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# -*- coding: utf-8 -*- 

 

u'''Wrapper to invoke I{Karney}'s U{GeodSolve 

<https://GeographicLib.SourceForge.io/html/GeodSolve.1.html>} utility 

as an (exact) geodesic, but intended I{for testing purposes only}. 

 

Set env variable C{PYGEODESY_GEODSOLVE} to the (fully qualified) path 

of the C{GeodSolve} executable. 

''' 

 

from pygeodesy.basics import map2, ub2str, _xinstanceof 

from pygeodesy.geodesicx.gxbases import _all_caps, Caps, _GeodesicBase 

from pygeodesy.interns import DIG, NN, _0_, _COMMASPACE_, _EQUAL_, \ 

_SLASH_, _SPACE_ 

from pygeodesy.interns import _not_ # PYCHOK used! 

from pygeodesy.karney import callername, _ellipsoid, _EWGS84, GDict, \ 

GeodesicError, GeodSolve12Tuple 

from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, \ 

_getenv, printf, _sys_version_info2 

# from pygeodesy.named import callername # from .karney 

from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple 

from pygeodesy.props import Property, Property_RO, property_RO 

from pygeodesy.streprs import Fmt, fstr, fstrzs, pairs, strs 

from pygeodesy.units import Precision_ 

from pygeodesy.utily import sincos2d, unroll180, wrap360 

 

from subprocess import PIPE as _PIPE, Popen as _Popen, STDOUT as _STDOUT 

 

__all__ = _ALL_LAZY.geodsolve 

__version__ = '22.05.04' 

 

_PYGEODESY_GEODSOLVE_ = 'PYGEODESY_GEODSOLVE' # PYCHOK used! 

 

_Error_ = 'Error' 

_ERROR_ = 'ERROR' 

_len_N = len(GeodSolve12Tuple._Names_) 

_stdin_ = 'stdin' 

 

 

def _cmd_stdin_(cmd, stdin): # PYCHOK no cover 

'''(INTERNAL) Cmd line, stdin and caller as sC{str}. 

''' 

c = Fmt.PAREN(callername(up=3)) 

t = (c,) if stdin is None else (_SLASH_, str(stdin), c) 

return _SPACE_.join(cmd + t) 

 

 

class _GeodesicSolveBase(_GeodesicBase): 

'''(NTERNAL) Base class for L{GeodesicSolve} and L{GeodesicLineSolve}. 

''' 

_E = _EWGS84 

_Exact = True 

_GeodSolve = _getenv(_PYGEODESY_GEODSOLVE_, _PYGEODESY_GEODSOLVE_) 

_invokation = 0 

_prec = Precision_(prec=DIG) 

_reverse2 = False 

_status = None 

_text_True = dict() if _sys_version_info2 < (3, 7) else dict(text=True) 

_unroll = False 

_verbose = False 

 

@Property_RO 

def a(self): 

'''Get the I{equatorial} radius, semi-axis (C{meter}). 

''' 

return self.ellipsoid.a 

 

@Property_RO 

def _b_option(self): 

return ('-b',) if self.reverse2 else () 

 

@Property_RO 

def _cmdBasic(self): 

'''(INTERNAL) Get the C{GeodSolve} basic cmd (C{tuple}). 

''' 

return (self.GeodSolve,) + self._b_option \ 

+ self._e_option \ 

+ self._E_option \ 

+ self._p_option \ 

+ self._u_option + ('-f',) 

 

@Property_RO 

def ellipsoid(self): 

'''Get the ellipsoid (C{Ellipsoid}). 

''' 

return self._E 

 

@Property_RO 

def _e_option(self): 

E = self.ellipsoid 

if E is _EWGS84: 

return () # default 

a, f = strs(E.a_f, fmt=Fmt.F, prec=DIG + 3) # not .G! 

return ('-e', a, f) 

 

@Property_RO 

def _E_option(self): 

return ('-E',) if self.Exact else () 

 

@Property 

def Exact(self): 

'''Get the C{GeodesicExact} usage (C{bool}). 

