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# -*- coding: utf-8 -*- 

 

u'''I{Charles F.F. Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>} C{geodesic}, wrapped. 

 

Wrapper around Python classes C{Geodesic} and C{GeodesicLine} and several C{Math} functions from 

I{Karney}'s Python package U{geographiclib<https://PyPI.org/project/geographiclib>}, provided 

that package is installed. 

 

The I{wrapped} class methods return a L{GDict} instance offering access to the C{dict} items either 

by C{key} or by C{attribute} name. 

 

With env variable C{PYGEODESY_GEOGRAPHICLIB} left undefined or set to C{"2"}, this module and 

L{pygeodesy.geodesicx} will use U{GeographicLib 2.0<https://GeographicLib.SourceForge.io/C++/doc/>} 

transcoding, otherwise C{1.52} or older. 

 

Karney-based functionality 

========================== 

 

1. The following classes and functions in C{pygeodesy} 

 

- L{AlbersEqualArea}, L{AlbersEqualArea2}, L{AlbersEqualArea4}, 

L{AlbersEqualAreaCylindrical}, L{AlbersEqualAreaNorth}, L{AlbersEqualAreaSouth} -- 

U{AlbersEqualArea<https://GeographicLib.SourceForge.io/html/ 

classGeographicLib_1_1AlbersEqualArea.html>} 

 

- L{CassiniSoldner} -- U{CassiniSoldner<https://GeographicLib.SourceForge.io/html/ 

classGeographicLib_1_1CassiniSoldner.html>} 

 

- L{EcefKarney} -- U{Geocentric<https://GeographicLib.SourceForge.io/html/ 

classGeographicLib_1_1Geocentric.html>} 

 

- L{Elliptic} -- U{EllipticFunction<https://GeographicLib.SourceForge.io/html/ 

classGeographicLib_1_1EllipticFunction.html>} 

 

- L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney} -- U{AzimuthalEquidistant 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1AzimuthalEquidistant.html>} 

 

- L{Etm}, L{ExactTransverseMercator} -- U{TransverseMercatorExact 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1TransverseMercatorExact.html>} 

 

- L{GeodesicAreaExact}, L{PolygonArea} -- U{PolygonArea<https://GeographicLib.SourceForge.io/ 

html/classGeographicLib_1_1PolygonAreaT.html>} 

 

- L{GeodesicExact}, L{GeodesicLineExact} -- U{GeodesicExact<https://GeographicLib.SourceForge.io/ 

html/classGeographicLib_1_1GeodesicExact.html>}, U{GeodesicLineExact<https://GeographicLib.SourceForge.io/ 

html/classGeographicLib_1_1GeodesicLineExact.html>} 

 

- L{GeoidKarney} -- U{Geoid<https://GeographicLib.SourceForge.io/html/geoid.html>} 

 

- L{Georef} -- U{Georef<https://GeographicLib.SourceForge.io/html/ 

classGeographicLib_1_1Georef.html>} 

 

- L{GnomonicExact}, L{GnomonicGeodSolve}, L{GnomonicKarney} -- U{Gnomonic 

<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Gnomonic.html>} 

 

- L{LocalCartesian}, L{Ltp} -- U{LocalCartesian<https://GeographicLib.SourceForge.io/html/ 

classGeographicLib_1_1LocalCartesian.html>} 

 

- L{Ups} -- U{PolarStereographic<https://GeographicLib.SourceForge.io/html/ 

classGeographicLib_1_1PolarStereographic.html>} 

 

- L{Utm} -- U{TransverseMercator<https://GeographicLib.SourceForge.io/html/ 

classGeographicLib_1_1TransverseMercator.html>} 

 

- L{UtmUps}, L{Epsg} -- U{UTMUPS<https://GeographicLib.SourceForge.io/html/ 

classGeographicLib_1_1UTMUPS.html>} 

 

- L{pygeodesy.atand}, L{pygeodesy.atan2d}, L{pygeodesy.sincos2}, L{pygeodesy.sincos2d} -- U{ 

Math<https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Math.html>} 

 

are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/html/annotated.html>}. 

