Coverage for pygeodesy/geodsolve.py: 98%
83 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, _UNDER_
16from pygeodesy.karney import Caps, GeodesicError, GeodSolve12Tuple, \
17 _sincos2d, _Xables, _0_0, NAN
18from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
19from pygeodesy.named import _name1__
20from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple
21from pygeodesy.props import Property, Property_RO, property_RO
22from pygeodesy.solveBase import _SolveGDictBase, _SolveGDictLineBase
23from pygeodesy.utily import _unrollon, _Wrap, wrap360
25__all__ = _ALL_LAZY.geodsolve
26__version__ = '24.11.02'
29class _GeodesicSolveBase(_SolveGDictBase):
30 '''(INTERNAL) Base class for L{GeodesicSolve} and L{GeodesicLineSolve}.
31 '''
32 _Error = GeodesicError
33 _Names_Direct = \
34 _Names_Inverse = GeodSolve12Tuple._Names_
35 _Xable_name = _Xables.GeodSolve.__name__
36 _Xable_path = _Xables.GeodSolve()
38 @Property_RO
39 def _b_option(self):
40 return ('-b',) if self.reverse2 else ()
42 @Property_RO
43 def _cmdBasic(self):
44 '''(INTERNAL) Get the basic C{GeodSolve} cmd (C{tuple}).
45 '''
46 return (self.GeodSolve, '-f') + (self._b_option +
47 self._e_option +
48 self._E_option +
49 self._p_option +
50 self._u_option)
52 @Property
53 def GeodSolve(self):
54 '''Get the U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
55 executable (C{filename}).
56 '''
57 return self._Xable_path
59 @GeodSolve.setter # PYCHOK setter!
60 def GeodSolve(self, path):
61 '''Set the U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
62 executable (C{filename}), the (fully qualified) path to the C{GeodSolve} executable.
64 @raise GeodesicError: Invalid B{C{path}}, B{C{path}} doesn't exist or
65 isn't the C{GeodSolve} executable.
66 '''
67 self._setXable(path)
69 def toStr(self, **prec_sep): # PYCHOK signature
70 '''Return this C{GeodesicSolve} as string.
72 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}
73 for the C{float} C{prec}ision, number of decimal digits
74 (0..9) and the C{sep}arator string to join. Trailing
75 zero decimals are stripped for B{C{prec}} values of 1
76 and above, but kept for negative B{C{prec}} values.
78 @return: GeodesicSolve items (C{str}).
79 '''
80 return _SolveGDictBase._toStr(self, GeodSolve=self.GeodSolve, **prec_sep)
82 @Property_RO
83 def _u_option(self):
84 return ('-u',) if self.unroll else ()
87class GeodesicSolve(_GeodesicSolveBase):
88 '''Wrapper to invoke I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
89 as an C{Exact} version of I{Karney}'s Python class U{Geodesic<https://GeographicLib.SourceForge.io/C++/doc/
90 python/code.html#geographiclib.geodesic.Geodesic>}.
92 @note: Use property C{GeodSolve} or env variable C{PYGEODESY_GEODSOLVE} to specify the (fully
93 qualified) path to the C{GeodSolve} executable.
95 @note: This C{geodesic} is intended I{for testing purposes only}, it invokes the C{GeodSolve}
96 executable for I{every} method call.
97 '''
99 def Area(self, polyline=False, **name):
100 '''Set up a L{GeodesicAreaExact} to compute area and perimeter
101 of a polygon.
103 @kwarg polyline: If C{True}, compute the perimeter only, otherwise
104 perimeter and area (C{bool}).
105 @kwarg name: Optional C{B{name}=NN} (C{str}).
107 @return: A L{GeodesicAreaExact} instance.
109 @note: The B{C{debug}} setting is passed as C{verbose}
110 to the returned L{GeodesicAreaExact} instance.
111 '''
112 gaX = _MODS.geodesicx.GeodesicAreaExact(self, polyline=polyline, **name)
113 if self.verbose or self.debug: # PYCHOK no cover
114 gaX.verbose = True
115 return gaX
117 Polygon = Area # for C{geographiclib} compatibility
119 def Direct3(self, lat1, lon1, azi1, s12): # PYCHOK outmask
120 '''Return the destination lat, lon and reverse azimuth (final bearing)
121 in C{degrees}.
123 @return: L{Destination3Tuple}C{(lat, lon, final)}.