''' 

return self._Exact 

 

@Exact.setter # PYCHOK setter! 

def Exact(self, Exact): 

'''Set the C{GeodesicExact} usage (C{bool}). 

 

@arg Exact: If C{True} use C{GeodesicExact}, 

otherwise use C{Geodesic} (C{bool}). 

''' 

Exact = bool(Exact) 

self._update(Exact != self.Exact) 

self._Exact = Exact 

 

@Property_RO 

def f(self): 

'''Get the ellipsoid's I{flattening} (C{float}), M{(a - b) / a}, C{0} for spherical, negative for prolate. 

''' 

return self.ellipsoid.f 

 

def _GDictInvoke(self, cmd, floats, *args): 

'''(INTERNAL) Invoke C{GeodSolve}, return results as C{GDict}. 

''' 

i = fstr(args, prec=DIG, fmt=Fmt.F, sep=_SPACE_) if args else None # not Fmt.G! 

t = self._invoke(cmd, stdin=i).lstrip().split() # 12-/+ tuple 

if len(t) > _len_N: # PYCHOK no cover 

# unzip instrumented name=value pairs to names and values 

n, v = zip(*(p.split(_EQUAL_) for p in t[:-_len_N])) 

v += tuple(t[-_len_N:]) 

n += GeodSolve12Tuple._Names_ 

else: 

n, v = GeodSolve12Tuple._Names_, t 

if self.verbose: # PYCHOK no cover 

self._print(_COMMASPACE_.join(map(Fmt.EQUAL, n, map(fstrzs, v)))) 

if floats: 

v = map(float, v) 

return GDict(zip(n, v)) 

 

@Property 

def GeodSolve(self): 

'''Get the U{GeodSolve<https://GeographicLib.SourceForge.io/html/GeodSolve.1.html>} 

executable (C{filename}). 

''' 

return self._GeodSolve 

 

@GeodSolve.setter # PYCHOK setter! 

def GeodSolve(self, path): 

'''Set the U{GeodSolve<https://GeographicLib.SourceForge.io/html/GeodSolve.1.html>} 

executable (C{filename}). 

 

@arg path: The (fully qualified) path to the C{GeodSolve} executable (C{str}). 

 

@raise GeodesicError: Invalid B{C{path}}, B{C{path}} doesn't exist or 

isn't the C{GeodSolve} executable. 

''' 

hold = self.GeodSolve 

self._update(path != hold) 

self._GeodSolve = path 

try: 

self.version # test path and ... 

if self.status: # ... return code 

raise GeodesicError(GeodSolve=path, status=self.status, txt=_not_(_0_)) 

hold = path 

finally: # restore in case of error 

self._update(hold != self.GeodSolve) 

self._GeodSolve = hold 

 

@property_RO 

def invokation(self): 

'''Get the most recent C{GeodSolve} invokation number (C{int}). 

''' 

return self._invokation 

 

def invoke(self, *options, **stdin): 

'''Invoke the C{GeodSolve} executable and return the result. 

 

@arg options: No, one or several C{GeodSolve} command line 

options (C{str}s). 

@kwarg stdin: Optional input to pass to C{GeodSolve.stdin} (C{str}). 

 

@return: The C{GeodSolve.stdout} and C{.stderr} output (C{str}). 

 

@raise GeodesicError: On any error, including a non-zero return 

code from C{GeodSolve}. 

 

@note: The C{GeodSolve} return code is in property L{status}. 

''' 

c = (self.GeodSolve,) + map2(str, options) 

i = stdin.get(_stdin_, None) 

r = self._invoke(c, stdin=i) 

s = self.status 

if s: 

raise GeodesicError(cmd=_cmd_stdin_(c, i), status=s, 

txt=_not_(_0_)) 

if self.verbose: # PYCHOK no cover 

self._print(r) 

return r 

 

def _invoke(self, cmd, stdin=None): 

'''(INTERNAL) Invoke the C{GeodSolve} executable, with the 

given B{C{cmd}} line and optional input to B{C{stdin}}. 

