O i%dZddlZddlZddlmZddlmZddlmZGddZ e ej ej e _ dS)aODefine the :class:`~geographiclib.geodesic.Geodesic` class The ellipsoid parameters are defined by the constructor. The direct and inverse geodesic problems are solved by * :meth:`~geographiclib.geodesic.Geodesic.Inverse` Solve the inverse geodesic problem * :meth:`~geographiclib.geodesic.Geodesic.Direct` Solve the direct geodesic problem * :meth:`~geographiclib.geodesic.Geodesic.ArcDirect` Solve the direct geodesic problem in terms of spherical arc length :class:`~geographiclib.geodesicline.GeodesicLine` objects can be created with * :meth:`~geographiclib.geodesic.Geodesic.Line` * :meth:`~geographiclib.geodesic.Geodesic.DirectLine` * :meth:`~geographiclib.geodesic.Geodesic.ArcDirectLine` * :meth:`~geographiclib.geodesic.Geodesic.InverseLine` :class:`~geographiclib.polygonarea.PolygonArea` objects can be created with * :meth:`~geographiclib.geodesic.Geodesic.Polygon` The public attributes for this class are * :attr:`~geographiclib.geodesic.Geodesic.a` :attr:`~geographiclib.geodesic.Geodesic.f` *outmask* and *caps* bit masks are * :const:`~geographiclib.geodesic.Geodesic.EMPTY` * :const:`~geographiclib.geodesic.Geodesic.LATITUDE` * :const:`~geographiclib.geodesic.Geodesic.LONGITUDE` * :const:`~geographiclib.geodesic.Geodesic.AZIMUTH` * :const:`~geographiclib.geodesic.Geodesic.DISTANCE` * :const:`~geographiclib.geodesic.Geodesic.STANDARD` * :const:`~geographiclib.geodesic.Geodesic.DISTANCE_IN` * :const:`~geographiclib.geodesic.Geodesic.REDUCEDLENGTH` * :const:`~geographiclib.geodesic.Geodesic.GEODESICSCALE` * :const:`~geographiclib.geodesic.Geodesic.AREA` * :const:`~geographiclib.geodesic.Geodesic.ALL` * :const:`~geographiclib.geodesic.Geodesic.LONG_UNROLL` :Example: >>> from geographiclib.geodesic import Geodesic >>> # The geodesic inverse problem ... Geodesic.WGS84.Inverse(-41.32, 174.81, 40.96, -5.50) {'lat1': -41.32, 'a12': 179.6197069334283, 's12': 19959679.26735382, 'lat2': 40.96, 'azi2': 18.825195123248392, 'azi1': 161.06766998615882, 'lon1': 174.81, 'lon2': -5.5} N)Math) Constants)GeodesicCapabilitycBeZdZUdZded<dZeZeZeZeZ eZ eZ e Z eZ e e dz zdzZeZeedzzdzZdZeejjzdzZejejjZejjZdezZejeZeZd ezZe j!Z!e j"Z"e j#Z#e j$Z$e j%Z%e j&Z&e j'Z'e j(Z(e j)Z)e j*Z*e+d Z,e+d Z-e+d Z.e+d Z/e+dZ0e+dZ1e+dZ2dZ3dZ4dZ5dZ6dZ7dZ8dZ9dZ:dZ;dZfdZ?dZ@e j>fdZAe j>fdZBe j>e jCzfd ZDe j>e jCzfd!ZEe j>e jCzfd"ZFe j>e jCzfd#ZGe j>e jCzfd$ZHd(d&ZIe jJZJ e jKZK e jLZL e jMZM e jNZN e j>Z> e jCZC e jOZO e jPZP e jQZQ e jRZR e jSZSd'S))GeodesiczSolve geodesic problemsWGS84 ict|}||z }d||z z||zz}d}|dzr|dz}||}nd}|dz}|r3|dz}|dz}||z|z ||z}|dz}||z|z ||z}|3|r d|z|z|zn|||z zS)z9Private: Evaluate a trig series using Clenshaw summation.r rr )len) sinpsinxcosxcknary1y0s N/srv/django_bis/venv311/lib/python3.11/site-packages/geographiclib/geodesic.py _SinCosSerieszGeodesic._SinCosSeries{s AA DA dTk dTk *B B1u 1fa1Q4bb b QA '1fa1fa27RA GC  rcgd}tj|}|}d}tdtjdzD]M}tj|z dz}|tj||||z|||zdzz ||<||dzz }||z}NdS)zPrivate: return C1.)r r8 rErrNrIrr r N)rr rangernC1_r;r=rr>eps2dolr?s r_C1fz Geodesic._C1f   E 73<A ! #a a400 05Q3C Cad1q5ja3haa rcgd}tjdz}tj||dtj|||dzz }||z d|zz S)zPrivate: return A2-1)iii@rr9r rr )rnA2_rr;r r<s r_A2m1fzGeodesic._A2m1frBrcgd}tj|}|}d}tdtjdzD]M}tj|z dz}|tj||||z|||zdzz ||<||dzz }||z}NdS)zPrivate: return C2)r r rF#r8r\rIPrKrerM?rOMrIrr r N)rr rPrnC2_r;rRs r_C2fz Geodesic._C2frXrc t||_ t||_ d|jz |_|jd|jz z|_|jt j|jz |_|jd|jz z |_|j|jz|_ t j|jt j|j |jdkrdn|jdkr+tj tj |jn+tj tj |j tj t|jz zzdz |_dt jztj t%dt|jt'dd|jdz z zdz z |_tj|jr |jdkst-dtj|j r |j dkst-dt/t1t j|_t/t1t j|_t/t1t j|_|| |!d S) aConstruct a Geodesic object :param a: the equatorial radius of the ellipsoid in meters :param f: the flattening of the ellipsoid An exception is thrown if *a* or the polar semi-axis *b* = *a* (1 - *f*) is not a finite positive quantity. r r r皙?gMbP??z!Equatorial radius is not positivezPolar semi-axis is not positiveN)"floataf_f1_e2rr _ep2_n_br!atanhr"atanabs_c2rtol2_maxmin_etol2isfinite ValueErrorlistrPnA3x__A3xnC3x__C3xnC4x__C4x_A3coeff_C3coeff_C4coeff)selfrqrrs r__init__zGeodesic.__init__sP1XXDF4 1XXDF#46zDHvTV$DH4748,,,DIfTV$DGftxDG$'$'"2"2h!mm59X\\$*TYtx00111)DItxi00113tx==))*#++-. .DH&Cs46{{4K4K47QtvaxZ4H4H5IKL5M*O*OODK = **++DIU8>**++DIU8>**++DIMMOOOMMOOOMMOOOOOrcgd}d}d}ttjdz ddD]b}ttj|z dz |}t j||||j|||zdzz |j|<|dz }||dzz }cdS)z#Private: return coefficients for A3)rr8rDrrDrdrrDrr rDr r r rr rDr N)rPrnA3_r~rr;rvr)rr>rUrjr?s rrzGeodesic._A3coeffDs   E Aq1 8=1$b" - - hma!#Q ' 'a\!UAtw77%A :JJdil1fa1q5jaa rcXgd}d}d}tdtjD]}ttjdz |dz dD]b}ttj|z dz |}t j||||j|||zdzz |j|<|dz }||dzz }cdS)z#Private: return coefficients for C3)-rrr rrDrrr8rDrr rrDr rrr9r rrrrrr8r rr rFrhrMirJr\rrGrrhrMirhrMi rr rDr N)rPrnC3_r~rr;rvrrr>rUrrVrr?s rrzGeodesic._C3coeffUs   E" Aq1 1hm $ $X]Q&Ar22!  !A%q ) )|Aua99E!a%!)EkR"WrBw./ H*X-CC DLQ &&++!c!frCF{*A %K811$ucJJ#11$ucJJK Lc''# bUU]#cUU]&;;emc!"d''=u}uu},f )uu} % 739 Ea a%i%#+-6< DIIcNN2TW<e# X  h %-%%-/GW--)- '47V#UUFCs .S):):%tR +dg56 6#$u99GaKK&475>>1DG; e# X  hn_  R(*;%;!;!; 6Q;;cA2,,%$)A4F*G*G(Ga8>/11ssta@@%)A.//%%H   a # #! qb1fa!enn$%2Q<>4&!!TXf-=-=,=6%%-$'&//9QZHH QJJYue,,leUUe %uc 11rcr|dkr|dkr tj }||z}tj|||z}|}||z}||zx}}t j||\}}||kr||z n|}||kst || krJtjt j||z|| kr ||z ||zzn ||z ||zzz|z nt |}|}||z}||zx}}t j||\}}tj td||z||zz dz||z||zz}td||z||zz dz}||z||zz}tj || z|| zz || z|| zz}t j||j z}|ddtjd|zzz|zz } | | |t d|||t d|||z }!|j || z|z||!zz}"||"z}#| rY|dkrd|jz|z|z }$nN|| |||||||||tj| | \}%}$}%}%}%|$|j||zz z}$n tj}$|#|||||||| |"|$f S)zPrivate: Solve hybrid problemrrr r Tr)rtiny_r!rrrrzr"r r$r}rurrrrrrsrrr)&rrrrrrrrrslam120clam120diffprrC3asalp0calp0rsomg1rcomg1rrrsomg2rcomg2rrretarr=B312domg12rdlam12rs& r _Lambda12zGeodesic._Lambda12qsT  zzeqjj~oe EME Jueem , ,E E55=5EM!EE9UE**LE5#e^^EEMME#e**"6"6Ytwuu}--=BeV^^55=99#em >@AACHII=@JJ E55=5EM!EE9UE**LE5 Js3  =>>D %  = ? ?Eeemeem3 4 4s :Femeem3F *Vg%(88g%(88 : :C $) #B Q1r6***+b0 1CIIc3  " "4s ; ;  " "4s ; ; tj%|7}>tj'|7}?