 

2. These C{pygeodesy} modules and classes 

 

- L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodsolve}, L{karney} 

- L{EquidistantKarney}, L{FrechetKarney}, L{GeodesicSolve}, L{GeodesicLineSolve}, L{GnomonicGeodSolve}, 

L{GnomonicKarney}, L{HeightIDWkarney} 

 

are or use I{wrappers} around I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} 

C{geodesic} or C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/html/GeodSolve.1.html>}. 

 

3. All C{pygeodesy} functions and methods to compute I{ellipsoidal} intersections and trilaterations 

 

- L{ellipsoidalExact.intersection3}, L{ellipsoidalExact.intersections2}, L{ellipsoidalExact.nearestOn}, 

L{ellipsoidalExact.LatLon.intersection3}, L{ellipsoidalExact.LatLon.intersections2}, 

L{ellipsoidalExact.LatLon.nearestOn}, L{ellipsoidalExact.LatLon.trilaterate5} 

 

- L{ellipsoidalKarney.intersection3}, L{ellipsoidalKarney.intersections2}, L{ellipsoidalKarney.nearestOn}, 

L{ellipsoidalKarney.LatLon.intersection3}, L{ellipsoidalKarney.LatLon.intersections2}, 

L{ellipsoidalKarney.LatLon.nearestOn}, L{ellipsoidalKarney.LatLon.trilaterate5} 

 

- L{ellipsoidalVincenty.intersection3}, L{ellipsoidalVincenty.intersections2}, L{ellipsoidalVincenty.nearestOn}, 

L{ellipsoidalVincenty.LatLon.intersection3}, L{ellipsoidalVincenty.LatLon.intersections2}, 

L{ellipsoidalVincenty.LatLon.nearestOn}, L{ellipsoidalVincenty.LatLon.trilaterate5} 

 

are implementations of I{Karney}'s solution posted under U{The B{ellipsoidal} case 

<https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} and in paper U{Geodesics 

on an ellipsoid of revolution<https://ArXiv.org/pdf/1102.1215.pdf>} (pp 20-21, section B{14. MARITIME BOUNDARIES}). 

 

4. Spherical functions 

 

- L{pygeodesy.excessKarney_}, L{sphericalTrigonometry.areaOf} 

 

in C{pygeodesy} are based on I{Karney}'s post U{Area of a spherical polygon 

<https://MathOverflow.net/questions/97711/the-area-of-spherical-polygons>}, 3rd Answer. 

''' 

 

from pygeodesy.basics import _copysign, _isfinite as _math_isfinite, unsigned0, \ 

_xgeographiclib, _xImportError, isodd # PYCHOK shared 

from pygeodesy.datums import Ellipsoid2, _ellipsoidal_datum, _WGS84 

# from pygeodesy.ellipsoids import Ellipsoid2 # from .datums 

from pygeodesy.fmath import cbrt, fremainder, norm2, unstr, \ 

hypot as _hypot # PYCHOK shared 

from pygeodesy.errors import _AssertionError, _or, _ValueError, _xkwds # PYCHOK shared 

from pygeodesy.interns import NAN, NN, _DOT_, _2_, _lat1_, _lat2_, _lon2_, \ 

_0_0, _1_0, _16_0, _180_0, _N_180_0, _360_0 

from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, _getenv 

from pygeodesy.named import callername, classname, _Dict, modulename, _NamedBase, \ 

_NamedTuple, _Pass # PYCHOK shared 

from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple 

from pygeodesy.props import Property, Property_RO 

# from pygeodesy.streps import unstr # from .fmath 

from pygeodesy.units import Bearing as _Azi, Degrees as _Deg, Lat, Lon, \ 

Meter as _M, Meter2 as _M2, _1mm as _TOL_M # PYCHOK shared 

from pygeodesy.utily import atan2d, sincos2d, unroll180, wrap360 

 

__all__ = _ALL_LAZY.karney 

__version__ = '22.05.04' 

 

_a12_ = 'a12' 

_azi1_ = 'azi1' 

_azi2_ = 'azi2' 

_lon1_ = 'lon1' 

_m12_ = 'm12' 

_M12_ = 'M12' 

_M21_ = 'M21' 

_s12_ = 's12' 

_S12_ = 'S12' 

 

_1_16th = _1_0 / _16_0 

_EWGS84 = _WGS84.ellipsoid # PYCHOK used! 

