+ iBF ^RIt]Pt^RIt^RIHt H t RR.t ^dt ] !R4t]P]P ]P"!]P$4]P&!]P(]P(]P$R7R4444t]P]P&!]P(]P$R 7]P&!]P$]P$R 7R 444t]P]P ]P&!]P(]P(]P(]P(R 7]P&!]P(]P(]P(]P(R 7R4444t]P]P ]P&!]P(]P(]P(]P(R7]P&!]P(]P(]P(]P(R 7R4444t]P]P ]P&!]P(]P(]P(]P(R7R444t]P&!]P(]P(]P(]P(]P4R7]P&!]P(]P(]P(]P(R 7]P&!]P$]P$]P$]P4R7]P&!]P(]P(]P(]P(R7R4444t]P]P ]P&!]P(]P(]P(]P(R7]P&!]P(]P(R7R4444t]P]P ]P&!]P(]P(]P(]P(R7]P&!]P(]P(]P(]P(R7R4444t]P]P ]P"!]P(4]P&!]P$]P(]P(]P(]P(R7]P&!]P(]P(R7R44444t]P]P ]P"!]P(4]P&!]P(]P(]P(]P(R 7]P&!]P(]P(]P(]P$R7R44444t]P]P"!]P44]P&!]P$]P(]P(]P(]P(R7]P&!]P(]P(R7R 4444t ]P]P ]P&!]P$R!7]P&!]P(]P(]P(]P(]P(R"7R#4444t!]P]P&!]P4]P$R$7]P&!]P4R%7]P&!]P4R&7]P&!]P(]P(]P(]P(R'7]P&!]P(]P(]P(]P(]P(R(7R)444444t"]P&!]P$R*7]P&!]P4R+7]P&!]P4R&7R/R,l444t#]P&!]P4]P4]P4R-7]P&!]P4R&7R/R.l44t$R# ]]3d ^RIHtE Lzi;i)0N)cython)ErrorApproxNotFoundErrorcurve_to_quadraticcurves_to_quadraticNaNv1v2resultcjWP4,Pp\V4R8dRpV#)zReturn the dot product of two vectors. Args: v1 (complex): First vector. v2 (complex): Second vector. Returns: double: Dot product. gV瞯! ' 'F 6{U M)zden)zrzicbVPpVPp\W!, W1, 4#)aLDivide complex by real using Python's method (two separate divisions). This ensures bit-exact compatibility with Python's complex division, avoiding C's multiply-by-reciprocal optimization that can cause 1 ULP differences on some platforms/compilers (e.g. clang on macOS arm64). https://github.com/fonttools/fonttools/issues/3928 )rimagcomplex)rrrrs&& r_complex_div_by_realr?s' B B 28RX &&r)abcd)_1_2_3_4cTp\VR4V,p\W,R4V,pW,V,V,pWEWg3#@)r)rrrrr r!r"r#s&&&& rcalc_cubic_pointsr'PsF B a % )B aeS )B .B QB 2>r)p0p1p2p3cW, R,pW!, R,V, pTpW6, V, V, pWuWF3#r%)r(r)r*r+rrrrs&&&& rcalc_cubic_parametersr.^s= CA C!A A  QA :rc hV^8Xd\\WW#44#V^8Xd\\WW#44#V^8Xdq\WW#4wrV\\V^,V^,V^,V^,4\V^,V^,V^,V^,4,4#V^8Xdq\WW#4wrV\\V^,V^,V^,V^,4\V^,V^,V^,V^,4,4#\WW#V4#)aSplit a cubic Bezier into n equal parts. Splits the curve into `n` equal parts by curve time. (t=0..1/n, t=1/n..2/n, ...) Args: p0 (complex): Start point of curve. p1 (complex): First handle of curve. p2 (complex): Second handle of curve. p3 (complex): End point of curve. Returns: An iterator yielding the control points (four complex values) of the subcurves. )itersplit_cubic_into_twosplit_cubic_into_three_split_cubic_into_n_gen)r(r)r*r+nrrs&&&&& rsplit_cubic_into_n_iterr5ls, Av(899Av*22:;;Av#BB3 1qtQqT1Q4 8"1Q41qtQqT: ;   Av#BB3 "1Q41qtQqT :$QqT1Q41qt< =  #221 55r)r(r)r*r+r4)dtdelta_2delta_3i)a1b1c1d1c#"\WW#4wrVrx^V, p W,p W,p \V4Fp W,p W,pW[,p^V,V ,V,V ,p^V,V ,V,^V,V,,V ,pW],V,Wn,,W},,V,p\VVVV4xK R#5i)N)r.ranger')r(r)r*r+r4rrrrr6r7r8r9t1t1_2r:r;r<r=s&&&&& rr3r3s'rr6JA! QBgGlG 1X Vw [!ebj1n '!ebj1nq1ut|+r 1 Vd]QX % . 