Coverage for pygeodesy/geodsolve.py: 88%
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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__ = '24.10.14'
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 _InverseLine2(self, lat1, lon1, lat2, lon2, **caps_name): # in .geodesici
185# '''(INTERNAL) Helper for L{InverseLine} and L{_InverseLine}.
186# '''
187# r = self.Inverse(lat1, lon1, lat2, lon2)
188# gl = GeodesicLineSolve(self, lat1, lon1, r.azi1, **_name1__(caps_name, _or_nameof=self))
189# gl._a13 = r.a12 # gl.SetArc(r.a12)
190# gl._s13 = r.s12 # gl.SetDistance(r.s12)
191# return gl, r
193 def InverseLine(self, lat1, lon1, lat2, lon2, **caps_name): # PYCHOK no cover
194 '''Set up a L{GeodesicLineSolve} to compute several points
195 on a single geodesic.
197 @arg lat1: Latitude of the first point (C{degrees}).
198 @arg lon1: Longitude of the first point (C{degrees}).
199 @arg lat2: Latitude of the second point (C{degrees}).
200 @arg lon2: Longitude of the second point (C{degrees}).
201 @kwarg caps_name: Optional C{B{name}=NN} (C{str}) and keyword
202 argument C{B{caps}=Caps.ALL}, bit-or'ed combination
203 of L{Caps} values specifying the capabilities the
204 L{GeodesicLineSolve} instance should possess.
206 @return: A L{GeodesicLineSolve} instance.
208 @note: Both B{C{lat1}} and B{C{lat2}} should in the range C{[-90, +90]}.
210 @see: C++ U{GeodesicExact.InverseLine
211 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicExact.html>} and
212 Python U{Geodesic.InverseLine<https://GeographicLib.SourceForge.io/Python/doc/code.html>}.
213 '''
214 r = self.Inverse(lat1, lon1, lat2, lon2)
215 gl = GeodesicLineSolve(self, lat1, lon1, r.azi1, **_name1__(caps_name, _or_nameof=self))
216 gl._a13 = r.a12 # gl.SetArc(r.a12)
217 gl._s13 = r.s12 # gl.SetDistance(r.s12)
218 return gl
221class GeodesicLineSolve(_GeodesicSolveBase, _SolveGDictLineBase):
222 '''Wrapper to invoke I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
223 as an C{Exact} version of I{Karney}'s Python class U{GeodesicLine<https://GeographicLib.SourceForge.io/C++/doc/
224 python/code.html#geographiclib.geodesicline.GeodesicLine>}.
226 @note: Use property C{GeodSolve} or env variable C{PYGEODESY_GEODSOLVE} to specify the (fully
227 qualified) path to the C{GeodSolve} executable.
229 @note: This C{geodesic} is intended I{for testing purposes only}, it invokes the C{GeodSolve}
230 executable for I{every} method call.
231 '''
232 _a13 = \
233 _s13 = NAN # see GeodesicSolve._InverseLine
235 def __init__(self, geodesic, lat1, lon1, azi1, caps=Caps.ALL, **name):
236 '''New L{GeodesicLineSolve} instance, allowing points to be found along
237 a geodesic starting at C{(B{lat1}, B{lon1})} with azimuth B{C{azi1}}.
239 @arg geodesic: The geodesic to use (L{GeodesicSolve}).
240 @arg lat1: Latitude of the first point (C{degrees}).
241 @arg lon1: Longitude of the first point (C{degrees}).
242 @arg azi1: Azimuth at the first points (compass C{degrees}).
243 @kwarg caps: Bit-or'ed combination of L{Caps} values specifying the
244 capabilities the L{GeodesicLineSolve} instance should possess,
245 C{B{caps}=Caps.ALL} always. Include C{Caps.LINE_OFF} if
246 updates to the B{C{geodesic}} should I{not} be reflected in
247 this L{GeodesicLineSolve} instance.
248 @kwarg name: Optional C{B{name}=NN} (C{str}).
250 @raise GeodesicError: Invalid path for the C{GeodSolve} executable
251 or isn't the C{GeodSolve} executable, see
252 property C{geodesic.GeodSolve}.
254 @raise TypeError: Invalid B{C{geodesic}}.
255 '''
256 _xinstanceof(GeodesicSolve, geodesic=geodesic)
257 if (caps & Caps.LINE_OFF): # copy to avoid updates
258 geodesic = geodesic.copy(deep=False, name=_UNDER_(NN, geodesic.name)) # NOT _under!