_K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_ 

 

 

def _ellipsoid(a_ellipsoid, f, name=NN, raiser=True): # in .geodesicx.gx and .geodsolve 

'''(INTERNAL) Get an ellipsoid from C{(B{a_..}, B{f})} or C{B{.._ellipsoid}}. 

''' 

return Ellipsoid2(a_ellipsoid, f, name=name) if f is not None else \ 

_ellipsoidal_datum(a_ellipsoid, name=name, raiser=raiser).ellipsoid 

 

 

def _Lat(*lat, **Error_name): 

'''(INTERNAL) Latitude B{C{lat}}. 

''' 

kwds = _xkwds(Error_name, clip=0, Error=GeodesicError) 

return Lat(*lat, **kwds) 

 

 

def _Lon(*lon, **Error_name): 

'''(INTERNAL) Longitude B{C{lon}}. 

''' 

kwds = _xkwds(Error_name, clip=0, Error=GeodesicError) 

return Lon(*lon, **kwds) 

 

 

def _raiseX(inst, x, *args): # PYCHOK no cover 

'''(INTERNAL) Throw a C{GeodesicError} for C{geographiclib} issue B{C{x}} . 

''' 

n = _DOT_(classname(inst), callername(up=2, underOK=True)) 

raise GeodesicError(unstr(n, *args), txt=str(x)) 

 

 

class _GTuple(_NamedTuple): # in .testNamedTuples 

'''(INTERNAL) Helper. 

''' 

def toGDict(self, **updates): 

'''Convert this C{*Tuple} to a L{GDict}. 

 

@kwarg updates: Optional items to apply (C{nam=value} pairs) 

''' 

r = GDict(zip(self._Names_, self)) 

if updates: 

r.update(updates) 

return r 

 

 

class Direct9Tuple(_GTuple): 

'''9-Tuple C{(a12, lat2, lon2, azi2, s12, m12, M12, M21, S12)} with arc 

length C{a12}, angles C{lat2}, C{lon2} and azimuth C{azi2} in C{degrees}, 

distance C{s12} and reduced length C{m12} in C{meter} and area C{S12} in 

C{meter} I{squared}. 

''' 

_Names_ = (_a12_, _lat2_, _lon2_, _azi2_, _s12_, _m12_, _M12_, _M21_, _S12_) 

_Units_ = (_Azi, _Lat, _Lon, _Azi, _M, _Pass, _Pass, _Pass, _M2) 

 

 

class GDict(_Dict): 

'''Basic C{dict} with both key I{and} attribute access 

to the C{dict} items. 

 

Results of all C{geodesic} methods are returned as a 

L{GDict} instance. 

''' 

def toDirect9Tuple(self, dflt=NAN): 

'''Convert this L{GDict} result to a 9-tuple, like I{Karney}'s 

method C{geographiclib.geodesic.Geodesic._GenDirect}. 

 

@kwarg dflt: Default value for missing items (C{any}). 

 

@return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, 

s12, m12, M12, M21, S12)} 

''' 

return self._toTuple(Direct9Tuple, dflt) 

 

def toGeodSolve12Tuple(self, dflt=NAN): # PYCHOK 12 args 

'''Convert this L{GDict} result to a 12-Tuple, compatible with I{Karney}'s 

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

result. 

 

@kwarg dflt: Default value for missing items (C{any}). 

 

@return: L{GeodSolve12Tuple}C{(lat1, lon1, azi1, lat2, lon2, azi2, 

s12, a12, m12, M12, M21, S12)}. 

''' 

return self._toTuple(GeodSolve12Tuple, dflt) 

 

def toInverse10Tuple(self, dflt=NAN): 

'''Convert this L{GDict} result to a 10-tuple, like I{Karney}'s 

method C{geographiclib.geodesic.Geodesic._GenInverse}. 

 

@kwarg dflt: Default value for missing items (C{any}). 

 

@return: L{Inverse10Tuple}C{(a12, s12, salp1, calp1, 

salp2, calp2, m12, M12, M21, S12)}. 

