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, _0_0, NAN
18from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, \
19 _getenv, _PYGEODESY_GEODSOLVE_
20from pygeodesy.named import _name1__
21from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple
22from pygeodesy.props import Property, Property_RO, property_RO
23from pygeodesy.solveBase import _SolveGDictBase, _SolveGDictLineBase
24from pygeodesy.utily import _unrollon, _Wrap, wrap360
26__all__ = _ALL_LAZY.geodsolve
27__version__ = '24.07.11'
30class _GeodesicSolveBase(_SolveGDictBase):
31 '''(INTERNAL) Base class for L{GeodesicSolve} and L{GeodesicLineSolve}.
32 '''
33 _Error = GeodesicError
34 _Names_Direct = \
35 _Names_Inverse = GeodSolve12Tuple._Names_
36 _Xable_name = 'GeodSolve'
37 _Xable_path = _getenv(_PYGEODESY_GEODSOLVE_, _PYGEODESY_GEODSOLVE_)
39 @Property_RO
40 def _b_option(self):
41 return ('-b',) if self.reverse2 else ()
43 @Property_RO
44 def _cmdBasic(self):
45 '''(INTERNAL) Get the basic C{GeodSolve} cmd (C{tuple}).
46 '''
47 return (self.GeodSolve, '-f') + (self._b_option +
48 self._e_option +
49 self._E_option +
50 self._p_option +
51 self._u_option)
53 @Property
54 def GeodSolve(self):
55 '''Get the U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
56 executable (C{filename}).
57 '''
58 return self._Xable_path
60 @GeodSolve.setter # PYCHOK setter!
61 def GeodSolve(self, path):
62 '''Set the U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
63 executable (C{filename}), the (fully qualified) path to the C{GeodSolve} executable.
65 @raise GeodesicError: Invalid B{C{path}}, B{C{path}} doesn't exist or
66 isn't the C{GeodSolve} executable.
67 '''
68 self._setXable(path)
70 def toStr(self, **prec_sep): # PYCHOK signature
71 '''Return this C{GeodesicSolve} as string.
73 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}
74 for the C{float} C{prec}ision, number of decimal digits
75 (0..9) and the C{sep}arator string to join. Trailing
76 zero decimals are stripped for B{C{prec}} values of 1
77 and above, but kept for negative B{C{prec}} values.
79 @return: GeodesicSolve items (C{str}).
80 '''
81 return _SolveGDictBase._toStr(self, GeodSolve=self.GeodSolve, **prec_sep)
83 @Property_RO
84 def _u_option(self):
85 return ('-u',) if self.unroll else ()
88class GeodesicSolve(_GeodesicSolveBase):
89 '''Wrapper to invoke I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
90 as an C{Exact} version of I{Karney}'s Python class U{Geodesic<https://GeographicLib.SourceForge.io/C++/doc/
91 python/code.html#geographiclib.geodesic.Geodesic>}.
93 @note: Use property C{GeodSolve} or env variable C{PYGEODESY_GEODSOLVE} to specify the (fully
94 qualified) path to the C{GeodSolve} executable.
96 @note: This C{geodesic} is intended I{for testing purposes only}, it invokes the C{GeodSolve}
97 executable for I{every} method call.
98 '''
100 def Area(self, polyline=False, **name):
101 '''Set up a L{GeodesicAreaExact} to compute area and perimeter
102 of a polygon.
104 @kwarg polyline: If C{True} perimeter only, otherwise area
105 and perimeter (C{bool}).
106 @kwarg name: Optional C{B{name}=NN} (C{str}).
108 @return: A L{GeodesicAreaExact} instance.
110 @note: The B{C{debug}} setting is passed as C{verbose}
111 to the returned L{GeodesicAreaExact} instance.
112 '''
113 gaX = _MODS.geodesicx.GeodesicAreaExact(self, polyline=polyline, **name)
114 if self.verbose or self.debug: # PYCHOK no cover
115 gaX.verbose = True
116 return gaX
118 Polygon = Area # for C{geographiclib} compatibility
120 def Direct3(self, lat1, lon1, azi1, s12): # PYCHOK outmask
121 '''Return the destination lat, lon and reverse azimuth (final bearing)
122 in C{degrees}.
124 @return: L{Destination3Tuple}C{(lat, lon, final)}.
125 '''
126 r = self._GDictDirect(lat1, lon1, azi1, False, s12, floats=False)
127 return Destination3Tuple(float(r.lat2), float(r.lon2), wrap360(r.azi2),
128 iteration=r._iteration)
130 def _DirectLine(self, ll1, azi12, **caps_name): # PYCHOK no cover
131 '''(INTERNAL) Short-cut version.