''' 

self._invokation += 1 

self._status = t = None 

if self.verbose: # PYCHOK no cover 

t = _cmd_stdin_(cmd, stdin) 

self._print(t) 

try: 

p = _Popen(cmd, creationflags=0, 

# executable =sys.executable, 

# shell =True, 

stdin =_PIPE, 

stdout =_PIPE, # PYCHOK kwArgs 

stderr =_STDOUT, 

**self._text_True) 

# invoke and write to stdin 

r = ub2str(p.communicate(stdin)[0]) 

if len(r) < 6 or r[:5] in (_Error_, _ERROR_): 

raise ValueError(r) 

 

self._status = p.returncode 

except (IOError, OSError, TypeError, ValueError) as x: 

raise GeodesicError(cmd=t or _cmd_stdin_(cmd, stdin), 

txt=str(x)) 

return r.strip() 

 

@Property_RO 

def _p_option(self): 

return '-p', str(self.prec - 5) # -p is distance prec 

 

@Property 

def prec(self): 

'''Get the precision, number of (decimal) digits (C{int}). 

''' 

return self._prec 

 

@prec.setter # PYCHOK setter! 

def prec(self, prec): 

'''Set the precision for C{angles} in C{degrees}, like C{lat}, 

C{lon}, C{azimuth} and C{arc}. 

 

@arg prec: Number of decimal digits (C{int}, C{0}..L{DIG}). 

 

@note: The precision for C{distance = B{prec} - 5} or up to 

10 decimal digits for C{nanometer} and for C{area = 

B{prec} - 12} or at most C{millimeter} I{squared}. 

''' 

prec = Precision_(prec=prec, high=DIG) 

self._update(prec != self.prec) 

self._prec = prec 

 

def _print(self, line): # PYCHOK no cover 

'''(INTERNAL) Print a status line. 

''' 

if self.status is not None: 

line = _SPACE_(line, Fmt.PAREN(self.status)) 

printf('%s %d: %s', self.named2, self.invokation, line) 

 

@Property 

def reverse2(self): 

'''Get the C{azi2} direction (C{bool}). 

''' 

return self._reverse2 

 

@reverse2.setter # PYCHOK setter! 

def reverse2(self, reverse2): 

'''Set the direction for C{azi2} (C{bool}). 

 

@arg reverse2: If C{True} reverse C{azi2} (C{bool}). 

''' 

reverse2 = bool(reverse2) 

self._update(reverse2 != self.reverse2) 

self._reverse2 = reverse2 

 

@property_RO 

def status(self): 

'''Get the most recent C{GeodSolve} return code (C{int}, C{str}) 

or C{None}. 

''' 

return self._status 

 

def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature 

'''Return this C{GeodesicSolve} as string. 

 

@kwarg prec: The C{float} precision, number of decimal digits (0..9). 

Trailing zero decimals are stripped for B{C{prec}} values 

of 1 and above, but kept for negative B{C{prec}} values. 

@kwarg sep: Separator to join (C{str}). 

 

@return: GeodesicSolve items (C{str}). 

''' 

d = dict(ellipsoid=self.ellipsoid, GeodSolve=self.GeodSolve, 

invokation=self.invokation, status=self.status) 

return sep.join(pairs(d, prec=prec)) 

 

@Property 

def unroll(self): 

'''Get the C{lon2} unroll'ing (C{bool}). 

''' 

return self._unroll 

 

@unroll.setter # PYCHOK setter! 

def unroll(self, unroll): 

'''Set unroll'ing for C{lon2} (C{bool}). 

 

@arg unroll: If C{True} unroll C{lon2}, 

otherwise don't (C{bool}). 

''' 

unroll = bool(unroll) 

self._update(unroll != self.unroll) 

self._unroll = unroll 

 

@Property_RO 

def _u_option(self): 

return '-u' if self.unroll else () 

 

@Property 

def verbose(self): 

'''Get the C{verbose} option (C{bool}). 