124 '''
125 r = self._GDictDirect(lat1, lon1, azi1, False, s12, floats=False)
126 return Destination3Tuple(float(r.lat2), float(r.lon2), wrap360(r.azi2),
127 iteration=r._iteration)
129 def _DirectLine(self, ll1, azi12, **caps_name): # PYCHOK no cover
130 '''(INTERNAL) Short-cut version.
131 '''
132 return self.DirectLine(ll1.lat, ll1.lon, azi12, **caps_name)
134 def DirectLine(self, lat1, lon1, azi1, **caps_name):
135 '''Set up a L{GeodesicLineSolve} to compute several points
136 on a single geodesic.
138 @arg lat1: Latitude of the first point (C{degrees}).
139 @arg lon1: Longitude of the first point (C{degrees}).
140 @arg azi1: Azimuth at the first point (compass C{degrees}).
141 @kwarg caps_name: Optional C{B{name}=NN} (C{str}) and keyword
142 argument C{B{caps}=Caps.ALL}, bit-or'ed combination
143 of L{Caps} values specifying the capabilities the
144 L{GeodesicLineSolve} instance should possess.
146 @return: A L{GeodesicLineSolve} instance.
148 @note: If the point is at a pole, the azimuth is defined by keeping
149 B{C{lon1}} fixed, writing C{B{lat1} = ±(90 − ε)}, and taking
150 the limit C{ε → 0+}.
152 @see: C++ U{GeodesicExact.Line
153 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicExact.html>}
154 and Python U{Geodesic.Line<https://GeographicLib.SourceForge.io/Python/doc/code.html>}.
155 '''
156 return GeodesicLineSolve(self, lat1, lon1, azi1, **_name1__(caps_name, _or_nameof=self))
158 Line = DirectLine
160 def _Inverse(self, ll1, ll2, wrap, **outmask): # PYCHOK no cover
161 '''(INTERNAL) Short-cut version, see .ellipsoidalBaseDI.intersecant2.
162 '''
163 if wrap:
164 ll2 = _unrollon(ll1, _Wrap.point(ll2))
165 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask)
167 def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask
168 '''Return the distance in C{meter} and the forward and
169 reverse azimuths (initial and final bearing) in C{degrees}.
171 @return: L{Distance3Tuple}C{(distance, initial, final)}.
172 '''
173 r = self._GDictInverse(lat1, lon1, lat2, lon2, floats=False)
174 return Distance3Tuple(float(r.s12), wrap360(r.azi1), wrap360(r.azi2),
175 iteration=r._iteration)
177 def _InverseLine(self, ll1, ll2, wrap, **caps_name): # PYCHOK no cover
178 '''(INTERNAL) Short-cut version.
179 '''
180 if wrap:
181 ll2 = _unrollon(ll1, _Wrap.point(ll2))
182 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name)
184 def InverseLine(self, lat1, lon1, lat2, lon2, **caps_name): # PYCHOK no cover
185 '''Set up a L{GeodesicLineSolve} to compute several points
186 on a single geodesic.
188 @arg lat1: Latitude of the first point (C{degrees}).
189 @arg lon1: Longitude of the first point (C{degrees}).
190 @arg lat2: Latitude of the second point (C{degrees}).
191 @arg lon2: Longitude of the second point (C{degrees}).
192 @kwarg caps_name: Optional C{B{name}=NN} (C{str}) and keyword
193 argument C{B{caps}=Caps.ALL}, bit-or'ed combination
194 of L{Caps} values specifying the capabilities the
195 L{GeodesicLineSolve} instance should possess.
197 @return: A L{GeodesicLineSolve} instance.
199 @note: Both B{C{lat1}} and B{C{lat2}} should in the range C{[-90, +90]}.
201 @see: C++ U{GeodesicExact.InverseLine
202 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicExact.html>} and
203 Python U{Geodesic.InverseLine<https://GeographicLib.SourceForge.io/Python/doc/code.html>}.
204 '''
205 r = self.Inverse(lat1, lon1, lat2, lon2)
206 gl = GeodesicLineSolve(self, lat1, lon1, r.azi1, **_name1__(caps_name, _or_nameof=self))
207 gl._a13 = r.a12 # gl.SetArc(r.a12)
208 gl._s13 = r.s12 # gl.SetDistance(r.s12)
209 return gl
212class GeodesicLineSolve(_GeodesicSolveBase, _SolveGDictLineBase):
213 '''Wrapper to invoke I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
214 as an C{Exact} version of I{Karney}'s Python class U{GeodesicLine<https://GeographicLib.SourceForge.io/C++/doc/
215 python/code.html#geographiclib.geodesicline.GeodesicLine>}.