''' 

return self._toTuple(Inverse10Tuple, dflt) 

 

def _toTuple(self, nTuple, dflt): 

'''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}. 

''' 

return nTuple(getattr(self, n, dflt) for n in nTuple._Names_) # *(getattr ...) 

 

 

class GeodesicError(_ValueError): 

'''Error raised for L{pygeodesy.geodesicx} lack of convergence 

or other L{pygeodesy.geodesicx} or L{pygeodesy.karney} issues. 

''' 

pass 

 

 

class GeodSolve12Tuple(_GTuple): 

'''12-Tuple C{(lat1, lon1, azi1, lat2, lon2, azi2, s12, a12, m12, M12, M21, S12)} with 

angles C{lat1}, C{lon1}, C{azi1}, C{lat2}, C{lon2} and C{azi2} and arc C{a12} all in 

C{degrees}, initial C{azi1} and final C{azi2} forward azimuths, distance C{s12} and 

reduced length C{m12} in C{meter}, area C{S12} in C{meter} I{squared} and geodesic 

scale factors C{M12} and C{M21}, both C{scalar}, see U{GeodSolve 

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

''' 

# from GeodSolve --help option -f ... lat1 lon1 azi1 lat2 lon2 azi2 s12 a12 m12 M12 M21 S12 

_Names_ = (_lat1_, _lon1_, _azi1_, _lat2_, _lon2_, _azi2_, _s12_, _a12_, _m12_, _M12_, _M21_, _S12_) 

_Units_ = (_Lat, _Lon, _Azi, _Lat, _Lon, _Azi, _M, _Deg, _Pass, _Pass, _Pass, _M2) 

 

 

class Inverse10Tuple(_GTuple): 

'''10-Tuple C{(a12, s12, salp1, calp1, salp2, calp2, m12, M12, M21, S12)} with arc length 

C{a12} in C{degrees}, distance C{s12} and reduced length C{m12} in C{meter}, area 

C{S12} in C{meter} I{squared} and the sines C{salp1}, C{salp2} and cosines C{calp1}, 

C{calp2} of the initial C{1} and final C{2} foward azimuths. 

''' 

_Names_ = (_a12_, _s12_, 'salp1', 'calp1', 'salp2', 'calp2', _m12_, _M12_, _M21_, _S12_) 

_Units_ = (_Azi, _M, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _Pass, _M2) 

 

def toGDict(self, **updates): 

'''Convert this C{Inverse10Tuple} to a L{GDict}. 

 

@kwarg updates: Optional items to apply (C{nam=value} pairs) 

''' 

return _GTuple.toGDict(self, azi1=atan2d(self.salp1, self.calp1), # PYCHOK indent, namedTuple 

azi2=atan2d(self.salp2, self.calp2), # PYCHOK namedTuple 

**updates) # PYCHOK indent 

 

 

class _Wrapped(object): 

''''(INTERNAL) Wrapper for some of I{Karney}'s U{geographiclib 

<https://PyPI.org/project/geographiclib>} classes. 

''' 

 

@Property_RO # MCCABE 24 

def Geodesic(self): 

'''Get the I{wrapped} C{Geodesic} class, provided the U{geographiclib 

<https://PyPI.org/project/geographiclib>} package is installed, 

otherwise an C{ImportError}. 

''' 

_Geodesic = self.geographiclib.Geodesic 

_DIRECT3 = _Geodesic.AZIMUTH | _Geodesic.LATITUDE | _Geodesic.LONGITUDE 

_INVERSE3 = _Geodesic.AZIMUTH | _Geodesic.DISTANCE 

 

class Geodesic(_Geodesic): 

'''I{Karney}'s U{Geodesic<https://GeographicLib.SourceForge.io/html/ 

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

''' 

_debug = 0 # like .geodesicx.bases._GeodesicBase 

_E = _EWGS84 

LINE_OFF = 0 # in .azimuthal._GnomonicBase and .css.CassiniSoldner 

 

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

'''New C{Geodesic} instance. 

 

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

(L{Datum}) or the equatorial radius 

of the ellipsoid (C{meter}). 

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

B{C{a_ellipsoid}) is specified as C{meter}. 