''' 

return self._verbose 

 

@verbose.setter # PYCHOK setter! 

def verbose(self, verbose): 

'''Set the C{verbose} option. 

 

@arg verbose: Print a message around each 

C{GeodSolve} invokation (C{bool}). 

''' 

self._verbose = bool(verbose) 

 

@property_RO 

def version(self): 

'''Get the result of C{"GeodSolve --version"}. 

''' 

return self.invoke('--version') 

 

 

class GeodesicSolve(_GeodesicSolveBase): 

'''Wrapper to invoke I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/html/GeodSolve.1.html>} 

as an C{Exact} version of I{Karney}'s Python class U{Geodesic<https://GeographicLib.SourceForge.io/html/ 

python/code.html#geographiclib.geodesic.Geodesic>}. 

 

@note: Use property C{GeodSolve} or env variable C{PYGEODESY_GEODSOLVE} to specify the (fully 

qualified) path to the C{GeodSolve} executable. 

 

@note: This C{geodesic} is intended I{for testing purposes only}, it invokes the C{GeodSolve} 

executable for I{every} method call. 

''' 

def __init__(self, a_ellipsoid=_EWGS84, f=None, name=NN): 

'''New L{GeodesicSolve} instance. 

 

@arg a_ellipsoid: An ellipsoid (L{Ellipsoid}) or datum (L{Datum}) or 

the equatorial radius of the ellipsoid (C{scalar}, 

conventionally in C{meter}), see B{C{f}}. 

@arg f: The flattening of the ellipsoid (C{scalar}) if B{C{a_ellipsoid}} 

is specified as C{scalar}. 

@kwarg name: Optional name (C{str}). 

''' 

if a_ellipsoid not in (GeodesicSolve._E, None): 

self._E = _ellipsoid(a_ellipsoid, f, name=name) 

 

if name: 

self.name = name 

 

def Area(self, polyline=False, name=NN): 

'''Set up an L{GeodesicAreaExact} to compute area and 

perimeter of a polygon. 

 

@kwarg polyline: If C{True} perimeter only, otherwise 

area and perimeter (C{bool}). 

@kwarg name: Optional name (C{str}). 

 

@return: A L{GeodesicAreaExact} instance. 

 

@note: The B{C{debug}} setting is passed as C{verbose} 

to the returned L{GeodesicAreaExact} instance. 

''' 

gaX = _MODS.geodesicx.GeodesicAreaExact(self, polyline=polyline, 

name=name or self.name) 

if self.verbose or self.debug: # PYCHOK no cover 

gaX.verbose = True 

return gaX 

 

Polygon = Area # for C{geographiclib} compatibility 

 

@Property_RO 

def _cmdDirect(self): 

'''(INTERNAL) Get the C{GeodSolve} I{Direct} cmd (C{tuple}). 

''' 

return self._cmdBasic 

 

@Property_RO 

def _cmdInverse(self): 

'''(INTERNAL) Get the C{GeodSolve} I{Inverse} cmd (C{tuple}). 

''' 

return self._cmdBasic + ('-i',) 

 

def Direct(self, lat1, lon1, azi1, s12, *unused): 

'''Return the C{Direct} result. 

''' 

return self._GDictInvoke(self._cmdDirect, True, lat1, lon1, azi1, s12) 

 

def Direct3(self, lat1, lon1, azi1, s12): # PYCHOK outmask 

'''Return the destination lat, lon and reverse azimuth 

(final bearing) in C{degrees}. 

 

@return: L{Destination3Tuple}C{(lat, lon, final)}. 

''' 

d = self._GDictInvoke(self._cmdDirect, False, lat1, lon1, azi1, s12) 

return Destination3Tuple(float(d.lat2), float(d.lon2), wrap360(d.azi2)) 

 

def _GDictDirect(self, lat, lon, azi, arcmode, s12_a12, *unused): # for .geodesicx.gxarea 

'''(INTERNAL) Get C{_GenDirect}-like result as C{GDict}. 

