(self._cmdDistance, True, self._Names_Direct, s12)._unCaps(outmask)
355 @Property_RO
356 def s13(self):
357 '''Get the distance to reference point 3 (C{meter} or C{NAN}).
359 @see: Methods L{Distance} and L{SetDistance}.
360 '''
361 return self._s13
363 def SetArc(self, a13):
364 '''Set reference point 3 in terms relative to the first point.
366 @arg a13: Spherical arc length from the first to the reference
367 point (C{degrees}).
369 @return: The distance C{s13} (C{meter}) between the first and
370 the reference point or C{NAN}.
371 '''
372 if self._a13 != a13:
373 self._a13 = a13
374 self._s13 = self.ArcPosition(a13, outmask=Caps.DISTANCE).s12 # if a13 else _0_0
375# _update_all(self)
376 return self._s13
378 def SetDistance(self, s13):
379 '''Set reference point 3 in terms relative to the first point.
381 @arg s13: Distance from the first to the reference point (C{meter}).
383 @return: The arc length C{a13} (C{degrees}) between the first
384 and the reference point or C{NAN}.
385 '''
386 if self._s13 != s13:
387 self._s13 = s13
388 self._a13 = self.Position(s13, outmask=Caps.DISTANCE).a12 if s13 else _0_0
389# _update_all(self)
390 return self._a13 # NAN for GeodesicLineExact without Cap.DISTANCE_IN
392 def toStr(self, **prec_sep): # PYCHOK signature
393 '''Return this C{GeodesicLineSolve} as string.
395 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=', '}
396 for the C{float} C{prec}ision, number of decimal digits
397 (0..9) and the C{sep}arator string to join. Trailing
398 zero decimals are stripped for B{C{prec}} values of
399 1 and above, but kept for negative B{C{prec}} values.
401 @return: GeodesicLineSolve items (C{str}).
402 '''
403 return _SolveLineBase._toStr(self, azi1=self.azi1, geodesic=self._solve,
404 GeodSolve=self.GeodSolve, **prec_sep)
407__all__ += _ALL_DOCS(_GeodesicSolveBase)
409if __name__ == '__main__':
411 from pygeodesy import printf
412 from sys import argv
414 gS = GeodesicSolve(name='Test')
415 gS.verbose = '--verbose' in argv # or '-v' in argv
417 if gS.GeodSolve in (_PYGEODESY_GEODSOLVE_, None): # not set
418 gS.GeodSolve = '/opt/local/bin/GeodSolve' # '/opt/local/Cellar/geographiclib/1.51/bin/GeodSolve' # HomeBrew
419 printf('version: %s', gS.version)
421 r = gS.Direct(40.6, -73.8, 51, 5.5e6)
422 printf('Direct: %r', r, nl=1)
423 printf('Direct3: %r', gS.Direct3(40.6, -73.8, 51, 5.5e6))
425 printf('Inverse: %r', gS.Inverse( 40.6, -73.8, 51.6, -0.5), nl=1)
426 printf('Inverse1: %r', gS.Inverse1(40.6, -73.8, 51.6, -0.5))
427 printf('Inverse3: %r', gS.Inverse3(40.6, -73.8, 51.6, -0.5))
429 glS = GeodesicLineSolve(gS, 40.6, -73.8, 51, name='LineTest')
430 p = glS.Position(5.5e6)
431 printf('Position: %s %r', p == r, p, nl=1)
432 p = glS.ArcPosition(49.475527)
433 printf('ArcPosition: %s %r', p == r, p)
436# % python3 -m pygeodesy.geodsolve
438# version: /opt/local/bin/GeodSolve: GeographicLib version 2.2
440# 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)
441# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
443# 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)
444# Inverse1: 49.94131021789904
445# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
447# 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)
448# 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)
451# % python3 -m pygeodesy.geodsolve --verbose
453# GeodesicSolve 'Test' 1: /opt/local/bin/GeodSolve --version (invoke)
454# GeodesicSolve 'Test' 1: /opt/local/bin/GeodSolve: GeographicLib version 2.2 (0)
455# version: /opt/local/bin/GeodSolve: GeographicLib version 2.2
456# GeodesicSolve 'Test' 2: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct)
457# 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)
459# 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)
460# GeodesicSolve 'Test' 3: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct3)
461# 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)
462# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
463# GeodesicSolve 'Test' 4: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse)
464# 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)
466# 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)
467# GeodesicSolve 'Test' 5: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse1)
468# 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)
469# Inverse1: 49.94131021789904
470# GeodesicSolve 'Test' 6: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse3)
471# 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)
472# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
474# 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)
475# 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)
477# **) MIT License
478#
479# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
480#
481# Permission is hereby granted, free of charge, to any person obtaining a
482# copy of this software and associated documentation files (the "Software"),
483# to deal in the Software without restriction, including without limitation
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485# and/or sell copies of the Software, and to permit persons to whom the
486# Software is furnished to do so, subject to the following conditions:
487#
488# The above copyright notice and this permission notice shall be included
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492# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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