Coverage for pygeodesy/rhumb/solve.py: 93%
96 statements
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2# -*- coding: utf-8 -*-
4u'''Wrapper to invoke I{Karney}'s U{RhumbSolve
5<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>} utility
6as an (exact) rhumb or rhumb line from I{either GeographicLib 2.0 or 2.2+}.
8@note: Set env variable C{PYGEODESY_RHUMBSOLVE} to the (fully qualified)
9 path of the C{RhumbSolve} executable.
10'''
11from pygeodesy.basics import _xinstanceof
12from pygeodesy.constants import _0_0, _180_0, _N_180_0, _over, _90_0 # PYCHOK used!
13from pygeodesy.errors import RhumbError # PYCHOK used!
14from pygeodesy.interns import NN, _a12_, _azi12_, _DMAIN_, _lat2_, _lon2_, _s12_, \
15 _S12_, _UNDER_
16from pygeodesy.karney import Caps, GDict, _norm180, Rhumb8Tuple, _sincos2d, _Xables
17from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
18from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple
19from pygeodesy.props import deprecated_method, Property, Property_RO
20from pygeodesy.solveBase import _SolveGDictBase, _SolveGDictLineBase
21from pygeodesy.utily import _unrollon, _Wrap, wrap360
23__all__ = _ALL_LAZY.rhumb_solve
24__version__ = '25.04.12'
27class _RhumbSolveBase(_SolveGDictBase):
28 '''(INTERNAL) Base class for L{RhumbSolve} and L{RhumbLineSolve}.
29 '''
30 _Error = RhumbError
31 _Names_Direct = _lat2_, _lon2_, _S12_
32 _Names_Inverse = _azi12_, _s12_, _S12_
33 _Xable_name = _Xables.RhumbSolve.__name__ # typename
34 _Xable_path = _Xables.RhumbSolve()
36 @Property_RO
37 def _cmdBasic(self):
38 '''(INTERNAL) Get the basic C{RhumbSolve} cmd (C{tuple}).
39 '''
40 return (self.RhumbSolve,) + (self._e_option +
41 self._p_option +
42 self._s_option)
44 @Property
45 def RhumbSolve(self):
46 '''Get the U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}
47 executable (C{filename}).
48 '''
49 return self._Xable_path
51 @RhumbSolve.setter # PYCHOK setter!
52 def RhumbSolve(self, path):
53 '''Set the U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}
54 executable (C{filename}), the (fully qualified) path to the C{RhumbSolve} executable.
56 @raise RhumbError: Invalid B{C{path}}, B{C{path}} doesn't exist or isn't
57 the C{RhumbSolve} executable.
58 '''
59 self._setXable(path)
61 @Property_RO
62 def _s_option(self): # == not -E for GeodSolve
63 return () if self.Exact else ('-s',)
65 def toStr(self, **prec_sep): # PYCHOK signature
66 '''Return this C{RhumbSolve} as string.
68 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}
69 for the C{float} C{prec}ision, number of decimal digits
70 (0..9) and the C{sep}arator string to join. Trailing
71 zero decimals are stripped for B{C{prec}} values of 1
72 and above, but kept for negative B{C{prec}} values.
74 @return: RhumbSolve items (C{str}).
75 '''
76 return self._toStr(RhumbSolve=self.RhumbSolve, **prec_sep)
78# @Property_RO
79# def _u_option(self):
80# return '-u' if self.unroll else ()
83class RhumbSolve(_RhumbSolveBase):
84 '''Wrapper to invoke I{Karney}'s U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}
85 like a class, similar to L{pygeodesy.Rhumb} and L{pygeodesy.RhumbAux}.
87 @note: Use property C{RhumbSolve} or env variable C{PYGEODESY_RHUMBSOLVE} to specify the (fully
88 qualified) path to the C{RhumbSolve} executable.
90 @note: This C{rhumb} is intended I{for testing purposes only}, it invokes the C{RhumbSolve}
91 executable for I{every} method call.
92 '''
93# def Area(self, polyline=False, **name):
94# '''Set up a L{RhumbArea} to compute area and
95# perimeter of a polygon.
96#
97# @kwarg polyline: If C{True}, compute the perimeter only,
98# otherwise perimeter and area (C{bool}).
99# @kwarg name: Optional C{B{name}=NN} (C{str}).
100#
101# @return: A L{RhumbArea} instance.
102#
103# @note: The B{C{debug}} setting is passed as C{verbose}
104# to the returned L{RhumbAreaExact} instance.