''' 

if arcmode: 

raise GeodesicError(arcmode=arcmode, txt=str(NotImplemented)) 

return self._GDictInvoke(self._cmdDirect, True, lat, lon, azi, s12_a12) 

 

def _GDictInverse(self, lat1, lon1, lat2, lon2, *unused): # for .geodesicx.gxarea 

'''(INTERNAL) Get C{_GenInverse}-like result as C{GDict}, but 

I{without} C{_SALPs_CALPs_}. 

''' 

return self._GDictInvoke(self._cmdInverse, True, lat1, lon1, lat2, lon2) 

 

def Inverse(self, lat1, lon1, lat2, lon2, *unused): 

'''Return the C{Inverse} result. 

''' 

return self._GDictInvoke(self._cmdInverse, True, lat1, lon1, lat2, lon2) 

 

def Inverse1(self, lat1, lon1, lat2, lon2, wrap=False): 

'''Return the non-negative, I{angular} distance in C{degrees}. 

''' 

# see .FrechetKarney.distance, .HausdorffKarney._distance 

# and .HeightIDWkarney._distances 

_, lon2 = unroll180(lon1, lon2, wrap=wrap) # self.LONG_UNROLL 

d = self._GDictInvoke(self._cmdInverse, False, lat1, lon1, lat2, lon2) 

# XXX self.DISTANCE needed for 'a12'? 

return abs(float(d.a12)) 

 

def Inverse3(self, lat1, lon1, lat2, lon2): # PYCHOK outmask 

'''Return the distance in C{meter} and the forward and 

reverse azimuths (initial and final bearing) in C{degrees}. 

 

@return: L{Distance3Tuple}C{(distance, initial, final)}. 

''' 

d = self._GDictInvoke(self._cmdInverse, False, lat1, lon1, lat2, lon2) 

return Distance3Tuple(float(d.s12), wrap360(d.azi1), wrap360(d.azi2)) 

 

def Line(self, lat1, lon1, azi1, caps=Caps.ALL): 

'''Set up an L{GeodesicLineSolve} to compute several points 

on a single geodesic. 

 

@arg lat1: Latitude of the first point (C{degrees}). 

@arg lon1: Longitude of the first point (C{degrees}). 

@arg azi1: Azimuth at the first point (compass C{degrees}). 

@kwarg caps: Bit-or'ed combination of L{Caps} values specifying 

the capabilities the L{GeodesicLineSolve} instance 

should possess, always C{Caps.ALL}. 

 

@return: A L{GeodesicLineSolve} instance. 

 

@note: If the point is at a pole, the azimuth is defined by keeping 

B{C{lon1}} fixed, writing C{B{lat1} = ±(90 − ε)}, and taking 

the limit C{ε → 0+}. 

 

@see: C++ U{GeodesicExact.Line 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1GeodesicExact.html>} 

and Python U{Geodesic.Line<https://GeographicLib.SourceForge.io/html/python/code.html>}. 

''' 

return GeodesicLineSolve(self, lat1, lon1, azi1, caps=caps, name=self.name) 

 

 

class GeodesicLineSolve(_GeodesicSolveBase): 

'''Wrapper to invoke I{Karney}'s U{GeodSolve<https://GeographicLib.SourceForge.io/html/GeodSolve.1.html>} 

as an C{Exact} version of I{Karney}'s Python class U{GeodesicLine<https://GeographicLib.SourceForge.io/html/ 

python/code.html#geographiclib.geodesicline.GeodesicLine>}. 

 

@note: Use property C{GeodSolve} or env variable C{PYGEODESY_GEODSOLVE} to specify the (fully 

qualified) path to the C{GeodSolve} executable. 

 

@note: This C{geodesic} is intended I{for testing purposes only}, it invokes the C{GeodSolve} 

executable for I{every} method call. 

