>> 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)GeodesicCapabilityceZdZUdZded<dZeZeZeZeZ eZ eZ e Z eZ e e dz zdzZeZeedzzdzZdZeej&j(zdzZej.ej&j0Zej&j4ZdezZej.eZeZd ezZe jBZ!e jDZ"e jFZ#e jHZ$e jJZ%e jLZ&e jNZ'e jPZ(e jRZ)e jTZ*e+d Z,e+d Z-e+d Z.e+d Z/e+dZ0e+dZ1e+dZ2dZ3dZ4dZ5dZ6dZ7dZ8dZ9dZ:dZ;dZ e jZC e jZO e jZP e jZQ e jZR e jZSy&)(GeodesiczSolve geodesic problemsWGS84 ict|}||z }d||z z||zz}d}|dzr |dz}||}nd}|dz}|r.|dz}|dz}||z|z ||z}|dz}||z|z ||z}|r.|r d|z|z|zS|||z zS)z9Private: Evaluate a trig series using Clenshaw summation.r rr )len) sinpsinxcosxcknary1y0s e/mounts/lovelace/software/anaconda3/envs/py312/lib/python3.12/site-packages/geographiclib/geodesic.py _SinCosSerieszGeodesic._SinCosSeries{s AA DA dTk dTk *B B1u1fa1Q4b b QA 1fa1fa27RA GC  rcgd}tj|}|}d}tdtjdzD]O}tj|z dz}|tj ||||z|||zdzz ||<||dzz }||z}Qy)zPrivate: return C1.)r r8 rErrNrIrr r N)rr rangernC1_r;r=rr>eps2dolr?s r_C1fz Geodesic._C1f E 773>A ! #a a40 05Q3C Cad1q5ja3ha rcgd}tjdz}tj||dtj|||dzz }||z d|zz S)zPrivate: return A2-1)iii@rr9r rr )rnA2_rr;r r<s r_A2m1fzGeodesic._A2m1frBrcgd}tj|}|}d}tdtjdzD]O}tj|z dz}|tj ||||z|||zdzz ||<||dzz }||z}Qy)zPrivate: return C2)r r rF#r8r\rIPrKrerM?rOMrIrr r N)rr rPrnC2_r;rRs r_C2fz Geodesic._C2frXrc t||_ t||_ d|jz |_|jd|jz z|_|jt j |jz |_|jd|jz z |_|j|jz|_ t j |jt j |j|jdk(rdn|jdkDr2tjtj|jn2tjtj|j tjt|jz zzdz |_dt j"ztjt%dt|jt'dd|jdz z zdz z |_tj*|jr|jdkDs t-dtj*|jr|jdkDs t-dt/t1t j2|_t/t1t j6|_t/t1t j:|_|j?|jA|jCy ) aConstruct a Geodesic object :param a: the equatorial radius of the ellipsoid in meters :param f: the flattening of the ellipsoid An exception is thrown if *a* or the polar semi-axis *b* = *a* (1 - *f*) is not a finite positive quantity. r r r皙?gMbP??z!Equatorial radius is not positivezPolar semi-axis is not positiveN)"floataf_f1_e2rr _ep2_n_br!atanhr"atanabs_c2rtol2_maxmin_etol2isfinite ValueErrorlistrPnA3x__A3xnC3x__C3xnC4x__C4x_A3coeff_C3coeff_C4coeff)selfrqrrs r__init__zGeodesic.__init__s*1XDF4 1XDF#466zDHvvTVV$DH477488,,DIffTVV$DGfftxxDG$''$''"2hh!m59XX\$**TYYtxx01))DIItxxi013txx=)*#++-. .DH&Cs466{4K47QtvvaxZ4H5IKL5M*OODK == TVVaZ : ;; == !dggk 8 99U8>>*+DIU8>>*+DIU8>>*+DIMMOMMOMMOrc*gd}d}d}ttjdz ddD]j}ttj|z dz |}t j ||||j |||zdzz |j|<|dz }||dzz }ly)z#Private: return coefficients for A3)rr8rDrrDrdrrDrr rDr r r rr rDr N)rPrnA3_r~rr;rvr)rr>rUrjr?s rrzGeodesic._A3coeffDs E Aq1 8==1$b" - hmma!#Q 'a\\!UAtww7%A :JJdiil1fa1q5ja rcngd}d}d}tdtjD]}ttjdz |dz dD]j}ttj|z dz |}t j ||||j |||zdzz |j|<|dz }||dzz }ly)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 1hmm $X]]Q&Ar2!  !A%q )||Aua9E!a%!)EkR"WrBw./ H**X-C-CC DQ &+!c!frCF{*A+ %K811$ucJ#11$ucJK Lc''' bUU]#cUU]&;;emc!"d'''u}uu},f ))uu} % 739 Ea a%i%#+-6< DIIcN2TWW<e# X  h %-%%-/GW-)- ''477V#UUFCs ..S):%tR +dgg56 6#$u9GaK&&4775>1DGG; e# X  hnn_ R(*;*;%;!; 66Q;cA2,%$))A4F*G(Ga8>>/1sta@%))A./%H   a #! qb1fa!en$%2Q<>4&!TXXf-=,=6%%-$''&/9QZHH QJYYue,leUe %uc 11rcj|dk(r|dk(rtj }||z}tj|||z}|}||z}||zx}}t j ||\}}||k7r||z n|}||k7st || k7rKtjt j||z|| kr ||z ||zzn ||z ||zzz|z n t |}|}||z}||zx}}t j ||\}}tjtd||z||zz dz||z||zz}td||z||zz dz}||z||zz}tj|| z|| zz || z|| zz}t j||jz}|ddtjd|zzz|zz } |j| |tjd|||tjd|||z }!|j |j| z|z||!zz}"||"z}#| rb|dk(rd|j z|z|z }$nW|j#| |||||||||tj$| | \}%}$}%}%}%|$|j ||zz z}$ntj&}$|#|||||||| |"|$f S)zPrivate: Solve hybrid problemrrr r Tr)rtiny_r!rrrrzr"r r$r}rurrrrrrsrrr)&rrrrrrrrrslam120clam120diffprrC3asalp0calp0rsomg1rcomg1rrrsomg2rcomg2rrretarr=B312domg12rdlam12rs& r _Lambda12zGeodesic._Lambda12qs  zeqj~~oe EME JJueem ,E E55=5EM!EE99UE*LE5#e^EEME#e*"6YYtwwuu}-=BeV^55=9#em >@ACHI=@J E55=5EM!EE99UE*LE5 JJs3  =>D %  = ?Eeemeem3 4s :Femeem3F **Vg%(88g%(88 :C $)) #B Q1r6**+b0 1CIIc3  " "4s ;  " "4s ; ks|(dk\rm|&dtj"zks|&tj@kr|'dks|(dkrdx}&x}(}'|(|jBz}(|'|jBz}'tjD|&}nd }d }*d}+d},|s|dk(r|jFdks| |jFdzk\rdx}} dx}}!|jH|z}'||jz x}&},|jBtjJ|&z}(|tjLzrtjN|&x} } | |jz }n|s|jQ||||||||||| \}&}}}!} }-|&dk\r|&|jBz|-z}'t j(|-|jBztjJ|&|-z z}(|tjLzrtjN|&|-z x} } tjD|&}||j|-zz },nd}.d x}/}0tj"}1d}2tj"}3d }4 |jS|||||||||||.tjTk|||\ }5}!} }&}"}#}$}%}6}7}8|0s6t|5|/rd ndtj@zk\r|.tjVk(rn|5dkDr#|.tjTkDs ||z |4|3z kDr|}3|}4n'|5dkr"|.tjTkDs ||z |2|1z kr|}1|}2|.dz }.|.tjTkr|8dkDr|5 |8z }9t|9tjXkrtjJ|9}:tjN|9};||;z||:zz}<|tjN|7}?||?z||>zz }*||?z||>zz}+|tj:zrd'z}|tj<zrd(z}|tj^zr?|z}@tj`||z}A|Adk7r+@dk7r%|}"||z}#|}$ |z}%t j(A|j&z}B|Bddtj$d|Bzzz|Bzz }6t j(|jH|Az@z|jbz}Ct j|"|#\}"}#t j|$|%\}$}%t+t-tjd}D|jg|6|Dtjid |"|#|D}Etjid |$|%|D}F|C|F|Ez z} nd} |s/|*d k(r*tjJ|,}*tjN|,}+|sN|+dkDrI||z dkrAd|+z}7d|z}Gd|z}Hdtj4|*||Hz||Gzzz|7||z|G|Hzzzz}InK!|z |zz }J| |z|!|zz}K|Jdk(rKdkrtj"|z}Jd }Ktj4JK}I| |jjIzz } | ||z|zz} | dz } |dkr!}}! }} |tjLzr| | } } ||zz}||zz}!||zz}! ||zz} |||||!| || | | f S)z/Private: General version of the inverse problemr rDrirorrFg@rrrdr g -g?)6r!rrrrAngDiffcopysignradianssincosdeAngRoundLatFixrzisnansincosdrsrr}rr"rur rrPrQrkrr$rrvrrr|tol0_rwdegreesrrrqrrr%rrmaxit1_maxit2_rtolb_EMPTYAREArrtrrrr{)Lrlat1lon1lat2lon2ra12s12m12rrS12lon12lon12slonsignrrrswapplatsignrrrrrrrrrmeridianrrrrrrrrrs12xm12xrrrrrnumittripntripbsalp1acalp1asalp1bcalp1br3r=rdvdalp1sdalp1cdalp1nsalp1 lengthmasksdomg12cdomg12rrrA4C4aB41B42dbet1dbet2alp12salp12calp12sL r _GenInversezGeodesic._GenInversesf (,0C0#00c0C# x   GLLt,ME6mmAu%G eOEg&6V LL E]]5&1NFFEkV #F ==T* +D ==T* +Dd)c$i'4::d+;BE qy mgDdmmAu%GGODGOD<<%LE5u'8u99UE*LE5C4NE<<%LE5u'8u99UE*LE5C4NE v~ % eU+ Uv  ))A DGGEN22 3C ))A DGGEN22 3C uX]]Q&' (C uX]]Q&' (C uX]]# $Cs{)fkH efee35eUU]UeUU]UjjS%%-%%-"?