o:i0hSSKr\RrSSKJr SSKJ r SSK r SSK J r J r Jr S/r\R \R""\R$5\R&"\R(\R*\R*\R*\R*S9\R&"\R*\R*S9S 5555r\R&"\R*\R*\R*\R*S 9S 5r\R \R&"\R$\R$\R$\R(\R(\R(\R(\R*\R*\R*\R*S 9 S 55r\R&"\R$\R$\R$\R*\R*\R*S9S5r\\ \\4\4r\R&"\R$\R$S9S0S\ \ \S\S\S\ \ \S44Sjj5r\ "S/SQ5r\R&"S10S\R$_S\R$_S\R$_S\R$_S\R$_S\R$_S\R$_S \R(_S!\R(_S"\R(_S#\R(_S$\R(_S\R$_S%\R$_S&\R$_S'\R*_S(\R*_S)\R*_S*\R*_S+\R*_S,\R*_6S0S-j5rS.r \!S/:Xa\ "5 gg!\\4a SSKJr GNf=f)2N)cython)splitCubicAtTC) namedtuple)ListTupleUnionquadratic_to_curves) tolerancep0p1p2p3)midderiv3c[U5U::a[U5U::agUSX---U-S-n[U5U:agX2-U- U- S-n[XU-S-XV- XT5=(a [XUU-X#-S-X45$)a\Check if a cubic Bezier lies within a given distance of the origin. "Origin" means *the* origin (0,0), not the start of the curve. Note that no checks are made on the start and end positions of the curve; this function only checks the inside of the curve. Args: p0 (complex): Start point of curve. p1 (complex): First handle of curve. p2 (complex): Second handle of curve. p3 (complex): End point of curve. tolerance (double): Distance from origin. Returns: bool: True if the cubic Bezier ``p`` entirely lies within a distance ``tolerance`` of the origin, False otherwise. Tg?F?)abscubic_farthest_fit_inside)r r r rr rrs X/srv/projetos/modelo_ml_acdoc/venv/lib/python3.13/site-packages/fontTools/qu2cu/qu2cu.pyrr(s: 2w)B9 4 RW  "e +C 3x)glR5 (F $ "WOS\3  W #Cv3 VWr r r p1_2_3c0US-nUUS-U-US-U-U4$)zAGiven a quadratic bezier curve, return its degree-elevated cubic.gUUUUUU?gUUUUUU?rs relevate_quadraticrRs55\F u  u   r) startnk prod_ratio sum_ratioratiotr r r rcSnSnS/n[SU5HdnXU-nXU-S- nUSUS:Xde[USUS- 5[USUS- 5- n X9-nXC- nURU5 Mf USSV s/sHoU- PM nn XSn XSn XU-S- Sn XU-S- SnXU - U(aUSOS- -n XU- U(aSUS- OS- -n XX4nX4$s sn f)z}Give a cubic-Bezier spline, reconstruct one cubic-Bezier that has the same endpoints and tangents and approxmates the spline.g?rrN)rangerappend)curvesrrr r!tsrckc_beforer"r#r r r rcurves r merge_curvesr/esQ(JI B 1a[ AI !)a-(!u ###BqEBqEM"S!x{)B%CC   )"$CR )Ai-B ) q B q B  A q !B  A q !B BwB2a5A. .B Bw2A2J15 5B R E 9 *sC1)count num_offcurvesioff1off2onc[U5nSn[U5S- n[SU5H5nXnXS-nXVU- S--nURUS-U-U5 US- nM7 U$)Nrr&r%r)listlenr(insert)pqr0r1r2r3r4r5s radd_implicit_on_curvesr<sy QA EFQJM 1m $tQx D[C' ' Q#   % Hr)cost is_complexquadsmax_err all_cubicreturn.c [USS5[LnU(d3UVVVs/sH"oDVVs/sHupV[XV5PM snnPM$ nnnnUSS/nS/nSn UHnUSUS:Xde[[U5S- 5H*n U S- n UR U 5 UR U 5 M, [ U5SSn UR 5 URU 5 U S- n UR U 5 M [XxX5n U(d"U V s/sHn [SU 55PM n n U $s snnfs snnnfs sn f)aConverts a connecting list of quadratic splines to a list of quadratic and cubic curves. A quadratic spline is specified as a list of points. Either each point is a 2-tuple of X,Y coordinates, or each