''' 

_caps = 0 

_gS = None # Solve only 

_lla1 = () 

 

def __init__(self, geodesic, lat1, lon1, azi1, caps=Caps.ALL, name=NN): 

'''New L{GeodesicLineSolve} instance, allowing points to be found along 

a geodesic starting at C{(B{lat1}, B{lon1})} with azimuth B{C{azi1}}. 

 

@arg geodesic: The geodesic to use (L{GeodesicSolve}). 

@arg lat1: Latitude of the first point (C{degrees}). 

@arg lon1: Longitude of the first point (C{degrees}). 

@arg azi1: Azimuth at the first points (compass C{degrees}). 

@kwarg caps: Bit-or'ed combination of L{Caps} values specifying 

the capabilities the L{GeodesicLineSolve} instance 

should possess, always C{Caps.ALL}. 

@kwarg name: Optional name (C{str}). 

 

@raise TypeError: Invalid B{C{geodesic}}. 

''' 

_xinstanceof(GeodesicSolve, geodesic=geodesic) 

 

self._gS = gS = geodesic 

self._lla1 = lat1, lon1, azi1 

self._caps = caps | Caps._LINE 

 

n = name or gS.name 

if n: 

self.name = n 

 

self._debug = gS._debug 

 

self.Exact = gS.Exact 

self.prec = gS.prec 

self.reverse2 = gS.reverse2 

self.unroll = gS.unroll 

self.verbose = gS.verbose 

try: 

self.GeodSolve = gS.GeodSolve 

except GeodesicError: 

pass 

 

def ArcPosition(self, a12, *unused): 

'''Find the position on the line given B{C{a12}}. 

 

@arg a12: Spherical arc length from the first point to the 

second point (C{degrees}). 

 

@return: A C{dict} with 12 items C{lat1, lon1, azi1, lat2, lon2, 

azi2, m12, a12, s12, M12, M21, S12}. 

''' 

return self._GDictInvoke(self._cmdArc, True, a12) 

 

@Property_RO 

def azi1(self): 

'''Get the azimuth at the first point (compass C{degrees}). 

''' 

return self._lla1[2] 

 

@Property_RO 

def azi1_sincos2(self): 

'''Get the sine and cosine of the first point's azimuth (2-tuple C{(sin, cos)}). 

''' 

return sincos2d(self.azi1) 

 

@Property_RO 

def caps(self): 

'''Get the capabilities (bit-or'ed C{Caps}). 

''' 

return self._caps 

 

def caps_(self, caps): 

'''Check the available capabilities. 

 

@arg caps: Bit-or'ed combination of L{Caps} values 

for all capabilities to be checked. 

 

@return: C{True} if I{all} B{C{caps}} are available, 

C{False} otherwise (C{bool}). 

''' 

return _all_caps(self.caps, caps) 

 

@Property_RO 

def _cmdArc(self): 

'''(INTERNAL) Get the C{GeodSolve} I{-a -L} cmd (C{tuple}). 

''' 

return self._cmdDistance + ('-a',) 

 

@Property_RO 

def _cmdDistance(self): 

'''(INTERNAL) Get the C{GeodSolve} I{-L} cmd (C{tuple}). 

''' 

return self._cmdBasic + ('-L',) + strs(self._lla1, prec=DIG, fmt=Fmt.F) 

 

@Property_RO 

def ellipsoid(self): 

'''Get the ellipsoid (C{Ellipsoid}). 

''' 

return self._gS.ellipsoid 

 

@Property_RO 

def lat1(self): 

'''Get the latitude of the first point (C{degrees}). 

''' 

return self._lla1[0] 

 

@Property_RO 

def lon1(self): 

'''Get the longitude of the first point (C{degrees}). 

''' 

return self._lla1[1] 

 

def Position(self, s12, *unused): 

'''Find the position on the line given B{C{s12}}. 

 

@arg s12: Distance from the first point to the second (C{meter}). 