259 _SolveGDictLineBase.__init__(self, geodesic, lat1, lon1, caps, azi1=azi1, **name)
260 try:
261 self.GeodSolve = geodesic.GeodSolve # geodesic or copy of geodesic
262 except GeodesicError:
263 pass
265 @Property_RO
266 def a13(self):
267 '''Get the arc length to reference point 3 (C{degrees}).
269 @see: Methods L{Arc} and L{SetArc}.
270 '''
271 return self._a13
273 def Arc(self):
274 '''Return the arc length to reference point 3 (C{degrees} or C{NAN}).
276 @see: Method L{SetArc} and property L{a13}.
277 '''
278 return self.a13
280 def ArcPosition(self, a12, outmask=Caps.STANDARD): # PYCHOK unused
281 '''Find the position on the line given B{C{a12}}.
283 @arg a12: Spherical arc length from the first point to the
284 second point (C{degrees}).
286 @return: A C{GDict} with 12 items C{lat1, lon1, azi1, lat2, lon2,
287 azi2, m12, a12, s12, M12, M21, S12}.
288 '''
289 return self._GDictInvoke(self._cmdArc, self._Names_Direct, a12)._unCaps(outmask)
291 @Property_RO
292 def azi1(self):
293 '''Get the azimuth at the first point (compass C{degrees}).
294 '''
295 return self._lla1.azi1
297 azi12 = azi1 # like RhumbLineSolve
299 @Property_RO
300 def azi1_sincos2(self):
301 '''Get the sine and cosine of the first point's azimuth (2-tuple C{(sin, cos)}).
302 '''
303 return _sincos2d(self.azi1)
305 azi12_sincos2 = azi1_sincos2
307 @Property_RO
308 def _cmdArc(self):
309 '''(INTERNAL) Get the C{GeodSolve} I{-a -L} cmd (C{tuple}).
310 '''
311 return self._cmdDistance + ('-a',)
313 def Distance(self):
314 '''Return the distance to reference point 3 (C{meter} or C{NAN}).
315 '''
316 return self.s13
318 @property_RO
319 def geodesic(self):
320 '''Get the geodesic (L{GeodesicSolve}).
321 '''
322 return self._solve # see .solveBase._SolveLineBase
324 def Intersecant2(self, lat0, lon0, radius, **kwds): # PYCHOK no cover
325 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
326 self._notImplemented(lat0, lon0, radius, **kwds)
328 def PlumbTo(self, lat0, lon0, **kwds): # PYCHOK no cover
329 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
330 self._notImplemented(lat0, lon0, **kwds)
332 def Position(self, s12, outmask=Caps.STANDARD):
333 '''Find the position on the line given B{C{s12}}.
335 @arg s12: Distance from the first point to the second (C{meter}).
337 @return: A C{GDict} with 12 items C{lat1, lon1, azi1, lat2, lon2,
338 azi2, m12, a12, s12, M12, M21, S12}, possibly C{a12=NAN}.
339 '''
340 return self._GDictInvoke(self._cmdDistance, self._Names_Direct, s12)._unCaps(outmask)
342 @Property_RO
343 def s13(self):
344 '''Get the distance to reference point 3 (C{meter} or C{NAN}).
346 @see: Methods L{Distance} and L{SetDistance}.
347 '''
348 return self._s13
350 def SetArc(self, a13):
351 '''Set reference point 3 in terms relative to the first point.
353 @arg a13: Spherical arc length from the first to the reference
354 point (C{degrees}).
356 @return: The distance C{s13} (C{meter}) between the first and
357 the reference point or C{NAN}.
358 '''
359 if self._a13 != a13:
360 self._a13 = a13
361 self._s13 = self.ArcPosition(a13, outmask=Caps.DISTANCE).s12 # if a13 else _0_0
362# _update_all(self)
363 return self._s13
365 def SetDistance(self, s13):
366 '''Set reference point 3 in terms relative to the first point.
368 @arg s13: Distance from the first to the reference point (C{meter}).
370 @return: The arc length C{a13} (C{degrees}) between the first
371 and the reference point or C{NAN}.
372 '''
373 if self._s13 != s13:
374 self._s13 = s13
375 self._a13 = self.Position(s13, outmask=Caps.DISTANCE).a12 if s13 else _0_0
376# _update_all(self)
377 return self._a13 # NAN for GeodesicLineExact without Cap.DISTANCE_IN
379 def toStr(self, **prec_sep): # PYCHOK signature
380 '''Return this C{GeodesicLineSolve} as string.