point is a complex number with real/imaginary components representing X,Y coordinates. The first and last points are on-curve points and the rest are off-curve points, with an implied on-curve point in the middle between every two consequtive off-curve points. Returns: The output is a list of tuples of points. Points are represented in the same format as the input, either as 2-tuples or complex numbers. Each tuple is either of length three, for a quadratic curve, or four, for a cubic curve. Each curve's last point is the same as the next curve's first point. Args: quads: quadratic splines max_err: absolute error tolerance; defaults to 0.5 all_cubic: if True, only cubic curves are generated; defaults to False rr%r'r&Nc3P# UHoRUR4v M g7fN)realimag).0cs r &quadratic_to_curves..s8%Q(%s$&) typecomplexr(r8r)r<popextendspline_to_curvestuple)r?r@rAr>r:xyr;costsr=r2qqr*r.s rr r s8FeAhqk"g-J :?@%Qa0aFQ'!-a0%@ q! A CE D u!}}s1vz"A AID LL  LL #$A &qr *      Ta ;F FLMfU%8%88fM M+1@(Ns D>D8D>E8D>Solution) num_pointserror start_indexis_cubicr2jrr i_sol_count j_sol_countthis_sol_countr errrX i_sol_error j_sol_errorrZr0r r r rvuc z[U5S:dS5e[S[U5S- S5Vs/sHn[XUS-6PM nn[5n[S[U55H[nXTS- SnXTSnXTSn [ X- 5[ X- 5-U[ X- 5-:dMJUR U5 M] [ SSSS5/n [ [U5S-S-SSS5n Sn [S[U5S-5GHnU n [X5GHunXRXRnnU(d>USU-S- USU-- S-nUU-nUn[ UUXN- S5nUU :aUn US::aMe[X^XN- 5unn[/UQUQ76n/nSn[U5HFunnX^U-n[ USUS- 5n[UU5nUU:a OURU5 MH UU:aM[U5HGunnX^U-n[S[!UU555upxn n[#XxU UU5(aMBUS-n O UU:aGMDUS-n[UU5n[ UUXN- S5nUU :aUn US:XdGMv O U RU 5 XF;dGMUn GM /n/n [U 5S- nU(aLXR$XR&n"n!URU5 U RU"5 UU!-nU(aML/n#Sn[)[+[!UU 555H_unn"U"(a!U#R[X^XN- 5S5 O/[X5H nU#RUUS-US-S-5 M" UnMa U#$s snf![a GMf=f) a. q: quadratic spline with alternating on-curve / off-curve points. costs: cumulative list of encoding cost of q in terms of number of points that need to be encoded. Implied on-curve points do not contribute to the cost. If all points need to be encoded, then costs will be range(1, len(q)+1). rz+quadratic spline requires at least 3 pointsrr&r%Fc3.# UH upX- v M g7frEr)rHrbrcs rrJ#spline_to_curves..Ts&L9Kqu9KsT)r8r(rsetraddrVrWrXr/ZeroDivisionErrorr enumeratemaxr)rQziprrYrZreversedr7)$r;rTr rAr2elevated_quadraticsforcedr r r sols impossiblerbest_solr[r]ra this_countr\r`i_solr.r+reconstructed_iter reconstructedrXrreconstorigr_rsplitscubicr0rZr*s$ rrPrPsB q6Q;EEE;383q6A:q2I2IQ1Q<(2I UF 1c-. / Q ' * #A & #A & rw<#bg, &S\)A A JJqM 0 Q1e $ %D#12Q6:Aq%HJ E 1c-.2 3uA'+w'9'947==K"1q519-a!e rs&& ??5"  ! ! mm ~~ ~~ ~~ ~~ 6>>&..9W:W@ ~~ ~~ ~~ >>     ** jj jj}}mm -- mm ~~ ~~ ~~ ~~ $ $N **** jj   ~~      eE5L!7*+ zz 6 U 6 66 %s  6 6r j"T U jj jj jj **     ::mm   --  jjZZ ** ~~!"~~#$~~%&~~'( nn)* nn+.v/.vr-$ zF  $&%%&sNN10N1