+ i0v^RIt]Pt^RIHt^RIH t ^RI t ^RI H t H t HtR.t]P ]P"!]P$4]P&!]P(]P*]P*]P*]P*R7]P&!]P*]P*R7R 4444t]P&!]P*]P*]P*]P*R 7R 4t]P ]P&!]P$]P$]P$]P(]P(]P(]P(]P*]P*]P*]P*R 7 R 44t]P&!]P$]P$]P$]P*]P*]P*R7R4t]] ]]3,]3,t]P&!]P$]P$R7R,RRll4t] !R.R-O4t]P&!R./R]P$bR]P$bR]P$bR]P$bR]P$bR]P$bR]P$bR]P(bR]P(bR]P(bR]P(bR ]P(bR!]P$bR]P$bR"]P$bR#]P*bR$]P*bR%]P*bR&]P*bR']P*bR(]P*bR,R)l4tR*t] R+8Xd ]!4R#R# ]]3d ^RIHtELi;i)/N)cython)splitCubicAtTC) namedtuple)ListTupleUnionquadratic_to_curves) tolerancep0p1p2p3)midderiv3c\V4V8:d\V4V8:dR#V^W,,,V,R,p\V4V8dR#W2,V, V, R,p\WV,R,WV, WT4;'d"\WUV,W#,R,W44#)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&&&&& u/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/fontTools/qu2cu/qu2cu.pyrr(s: 2w)B9 4 RW  "e +C 3x)glR5 (F $ "WOS\3  W W #Cv3 VWr r r p1_2_3cXVR,pVVR,V,VR,V,V3#)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 rc RpRp^.p\^V4FpWV,,pWV,^, ,pV^,V^,8XgQh\V^,V^,, 4\V^,V^,, 4, p W9,pWC, pVPV4K VRRU u.uF qV, NK pp W,^,p W,^,p WV,^, ,^,p WV,^, ,^,pYV , V'd V^,M^, ,p YV, V'd^VR,, M^, ,p WW3pW3#uup i)z}Give a cubic-Bezier spline, reconstruct one cubic-Bezier that has the same endpoints and tangents and approxmates the spline.g?N)rangerappend)curvesrrrr tsrckc_beforer!r"r r r rcurves&&& r merge_curvesr,esS(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 *sF )count num_offcurvesioff1off2onc\V4p^p\V4^, p\^V4FYpW,pW^,,pWVV, R,,pVPV^,V,V4V^, pK[ V#)rr)listlenr%insert)pqr-r.r/r0r1r2s& radd_implicit_on_curvesr9sy QA EFQJM 1m $tQx D[C' ' Q#   % Hr)cost is_complexc V^8dQhR\\\,,R\R\R\\\R3,,/#)quadsmax_err all_cubicreturn.)rPointfloatboolr)formats"r __annotate__rFsG66 U 6 66 %s  6rc \V^,^,4\JpV'g2VUUUu.uF!qDUUu.uFwrV\WV4NK uppNK# ppppV^,^,.p^.p^p VFpVR,V^,8XgQh\\V4^, 4F.p V ^, p VP V 4VP V 4K0 \ V4R,p VP 4VPV 4V ^, p VP V 4K \WxW4p V'g<V U u.uF/p \;QJd.RV 4FNK 5M !RV 44NK1 p p V #uuppiuupppiuup i)aConverts a connecting list of quadratic splines to a list of quadratic and cubic curves. A quadratic spline is specified as a list of points. Either each point is a 2-tuple of X,Y coordinates, or each point is a complex number with real/imaginary components representing X,Y coordinates. The first and last points are on-curve points and the rest are off-curve points, with an implied on-curve point in the middle between every two consequtive off-curve points. Returns: The output is a list of tuples of points. Points are represented in the same format as the input, either as 2-tuples or complex numbers. Each tuple is either of length three, for a quadratic curve, or four, for a cubic curve. Each curve's last point is the same as the next curve's first point. Args: quads: quadratic splines max_err: absolute error tolerance; defaults to 0.5 all_cubic: if True, only cubic curves are generated; defaults to False :NNc3P"TFqPVP3xK R#5iN)realimag).0cs& r &quadratic_to_curves..s8%Q(%s$&r$) typecomplexr%r5r&r9popextendspline_to_curvestuple)r>r?r@r;r7xyr8costsr:r/qqr'r+s&&& rr r sDFeAhqk"g-J :?@%Qa0aFQ'!-a0%@ q! A CE D u!}}s1vz"A AID LL  LL #$A &r *      Ta ;F FLMfU%%8%8%%8%88fM M+1@(Ns" FE: FF%F:FSolutionerroris_cubicr/jrr i_sol_count j_sol_countthis_sol_countr err i_sol_error j_sol_errorr@r-r r r rvuc V \V4^8gQR4h\^\V4^, ^4Uu.uFp\WV^,!NK pp\4p\^\V44FpWT^, ,^,pWT,^,pWT,^,p \ W, 4\ W, 4,V\ W, 4,8gK{VP V4K \ ^^^R4.p \ \V4^,^,^^R4p ^p \^\V4^,4EF.pT p \W4EFpW,PW,PppV'geV^V,^, ,V^V,,, ^,pVV,pTp\ VVWN, R4pVV 8dTp V^8:dK\W^WN, 4wpp\.TOTO5!p.p^p\T4F[wppY^T,,p\ T^,T^,, 4p\TT4pTT8dMTPT4K] TT8dEK0\T4FxwppY^T,,p\;QJd.R\!TT44FNK 5M!R\!TT444wrxp p\#YxT TT4'dKoT^,pM TT8dEKT^,p\TT4p\ TTYN, R4pTT 8dTp T^8XgEKM V PV 4WF9gEK,Tp EK1 .p.p \V 4^, pV'dRW,P$W,P&p"p!VPV4V PV"4VV!,pKY.p#^p\)\+\!VV 444Ftwpp"V"'d*V#P\W^WN, 4^,4M;\W4F,pV#PVV^,V^,^,4K. TpKv V##uupi \dEKAi;i)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). z+quadratic spline requires at least 3 pointsFc36"TFwrW, xK R#5irJr)rMrerfs& rrO#spline_to_curves..Ts&L9Kquu9KsT)r5r%rsetraddr[ num_pointsr\r,ZeroDivisionErrorr enumeratemaxr&rVzipr start_indexr]reversedr4)$r8rYr r@r/elevated_quadraticsforcedr r r sols impossiblerbest_solr^r`rd this_countr_rci_solr+r(reconstructed_iter reconstructedr\rreconstorigrbrsplitscubicr-r]r's$&&&& rrUrUsB 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 rsz&& ??5"  ! ! mm ~~ ~~ ~~ ~~ 6>>&..9W:W@ ~~ ~~ ~~ >>     ** jj jj}}mm -- mm ~~ ~~ ~~ ~~ $ $N **** jj   ~~      eE5L!7*+ zz6 6r j"T U jj jj jj **     ::mm   --  jjZZ ** ~~!"~~#$~~%&~~'( nn)* nn+.v/.vr-$ zF  $&%%&sN%%N87N8