217 @note: Use property C{GeodSolve} or env variable C{PYGEODESY_GEODSOLVE} to specify the (fully
218 qualified) path to the C{GeodSolve} executable.
220 @note: This C{geodesic} is intended I{for testing purposes only}, it invokes the C{GeodSolve}
221 executable for I{every} method call.
222 '''
223 _a13 = \
224 _s13 = NAN # see GeodesicSolve._InverseLine
226 def __init__(self, geodesic, lat1, lon1, azi1, caps=Caps.ALL, **name):
227 '''New L{GeodesicLineSolve} instance, allowing points to be found along
228 a geodesic starting at C{(B{lat1}, B{lon1})} with azimuth B{C{azi1}}.
230 @arg geodesic: The geodesic to use (L{GeodesicSolve}).
231 @arg lat1: Latitude of the first point (C{degrees}).
232 @arg lon1: Longitude of the first point (C{degrees}).
233 @arg azi1: Azimuth at the first points (compass C{degrees}).
234 @kwarg caps: Bit-or'ed combination of L{Caps} values specifying the
235 capabilities the L{GeodesicLineSolve} instance should possess,
236 C{B{caps}=Caps.ALL} always. Include C{Caps.LINE_OFF} if
237 updates to the B{C{geodesic}} should I{not} be reflected in
238 this L{GeodesicLineSolve} instance.
239 @kwarg name: Optional C{B{name}=NN} (C{str}).
241 @raise GeodesicError: Invalid path for the C{GeodSolve} executable
242 or isn't the C{GeodSolve} executable, see
243 property C{geodesic.GeodSolve}.
245 @raise TypeError: Invalid B{C{geodesic}}.
246 '''
247 _xinstanceof(GeodesicSolve, geodesic=geodesic)
248 if (caps & Caps.LINE_OFF): # copy to avoid updates
249 geodesic = geodesic.copy(deep=False, name=_UNDER_(NN, geodesic.name)) # NOT _under!
250 _SolveGDictLineBase.__init__(self, geodesic, lat1, lon1, caps, azi1=azi1, **name)
251 try:
252 self.GeodSolve = geodesic.GeodSolve # geodesic or copy of geodesic
253 except GeodesicError:
254 pass
256 @Property_RO
257 def a13(self):
258 '''Get the arc length to reference point 3 (C{degrees}).
260 @see: Methods L{Arc} and L{SetArc}.
261 '''
262 return self._a13
264 def Arc(self): # PYCHOK no cover
265 '''Return the arc length to reference point 3 (C{degrees} or C{NAN}).
267 @see: Method L{SetArc} and property L{a13}.
268 '''
269 return self.a13
271 def ArcPosition(self, a12, outmask=Caps.STANDARD): # PYCHOK no cover
272 '''Find the position on the line given B{C{a12}}.
274 @arg a12: Spherical arc length from the first point to the
275 second point (C{degrees}).
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, self._Names_Direct, a12)._unCaps(outmask)
282 @Property_RO
283 def azi1(self):
284 '''Get the azimuth at the first point (compass C{degrees}).
285 '''
286 return self._lla1.azi1
288 azi12 = azi1 # like RhumbLineSolve
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)
296 azi12_sincos2 = azi1_sincos2
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',)
304 def Distance(self):
305 '''Return the distance to reference point 3 (C{meter} or C{NAN}).
306 '''
307 return self.s13
309 @property_RO
310 def geodesic(self):
311 '''Get the geodesic (L{GeodesicSolve}).
312 '''
313 return self._solve # see .solveBase._SolveLineBase
315 def Intersecant2(self, lat0, lon0, radius, **kwds): # PYCHOK no cover
316 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
317 self._notImplemented(lat0, lon0, radius, **kwds)
319 def PlumbTo(self, lat0, lon0, **kwds): # PYCHOK no cover
320 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
321 self._notImplemented(lat0, lon0, **kwds)
323 def Position(self, s12, outmask=Caps.STANDARD):
324 '''Find the position on the line given B{C{s12}}.
326 @arg s12: Distance from the first point to the second (C{meter}).
328 @return: A C{GDict} with 12 items C{lat1, lon1, azi1, lat2, lon2,
329 azi2, m12, a12, s12, M12, M21, S12}, possibly C{a12=NAN}.