@kwarg name: Optional name (C{str}). 

''' 

if a_ellipsoid not in (Geodesic._E, None): # spherical OK 

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

try: 

_Geodesic.__init__(self, *self.ellipsoid.a_f) 

except (TypeError, ValueError) as x: 

_raiseX(self, x, *self.ellipsoid.a_f) 

 

Area = _Geodesic.Polygon # like GeodesicExact.Area 

 

@Property 

def debug(self): 

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

''' 

return bool(self._debug) 

 

@debug.setter # PYCHOK setter! 

def debug(self, debug): 

'''Set the C{debug} option. 

 

@arg debug: Include more details in results (C{bool}). 

''' 

self._debug = _MODS.geodesicx.Caps._DEBUG_ALL if debug else 0 

 

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

'''Return the C{Direct} result. 

''' 

try: 

d = _Geodesic.Direct(self, lat1, lon1, azi1, s12, *outmask) 

except (TypeError, ValueError) as x: 

_raiseX(self, x, lat1, lon1, azi1, s12, *outmask) 

return GDict(d) 

 

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.Direct(lat1, lon1, azi1, s12, _DIRECT3) 

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

 

@Property_RO 

def ellipsoid(self): 

'''Get this geodesic's ellipsoid (C{Ellipsoid[2]}). 

''' 

return self._E 

 

@Property_RO 

def f1(self): # in .css.CassiniSoldner.reset 

'''Get the geodesic's ellipsoid I{1 - flattening} (C{float}). 

''' 

return getattr(self, '_f1', self.ellipsoid.f1) 

 

def _GDictDirect(self, lat, lon, azi, arcmode, s12_a12, 

outmask=_Geodesic.STANDARD): 

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

''' 

try: 

t = _Geodesic._GenDirect(self, lat, lon, azi, arcmode, s12_a12, outmask) 

except (TypeError, ValueError) as x: 

_raiseX(self, x, lat, lon, azi, arcmode, s12_a12, outmask) 

return Direct9Tuple(t).toGDict() # *t 

 

def _GDictInverse(self, lat1, lon1, lat2, lon2, outmask=_Geodesic.STANDARD): 

'''(INTERNAL) Get C{._GenInverse} result as C{GDict}. 

''' 

try: 

t = _Geodesic._GenInverse(self, lat1, lon1, lat2, lon2, outmask) 

except (TypeError, ValueError) as x: 

_raiseX(self, x, lat1, lon1, lat2, lon2, outmask) 

return Inverse10Tuple(t).toGDict(lon1=lon1, lon2=lon2) # *t 

 

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

'''Return the C{Inverse} result. 

''' 

try: 

d = _Geodesic.Inverse(self, lat1, lon1, lat2, lon2, *outmask) 

except (TypeError, ValueError) as x: 

_raiseX(self, x, lat1, lon1, lat2, lon2, *outmask) 

return GDict(d) 

 

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.Inverse(lat1, lon1, lat2, lon2) 

# XXX self.DISTANCE needed for 'a12'? 

return abs(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.Inverse(lat1, lon1, lat2, lon2, _INVERSE3) 

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

 

def Line(self, lat1, lon1, azi1, *caps): 

'''Set up a L{GeodesicLine} to compute several points on a 

single geodesic. 

''' 

return _wrapped.GeodesicLine(self, lat1, lon1, azi1, *caps) 

 

# Geodesic.Direct.__doc__ = _Geodesic.Direct.__doc__ 

# Geodesic.Inverse.__doc__ = _Geodesic.Inverse.__doc__ 

# Geodesic.Line.__doc__ = _Geodesic.Line.__doc__ 

return Geodesic 

 

@Property_RO # MCCABE 16 

def GeodesicLine(self): 

'''Get the I{wrapped} C{GeodesicLine} class, provided the U{geographiclib 

<https://PyPI.org/project/geographiclib>} package is installed, 

otherwise an C{ImportError}. 

