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# -*- coding: utf-8 -*- 

 

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

 

Wrapper around I{Charles Karney}'s Python classes C{Geodesic} and C{GeodesicLine} and C{Math} 

functions C{AngDiff}, C{AngNormalize}, C{LatFix} and C{sum} 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 providing access to the C{dict} items 

by C{key} or by C{attribute} name. 

 

Following are the U{PyGeodesy<https://PyPI.org/project/PyGeodesy>} classes and functions I{transcoded} 

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

 

- 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{atan2d}, L{sincos2}, L{sincos2d}-- U{Math<https://GeographicLib.sourceforge.io/html/ 

classGeographicLib_1_1Math.html>} 

 

The following U{PyGeodesy<https://PyPI.org/project/PyGeodesy>} module, classes and functions are I{wrappers} 

around some of I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>} or C++ U{Utility 

programs<https://GeographicLib.SourceForge.io/html/utilities.html>}: 

 

- L{karney}, L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{EquidistantKarney}, L{FrechetKarney}, 

L{geodsolve}, L{GeodesicSolve}, L{GeodesicLineSolve}, L{GnomonicGeodSolve}, L{GnomonicKarney}, 

L{HeightIDWkarney} 

 

Lastly, spherical functions: 

 

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

 

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

<http://OSGeo-org.1560.x6.Nabble.com/Area-of-a-spherical-polygon-td3841625.html>} and ellipsoidal 

functions and methods: 

 

- 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}). 

''' 

 

from pygeodesy.basics import copysign0, _xversion 

from pygeodesy.datums import _ellipsoidal_datum, _WGS84 # PYCHOK used! 

from pygeodesy.ellipsoids import Ellipsoid2 

from pygeodesy.errors import _ValueError, _xkwds # PYCHOK shared 

from pygeodesy.interns import MAX as _MAX, NAN, NN, _lat1_, \ 

_lat2_, _lon2_, _0_0, _1_0, _2_0, \ 

_16_0, _180_0, _360_0 

from pygeodesy.iters import PointsIter 

from pygeodesy.lazily import _ALL_LAZY 

from pygeodesy.named import _Dict, _NamedTuple, _Pass 

from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple 

from pygeodesy.props import Property, Property_RO 

from pygeodesy.units import Degrees as _Deg, Meter as _M, \ 

Meter2 as _M2, _1mm as _TOL_M # PYCHOK shared 

from pygeodesy.utily import atan2d, unroll180, wrap360 

 

from math import fmod 

 

 

__all__ = _ALL_LAZY.karney 

__version__ = '21.07.03' 

 

_16th = _1_0 / _16_0 

 

_a12_ = 'a12' 

_azi1_ = 'azi1' 

_azi2_ = 'azi2' 

_lon1_ = 'lon1' 

_m12_ = 'm12' 

_M12_ = 'M12' 

_M21_ = 'M21' 

_s12_ = 's12' 

_S12_ = 'S12' 

 

 

class _GTuple(_NamedTuple): # in .testNamedTuples 

'''(INTERNAL) Helper. 

''' 

def toGDict(self, **updates): 

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

 

@kwarg updates: Optional updates 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_ = (_Deg, _Deg, _Deg, _Deg, _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, compatible 

with I{Karney}'s C{geographiclib} method C{Direct}. 

 

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

s12, m12, M12, M21, S12)} 

''' 

 

def _9Tuple(a12=dflt, lat2=dflt, lon2=dflt, azi2=dflt, 

s12=dflt, m12=dflt, M12=dflt, M21=dflt, S12=dflt, 

**unused): 

return Direct9Tuple(a12, lat2, lon2, azi2, 

s12, m12, M12, M21, S12) 

 

return _9Tuple(**self) 

 

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. 

 

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

s12, a12, m12, M12, M21, S12)}. 

''' 

 

def _12Tuple(lat1=dflt, lon1=dflt, azi1=dflt, 

lat2=dflt, lon2=dflt, azi2=dflt, s12=dflt, a12=dflt, 

m12=dflt, M12=dflt, 

M21=dflt, S12=dflt, 

**unused): 

return GeodSolve12Tuple(lat1, lon1, azi1, lat2, lon2, azi2, 

s12, a12, m12, M12, M21, S12) 

 

return _12Tuple(**self) 

 

def toInverse10Tuple(self, dflt=NAN): 

'''Convert this L{GDict} result to a 10-tuple, compatible 

with I{Karney}'s C{geographiclib} method C{Indirect}. 

 

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

salp2, calp2, m12, M12, M21, S12)}. 

''' 

 

def _10Tuple(a12=dflt, s12=dflt, salp1=dflt, calp1=dflt, 

salp2=dflt, calp2=dflt, 

m12=dflt, M12=dflt, 

M21=dflt, S12=dflt, 

**unused): 

return Inverse10Tuple(a12, s12, salp1, calp1, salp2, calp2, 

m12, M12, M21, S12) 

 

return _10Tuple(**self) 

 

 

class GeodesicError(_ValueError): # PYCHOK exported 

'''Error raised for I{geodesicx}'s methods for lack of convergence 

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

C{meter} I{squared} and geodesic scales C{M12} and C{M21} 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_ = (_Deg, _Deg, _Deg, _Deg, _Deg, _Deg, _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 

sines and cosines of initial and final (forward) azimuths. 