132 '''
133 return self.DirectLine(ll1.lat, ll1.lon, azi12, **caps_name)
135 def DirectLine(self, lat1, lon1, azi1, **caps_name):
136 '''Set up a L{GeodesicLineSolve} to compute several points
137 on a single geodesic.
139 @arg lat1: Latitude of the first point (C{degrees}).
140 @arg lon1: Longitude of the first point (C{degrees}).
141 @arg azi1: Azimuth at the first point (compass C{degrees}).
142 @kwarg caps_name: Optional C{B{name}=NN} (C{str}) and keyword
143 argument C{B{caps}=Caps.ALL}, bit-or'ed combination
144 of L{Caps} values specifying the capabilities the
145 L{GeodesicLineSolve} instance should possess.
147 @return: A L{GeodesicLineSolve} instance.
149 @note: If the point is at a pole, the azimuth is defined by keeping
150 B{C{lon1}} fixed, writing C{B{lat1} = ±(90 − ε)}, and taking
151 the limit C{ε → 0+}.
153 @see: C++ U{GeodesicExact.Line
154 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicExact.html>}
155 and Python U{Geodesic.Line<https://GeographicLib.SourceForge.io/Python/doc/code.html>}.
156 '''
157 return GeodesicLineSolve(self, lat1, lon1, azi1, **_name1__(caps_name, _or_nameof=self))
159 Line = DirectLine
161 def _Inverse(self, ll1, ll2, wrap, **outmask): # PYCHOK no cover
162 '''(INTERNAL) Short-cut version, see .ellipsoidalBaseDI.intersecant2.
163 '''
164 if wrap:
165 ll2 = _unrollon(ll1, _Wrap.point(ll2))
166 return self.Inverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **outmask)
168 def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask
169 '''Return the distance in C{meter} and the forward and
170 reverse azimuths (initial and final bearing) in C{degrees}.
172 @return: L{Distance3Tuple}C{(distance, initial, final)}.
173 '''
174 r = self._GDictInverse(lat1, lon1, lat2, lon2, floats=False)
175 return Distance3Tuple(float(r.s12), wrap360(r.azi1), wrap360(r.azi2),
176 iteration=r._iteration)
178 def _InverseLine(self, ll1, ll2, wrap, **caps_name): # PYCHOK no cover
179 '''(INTERNAL) Short-cut version.
180 '''
181 if wrap:
182 ll2 = _unrollon(ll1, _Wrap.point(ll2))
183 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **caps_name)
185# def _InverseLine2(self, lat1, lon1, lat2, lon2, **caps_name): # in .geodesici
186# '''(INTERNAL) Helper for L{InverseLine} and L{_InverseLine}.
187# '''
188# r = self.Inverse(lat1, lon1, lat2, lon2)
189# gl = GeodesicLineSolve(self, lat1, lon1, r.azi1, **_name1__(caps_name, _or_nameof=self))
190# gl._a13 = r.a12 # gl.SetArc(r.a12)
191# gl._s13 = r.s12 # gl.SetDistance(r.s12)
192# return gl, r
194 def InverseLine(self, lat1, lon1, lat2, lon2, **caps_name): # PYCHOK no cover
195 '''Set up a L{GeodesicLineSolve} to compute several points
196 on a single geodesic.
198 @arg lat1: Latitude of the first point (C{degrees}).
199 @arg lon1: Longitude of the first point (C{degrees}).
200 @arg lat2: Latitude of the second point (C{degrees}).
201 @arg lon2: Longitude of the second point (C{degrees}).
202 @kwarg caps_name: Optional C{B{name}=NN} (C{str}) and keyword
203 argument C{B{caps}=Caps.ALL}, bit-or'ed combination
204 of L{Caps} values specifying the capabilities the
205 L{GeodesicLineSolve} instance should possess.
207 @return: A L{GeodesicLineSolve} instance.
209 @note: Both B{C{lat1}} and B{C{lat2}} should in the range C{[-90, +90]}.
211 @see: C++ U{GeodesicExact.InverseLine
212 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicExact.html>} and
213 Python U{Geodesic.InverseLine<https://GeographicLib.SourceForge.io/Python/doc/code.html>}.
214 '''
215 r = self.Inverse(lat1, lon1, lat2, lon2)
216 gl = GeodesicLineSolve(self, lat1, lon1, r.azi1, **_name1__(caps_name, _or_nameof=self))
217 gl._a13 = r.a12 # gl.SetArc(r.a12)
218 gl._s13 = r.s12 # gl.SetDistance(r.s12)
219 return gl
222class GeodesicLineSolve(_GeodesicSolveBase, _SolveGDictLineBase):
223 '''Wrapper to invoke I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>}
224 as an C{Exact} version of I{Karney}'s Python class U{GeodesicLine<https://GeographicLib.SourceForge.io/C++/doc/
225 python/code.html#geographiclib.geodesicline.GeodesicLine>}.