330 '''
331 return self._GDictInvoke(self._cmdDistance, self._Names_Direct, s12)._unCaps(outmask)
333 @Property_RO
334 def s13(self):
335 '''Get the distance to reference point 3 (C{meter} or C{NAN}).
337 @see: Methods L{Distance} and L{SetDistance}.
338 '''
339 return self._s13
341 def SetArc(self, a13): # PYCHOK no cover
342 '''Set reference point 3 in terms relative to the first point.
344 @arg a13: Spherical arc length from the first to the reference
345 point (C{degrees}).
347 @return: The distance C{s13} (C{meter}) between the first and
348 the reference point or C{NAN}.
349 '''
350 if self._a13 != a13:
351 self._a13 = a13
352 self._s13 = self.ArcPosition(a13, outmask=Caps.DISTANCE).s12 # if a13 else _0_0
353# _update_all(self)
354 return self._s13
356 def SetDistance(self, s13): # PYCHOK no cover
357 '''Set reference point 3 in terms relative to the first point.
359 @arg s13: Distance from the first to the reference point (C{meter}).
361 @return: The arc length C{a13} (C{degrees}) between the first and
362 the reference point or C{NAN}.
363 '''
364 if self._s13 != s13:
365 self._s13 = s13
366 self._a13 = self.Position(s13, outmask=Caps.DISTANCE).a12 if s13 else _0_0
367# _update_all(self)
368 return self._a13 # NAN for GeodesicLineExact without Cap.DISTANCE_IN
370 def toStr(self, **prec_sep): # PYCHOK signature
371 '''Return this C{GeodesicLineSolve} as string.
373 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}
374 for the C{float} C{prec}ision, number of decimal digits
375 (0..9) and the C{sep}arator string to join. Trailing
376 zero decimals are stripped for B{C{prec}} values of 1
377 and above, but kept for negative B{C{prec}} values.
379 @return: GeodesicLineSolve items (C{str}).
380 '''
381 return _SolveGDictLineBase._toStr(self, azi1=self.azi1, geodesic=self._solve,
382 GeodSolve=self.GeodSolve, **prec_sep)
385__all__ += _ALL_DOCS(_GeodesicSolveBase)
387if __name__ == '__main__':
389 def _main():
390 from pygeodesy import printf
391 from sys import argv
393 gS = GeodesicSolve(name='Test')
394 gS.verbose = '--verbose' in argv # or '-v' in argv
396 if not _Xables.X_OK(gS.GeodSolve): # not set
397 gS.GeodSolve = _Xables.GeodSolve(_Xables.bin_)
398 printf('version: %s', gS.version)
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))
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))
408 glS = GeodesicLineSolve(gS, 40.6, -73.8, 51, name='LineTest')
409 p = glS.Position(5.5e6)
410 printf('Position: %5s %r', p == r, p, nl=1)
411 p = glS.ArcPosition(49.475527)
412 printf('ArcPosition: %5s %r', p == r, p)
414 _main()
416# % python3 -m pygeodesy.geodsolve
418# version: /opt/local/bin/GeodSolve: GeographicLib version 2.2
420# 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)
421# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
423# 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)
424# Inverse1: 49.94131021789904
425# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
427# 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)
428# 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)
431# % python3 -m pygeodesy.geodsolve
433# version: /opt/local/bin/GeodSolve: GeographicLib version 2.3
435# 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=39735075134877.078125)
436# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
438# 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)
439# Inverse1: 49.94131021789904
440# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
442# Position: False GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141173, s12=5500000.0)
443# ArcPosition: False GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141174, s12=5499999.948497)
446# % python3 -m pygeodesy.geodsolve --verbose
448# GeodesicSolve 'Test' 1: /opt/local/bin/GeodSolve --version (invoke)
449# GeodesicSolve 'Test' 1: /opt/local/bin/GeodSolve: GeographicLib version 2.2 (0)
450# version: /opt/local/bin/GeodSolve: GeographicLib version 2.2
451# GeodesicSolve 'Test' 2: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct)
452# 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)
454# 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)
455# GeodesicSolve 'Test' 3: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct3)
456# 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)
457# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
458# GeodesicSolve 'Test' 4: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse)
459# 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)
461# 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)
462# GeodesicSolve 'Test' 5: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse1)
463# 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)
464# Inverse1: 49.94131021789904