105# '''
106# rA = _MODS.rhumbs.rhumb*.RhumbArea(self, polyline=polyline,
107# name=self._name__(name))
108# if self.verbose or self.debug: # PYCHOK no cover
109# rA.verbose = True
110# return rA
112# Polygon = Area # for C{geographiclib} compatibility
114 def _azimuth_reverse(self, azimuth):
115 '''(INTERNAL) Reverse final azimuth C{azimuth}.
116 '''
117 z = _norm180(float(azimuth))
118 if self.reverse2: # like .utils.atan2d
119 z += _180_0 if z < 0 else _N_180_0
120 return z
122 def _Direct(self, ll1, azi12, s12, **outmask):
123 '''(INTERNAL) Short-cut version, see .latlonBase.
124 '''
125 return self.Direct(ll1.lat, ll1.lon, azi12, s12, **outmask)
127 def Direct3(self, lat1, lon1, azi1, s12): # PYCHOK outmask
128 '''Return the destination lat, lon and reverse azimuth
129 (final bearing) in C{degrees}.
131 @return: L{Destination3Tuple}C{(lat, lon, final)}.
132 '''
133 r = self._GDictDirect(lat1, lon1, azi1, False, s12, floats=False)
134 z = self._azimuth_reverse(r.azi12)
135 return Destination3Tuple(float(r.lat2), float(r.lon2), wrap360(z),
136 iteration=r._iteration)
138 def _DirectLine(self, ll1, azi12, **name_caps):
139 '''(INTERNAL) Short-cut version, see .latlonBase.
140 '''
141 return self.DirectLine(ll1.lat, ll1.lon, azi12, **name_caps)
143 def DirectLine(self, lat1, lon1, azi1, caps=Caps.STANDARD, **name):
144 '''Set up a L{RhumbLineSolve} in terms of the I{direct} rhumb
145 problem to compute several points on a single rhumb line.
147 @arg lat1: Latitude of the first point (C{degrees}).
148 @arg lon1: Longitude of the first point (C{degrees}).
149 @arg azi1: Azimuth at the first point (compass C{degrees}).
150 @kwarg caps: Bit-or'ed combination of L{Caps<pygeodesy.karney.Caps>}
151 values specifying the capabilities the L{RhumbLineSolve}
152 instance should possess, always C{Caps.ALL}.
153 @kwarg name: Optional C{B{name}=NN} (C{str}).
155 @return: A L{RhumbLineSolve} instance.
157 @note: If the point is at a pole, the azimuth is defined by keeping
158 B{C{lon1}} fixed, writing C{B{lat1} = ±(90 − ε)}, and taking
159 the limit C{ε → 0+}.
161 @see: C++ U{RhumbExact.Line
162 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbExact.html>}
163 and Python U{Rhumb.Line<https://GeographicLib.SourceForge.io/Python/doc/code.html>}.
164 '''
165 return RhumbLineSolve(self, lat1, lon1, azi1, caps=caps, name=self._name__(name))
167 def _GDictDirect(self, lat, lon, azi1, arcmode, s12_a12, *unused, **floats): # PYCHOK signature
168 '''(INTERNAL) Get C{_GenDirect}-like result as an 8-item C{GDict}.
169 '''
170 d = _RhumbSolveBase._GDictDirect(self, lat, lon, azi1, arcmode, s12_a12, **floats)
171 r = GDict(lat1=lat, lon1=lon, azi12=azi1, s12=s12_a12) # a12=_over(s12_a12, self._mpd)
172 r.update(d)
173 return r
175 def _GDictInverse(self, lat1, lon1, lat2, lon2, *unused, **floats): # PYCHOK signature
176 '''(INTERNAL) Get C{_GenInverse}-like result as an 8-item C{GDict}, but I{without} C{_SALP_CALPs_}.
177 '''
178 i = _RhumbSolveBase._GDictInverse(self, lat1, lon1, lat2, lon2, **floats)
179 a = _over(float(i.s12), self._mpd) # for .Inverse1
180 r = GDict(lat1=lat1, lon1=lon1, lat2=lat2, lon2=lon2, a12=a)
181 r.update(i)
182 return r
184 def _Inverse(self, ll1, ll2, wrap, **unused):
185 '''(INTERNAL) Short-cut version, see .latlonBase.
186 '''
187 if wrap: # PYCHOK no cover
188 ll2 = _unrollon(ll1, _Wrap.point(ll2))
189 return self._GDictInverse(ll1.lat, ll1.lon, ll2.lat, ll2.lon)
191 def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask
192 '''Return the distance in C{meter} and the forward and
193 reverse azimuths (initial and final bearing) in C{degrees}.