 

@return: A C{dict} with 12 items C{lat1, lon1, azi1, lat2, lon2, 

azi2, m12, a12, s12, M12, M21, S12}, possibly C{a12=NAN}. 

''' 

return self._GDictInvoke(self._cmdDistance, True, s12) 

 

 

__all__ += _ALL_DOCS(_GeodesicSolveBase) 

 

if __name__ == '__main__': 

 

gS = GeodesicSolve(name='Test') 

if gS.GeodSolve in (_PYGEODESY_GEODSOLVE_, None): # not set 

gS.GeodSolve = '/opt/local/Cellar/geographiclib/1.51/bin/GeodSolve' # HomeBrew 

# gS.verbose = True 

printf('version: %s', gS.version) 

 

r = gS.Direct(40.6, -73.8, 51, 5.5e6) 

printf('Direct: %r', r, nl=1) # GDict(M12=0.650911, M21=0.651229, S12=39735075134877.09375, a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141173, m12=4844148.703101, s12=5500000.0) 

printf('Direct3: %r', gS.Direct3(40.6, -73.8, 51, 5.5e6)) # Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397) 

 

printf('Inverse: %r', gS.Inverse( 40.6, -73.8, 51.6, -0.5), nl=1) # GDict(M12=0.64473, M21=0.645046, S12=40041368848742.53125, a12=49.94131, azi1=51.198883, azi2=107.821777, lat1=40.6, lat2=51.6, lon1=-73.8, lon2=-0.5, m12=4877684.602706, s12=5551759.400319) 

printf('Inverse1: %r', gS.Inverse1(40.6, -73.8, 51.6, -0.5)) # 49.94131021789904 

printf('Inverse3: %r', gS.Inverse3(40.6, -73.8, 51.6, -0.5)) # Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777) 

 

glS = GeodesicLineSolve(gS, 40.6, -73.8, 51) 

p = glS.Position(5.5e6) 

printf('Position: %s %r', p == r, p, nl=1) 

p = glS.ArcPosition(49.475527) 

printf('ArcPosition: %s %r', p == r, p) 

 

# % python3 -m pygeodesy.geodsolve 

 

# version: /opt/local/Cellar/geographiclib/1.51/bin/GeodSolve: GeographicLib version 1.51 

 

# Direct: GDict(M12=0.650911, M21=0.651229, S12=39735075134877.09375, a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141173, m12=4844148.703101, s12=5500000.0) 

# Direct3: Destination3Tuple(lat=51.884565, lon=-1.141173, final=107.189397) 

 

# Inverse: GDict(M12=0.64473, M21=0.645046, S12=40041368848742.53125, a12=49.94131, azi1=51.198883, azi2=107.821777, lat1=40.6, lat2=51.6, lon1=-73.8, lon2=-0.5, m12=4877684.602706, s12=5551759.400319) 

# Inverse1: 49.94131021789904 

# Inverse3: Distance3Tuple(distance=5551759.400319, initial=51.198883, final=107.821777) 

 

# Position: True GDict(M12=0.650911, M21=0.651229, S12=39735075134877.09375, a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141173, m12=4844148.703101, s12=5500000.0) 

# ArcPosition: False GDict(M12=0.650911, M21=0.651229, S12=39735074737272.734375, a12=49.475527, azi1=51.0, azi2=107.189397, lat1=40.6, lat2=51.884565, lon1=-73.8, lon2=-1.141174, m12=4844148.669561, s12=5499999.948497) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2022 -- mrJean1 at Gmail -- All Rights Reserved. 

# 

# Permission is hereby granted, free of charge, to any person obtaining a 

# copy of this software and associated documentation files (the "Software"), 

# to deal in the Software without restriction, including without limitation 

# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

# and/or sell copies of the Software, and to permit persons to whom the 

# Software is furnished to do so, subject to the following conditions: 

# 

# The above copyright notice and this permission notice shall be included 

# in all copies or substantial portions of the Software. 

# 

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

# OTHER DEALINGS IN THE SOFTWARE.