# Coverage for pygeodesy/karney.py : 97%

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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. 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 copysign0, unsigned0, _xgeographiclib, \ _xImportError, isodd # PYCHOK shared from pygeodesy.datums import Ellipsoid2, _ellipsoidal_datum, _WGS84 # from pygeodesy.ellipsoids import Ellipsoid2 # from .datums from pygeodesy.errors import _AssertionError, _or, _ValueError, _xkwds # PYCHOK shared from pygeodesy.interns import MAX as _MAX, NAN, NN, _DOT_, _lat1_, _lat2_, _lon2_, \ _0_0, _1_0, _2_0, _16_0, _180_0, _N_180_0, _360_0 from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS from pygeodesy.named import callername, classname, _Dict, _NamedBase, \ _NamedTuple, _Pass, unstr # PYCHOK shared from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple from pygeodesy.props import Property, Property_RO # from pygeodesy.streps import unstr # from .named 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, unroll180, wrap360 from math import fmod as _fmod __all__ = _ALL_LAZY.karney __version__ = '22.02.28' _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! 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 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 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) _LineTemp = Line # for .azimuthal._GnomonicBase.reverse, matching # PYCHOK .geodesicx.GeodesictExact._LineTemp 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}. ''' _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) 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) 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 def Math(self): '''Get the C{Math} class, provided the U{geographiclib <https://PyPI.org/project/geographiclib>} package is installed, otherwise C{None}. ''' try: M = self.geographiclib.Math # replace karney. with Math. functions k = _MODS.karney k._around = M.AngRound k._diff182 = M.AngDiff k._fix90 = M.LatFix k._isfinite = M.isfinite k._norm180 = M.AngNormalize k._sum2 = M.sum try: # geographiclib 1.49 k._remainder = M.remainder except AttributeError: pass except ImportError: M = None return M _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 = _1_16th - abs(x) if y > 0: # abs(x) < _1_16th x = copysign0(_1_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 = _N_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: # 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. ''' M = _wrapped.Math return M.LatFix(deg) if M else (NAN if abs(deg) > 90 else deg) def _isfinite(x): # mimick Math.AngNormalize '''Check finiteness of C{x}. @return: C{True} if finite. ''' M = _wrapped.Math return M.isfinite(x) if M else (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 return M.AngNormalize(deg) if M else _remod(deg, _360_0, _180_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) 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]}. ''' M = _wrapped.Math if M: try: # geographiclib 1.49 return M.remainder(x, y) except AttributeError: pass return _remod(x, y, 0) def _remod(x, y, y_2): '''(INTERNAL) Remainder/modulo in the range C{[-B{y_2}, B{y_2}]}. ''' # with Python 2.7.16 and 3.7.3 on macOS 10.13.6 and # with Python 3.10.2 on macOS 12.2.1 M1 arm64 native # 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 == (-360) % 360 # -0.0 % 360 == 0.0 == (-0.0) % 360 # -360.0 % 360 == 0.0 == (-360.0) % 360 # 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. if x: if _isfinite(x): h = y_2 if y_2 else (y / _2_0) z = _fmod(x, y) x = (z + y) if z < -h else (z if z < h else (z - y)) else: # PYCHOK no cover x = NAN return x # maintain -0.0 signed 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>}. ''' M = _wrapped.Math if M: return M.sum(u, v) 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}. ''' for v in vs: if v: t, u = _sum2(t, v) # start at least- if s: s, t = _sum2(s, t) # significant end if s: t += u # accumulate u to t # elif t: # s == 0 implies t == 0 # raise _AssertionError(t=t, txt=_not(_0_)) else: s = unsigned0(u) # result is u, t = 0 else: s, t = unsigned0(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.