''' 

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

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

 

 

class _Wrapped(object): 

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

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

''' 

_geographiclib = None 

 

@Property_RO # MCCABE 14 

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}. 

''' 

self._xgeographiclib(_Wrapped.Geodesic) 

from geographiclib.geodesic import Geodesic as _Geodesic 

 

class Geodesic(_Geodesic): 

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

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

''' 

 

def __init__(self, a_ellipsoid, 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 f is None: 

self._E = _ellipsoidal_datum(a_ellipsoid, name=name).ellipsoid 

else: 

self._E = Ellipsoid2(a_ellipsoid, f, name=name) 

_Geodesic.__init__(self, self.ellipsoid.a, self.ellipsoid.f) 

 

Area = _Geodesic.Polygon # like GeodesicExact.Area 

 

_debug = 0 # like .geodesicx.bases._GeodesicBase 

 

@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}). 

''' 

from pygeodesy.geodesicx.gxbases import Caps 

self._debug = Caps._DEBUG_ALL if debug else 0 

 

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

'''Return the C{Direct} result. 

''' 

d = _Geodesic.Direct(self, 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)}. 

''' 

m = self.AZIMUTH | self.LATITUDE | self.LONGITUDE 

d = self.Direct(lat1, lon1, azi1, s12, m) 

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

 

@Property_RO 

def ellipsoid(self): 

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

''' 

return self._E 

 

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

outmask=_Geodesic.STANDARD): 

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

''' 

def _toGdict(a12, lat2, lon2, azi2, 

s12, m12, M12, M21, S12): 

return GDict(a12=a12, lat2=lat2, lon2=lon2, azi2=azi2, 

s12=s12, m12=m12, M12=M12, M21=M21, S12=S12) 

 

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

return _toGdict(*t) 

 

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

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

''' 

def _toGdict(a12, s12, salp1, calp1, salp2, calp2, 

m12, M12, M21, S12): 

return GDict(a12=a12, s12=s12, 

salp1=salp1, calp1=calp1, azi1=atan2d(salp1, calp1), 

salp2=salp2, calp2=calp2, azi2=atan2d(salp2, calp2), 

m12=m12, M12=M12, M21=M21, S12=S12, lon1=lon1) 

 

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

return _toGdict(*t) 

 

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

'''Return the C{Inverse} result. 

''' 

d = _Geodesic.Inverse(self, 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)}. 

''' 

m = self.DISTANCE | self.AZIMUTH 

d = self.Inverse(lat1, lon1, lat2, lon2, m) 

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

 

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

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

 

_Line = Line # for .azimuthal._GnomonicBase.reverse, matching 

# PYCHOK .geodesicx.GeodesictExact._Line and -._GDictDirect 

 

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

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

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

return Geodesic 

 

@Property_RO 

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}. 

''' 

self._xgeographiclib(_Wrapped.GeodesicLine) 

from geographiclib.geodesicline import GeodesicLine as _GeodesicLine 

 

class GeodesicLine(_GeodesicLine): 

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

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

''' 

def ArcPosition(self, a12, *outmask): 

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

return GDict(d) 

 

def Position(self, s12, *outmask): 

d = _GeodesicLine.Position(self, 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 _WGS84.ellipsoid.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}. 

''' 

return self._xgeographiclib(_Wrapped.geographiclib) 

 

@Property_RO 

def Math(self): 

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

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

installed, otherwise C{None}. 

''' 

try: 

self._xgeographiclib(_Wrapped.Math) 

from geographiclib.geomath import Math 

# replace karney. with Math. functions 

from pygeodesy import karney 

karney._around = Math.AngRound 

karney._diff182 = Math.AngDiff 

karney._fix90 = Math.LatFix 

karney._isfinite = Math.isfinite 

karney._norm180 = Math.AngNormalize 

karney._sum2 = Math.sum 

try: # geographiclib 1.49 

karney._remainder = Math.remainder 

except AttributeError: 

pass 

except ImportError: 

Math = None 

return Math 

 

def _xgeographiclib(self, where): 

'''(INTERNAL) Import C{geographiclib}. 

''' 

if self._geographiclib is None: 

import geographiclib as g 

self._geographiclib = _xversion(g, _Wrapped, 1, 49, name=where.name) 

return self._geographiclib 

 

_wrapped = _Wrapped() # PYCHOK singleton, .datum 

 

 

def _around(x): 

'''Coarsen a scalar to zero. 

 

@return: Coarsened value (C{float}). 