@3F"'%-%%-"?Ae%)MM uc5%eU(###h&<&<> X++ +hhus{+ +#ll5!C(#$#nn E3uc E66583C3C+C #s 1eUE5%  CFEqqHNN&JJx'''  U 0 00e fVm3FUF1u%("2"22+v 5FUF 1*% X%% %"q&BrEE5zDGG#xxf%v~6f!7#yy6 uA"x~~"55F?A%%F?A%%5%0,%%v~&&5.9HNNJKuv~&%&.9HNNJ _d"h&<&<&.&<&<'=> ((%NN , '+mm ueUCsE5 c3' #dE3  ll5! X]] "HHV$'0@gG#fw&66&G#fw&66&""" $Jc''' $Jcemejj .e ! uu}uuu}u WWU^dii 'ATYYq2v../"45 WWTVV_u $u ,txx 7yy. uyy. u5'( #s$$UE5#>$$UE5#>C#I &C-%488E?& 7  %-$ VQYUE DJJ55=55=+H J &55=55=+H JMM.. Q;6A:>>E)&& 66* TXX c UW_w &&c Sjc qyEUeEUe 8)) )S UW_Eeuw6e UW_Eeuw6e UE5%c3 CCrc |j|||||\ }}}} } } } } }}|tjz}|tjzr"t j ||\}}||z|z}nt j |}t j||tjzr|nt j |t j||d}||d<|tjzr||d<|tjzr2t j|| |d<t j| | |d<|tjzr| |d<|tjzr | |d<||d<|tjzr||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.Inversesj$>B=M=M D$g>':CeE5S#s x   G%%%dD)heQUla d   t $dkk$'%(<(<arcmodes12_a12rrIlines r _GenDirectzGeodesic._GenDirect"s>7 Gx333G dD$ 8D   Wgw 77rc J|j|||d||\ }}}} }} } } } |tjz}tj||tj zr|ntj |tj ||d}||d<|tjzr||d<|tjzr||d<|tjzr| |d<|tjzr| |d<|tjzr | |d<| |d <|tjzr| |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$sG6-2CtT3S#s x   Gkk$'%(<(<''''''fUm36%=u Mrc p|j|||d||\ }}}}} } } } } |tjz}tj||tj zr|ntj |tj ||d}|tjzr| |d<|tjzr||d<|tjzr||d<|tjzr||d<|tjzr| |d<|tjzr | |d<| |d <|tjzr| |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$c76,2CtT3S#s x   Gkk$'%(<(<''''''fUm36%=u 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$8 dD$ 55rcddlm}|s|tjz}||||||}|r|j ||S|j ||S)z#Private: general form of DirectLinerrH)rJrIrrKSetArc SetDistance) rrrr>rMrNrXrIrOs r_GenDirectLinezGeodesic._GenDirectLinesV8 DH000D dD$ 5D kk' K w Krc.|j|||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 BBrc.|j|||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 AArc *ddlm}|j||||d\ }}} } }}}}}}tj| | } |t j t jzzr|t jz}||||| || | } | j|| 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&8-1-=-= D$a.!*CE5!Q1a ;;ue $D x  8#7#778 hd dD$eU CDKK Krc 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.Polygons6 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@rrrrVs !" %$ %$ &% %$ %$ %$ % %$ 4!8  "% %$ 4!8  "% ' cnn-- - 2' $))CNN&& '% .. % +% $))E % % E\(  ( ((  & &&  ' ''  & &&  & &&  & &&  ' ''  ( ((  ' ''  ( ((%%2, , \!!&&!!&.`"6B>  3$lH2XJZwDt +33(V8*22#L-55#L%--  ) )*6,/77'334 +33#//0C0+33#//0B0,44$001: '%**%#$--("$..)#$,,'-$--(!$--($00+$22-'$22-2$))$$((#$00+rr) rnr!rqgeographiclib.geomathrgeographiclib.constantsr geographiclib.geodesiccapabilityrrWGS84_aWGS84_frrrrrsH;^ &-?ssj%)++Y->->?+r