# Coverage for pygeodesy/karney.py : 95%

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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. 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/C++/doc/ classGeographicLib_1_1AlbersEqualArea.html>} - L{CassiniSoldner} -- U{CassiniSoldner<https://GeographicLib.SourceForge.io/C++/doc/ classGeographicLib_1_1CassiniSoldner.html>} - L{EcefKarney} -- U{Geocentric<https://GeographicLib.SourceForge.io/C++/doc/ classGeographicLib_1_1Geocentric.html>} - L{Elliptic} -- U{EllipticFunction<https://GeographicLib.SourceForge.io/C++/doc/ classGeographicLib_1_1EllipticFunction.html>} - L{EquidistantExact}, L{EquidistantGeodSolve}, L{EquidistantKarney} -- U{AzimuthalEquidistant <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1AzimuthalEquidistant.html>} - L{Etm}, L{ExactTransverseMercator} -- U{TransverseMercatorExact <https://GeographicLib.SourceForge.io/C++/doc/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/C++/doc/ classGeographicLib_1_1GeodesicExact.html>}, U{GeodesicLineExact<https://GeographicLib.SourceForge.io/C++/doc/ classGeographicLib_1_1GeodesicLineExact.html>} - L{GeoidKarney} -- U{Geoid<https://GeographicLib.SourceForge.io/C++/doc/geoid.html>} - L{Georef} -- U{Georef<https://GeographicLib.SourceForge.io/C++/doc/ classGeographicLib_1_1Georef.html>} - L{GnomonicExact}, L{GnomonicGeodSolve}, L{GnomonicKarney} -- U{Gnomonic <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Gnomonic.html>} - L{KTransverseMercator} - U{TransverseMercator <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>} - L{LocalCartesian}, L{Ltp} -- U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/ classGeographicLib_1_1LocalCartesian.html>} - L{Osgr} -- U{OSGB<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1OSGB.html>}. - L{Rhumb}, L{RhumbLine} -- U{Rhumb<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Rhumb.html>}, U{RhumbLine<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1RhumbLine.html>}, U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1TransverseMercator.html>} - L{Ups} -- U{PolarStereographic<https://GeographicLib.SourceForge.io/C++/doc/ classGeographicLib_1_1PolarStereographic.html>} - L{Utm} -- U{TransverseMercator<https://GeographicLib.SourceForge.io/C++/doc/ classGeographicLib_1_1TransverseMercator.html>} - L{UtmUps}, L{Epsg} -- U{UTMUPS<https://GeographicLib.SourceForge.io/C++/doc/ classGeographicLib_1_1UTMUPS.html>} - L{pygeodesy.atand}, L{pygeodesy.atan2d}, L{pygeodesy.sincos2}, L{pygeodesy.sincos2d}, L{pygeodesy.tand} -- U{ Math<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>} are I{transcoded} from C++ classes in I{Karney}'s U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/annotated.html>}. 2. These C{pygeodesy} modules and classes - L{ellipsoidalGeodSolve}, L{ellipsoidalKarney}, L{geodsolve}, L{karney}, L{rhumbsolve} - 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}, C++ utility U{GeodSolve<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} or C++ utility U{RhumbSolve<https://GeographicLib.SourceForge.io/C++/doc/RhumbSolve.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, neg, unsigned0, _xgeographiclib, \ _xImportError, _xversion_info, _xinstanceof, \ _zip, isodd # PYCHOK shared from pygeodesy.constants import NAN, _isfinite as _math_isfinite, _0_0, _1_16th, \ _180_0, _N_180_0, _360_0 from pygeodesy.datums import _a_ellipsoid, _WGS84 from pygeodesy.errors import _AssertionError, _ValueError, _xkwds, _xkwds_get, \ _or # PYCHOK shared from pygeodesy.fmath import cbrt, fremainder, norm2, hypot as _hypot, unstr # PYCHOK shared from pygeodesy.interns import NN, _2_, _a12_, _area_, _azi2_, _DOT_, _lat2_, \ _lon2_, _m12_, _M12_, _M21_, _number_, _s12_, _S12_ from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS, _getenv from pygeodesy.named import callername, classname, _Dict, _NamedBase, \ _NamedTuple, _Pass from pygeodesy.namedTuples import Destination3Tuple, Distance3Tuple from pygeodesy.props import deprecated_method, Property, Property_RO, 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, Number_, \ Precision_, _1mm as _TOL_M # PYCHOK shared from pygeodesy.utily import atan2d, sincos2d, tand, unroll180, wrap360 __all__ = _ALL_LAZY.karney __version__ = '22.09.14' _EWGS84 = _WGS84.ellipsoid # PYCHOK in .geodesicx.gx, .ktm, .rhumbx, .solveBase _K_2_0 = _getenv('PYGEODESY_GEOGRAPHICLIB', _2_) == _2_ _perimeter_ = 'perimeter' 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)) # strict=True if updates: r.update(updates) if self._iteration is not None: r._iteration = self._iteration return r class _Lat(Lat): '''(INTERNAL) Latitude B{C{lat}}. ''' def __init__(self, *lat, **Error_name): kwds = _xkwds(Error_name, clip=0, Error=GeodesicError) Lat.