''' 

_GeodesicLine = self.geographiclib.GeodesicLine 

 

class GeodesicLine(_GeodesicLine): 

'''I{Karney}'s U{GeodesicLine <https://GeographicLib.SourceForge.io/html/ 

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

''' 

def __init__(self, lat1, lon1, azi1, *caps): 

try: 

_GeodesicLine.__init__(self, lat1, lon1, azi1, *caps) 

except (TypeError, ValueError) as x: 

_raiseX(self, x, lat1, lon1, azi1, *caps) 

 

@Property_RO 

def a1(self): 

'''Get the I{equatorial arc} (C{degrees}), the arc length between 

the northward equatorial crossing and point C{(lat1, lon1)}. 

 

@see: U{EquatorialArc<https://GeographicLib.SourceForge.io/ 

C++/doc/classGeographicLib_1_1GeodesicLine.html>} 

''' 

try: 

return _atan2d(self._ssig1, self._csig1) 

except AttributeError: 

return NAN # see .geodesicx.gxline._GeodesicLineExact 

 

equatorarc = a1 

 

def ArcPosition(self, a12, *outmask): 

try: 

d = _GeodesicLine.ArcPosition(self, a12, *outmask) 

except (TypeError, ValueError) as x: 

_raiseX(self, x, a12, *outmask) 

return GDict(d) 

 

@Property_RO 

def azi0(self): # see .css.CassiniSoldner.forward4 

'''Get the I{equatorial azimuth} (C{degrees}), the azimuth of the 

geodesic line as it crosses the equator in a northward direction. 

 

@see: U{EquatorialAzimuth<https://GeographicLib.SourceForge.io/ 

C++/doc/classGeographicLib_1_1GeodesicLine.html>} 

''' 

try: 

return _atan2d(self._salp0, self._calp0) 

except AttributeError: 

return NAN # see .geodesicx.gxline._GeodesicLineExact 

 

equatorazimuth = azi0 

 

def Position(self, s12, *outmask): 

try: 

d = _GeodesicLine.Position(self, s12, *outmask) 

except (TypeError, ValueError) as x: 

_raiseX(self, x, s12, *outmask) 

return GDict(d) 

 

# GeodesicLine.ArcPosition.__doc__ = _GeodesicLine.ArcPosition.__doc__ 

# GeodesicLine.Position.__doc__ = _GeodesicLine.Position.__doc__ 

return GeodesicLine 

 

@Property_RO 

def Geodesic_WGS84(self): 

'''Get the I{wrapped} C{Geodesic.WGS84} I{instance} provided the 

U{geographiclib<https://PyPI.org/project/geographiclib>} package 

is installed, otherwise an C{ImportError}. 

''' 

return _EWGS84.geodesic 

 

@Property_RO 

def geographiclib(self): 

'''Get the imported C{geographiclib}, provided the U{geographiclib 

<https://PyPI.org/project/geographiclib>} package is installed, 

otherwise an C{ImportError}. 

''' 

g = _xgeographiclib(self.__class__, 1, 49) 

from geographiclib.geodesic import Geodesic 

g.Geodesic = Geodesic 

from geographiclib.geodesicline import GeodesicLine 

g.GeodesicLine = GeodesicLine 

from geographiclib.geomath import Math 

g.Math = Math 

return g 

 

@Property_RO # MCCABE 13 

def Math(self): 

'''Get the C{Math} class, provided the U{geographiclib 

<https://PyPI.org/project/geographiclib>} package is 

installed, otherwise C{None}. 

''' 

try: 

g = self.geographiclib 

M = g.Math 

if g.__version_info__ < (2,): 

if _K_2_0: 

M = None 

# elif not _K_2_0: # XXX 2.0? 

# _K_2_0 = False 

except (AttributeError, ImportError): 

M = None 

return M 

 

_wrapped = _Wrapped() # PYCHOK singleton, .datum, .test/base.py 

 

 

def _around(x): # in .utily.sincos2d 

'''I{Coarsen} a scalar by rounding small values to underflow to C{0.0}. 

 

@return: Coarsened value (C{float}). 

 

@see: I{Karney}'s U{Math.AngRound<https://SourceForge.net/p/ 

geographiclib/code/ci/release/tree/python/geographiclib/geomath.py>} 

''' 

try: 

return _wrapped.Math.AngRound(x) 

except AttributeError: 

pass 

if x: 

y = _1_16th - abs(x) 

if y > 0: # abs(x) < _1_16th 

x = _copysign(_1_16th - y, x) 

else: 

x = _0_0 # -0 to 0 

return x 

 

 

def _atan2d(y, x): 

'''Return C{atan2(B{y}, B{x})} in C{degrees}. 