''' 

M = _wrapped.Math 

if M: 

return M.AngRound(x) 

 

if x: 

y = abs(x) 

if y < _16th: 

y = _16th - y 

x = copysign0(_16th - y, x) 

else: 

x = _0_0 # -0 to 0 

return x 

 

 

def _diff182(deg0, deg): # mimick Math.AngDiff 

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

 

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

''' 

M = _wrapped.Math 

if M: 

return M.AngDiff(deg0, deg) 

 

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

d = _norm180(d) 

if t > 0 and d == _180_0: 

d = -_180_0 

return _sum2(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: 

# from pygeodesy.azimuthal import EquidistantExact as equidistant 

# elif geodsolve: 

# from pygeodesy.azimuthal import EquidistantGeodSolve as equidistant 

# else: 

# from pygeodesy.azimuthal import EquidistantKarney as equidistant 

# return equidistant 

 

 

def _fix90(deg): # mimick Math.LatFix 

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

 

@return: Angle C{degrees} or NAN. 

''' 

M = _wrapped.Math 

if M: 

return M.LatFix(deg) 

 

return NAN if abs(deg) > 90 else deg 

 

 

def _fsum2_(*vs): # see .test/testKarney.py 

'''Cascaded summation, like C{.fmath.fsum_}. 

 

@arg vs: Values to be added (C{scalar}[]). 

 

@return: 2-Tuple C{(sum_of_vs, residual)}. 

 

@note: NOT "error-free", see .test/testKarney.py. 

 

@see: U{Algorithm 4.1<http://www.ti3.TUHH.De/paper/rump/OgRuOi05.pdf>}. 

''' 

s = t = _0_0 

for v in vs: 

s, t = _3sum2(s, t, v) 

return _sum2(s, t) 

 

 

def _isfinite(x): # mimick Math.AngNormalize 

'''Check finitenessof C{x}. 

 

@return: True if finite. 

''' 

M = _wrapped.Math 

if M: 

return M.isfinite(x) 

 

return abs(x) <= _MAX 

 

 

def _norm180(deg): # mimick Math.AngNormalize 

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

 

@return: Reduced angle C{degrees}. 

''' 

M = _wrapped.Math 

if M: 

return M.AngNormalize(deg) 

 

# with Python 2.7.16 and 3.7.3 on macOS 10.13.6 

# fmod( 0, 360) == 0.0 

# fmod( 360, 360) == 0.0 

# fmod(-0, 360) == 0.0 

# fmod(-0.0, 360) == -0.0 

# fmod(-360, 360) == -0.0 

# however, using the % operator ... 

# 0 % 360 == 0 

# 360 % 360 == 0 

# 360.0 % 360 == 0.0 

# -0 % 360 == 0 

# -360 % 360 == 0 

# -0.0 % 360 == 0.0 

# -360.0 % 360 == 0.0 

 

# On Windows 32-bit with Python 2.7, math.fmod(-0.0, 360) 

# == +0.0. This fixes this bug. See also Math::AngNormalize 

# in the C++ library, Math::sincosd has a similar fix. 

d = (fmod(deg, _360_0) if _isfinite(deg) else NAN) if deg else deg 

return (d + _360_0) if d < -_180_0 else (d # XXX was <= twice 

if d < _180_0 else (d - _360_0)) 

 

 

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) 

p_ = gP.AddPoint 

 

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

p0 = Ps[0] 

 

# note, lon deltas are unrolled, by default 

p_(p0.lat, p0.lon) 

for p in Ps.iterate(closed=closed): 

p_(p.lat, p.lon) 

if closed and line and p != p0: 

p_(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]}. 

''' 

M = _wrapped.Math 

if M: 

try: # geographiclib 1.49 

return M.remainder(x, y) 

except AttributeError: 

pass 

 

z = (fmod(x, y) if _isfinite(x) else NAN) if x else x 

# On Windows 32-bit with python 2.7, math.fmod(-0.0, 360) 

# == +0.0. This fixes this bug. See also Math::AngNormalize 

# in the C++ library, Math.sincosd has a similar fix. 

h = y / _2_0 

return (z + y) if z < -h else (z 

if z < h else (z - y)) 

 

 

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

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

 

@return: 2-Tuple C{(sum_u_plus_v, residual)}. 

 

@note: The C{residual} can be the same as 

B{C{u}} or B{C{v}}. 

 

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

''' 

M = _wrapped.Math 

if M: 

return M.sum(u, v) 

 

s = u + v 

r = s - v 

t = s - r 

# if True: # Algorithm 3.1 

t = (u - r) + (v - t) 

 

# else: # in Math C/C++ 

# r -= u 

# t -= v 

# t = -(r + t) 

 

# u + v = s + t 

# = round(u + v) + t 

return s, t 

 

 

def _3sum2(s, t, x): 

'''Accumulate B{C{x}} into C{_sum2(s, t)}. 

 

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

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

''' 

if x: 

t, u = _sum2(t, x) # start at least- 

s, t = _sum2(s, t) # significant end 

if s: 

t += u # accumulate u to t 

else: 

s = u # result is 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{(lon2 - lon1, lon2)} with B{C{lon2}} unrolled 

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

''' 

if wrap: 

d, t = _diff182(lon1, lon2) 

lon2 = (lon1 + d) + t # _fsum2_(lon1, d, t) 

else: 

lon2 = _norm180(lon2) 

return (lon2 - lon1), lon2 

 

# **) MIT License 

# 

# Copyright (C) 2016-2021 -- 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.