195 @return: L{Distance3Tuple}C{(distance, initial, final)}.
196 '''
197 r = self._GDictInverse(lat1, lon1, lat2, lon2, floats=False)
198 z = self._azimuth_reverse(r.azi12)
199 return Distance3Tuple(float(r.s12), wrap360(r.azi12), wrap360(z),
200 iteration=r._iteration)
202 def _InverseLine(self, ll1, ll2, wrap, **name_caps):
203 '''(INTERNAL) Short-cut version, see .latlonBase.
204 '''
205 if wrap: # PYCHOK no cover
206 ll2 = _unrollon(ll1, _Wrap.point(ll2))
207 return self.InverseLine(ll1.lat, ll1.lon, ll2.lat, ll2.lon, **name_caps)
209 def InverseLine(self, lat1, lon1, lat2, lon2, caps=Caps.STANDARD, **name):
210 '''Define a L{RhumbLineSolve} in terms of the I{inverse}
211 rhumb problem.
213 @arg lat1: Latitude of the first point (C{degrees90}).
214 @arg lon1: Longitude of the first point (C{degrees180}).
215 @arg lat2: Latitude of the second point (C{degrees90}).
216 @arg lon2: Longitude of the second point (C{degrees180}).
217 @kwarg caps: Optional C{caps}, see L{RhumbLine} C{B{caps}}.
218 @kwarg name: Optional C{B{name}=NN} (C{str}).
220 @return: A L{RhumbLineSolve} instance and invoke its method
221 L{RhumbLine.Position} to compute each point.
223 @note: Updates to this rhumb are reflected in the returned
224 rhumb line.
225 '''
226 r = self.Inverse(lat1, lon1, lat2, lon2) # outmask=Caps.AZIMUTH
227 return RhumbLineSolve(self, lat1, lon1, r.azi12, caps=caps,
228 name=self._name__(name))
230 Line = DirectLine
233class RhumbLineSolve(_RhumbSolveBase, _SolveGDictLineBase):
234 '''Wrapper to invoke I{Karney}'s U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.1.html>}
235 like a class, similar to L{pygeodesy.RhumbLine} and L{pygeodesy.RhumbLineAux}.
237 @note: Use property C{RhumbSolve} or env variable C{PYGEODESY_RHUMBSOLVE} to specify the (fully
238 qualified) path to the C{RhumbSolve} executable.
240 @note: This C{rhumb line} is intended I{for testing purposes only}, it invokes the C{RhumbSolve}
241 executable for I{every} method call.
242 '''
243 def __init__(self, rhumb, lat1, lon1, azi12, caps=Caps.STANDARD, **name):
244 '''New L{RhumbLineSolve} instance, allowing points to be found along
245 a rhumb starting at C{(B{lat1}, B{lon1})} with azimuth B{C{azi12}}.
247 @arg rhumb: The rhumb to use (L{RhumbSolve}).
248 @arg lat1: Latitude of the first point (C{degrees90}).
249 @arg lon1: Longitude of the first point (C{degrees180}).
250 @arg azi12: Azimuth of the rhumb line (compass C{degrees180}).
251 @kwarg caps: Bit-or'ed combination of L{Caps<pygeodesy.karney.Caps>}
252 values specifying the capabilities the L{RhumbLineSolve}
253 instance should possess, always C{Caps.ALL}. Include
254 C{Caps.LINE_OFF} if updates to the B{C{rhumb}} should
255 I{not be reflected} in this L{RhumbLineSolve} instance.
256 @kwarg name: Optional C{B{name}=NN} (C{str}).
258 @kwarg name: Optional name (C{str}).
260 @raise RhumbError: Invalid path for C{RhumbSolve} executable or isn't the
261 C{RhumbSolve} executable, see property C{B{rhumb}.RhumbSolve}.
263 @raise TypeError: Invalid B{C{rhumb}}.
264 '''
265 _xinstanceof(RhumbSolve, rhumb=rhumb)
266 if (caps & Caps.LINE_OFF): # copy to avoid updates
267 rhumb = rhumb.copy(deep=False, name=NN(_UNDER_, rhumb.name))
268 _SolveGDictLineBase.__init__(self, rhumb, lat1, lon1, caps, azi12=azi12, **name)
269 try:
270 self.RhumbSolve = rhumb.RhumbSolve # rhumb or copy of rhumb
271 except RhumbError:
272 pass
274# def ArcPosition(self, a12, *unused):
275# '''Find the position on the line given B{C{a12}}.