||?z||>zz }*||?z||>zz}+|tjzrd|'z}|tjzrd|(z}|tj/zr6||z}@tj0|||z}A|Adkr*|@dkr#|}"||z}#|}$| |z}%t j|A|jz}B|Bddtjd|Bzzz|Bzz }6t j|j$|Az|@z|j1z}Ct j|"|#\}"}#t j|$|%\}$}%t+t-tj2}D|3|6|Dt4d |"|#|D}Et4d |$|%|D}F|C|F|Ez z} nd} |s.|*d kr(tj%|,}*tj'|,}+|sO|+dkrI||z dkr@d|+z}7d|z}Gd|z}Hdtj|*||Hz||Gzzz|7||z|G|Hzzzz}InH|!|z| |zz }J| |z|!|zz}K|Jdkr|Kdkrtj|z}Jd }Ktj|J|K}I| |j5|Izz } | ||z|zz} | dz } |dkr||!}}!|| }} |tj&zr| | } } |||zz}|||zz}|!||zz}!| ||zz} |||||!| || | | f S)z/Private: General version of the inverse problemr rDrirorrFg@rTrrdr g -g?)6r!rrrrAngDiffcopysignradianssincosdeAngRoundLatFixrzisnansincosdrsrr}rr"rur rrPrQrkrr$rrvrrr|tol0_rwdegreesrrrqrrr%rrmaxit1_maxit2_rtolb_EMPTYAREArrtrrrr{)Lrlat1lon1lat2lon2ra12s12m12rrS12lon12lon12slonsignrrrswapplatsignrrrrrrrrrmeridianrrrrrrrrrs12xm12xrrrrrnumittripntripbsalp1acalp1asalp1bcalp1br3r=rdvdalp1sdalp1cdalp1nsalp1 lengthmasksdomg12cdomg12rrrA4C4aB41B42dbet1dbet2alp12salp12calp12sL r _GenInversezGeodesic._GenInverses (,0C0#00c0C# x  GLt,,ME6mAu%%G eOEg&6V L  E]5&11NFFEkV #F =T** + +D =T** + +Dd))c$ii''4:d+;+;'BBE qyy mgDdmAu%%GGODGOD<%%LE5u'8u9UE**LE5C4N4NE<%%LE5u'8u9UE**LE5C4N4NE v~~ % eU++ Uv   )A DGENN22 3 3C )A DGENN22 3 3C uX]Q&'' ( (C uX]Q&'' ( (C uX]## $ $Cs{)fkH% efee35eUU]UeUU]UjS%%-%%-"?@@3F"'%-%%-"?AAe%)MM uc5%eU(##h&<)>> X+ + ,hus{++ +#l5!!C(#$0 L#nn E3uc E66583C+C #s 1eUE5%   CFFE'8qqqHN&JJJx'''  UU 000e fVm33FUFF1uu%("222+v 55FUF 1*% X% % %"q&&BrEE5zzDG##xf%v~6f!7#y66 uA"x~"55F?A%%F?A%%5%00,%%v~&&&5.9HNJKuv~&&%&.9HNJ _0 Ld"h&<&.&<'=>+x((%N , '+mm ueUCsE5 c3' ' #dE3  l5!! X] " 7HV$$'0@0@gG#fw&66&G#fw&66&"" $Jc'' $Jc4emej ..e ! uu}uuu}u WU^^di 'ATYq2v.../"45 WTV__u $u ,tx 7y.. uy.. u5''(( #s$$UE5#>>$$UE5#>>C#I ;&C--%48E??&+ 7   %-$  VQYUE DJ55=55=+H J &55=55=+H JMMM.. Q;;6A::>E)&& 66** TX c UW_w &&c Sjc qyyEUeEUe 8) )S UW_Eeuw6e UW_Eeuw6e UE5%c3 CCrc ||||||\ }}}} } } } } }}|tjz}|tjzr!t j||\}}||z|z}nt j|}t j||tjzr|nt j|t j||d}||d<|tjzr||d<|tj zr0t j || |d<t j | | |d<|tj zr| |d<|tj zr | |d<||d<|tj zr||d <|S) a7Solve the inverse geodesic problem :param lat1: latitude of the first point in degrees :param lon1: longitude of the first point in degrees :param lat2: latitude of the second point in degrees :param lon2: longitude of the second point in degrees :param outmask: the :ref:`output mask ` :return: a :ref:`dict` Compute geodesic between (*lat1*, *lon1*) and (*lat2*, *lon2*). The default value of *outmask* is STANDARD, i.e., the *lat1*, *lon1*, *azi1*, *lat2*, *lon2*, *azi2*, *s12*, *a12* entries are returned. )rrrrrrazi1azi2rrrr)r<rr LONG_UNROLLrr AngNormalizer rAZIMUTHatan2drrr)rrrrrrrrrrrrrrrrreresults rInversezGeodesic.Inverses$>B=M=M D$g>'>':CeE5S#s x  G%%%dD))heQUla dd  t $ $dk$''%(<<&dd%%k$'' F F5M""7CF5M!!1{5%00fVn{5%00fVn''<''/fUm36%=3u Mrc|ddlm}|s|tjz}||||||}||||S)z*Private: General version of direct problemr GeodesicLine)geographiclib.geodesiclinerIr DISTANCE_IN _GenPosition) rrrr>arcmodes12_a12rrIlines r _GenDirectzGeodesic._GenDirect"sU777777 3Gx33G <dD$ 8 8D   Wgw 7 77rc  ||||d||\ }}}} }} } } } |tjz}tj||tjzr|ntj|tj||d}||d<|tjzr||d<|tjzr||d<|tj zr| |d<|tj zr| |d<|tj zr | |d<| |d <|tj zr| |d <|S) a_Solve the direct geodesic problem :param lat1: latitude of the first point in degrees :param lon1: longitude of the first point in degrees :param azi1: azimuth at the first point in degrees :param s12: the distance from the first point to the second in meters :param outmask: the :ref:`output mask ` :return: a :ref:`dict` Compute geodesic starting at (*lat1*, *lon1*) with azimuth *azi1* and length *s12*. The default value of *outmask* is STANDARD, i.e., the *lat1*, *lon1*, *azi1*, *lat2*, *lon2*, *azi2*, *s12*, *a12* entries are returned. F)rrr>rrrrr?rrrr) rPrrrr r@rALATITUDE LONGITUDErBrrr)rrrr>rrrrrr?rrrrrEs rDirectzGeodesic.Direct*s.&6:__ D$sG6-6-2CtT3S#s x  Gk$''%(<<&dd%%'-- F F5M""9TF6N##:dVF^!!8D6&>''<''/fUm36%=3u Mrc *||||d||\ }}}}} } } } } |tjz}tj||tjzr|ntj|tj||d}|tjzr| |d<|tjzr||d<|tj zr||d<|tj zr||d<|tj zr| |d<|tj zr | |d<| |d <|tj zr| |d <|S) aSolve the direct geodesic problem in terms of spherical arc length :param lat1: latitude of the first point in degrees :param lon1: longitude of the first point in degrees :param azi1: azimuth at the first point in degrees :param a12: spherical arc length from the first point to the second in degrees :param outmask: the :ref:`output mask ` :return: a :ref:`dict` Compute geodesic starting at (*lat1*, *lon1*) with azimuth *azi1* and arc length *a12*. The default value of *outmask* is STANDARD, i.e., the *lat1*, *lon1*, *azi1*, *lat2*, *lon2*, *azi2*, *s12*, *a12* entries are returned. T)rrr>rrrrr?rrrr)rPrrrr r@rArrRrSrBrrr)rrrr>rrrrr?rrrrrrEs r ArcDirectzGeodesic.ArcDirectOs;&6:__ D$c76,6,2CtT3S#s x  Gk$''%(<<&dd%%'-- F ""7CF5M""9TF6N##:dVF^!!8D6&>''<''/fUm36%=3u Mrc,ddlm}||||||S)aReturn a GeodesicLine object :param lat1: latitude of the first point in degrees :param lon1: longitude of the first point in degrees :param azi1: azimuth at the first point in degrees :param caps: the :ref:`capabilities ` :return: a :class:`~geographiclib.geodesicline.GeodesicLine` This allows points along a geodesic starting at (*lat1*, *lon1*), with azimuth *azi1* to be found. The default value of *caps* is STANDARD | DISTANCE_IN, allowing direct geodesic problem to be solved. rrH)rJrI)rrrr>capsrIs rLinez Geodesic.Linets.$877777 <dD$ 5 55rcddlm}|s|tjz}||||||}|r||n|||S)z#Private: general form of DirectLinerrH)rJrIrrKSetArc SetDistance) rrrr>rMrNrXrIrOs r_GenDirectLinezGeodesic._GenDirectLinesu877777 0DH00D <dD$ 5 5D  kk' w Krc6||||d||S)aDefine a GeodesicLine object in terms of the direct geodesic problem specified in terms of spherical arc length :param lat1: latitude of the first point in degrees :param lon1: longitude of the first point in degrees :param azi1: azimuth at the first point in degrees :param s12: the distance from the first point to the second in meters :param caps: the :ref:`capabilities ` :return: a :class:`~geographiclib.geodesicline.GeodesicLine` This function sets point 3 of the GeodesicLine to correspond to point 2 of the direct geodesic problem. The default value of *caps* is STANDARD | DISTANCE_IN, allowing direct geodesic problem to be solved. Fr])rrrr>rrXs r DirectLinezGeodesic.DirectLines"*   tT4T B BBrc6||||d||S)aDefine a GeodesicLine object in terms of the direct geodesic problem specified in terms of spherical arc length :param lat1: latitude of the first point in degrees :param lon1: longitude of the first point in degrees :param azi1: azimuth at the first point in degrees :param a12: spherical arc length from the first point to the second in degrees :param caps: the :ref:`capabilities ` :return: a :class:`~geographiclib.geodesicline.GeodesicLine` This function sets point 3 of the GeodesicLine to correspond to point 2 of the direct geodesic problem. The default value of *caps* is STANDARD | DISTANCE_IN, allowing direct geodesic problem to be solved. Tr_)rrrr>rrXs r ArcDirectLinezGeodesic.ArcDirectLines"*   tT4sD A AArc &ddlm}|||||d\ }}} } }}}}}}tj| | } |t jt jzzr|t jz}||||| || | } | || S)aDefine a GeodesicLine object in terms of the invese geodesic problem :param lat1: latitude of the first point in degrees :param lon1: longitude of the first point in degrees :param lat2: latitude of the second point in degrees :param lon2: longitude of the second point in degrees :param caps: the :ref:`capabilities ` :return: a :class:`~geographiclib.geodesicline.GeodesicLine` This function sets point 3 of the GeodesicLine to correspond to point 2 of the inverse geodesic problem. The default value of *caps* is STANDARD | DISTANCE_IN, allowing direct geodesic problem to be solved. rrH) rJrIr<rrCrrrKrr[) rrrrrrXrIr_rrr>rOs r InverseLinezGeodesic.InverseLines&877777-1-=-= D$a.!.!*CE5!Q1a ;ue $ $D x 8#778  hd <dD$eU C CDKK KrFc&ddlm}|||S)zReturn a PolygonArea object :param polyline: if True then the object describes a polyline instead of a polygon :return: a :class:`~geographiclib.polygonarea.PolygonArea` r) PolygonArea)geographiclib.polygonarearg)rpolylinergs rPolygonzGeodesic.Polygons(655555 ;tX & &&rN)F)T__name__ __module__ __qualname____doc____annotations__GEOGRAPHICLIB_GEODESIC_ORDERr:rQr^rarkrrrrrrrsys float_infomant_digrr!r"r~repsilonr rr|rrrCAP_NONECAP_C1CAP_C1pCAP_C2CAP_C3CAP_C4CAP_ALLCAP_MASKOUT_ALLr staticmethodrr6rArWr_rbrlrrrrrrrrrrr<STANDARDrFrPrTrVrKrYr]r`rbrerjrrRrSrBrrrrALLr@rrrrVso !" %$ %$ &% %$ %$ %$ % %$ 4!8  "% %$ 4!8  "% ' cn- - 2' $)CN& ' '% . % +% $)E  % % E\(  ((  &&  ''  &&  &&  &&  ''  ((  ''  ((%%<%2, , <, \!!<!<&<&!!<!<&...`"6B>>>      3$3$3$lH2H2H2XJJJZwDwDwDt +3((((V888*2####L-5####L%-  )*6666,/7'34    +3#/0CCCC0+3#/0BBBB0,4$01: ' ' ' '%*%#$-("$.)#$,'-$-(!$-($0+$2-'$2-2$)$$(#$0+rr) rnr!rqgeographiclib.geomathrgeographiclib.constantsr geographiclib.geodesiccapabilityrrWGS84_aWGS84_frrrrrs;;^ &&&&&&------??????ssssssssj%)+Y->??++r