382 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}
383 for the C{float} C{prec}ision, number of decimal digits
384 (0..9) and the C{sep}arator string to join. Trailing
385 zero decimals are stripped for B{C{prec}} values of 1
386 and above, but kept for negative B{C{prec}} values.
388 @return: GeodesicLineSolve items (C{str}).
389 '''
390 return _SolveGDictLineBase._toStr(self, azi1=self.azi1, geodesic=self._solve,
391 GeodSolve=self.GeodSolve, **prec_sep)
394__all__ += _ALL_DOCS(_GeodesicSolveBase)
396if __name__ == '__main__':
398 def _main():
399 from pygeodesy import printf
400 from sys import argv
402 gS = GeodesicSolve(name='Test')
403 gS.verbose = '--verbose' in argv # or '-v' in argv
405 if not _Xables.X_OK(gS.GeodSolve): # not set
406 gS.GeodSolve = _Xables.GeodSolve(_Xables.bin_)
407 printf('version: %s', gS.version)
409 r = gS.Direct(40.6, -73.8, 51, 5.5e6)
410 printf('Direct: %r', r, nl=1)
411 printf('Direct3: %r', gS.Direct3(40.6, -73.8, 51, 5.5e6))
413 printf('Inverse: %r', gS.Inverse( 40.6, -73.8, 51.6, -0.5), nl=1)
414 printf('Inverse1: %r', gS.Inverse1(40.6, -73.8, 51.6, -0.5))
415 printf('Inverse3: %r', gS.Inverse3(40.6, -73.8, 51.6, -0.5))
417 glS = GeodesicLineSolve(gS, 40.6, -73.8, 51, name='LineTest')
418 p = glS.Position(5.5e6)
419 printf('Position: %5s %r', p == r, p, nl=1)
420 p = glS.ArcPosition(49.475527)
421 printf('ArcPosition: %5s %r', p == r, p)
423 _main()
425# % python3 -m pygeodesy.geodsolve
427# version: /opt/local/bin/GeodSolve: GeographicLib version 2.2
429# 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)
430# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
432# 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)
433# Inverse1: 49.94131021789904
434# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
436# 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)
437# 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)
440# % python3 -m pygeodesy.geodsolve
442# version: /opt/local/bin/GeodSolve: GeographicLib version 2.3
444# 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)
445# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
447# 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)
448# Inverse1: 49.94131021789904
449# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
451# 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)
452# 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)
455# % python3 -m pygeodesy.geodsolve --verbose
457# GeodesicSolve 'Test' 1: /opt/local/bin/GeodSolve --version (invoke)
458# GeodesicSolve 'Test' 1: /opt/local/bin/GeodSolve: GeographicLib version 2.2 (0)
459# version: /opt/local/bin/GeodSolve: GeographicLib version 2.2
460# GeodesicSolve 'Test' 2: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct)
461# 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)
463# 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)
464# GeodesicSolve 'Test' 3: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct3)
465# 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)
466# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
467# GeodesicSolve 'Test' 4: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse)
468# 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)
470# 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)
471# GeodesicSolve 'Test' 5: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse1)
472# 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)
473# Inverse1: 49.94131021789904
474# GeodesicSolve 'Test' 6: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse3)
475# 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)
476# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
478# 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)
479# 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)
482# % python3 -m pygeodesy.geodsolve --verbose
484# GeodesicSolve 'Test'@1: /opt/local/bin/GeodSolve --version (invoke)
485# GeodesicSolve 'Test'@1: '/opt/local/bin/GeodSolve: GeographicLib version 2.3' (0, stdout/-err)
486# GeodesicSolve 'Test'@1: /opt/local/bin/GeodSolve: GeographicLib version 2.3 (0)
487# version: /opt/local/bin/GeodSolve: GeographicLib version 2.3
488# GeodesicSolve 'Test'@2: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct)
489# 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)
490# 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)
492# 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)
493# GeodesicSolve 'Test'@3: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct3)
494# 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)
495# 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)
496# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
497# GeodesicSolve 'Test'@4: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse)
498# 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)
499# 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)
501# 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)
502# GeodesicSolve 'Test'@5: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse1)
503# 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)
504# 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)
505# Inverse1: 49.94131021789904
506# GeodesicSolve 'Test'@6: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse3)
507# 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)
508# 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)
509# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
511# 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)
512# 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)
514# **) MIT License
515#
516# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
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518# Permission is hereby granted, free of charge, to any person obtaining a
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524#
525# The above copyright notice and this permission notice shall be included
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529# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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