276#
277# @arg a12: Spherical arc length from the first point to the
278# second point (C{degrees}).
279#
280# @return: A C{dict} with 8 items C{lat1, lon1, lat2, lon2,
281# azi12, a12, s12, S12}.
282# '''
283# s = a12 * self._mpd
284# a = self._GDictInvoke(self._cmdArc, self._Names_Direct, s)
285# r = GDict(a12=a12, s12=s, **self._lla1)
286# r.updated(a)
287# return r
289 @Property_RO
290 def azi12(self):
291 '''Get this rhumb line's azimuth (compass C{degrees}).
292 '''
293 return self._lla1.azi12
295 azi1 = azi12 # like GeodesicLineSolve
297 @Property_RO
298 def azi12_sincos2(self): # PYCHOK no cover
299 '''Get the sine and cosine of this rhumb line's azimuth (2-tuple C{(sin, cos)}).
300 '''
301 return _sincos2d(self.azi12)
303 azi1_sincos2 = azi12_sincos2
305# @Property_RO
306# def _cmdArc(self):
307# '''(INTERNAL) Get the C{RhumbSolve} I{-a -L} cmd (C{tuple}).
308# '''
309# return self._cmdDistance + ('-a',)
311 def Position(self, s12, **unused):
312 '''Find the position on the line given B{C{s12}}.
314 @arg s12: Distance from the first point to the second (C{meter}).
316 @return: A L{GDict} with 7 items C{lat1, lon1, lat2, lon2,
317 azi12, s12, S12}.
318 '''
319 d = self._GDictInvoke(self._cmdDistance, self._Names_Direct, s12)
320 r = GDict(s12=s12, **self._lla1) # a12=_over(s12, self._mpd)
321 r.update(d)
322 return r
324 def toStr(self, **prec_sep): # PYCHOK signature
325 '''Return this C{RhumbLineSolve} as string.
327 @kwarg prec_sep: Keyword argumens C{B{prec}=6} and C{B{sep}=", "}
328 for the C{float} C{prec}ision, number of decimal digits
329 (0..9) and the C{sep}arator string to join. Trailing
330 zero decimals are stripped for B{C{prec}} values of 1
331 and above, but kept for negative B{C{prec}} values.
333 @return: RhumbLineSolve items (C{str}).
334 '''
335 return _SolveGDictLineBase._toStr(self, azi12=self.azi12, rhumb=self._solve,
336 RhumbSolve=self.RhumbSolve, **prec_sep)
339class RhumbSolve7Tuple(Rhumb8Tuple):
340 '''7-Tuple C{(lat1, lon1, lat2, lon2, azi12, s12, S12)} with lat- C{lat1},
341 C{lat2} and longitudes C{lon1}, C{lon2} of both points, the azimuth of
342 the rhumb line C{azi12}, the distance C{s12} and the area C{S12} under
343 the rhumb line between both points.
344 '''
345 assert Rhumb8Tuple._Names_.index(_a12_) == 7
346 _Names_ = Rhumb8Tuple._Names_[:7] # drop a12
347 _Units_ = Rhumb8Tuple._Units_[:7]
349 @deprecated_method
350 def _to7Tuple(self): # PYCHOK no cover
351 '''DEPRECATED, I{don't use!}
352 '''
353 return _MODS.deprecated.classes.Rhumb7Tuple(self[:7])
356__all__ += _ALL_DOCS(_RhumbSolveBase)
358if __name__ == _DMAIN_:
360 from pygeodesy import printf
361 from sys import argv
363 def rhumb_intercept(rS, lat1, lon1, lat2, lon2, azi2, s23):
364 # using RhumbSolve and GeodesicExact for I{Karney}'s C++ U{rhumb-intercept.cpp
365 # <https://SourceForge.net/p/geographiclib/discussion/1026620/thread/2ddc295e/>
366 from pygeodesy.constants import EPS4 as _TOL
367 from pygeodesy.karney import _diff182
369 E = rS.ellipsoid
370 gX = E.geodesicx # == GeodesicExact(E)
371 m = gX.STANDARD | gX.REDUCEDLENGTH | gX.GEODESICSCALE
373 rlS = rS.Line(lat2, lon2, azi2)
374 sa, _ = rlS.azi12_sincos2 # aka _salp, _calp
375 for i in range(1, 16):
376 p = rlS.Position(s23) # outmask=gX.LATITUDE_LONGITUDE
377 r = gX.Inverse(lat1, lon1, p.lat2, p.lon2, outmask=m)
378 d, _ = _diff182(azi2, r.azi2, K_2_0=True)