''' 

try: 

return _wrapped.Math.atan2d(y, x) 

except AttributeError: 

return atan2d(y, x) 

 

 

def _cbrt(x): 

'''Return C{cubic root(B{x})}. 

''' 

try: 

return _wrapped.Math.cbrt(x) 

except AttributeError: 

return cbrt(x) 

 

 

def _diff182(deg0, deg): 

'''Compute C{deg - deg0}, reduced to C{[-180,180]} accurately. 

 

@return: 2-Tuple C{(delta_angle, residual)} in C{degrees}. 

''' 

try: 

return _wrapped.Math.AngDiff(deg0, deg) 

except AttributeError: 

pass 

if _K_2_0: # geographiclib 2.0 

d, t = _sum2(fremainder(-deg0, _360_0), 

fremainder( deg, _360_0)) 

d, t = _sum2(fremainder( d, _360_0), t) 

if d in (_0_0, _180_0, -_180_0): 

d = _copysign(d, -t if t else (deg - deg0)) 

else: 

d, t = _sum2(_norm180(-deg0), _norm180(deg)) 

d = _norm180(d) 

if t > 0 and d == _180_0: 

d = _N_180_0 

d, t = _sum2(d, t) 

return d, t 

 

 

# def _Equidistant(equidistant, exact=False, geodsolve=False): 

# # (INTERNAL) Get the C{EquidistantExact}, C{-GeodSolve} or 

# # C{-Karney} class if B{C{equidistant}} in not callable. 

# if equidistant is None or not callable(equidistant): 

# if exact: 

# equidistant = _MODS.azimuthal.EquidistantExact 

# elif geodsolve: 

# equidistant = _MODS.azimuthal.EquidistantGeodSolve 

# else: 

# equidistant = _MODS.azimuthal.EquidistantKarney 

# return equidistant 

 

 

def _fix90(deg): # mimick Math.LatFix 

'''Replace angle in C{degrees} outside [-90,90] by NAN. 

 

@return: Angle C{degrees} or NAN. 

''' 

try: 

return _wrapped.Math.LatFix(deg) 

except AttributeError: 

return NAN if abs(deg) > 90 else deg 

 

 

def _isfinite(x): # mimick Math.AngNormalize 

'''Check finiteness of C{x}. 

 

@return: C{True} if finite. 

''' 

try: 

return _wrapped.Math.isfinite(x) 

except AttributeError: 

return _math_isfinite(x) # and abs(x) <= _MAX 

 

 

def _norm180(deg): # mimick Math.AngNormalize 

'''Reduce angle in C{degrees} to (-180,180]. 

 

@return: Reduced angle C{degrees}. 

''' 

try: 

return _wrapped.Math.AngNormalize(deg) 

except AttributeError: 

pass 

d = fremainder(deg, _360_0) 

if d in (_180_0, -_180_0): 

d = _copysign(_180_0, deg) if _K_2_0 else _180_0 

return d 

 

 

def _norm2(x, y): # mimick Math.norm 

'''Normalize C{B{x}} and C{B{y}}. 

 

@return: 2-Tuple of C{(B{x}, B{y})}, normalized. 

''' 

try: 

return _wrapped.Math.norm(x, y) 

except AttributeError: 

return norm2(x, y) 

 

 

def _polygon(geodesic, points, closed, line, wrap): 

'''(INTERNAL) Compute the area or perimeter of a polygon, 

using a L{GeodesicExact}, L{GeodesicSolve} or (if the 

C{geographiclib} package is installed) a C{Geodesic} 

or C{_wrapped.Geodesic} instance. 