__new__(_Lat, *lat, **kwds) class _Lon(Lon): '''(INTERNAL) Longitude B{C{lon}}. ''' def __init__(self, *lon, **Error_name): kwds = _xkwds(Error_name, clip=0, Error=GeodesicError) Lon.__new__(_Lon, *lon, **kwds) class Area3Tuple(_NamedTuple): # in .geodesicx.gxarea '''3-Tuple C{(number, perimeter, area)} with the C{number} of points on the polygon or polyline, the C{perimeter} in C{meter} and the C{area} in C{meter} I{squared}. ''' _Names_ = (_number_, _perimeter_, _area_) _Units_ = ( Number_, _M, _M2) class Caps(object): # PYCHOK '''(INTERNAL) Overriden by C{Caps} below. ''' EMPTY = 0 # formerly aka NONE LATITUDE = 1 << 7 # compute latitude C{lat2} LONGITUDE = 1 << 8 # compute longitude C{lon2} AZIMUTH = 1 << 9 # azimuths C{azi1} and C{azi2} DISTANCE = 1 << 10 # compute distance C{s12} DISTANCE_IN = 1 << 11 # allow distance C{s12} in Direct REDUCEDLENGTH = 1 << 12 # compute reduced length C{m12} GEODESICSCALE = 1 << 13 # compute geodesic scales C{M12} and C{M21} AREA = 1 << 14 # compute area C{S12} STANDARD = AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE ALL = 0x7F80 # without LONG_UNROLL, LINE_OFF, REVERSE2 and _DEBUG_* LINE_OFF = 1 << 15 # Line without updates from parent geodesic or rhumb LONG_UNROLL = 1 << 16 # unroll C{lon2} in .Direct and .Position REVERSE2 = 1 << 17 # reverse C{azi2} LATITUDE_LONGITUDE = LATITUDE | LONGITUDE LATITUDE_LONGITUDE_AREA = LATITUDE | LONGITUDE | AREA AZIMUTH_DISTANCE = AZIMUTH | DISTANCE AZIMUTH_DISTANCE_AREA = AZIMUTH | DISTANCE | AREA _ANGLE_ONLY = 1 << 18 # angular distance C{a12} only _SALPs_CALPs = 1 << 19 # (INTERNAL) GeodesicExact._GenInverse _DEBUG_AREA = 1 << 20 # (INTERNAL) include Line details _DEBUG_DIRECT = 1 << 21 # (INTERNAL) include Direct details _DEBUG_INVERSE = 1 << 22 # (INTERNAL) include Inverse details _DEBUG_LINE = 1 << 23 # (INTERNAL) include Line details _DEBUG_ALL = _DEBUG_AREA | _DEBUG_DIRECT | _DEBUG_INVERSE | \ _DEBUG_LINE | _ANGLE_ONLY | _SALPs_CALPs _OUT_ALL = ALL _OUT_MASK = ALL | LONG_UNROLL | REVERSE2 | _DEBUG_ALL _AZIMUTH_LATITUDE_LONGITUDE = AZIMUTH | LATITUDE | LONGITUDE _DEBUG_DIRECT_LINE = _DEBUG_DIRECT | _DEBUG_LINE _DISTANCE_IN_OUT = DISTANCE_IN & _OUT_MASK _LINE = AZIMUTH | LATITUDE | LONG_UNROLL _REDUCEDLENGTH_GEODESICSCALE = REDUCEDLENGTH | GEODESICSCALE # _REDUCEDLENGTH_GEODESICSCALE_DISTANCE = REDUCEDLENGTH | GEODESICSCALE | DISTANCE Caps = Caps() # PYCHOK singleton '''I{Enum}-style masks to be bit-C{or}'ed to specify geodesic or rhumb capabilities (C{caps}) and expected results (C{outmask}). C{AREA} - compute area C{S12}, C{AZIMUTH} - include azimuths C{azi1} and C{azi2}, C{DISTANCE} - compute distance C{s12}, C{DISTANCE_IN} - allow distance C{s12} in C{.Direct}, C{EMPTY} - nothing, formerly aka C{NONE}, C{GEODESICSCALE} - compute geodesic scales C{M12} and C{M21}, C{LINE_OFF} - Line without updates from parent geodesic or rhumb. C{LATITUDE} - compute latitude C{lat2}, C{LONGITUDE} - compute longitude C{lon2}, C{LONG_UNROLL} - unroll C{lon2} in C{.Direct}, C{REDUCEDLENGTH} - compute reduced length C{m12}, C{REVERSE2} - reverse C{azi2}, and C{ALL} - all of the above. C{STANDARD} = C{AZIMUTH | DISTANCE | DISTANCE_IN | LATITUDE | LONGITUDE}''' class _CapsBase(_NamedBase): # in .geodesicx.gxbases, .rhumbx '''(INTERNAL) Base class for C{[_]Geodesic*Exact}. ''' ALL = Caps.ALL AREA = Caps.AREA AZIMUTH = Caps.AZIMUTH DISTANCE = Caps.DISTANCE DISTANCE_IN = Caps.DISTANCE_IN EMPTY = Caps.EMPTY # aka NONE GEODESICSCALE = Caps.GEODESICSCALE LATITUDE = Caps.LATITUDE LINE_OFF = Caps.LINE_OFF LONGITUDE = Caps.LONGITUDE LONG_UNROLL = Caps.LONG_UNROLL REDUCEDLENGTH = Caps.REDUCEDLENGTH STANDARD = Caps.STANDARD _caps = 0 # None _debug = 0 # or Caps._DEBUG_... @Property_RO def caps(self): '''Get the capabilities (bit-or'ed C{Caps}). ''' return self._caps def caps_(self, caps): '''Check the available capabilities. @arg caps: Bit-or'ed combination of L{Caps} values for all capabilities to be checked. @return: C{True} if I{all} B{C{caps}} are available, C{False} otherwise (C{bool}). ''' caps &= Caps._OUT_ALL return (self.caps & caps) == caps @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 (C{bool}) to include more details in L{GDict} results. ''' self._debug = Caps._DEBUG_ALL if debug else 0 def _iter2tion(self, r, s): '''(INTERNAL) Copy C{C{s}.iter} into C{B{r}._iteration}. ''' i = _xkwds_get(s, iter=None) if i is not None: self._iteration = r._iteration = i 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): # XXX _NamedDict '''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. ''' _iteration = None # Iteration number (C{int}) or C{None} @property_RO def iteration(self): # see .named._NamedBase '''Get the iteration number (C{int}) or C{None} if not available/applicable. ''' return self._iteration 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/C++/doc/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(_MODS.geodsolve.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) @deprecated_method def toRhumb7Tuple(self, dflt=NAN): '''DEPRECATED, used method C{toRhumb8Tuple}. @return: A I{DEPRECATED} L{Rhumb7Tuple}. ''' return self._toTuple(_MODS.deprecated.Rhumb7Tuple, dflt) def toRhumb8Tuple(self, dflt=NAN): '''Convert this L{GDict} result to a 8-tuple. @kwarg dflt: Default value for missing items (C{any}). @return: L{Rhumb8Tuple}C{(lat1, lon1, lat2, lon2, azi12, s12, S12, a12)}. ''' return self._toTuple(_MODS.rhumbx.Rhumb8Tuple, dflt) def toRhumbSolve7Tuple(self, dflt=NAN): '''Convert this L{GDict} result to a 8-tuple. @kwarg dflt: Default value for missing items (C{any}). @return: L{RhumbSolve7Tuple}C{(lat1, lon1, lat2, lon2, azi12, s12, S12)}. ''' return self._toTuple(_MODS.rhumbsolve.RhumbSolve7Tuple, dflt) def _toTuple(self, nTuple, dflt): '''(INTERNAL) Convert this C{GDict} to an B{C{nTuple}}. ''' _g = getattr t = tuple(_g(self, n, dflt) for n in nTuple._Names_) return nTuple(t, iteration=self._iteration) class GeodesicError(_ValueError): '''Error raised for L{pygeodesy.geodesicx} lack of convergence or other L{pygeodesy.geodesicx} or L{pygeodesy.karney} issues. ''' pass 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/C++/doc/ 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 = _a_ellipsoid(a_ellipsoid, f, name=name) # raiser=NN 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 (C{bool}) to include more details in L{GDict} results. ''' 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 r = self.Inverse(lat1, lon1, lat2, lon2) # XXX self.DISTANCE needed for 'a12'? return abs(r.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)}. ''' r = self.Inverse(lat1, lon1, lat2, lon2, _INVERSE3) return Distance3Tuple(r.s12, wrap360(r.azi1), wrap360(r.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/C++/doc/ 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 _xversion_info(g) < (2,): if _K_2_0: M = None # elif not _K_2_0: # XXX set 2.0? # _K_2_0 = True 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 _copyBit(x, y): '''Like C{copysign0(B{x}, B{y})}, with C{B{x} > 0}. ''' return (-x) if _signBit(y) else 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, _N_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 _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 _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 _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 _polynomial(x, cs, i, j): # PYCHOK shared '''(INTERNAL) Like C{GeographicLib.Math.hpp.polyval} but with a different signature and cascaded summation as C{karney._sum2_}. @return: M{sum(cs[k] * x**(j - k - 1) for k in range(i, j)} ''' s, t = cs[i], _0_0 _s2_ = _sum2_ for c in cs[i+1:j]: s, t = _s2_(s * x, t * x, c) return s # + t 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)) 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 pygeodesy.basics import signBit as _signBit 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 _signBit(x): '''(INTERNAL) GeographicLin 1.52-. ''' return x < 0 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} + sum(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 _tand(x): '''Return C{tan(B{x})} in C{degrees}. ''' try: return _wrapped.Math.tand(x) except AttributeError: return tand(x) 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 def _unsigned2(x): '''(INTERNAL) Unsign B{C{x}}. ''' return (neg(x), True) if _signBit(x) else (x, False) __all__ += _ALL_DOCS(_CapsBase) # **) 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.