379 s, c = _sincos2d(d)
380 printf('%2d %.3f %.8f, %.8f, %.8e',
381 i, s23, r.lat2, r.lon2, c)
382 s2, c2 = _sincos2d(r.lat2)
383 c2 *= E.rocTransverse(r.lat2)
384 if c2 and r.m12:
385 s *= (s2 * sa) / c2 - s * r.M21 / r.m12
386 t = (c / s) if s else _0_0
387 if abs(t) < _TOL:
388 break
389 s23 += t
390 else:
391 break
393 rS = RhumbSolve(name='Test')
394 rS.verbose = '--verbose' in argv # or '-v' in argv
396 if not _Xables.X_OK(rS.RhumbSolve): # not set
397 rS.RhumbSolve = _Xables.RhumbSolve(_Xables.bin_)
398 printf('version: %s', rS.version)
400 if len(argv) > 6: # 60 0 30 0 45 1e6
401 t = (14, 's23'), (7, 'lat3'), (11, 'lon3'), (13, 'cos()')
402 printf(' '.join('%*s' % _ for _ in t))
403 rhumb_intercept(rS, *map(float, argv[-6:]))
404 exit()
406 r = rS.Direct(40.6, -73.8, 51, 5.5e6)
407 printf('Direct: %r', r, nl=1)
408 printf('Direct3: %r', rS.Direct3(40.6, -73.8, 51, 5.5e6))
410 printf('Inverse: %r', rS.Inverse( 40.6, -73.8, 51.6, -0.5), nl=1)
411 printf('Inverse1: %r', rS.Inverse1(40.6, -73.8, 51.6, -0.5))
412 printf('Inverse3: %r', rS.Inverse3(40.6, -73.8, 51.6, -0.5))
414 printf('Inverse: %r', rS.Inverse( 40.6, -73.8, 35.8, 140.3), nl=1)
415 printf('Inverse1: %r', rS.Inverse1(40.6, -73.8, 35.8, 140.3))
416 printf('Inverse3: %r', rS.Inverse3(40.6, -73.8, 35.8, 140.3))
418 rlS = RhumbLineSolve(rS, 40.6, -73.8, 51, name='LineTest')
419 p = rlS.Position(5.5e6)
420 printf('Position: %s %r', p == r, p, nl=1)
421# p = rlS.ArcPosition(49.475527)
422# printf('ArcPosition: %s %r', p == r, p)
425# % python3 -m pygeodesy.rhumb.solve
427# version: /opt/local/bin/RhumbSolve: GeographicLib version 2.2
429# Direct: GDict(azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0, S12=44095641862956.109375)
430# Direct3: Destination3Tuple(lat=71.6889, lon=0.25552, final=51.0)
432# Inverse: GDict(a12=51.929543, azi12=77.76839, lat1=40.6, lat2=51.6, lon1=-73.8, lon2=-0.5, s12=5771083.383328, S12=37395209100030.390625)
433# Inverse1: 51.929542507561905
434# Inverse3: Distance3Tuple(distance=5771083.383328, initial=77.76839, final=77.76839)
436# Inverse: GDict(a12=115.02062, azi12=-92.388888, lat1=40.6, lat2=35.8, lon1=-73.8, lon2=140.3, s12=12782581.067684, S12=-63760642939072.5)
437# Inverse1: 115.02061966879248
438# Inverse3: Distance3Tuple(distance=12782581.067684, initial=267.611112, final=267.611112)
440# Position: True GDict(azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0, S12=44095641862956.109375)
443# % python3 -m pygeodesy.rhumb.solve --verbose
445# RhumbSolve 'Test' 1: /opt/local/bin/RhumbSolve --version (invoke)
446# RhumbSolve 'Test' 1: /opt/local/bin/RhumbSolve: GeographicLib version 2.2 (0)
447# version: /opt/local/bin/RhumbSolve: GeographicLib version 2.2
448# RhumbSolve 'Test' 2: /opt/local/bin/RhumbSolve -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct)
449# RhumbSolve 'Test' 2: lat2=71.688899882813018, lon2=0.255519824423402, S12=44095641862956.109 (0)
451# Direct: GDict(azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0, S12=44095641862956.109375)
452# RhumbSolve 'Test' 3: /opt/local/bin/RhumbSolve -p 10 \ 40.600000000000001 -73.799999999999997 51.0 5500000.0 (Direct3)
453# RhumbSolve 'Test' 3: lat2=71.688899882813018, lon2=0.255519824423402, S12=44095641862956.109 (0)
454# Direct3: Destination3Tuple(lat=71.6889, lon=0.25552, final=51.0)