227 @note: Use property C{GeodSolve} or env variable C{PYGEODESY_GEODSOLVE} to specify the (fully
228 qualified) path to the C{GeodSolve} executable.
230 @note: This C{geodesic} is intended I{for testing purposes only}, it invokes the C{GeodSolve}
231 executable for I{every} method call.
232 '''
233 _a13 = \
234 _s13 = NAN # see GeodesicSolve._InverseLine
236 def __init__(self, geodesic, lat1, lon1, azi1, caps=Caps.ALL, **name):
237 '''New L{GeodesicLineSolve} instance, allowing points to be found along
238 a geodesic starting at C{(B{lat1}, B{lon1})} with azimuth B{C{azi1}}.
240 @arg geodesic: The geodesic to use (L{GeodesicSolve}).
241 @arg lat1: Latitude of the first point (C{degrees}).
242 @arg lon1: Longitude of the first point (C{degrees}).
243 @arg azi1: Azimuth at the first points (compass C{degrees}).
244 @kwarg caps: Bit-or'ed combination of L{Caps} values specifying the
245 capabilities the L{GeodesicLineSolve} instance should possess,
246 C{B{caps}=Caps.ALL} always. Include C{Caps.LINE_OFF} if
247 updates to the B{C{geodesic}} should I{not} be reflected in
248 this L{GeodesicLineSolve} instance.
249 @kwarg name: Optional C{B{name}=NN} (C{str}).
251 @raise GeodesicError: Invalid path for the C{GeodSolve} executable
252 or isn't the C{GeodSolve} executable, see
253 property C{geodesic.GeodSolve}.
255 @raise TypeError: Invalid B{C{geodesic}}.
256 '''
257 _xinstanceof(GeodesicSolve, geodesic=geodesic)
258 if (caps & Caps.LINE_OFF): # copy to avoid updates
259 geodesic = geodesic.copy(deep=False, name=_UNDER_(NN, geodesic.name)) # NOT _under!
260 _SolveGDictLineBase.__init__(self, geodesic, lat1, lon1, caps, azi1=azi1, **name)
261 try:
262 self.GeodSolve = geodesic.GeodSolve # geodesic or copy of geodesic
263 except GeodesicError:
264 pass
266 @Property_RO
267 def a13(self):
268 '''Get the arc length to reference point 3 (C{degrees}).
270 @see: Methods L{Arc} and L{SetArc}.
271 '''
272 return self._a13
274 def Arc(self):
275 '''Return the arc length to reference point 3 (C{degrees} or C{NAN}).
277 @see: Method L{SetArc} and property L{a13}.
278 '''
279 return self.a13
281 def ArcPosition(self, a12, outmask=Caps.STANDARD): # PYCHOK unused
282 '''Find the position on the line given B{C{a12}}.
284 @arg a12: Spherical arc length from the first point to the
285 second point (C{degrees}).
287 @return: A C{GDict} with 12 items C{lat1, lon1, azi1, lat2, lon2,
288 azi2, m12, a12, s12, M12, M21, S12}.
289 '''
290 return self._GDictInvoke(self._cmdArc, self._Names_Direct, a12)._unCaps(outmask)
292 @Property_RO
293 def azi1(self):
294 '''Get the azimuth at the first point (compass C{degrees}).
295 '''
296 return self._lla1.azi1
298 azi12 = azi1 # like RhumbLineSolve
300 @Property_RO
301 def azi1_sincos2(self):
302 '''Get the sine and cosine of the first point's azimuth (2-tuple C{(sin, cos)}).
303 '''
304 return _sincos2d(self.azi1)
306 azi12_sincos2 = azi1_sincos2
308 @Property_RO
309 def _cmdArc(self):
310 '''(INTERNAL) Get the C{GeodSolve} I{-a -L} cmd (C{tuple}).
311 '''
312 return self._cmdDistance + ('-a',)
314 def Distance(self):
315 '''Return the distance to reference point 3 (C{meter} or C{NAN}).
316 '''
317 return self.s13
319 @property_RO
320 def geodesic(self):
321 '''Get the geodesic (L{GeodesicSolve}).