''' 

if not wrap: # capability LONG_UNROLL can't be off 

raise _ValueError(wrap=wrap) 

 

gP = geodesic.Polygon(line) 

pA = gP.AddPoint 

 

Ps = _MODS.iters.PointsIter(points, loop=1) # base=LatLonEllipsoidalBase(0, 0) 

p0 = Ps[0] 

 

# note, lon deltas are unrolled, by default 

pA(p0.lat, p0.lon) 

for p in Ps.iterate(closed=closed): 

pA(p.lat, p.lon) 

if closed and line and p != p0: 

pA(p0.lat, p0.lon) 

 

# gP.Compute returns (number_of_points, perimeter, signed area) 

return gP.Compute(False, True)[1 if line else 2] 

 

 

def _remainder(x, y): 

'''Remainder of C{x / y}. 

 

@return: Remainder in the range M{[-y / 2, y / 2]}, preserving signed 0.0. 

''' 

try: 

return _wrapped.Math.remainder(x, y) 

except AttributeError: 

return fremainder(x, y) 

 

 

if _K_2_0: 

from math import cos as _cos, sin as _sin 

 

def _sincos2(rad): 

return _sin(rad), _cos(rad) 

else: 

from pygeodesy.utily import sincos2 as _sincos2 # PYCHOK shared 

 

 

def _sincos2d(deg): 

'''Return sine and cosine of an angle in C{degrees}. 

 

@return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}. 

''' 

try: 

return _wrapped.Math.sincosd(deg) 

except AttributeError: 

return sincos2d(deg) 

 

 

def _sincos2de(deg, t): 

'''Return sine and cosine of a corrected angle in C{degrees}. 

 

@return: 2-Tuple C{(sin(B{deg}), cos(B{deg}))}. 

''' 

try: 

return _wrapped.Math.sincosde(deg, t) 

except AttributeError: 

return sincos2d(deg, adeg=t) 

 

 

def _sum2(u, v): # mimick Math::sum, actually sum2 

'''Error-free summation like C{Math::sum}. 

 

@return: 2-Tuple C{(B{u} + B{v}, residual)}. 

 

@note: The C{residual} can be the same as B{C{u}} or B{C{v}}. 

 

@see: U{Algorithm 3.1<https://www.TUHH.De/ti3/paper/rump/OgRuOi05.pdf>}. 

''' 

try: 

return _wrapped.Math.sum(u, v) 

except AttributeError: 

pass 

s = u + v 

r = s - v 

t = s - r 

# if Algorithm_3_1: 

# t = (u - t) + (v + r) 

# elif C_CPP: # Math::sum C/C++ 

# r -= u 

# t -= v 

# t += r 

# t = -t 

# else: 

t = (u - r) + (v - t) 

return s, t 

 

 

def _sum2_(s, t, *vs): 

'''Accumulate any B{C{vs}} into a previous C{_sum2(s, t)}. 

 

@return: 2-Tuple C{(B{s} + B{t} + B{vs}, residual)}. 

 

@see: I{Karney's} C++ U{Accumulator<https://GeographicLib.SourceForge.io/ 

html/Accumulator_8hpp_source.html>} comments for more details and 

function C{_sum2} above. 

 

@note: NOT "error-free", see C{pygeodesy.test/testKarney.py}. 

''' 

_s2, _u0 = _sum2, unsigned0 

for v in vs: 

if v: 

t, u = _s2(t, v) # start at the least- 

if s: 

s, t = _s2(s, t) # significant end 

if s: 

t += u # accumulate u into t 

# elif t: # s == 0 implies t == 0 

# raise _AssertionError(t=t, txt=_not_(_0_)) 

else: 

s = _u0(u) # result is u, t = 0 

else: 

s, t = _u0(t), u 

return s, t 

 

 

def _unroll2(lon1, lon2, wrap=False): # see .ellipsoidalBaseDI._intersects2 

'''Unroll B{C{lon2 - lon1}} like C{geodesic.Geodesic.Inverse}. 

 

@return: 2-Tuple C{(B{lon2} - B{lon1}, B{lon2})} with B{C{lon2}} 

unrolled if B{C{wrap}} is C{True}, normalized otherwise. 

''' 

if wrap: 

d, t = _diff182(lon1, lon2) 

lon2, _ = _sum2_(d, t, lon1) # (lon1 + d) + t 

else: 

lon2 = _norm180(lon2) 

return (lon2 - lon1), lon2 

 

# **) 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.