455# RhumbSolve 'Test' 4: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse)
456# RhumbSolve 'Test' 4: azi12=77.768389710255661, s12=5771083.383328028, S12=37395209100030.391 (0)
458# Inverse: GDict(a12=51.929543, azi12=77.76839, lat1=40.6, lat2=51.6, lon1=-73.8, lon2=-0.5, s12=5771083.383328, S12=37395209100030.390625)
459# RhumbSolve 'Test' 5: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse1)
460# RhumbSolve 'Test' 5: azi12=77.768389710255661, s12=5771083.383328028, S12=37395209100030.391 (0)
461# Inverse1: 51.929542507561905
462# RhumbSolve 'Test' 6: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 51.600000000000001 -0.5 (Inverse3)
463# RhumbSolve 'Test' 6: azi12=77.768389710255661, s12=5771083.383328028, S12=37395209100030.391 (0)
464# Inverse3: Distance3Tuple(distance=5771083.383328, initial=77.76839, final=77.76839)
465# RhumbSolve 'Test' 7: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 35.799999999999997 140.300000000000011 (Inverse)
466# RhumbSolve 'Test' 7: azi12=-92.388887981699654, s12=12782581.0676841699, S12=-63760642939072.5 (0)
468# Inverse: GDict(a12=115.02062, azi12=-92.388888, lat1=40.6, lat2=35.8, lon1=-73.8, lon2=140.3, s12=12782581.067684, S12=-63760642939072.5)
469# RhumbSolve 'Test' 8: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 35.799999999999997 140.300000000000011 (Inverse1)
470# RhumbSolve 'Test' 8: azi12=-92.388887981699654, s12=12782581.0676841699, S12=-63760642939072.5 (0)
471# Inverse1: 115.02061966879248
472# RhumbSolve 'Test' 9: /opt/local/bin/RhumbSolve -p 10 -i \ 40.600000000000001 -73.799999999999997 35.799999999999997 140.300000000000011 (Inverse3)
473# RhumbSolve 'Test' 9: azi12=-92.388887981699654, s12=12782581.0676841699, S12=-63760642939072.5 (0)
474# Inverse3: Distance3Tuple(distance=12782581.067684, initial=267.611112, final=267.611112)
476# Position: True GDict(azi12=51, lat1=40.6, lat2=71.6889, lon1=-73.8, lon2=0.25552, s12=5500000.0, S12=44095641862956.109375)
479# % python3 -m pygeodesy.rhumb.solve 60 0 30 0 45 1e6
481# version: /opt/local/bin/RhumbSolve: GeographicLib version 2.2
482# s23 lat3 lon3 cos()
483# 1 1000000.000 36.37559999, 7.58982303, -5.83098638e-01
484# 2 4532573.097 58.84251798, 41.57078946, 4.05349594e-01
485# 3 2233216.895 44.22871762, 17.86660260, -2.91432608e-01
486# 4 3168401.173 50.17678842, 26.60741388, 3.00555188e-02
487# 5 3082690.347 49.63189746, 25.76374255, -1.49446251e-04
488# 6 3083112.629 49.63458216, 25.76787599, -2.59865190e-09
489# 7 3083112.636 49.63458221, 25.76787606, 4.96052409e-16
490# 8 3083112.636 49.63458221, 25.76787606, -4.96052409e-16
491# 9 3083112.636 49.63458221, 25.76787606, 4.96052409e-16
492# 10 3083112.636 49.63458221, 25.76787606, -4.96052409e-16
493# 11 3083112.636 49.63458221, 25.76787606, 4.96052409e-16
494# 12 3083112.636 49.63458221, 25.76787606, -4.96052409e-16
495# 13 3083112.636 49.63458221, 25.76787606, 4.96052409e-16
496# 14 3083112.636 49.63458221, 25.76787606, -4.96052409e-16
497# 15 3083112.636 49.63458221, 25.76787606, 4.96052409e-16
500# **) MIT License
501#
502# Copyright (C) 2022-2025 -- mrJean1 at Gmail -- All Rights Reserved.
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509# Software is furnished to do so, subject to the following conditions:
510#
511# The above copyright notice and this permission notice shall be included
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