# Coverage for pygeodesy/karney.py : 94%

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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 U{geographiclib<https://PyPI.org/project/geographiclib>}, Python package, provided that package is installed. The I{wrapped} class methods return a C{named._NamedDict}-like instance providing access to the L{GDict} items by key or by attribute name. Following are 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.areaOf}, L{ellipsoidalExact.intersections2}, L{ellipsoidalExact.isclockwise}, L{ellipsoidalExact.nearestOn}, L{ellipsoidalExact.LatLon.intersections2}, L{ellipsoidalExact.LatLon.nearestOn}, L{ellipsoidalExact.perimeterOf} - L{ellipsoidalKarney.areaOf}, L{ellipsoidalKarney.intersections2}, L{ellipsoidalKarney.isclockwise}, L{ellipsoidalKarney.nearestOn}, L{ellipsoidalKarney.LatLon.intersections2}, L{ellipsoidalKarney.LatLon.nearestOn}, L{ellipsoidalKarney.perimeterOf} are implementations of I{Karney}'s post U{The B{ellipsoidal} case <https://GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>} and 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 _xversion from pygeodesy.datums import _ellipsoidal_datum, _WGS84 # PYCHOK used! from pygeodesy.ellipsoids import Ellipsoid2 from pygeodesy.errors import _ValueError 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 from pygeodesy.utily import atan2d, unroll180, wrap360 from math import copysign, fmod __all__ = _ALL_LAZY.karney __version__ = '21.06.09' _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}, 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}, {Clon1}, 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 lenght C{1a12} 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 = copysign(_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.