465# GeodesicSolve 'Test' 6: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse3)
466# 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)
467# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
469# 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)
470# 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)
473# % python3 -m pygeodesy.geodsolve --verbose
475# GeodesicSolve 'Test'@1: /opt/local/bin/GeodSolve --version (invoke)
476# GeodesicSolve 'Test'@1: '/opt/local/bin/GeodSolve: GeographicLib version 2.3' (0, stdout/-err)
477# GeodesicSolve 'Test'@1: /opt/local/bin/GeodSolve: GeographicLib version 2.3 (0)
478# version: /opt/local/bin/GeodSolve: GeographicLib version 2.3
479# GeodesicSolve 'Test'@2: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct)
480# GeodesicSolve 'Test'@2: '40.600000000000001 -73.799999999999997 51.000000000000000 51.884564505606761 -1.141172861200843 107.189397162605871 5500000.0000000000 49.475527463251460 4844148.7031014860 0.65091056699808614 0.65122865892196569 39735075134877.078' (0, stdout/-err)
481# GeodesicSolve 'Test'@2: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.0, lat2=51.884564505606761, lon2=-1.141172861200843, azi2=107.189397162605871, s12=5500000.0, a12=49.47552746325146, m12=4844148.703101486, M12=0.65091056699808614, M21=0.65122865892196569, S12=39735075134877.078 (0)
483# 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=39735075134877.078125)
484# GeodesicSolve 'Test'@3: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct3)
485# GeodesicSolve 'Test'@3: '40.600000000000001 -73.799999999999997 51.000000000000000 51.884564505606761 -1.141172861200843 107.189397162605871 5500000.0000000000 49.475527463251460 4844148.7031014860 0.65091056699808614 0.65122865892196569 39735075134877.078' (0, stdout/-err)
486# GeodesicSolve 'Test'@3: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.0, lat2=51.884564505606761, lon2=-1.141172861200843, azi2=107.189397162605871, s12=5500000.0, a12=49.47552746325146, m12=4844148.703101486, M12=0.65091056699808614, M21=0.65122865892196569, S12=39735075134877.078 (0)
487# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
488# GeodesicSolve 'Test'@4: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse)
489# GeodesicSolve 'Test'@4: '40.600000000000001 -73.799999999999997 51.198882845579824 51.600000000000001 -0.500000000000000 107.821776735514248 5551759.4003186813 49.941310217899037 4877684.6027061967 0.64472969205948238 0.64504567852134398 40041368848742.531' (0, stdout/-err)
490# GeodesicSolve 'Test'@4: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.198882845579824, lat2=51.600000000000001, lon2=-0.5, azi2=107.821776735514248, s12=5551759.4003186813, a12=49.941310217899037, m12=4877684.6027061967, M12=0.64472969205948238, M21=0.64504567852134398, S12=40041368848742.531 (0)
492# 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)
493# GeodesicSolve 'Test'@5: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse1)
494# GeodesicSolve 'Test'@5: '40.600000000000001 -73.799999999999997 51.198882845579824 51.600000000000001 -0.500000000000000 107.821776735514248 5551759.4003186813 49.941310217899037 4877684.6027061967 0.64472969205948238 0.64504567852134398 40041368848742.531' (0, stdout/-err)
495# GeodesicSolve 'Test'@5: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.198882845579824, lat2=51.600000000000001, lon2=-0.5, azi2=107.821776735514248, s12=5551759.4003186813, a12=49.941310217899037, m12=4877684.6027061967, M12=0.64472969205948238, M21=0.64504567852134398, S12=40041368848742.531 (0)
496# Inverse1: 49.94131021789904
497# GeodesicSolve 'Test'@6: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse3)
498# GeodesicSolve 'Test'@6: '40.600000000000001 -73.799999999999997 51.198882845579824 51.600000000000001 -0.500000000000000 107.821776735514248 5551759.4003186813 49.941310217899037 4877684.6027061967 0.64472969205948238 0.64504567852134398 40041368848742.531' (0, stdout/-err)
499# GeodesicSolve 'Test'@6: lat1=40.600000000000001, lon1=-73.799999999999997, azi1=51.198882845579824, lat2=51.600000000000001, lon2=-0.5, azi2=107.821776735514248, s12=5551759.4003186813, a12=49.941310217899037, m12=4877684.6027061967, M12=0.64472969205948238, M21=0.64504567852134398, S12=40041368848742.531 (0)
500# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
502# Position: False GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141173, s12=5500000.0)
503# ArcPosition: False GDict(a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141174, s12=5499999.948497)
505# **) MIT License
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507# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
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