322 '''
323 return self._solve # see .solveBase._SolveLineBase
325 def Intersecant2(self, lat0, lon0, radius, **kwds): # PYCHOK no cover
326 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
327 self._notImplemented(lat0, lon0, radius, **kwds)
329 def PlumbTo(self, lat0, lon0, **kwds): # PYCHOK no cover
330 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
331 self._notImplemented(lat0, lon0, **kwds)
333 def Position(self, s12, outmask=Caps.STANDARD):
334 '''Find the position on the line given B{C{s12}}.
336 @arg s12: Distance from the first point to the second (C{meter}).
338 @return: A C{GDict} with 12 items C{lat1, lon1, azi1, lat2, lon2,
339 azi2, m12, a12, s12, M12, M21, S12}, possibly C{a12=NAN}.
340 '''
341 return self._GDictInvoke(self._cmdDistance, self._Names_Direct, s12)._unCaps(outmask)
343 @Property_RO
344 def s13(self):
345 '''Get the distance to reference point 3 (C{meter} or C{NAN}).
347 @see: Methods L{Distance} and L{SetDistance}.
348 '''
349 return self._s13
351 def SetArc(self, a13):
352 '''Set reference point 3 in terms relative to the first point.
354 @arg a13: Spherical arc length from the first to the reference
355 point (C{degrees}).
357 @return: The distance C{s13} (C{meter}) between the first and
358 the reference point or C{NAN}.
359 '''
360 if self._a13 != a13:
361 self._a13 = a13
362 self._s13 = self.ArcPosition(a13, outmask=Caps.DISTANCE).s12 # if a13 else _0_0
363# _update_all(self)
364 return self._s13
366 def SetDistance(self, s13):
367 '''Set reference point 3 in terms relative to the first point.
369 @arg s13: Distance from the first to the reference point (C{meter}).
371 @return: The arc length C{a13} (C{degrees}) between the first
372 and the reference point or C{NAN}.
373 '''
374 if self._s13 != s13:
375 self._s13 = s13
376 self._a13 = self.Position(s13, outmask=Caps.DISTANCE).a12 if s13 else _0_0
377# _update_all(self)
378 return self._a13 # NAN for GeodesicLineExact without Cap.DISTANCE_IN
380 def toStr(self, **prec_sep): # PYCHOK signature
381 '''Return this C{GeodesicLineSolve} as string.
383 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}
384 for the C{float} C{prec}ision, number of decimal digits
385 (0..9) and the C{sep}arator string to join. Trailing
386 zero decimals are stripped for B{C{prec}} values of 1
387 and above, but kept for negative B{C{prec}} values.
389 @return: GeodesicLineSolve items (C{str}).
390 '''
391 return _SolveGDictLineBase._toStr(self, azi1=self.azi1, geodesic=self._solve,
392 GeodSolve=self.GeodSolve, **prec_sep)
395__all__ += _ALL_DOCS(_GeodesicSolveBase)
397if __name__ == '__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 gS.GeodSolve in (_PYGEODESY_GEODSOLVE_, None): # not set
406 gS.GeodSolve = '/opt/local/bin/GeodSolve' # '/opt/local/Cellar/geographiclib/2.3/bin/GeodSolve' # HomeBrew
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: %s %r', p == r, p, nl=1)
420 p = glS.ArcPosition(49.475527)
421 printf('ArcPosition: %s %r', p == r, p)
424# % python3 -m pygeodesy.geodsolve
426# version: /opt/local/bin/GeodSolve: GeographicLib version 2.2
428# 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)
429# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
431# 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)
432# Inverse1: 49.94131021789904
433# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
435# 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)
436# 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)
439# % python3 -m pygeodesy.geodsolve --verbose
441# GeodesicSolve 'Test' 1: /opt/local/bin/GeodSolve --version (invoke)
442# GeodesicSolve 'Test' 1: /opt/local/bin/GeodSolve: GeographicLib version 2.2 (0)
443# version: /opt/local/bin/GeodSolve: GeographicLib version 2.2
444# GeodesicSolve 'Test' 2: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct)
445# 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)
447# 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)
448# GeodesicSolve 'Test' 3: /opt/local/bin/GeodSolve -f -E -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct3)
449# 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)
450# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397)
451# GeodesicSolve 'Test' 4: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse)
452# 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)
454# 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)
455# GeodesicSolve 'Test' 5: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse1)
456# 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)
457# Inverse1: 49.94131021789904
458# GeodesicSolve 'Test' 6: /opt/local/bin/GeodSolve -f -E -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse3)
459# 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)
460# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777)
462# 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)
463# 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)
465# **) MIT License
466#
467# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
468#
469# Permission is hereby granted, free of charge, to any person obtaining a
470# copy of this software and associated documentation files (the "Software"),
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474# Software is furnished to do so, subject to the following conditions:
475#
476# The above copyright notice and this permission notice shall be included
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