2BB//sC&C()midderiv3cV^W,,,V,R,pW2,V, V, R,pWV,R,WE, V3WDV,W#,R,V33#)adSplit a cubic Bezier into two equal parts. Splits the curve into two equal parts at t = 0.5 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. Returns: tuple: Two cubic Beziers (each expressed as a tuple of four complex values). ??r-)r(r)r*r+rCrDs&&&& rr1r1se* RW  "e +CglR5 (F 2g_clC0 FlRWOR0 r)mid1deriv1mid2deriv2c^V,^ V,,^V,,V,R,pV^V,,^V,, R,pV^V,,^ V,,^V,,R,p^V,^V,, V, R,pV^V,V,R, WE, V3WDV,Wg, V3WfV,V^V,,R, V33#)avSplit a cubic Bezier into three equal parts. Splits the curve into three equal parts at t = 1/3 and t = 2/3 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. Returns: tuple: Three cubic Beziers (each expressed as a tuple of four complex values). r&gh/?r-)r(r)r*r+rHrIrJrKs&&&& rr2r2s: FR"W q2v % *v 6D1r6kAF"v .F RK"r' !AF *v 6D"fq2vo"v .F a"frkS $-6 f}dmT2 f}rAF{c126 r)tr(r)r*r+)_p1_p2cWV, R,,pWCV, R,,pWVV, V,,#)aTApproximate a cubic Bezier using a quadratic one. Args: t (double): Position of control point. p0 (complex): Start point of curve. p1 (complex): First handle of curve. p2 (complex): Second handle of curve. p3 (complex): End point of curve. Returns: complex: Location of candidate control point on quadratic curve. g?r-)rMr(r)r*r+rNrOs&&&&& rcubic_approx_controlrQs50 R3 C R3 C )q  r)abcdphcW, pW2, pVR,p\W`V, 4\We4, pY%T,,# \d.Y8XdY8XgY#8XdTu#\\\4u#i;i)aUCalculate the intersection of two lines. Args: a (complex): Start point of first line. b (complex): End point of first line. c (complex): Start point of second line. d (complex): End point of second line. Returns: complex: Location of intersection if one present, ``complex(NaN,NaN)`` if no intersection was found. y?)rZeroDivisionErrorrNAN)rrrrrRrSrTrUs&&&& rcalc_intersectrYsv$ B B RA ! q5MCJ & Av: ! 6qvHsC  !s"A B-BB) tolerancer(r)r*r+c\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. TrFFrG)rcubic_farthest_fit_inside)r(r)r*r+rZrCrDs&&&&& rr\r\8s: 2w)B9 4 RW  "e +C 3x)glR5 (F $ "WOS\3  W W #Cv3 VWr)rZ)q1c0r<c2c3c\V^,V^,V^,V^,4p\P!VP4'dR#V^,pV^,pW2V, R,,pWBV, R,,p\ ^WP^,, W`^,, ^V4'gR#W2V3#)aApproximate a cubic Bezier with a single quadratic within a given tolerance. Args: cubic (sequence): Four complex numbers representing control points of the cubic Bezier curve. tolerance (double): Permitted deviation from the original curve. Returns: Three complex numbers representing control points of the quadratic curve if it fits within the given tolerance, or ``None`` if no suitable curve could be calculated. NUUUUUU?)rYmathisnanrr\)cubicrZr]r^r`r<r_s&& rcubic_approx_quadraticrfbs0 a%(E!HeAh ?B zz"'' qB qB Bw5! !B Bw5! !B $Q1X r!H}a S S 2:r)r4rZ)r9) all_quadratic)r^r<r_r`)q0r]next_q1q2r=c \V^8Xd \W4#V^8Xd VR8XdV#\V^,V^,V^,V^,V4p\V4p\^V^,V^,V^,V^,4pV^,pRpV^,V.p \ ^V^,4Fp VwrrTpTpW8df\V4p\W^, , V^,V^,V^,V^,4pV P V4VV,R,pMTpTpW~, p\ V4V8gP\VVVV, R,,V , VVV, R,,V , VV4'dKR# V P V^,4V #)aApproximate a cubic Bezier curve with a spline of n quadratics. Args: cubic (sequence): Four complex numbers representing control points of the cubic Bezier curve. n (int): Number of quadratic Bezier curves in the spline. tolerance (double): Permitted deviation from the original curve. Returns: A list of ``n+2`` complex numbers, representing control points of the quadratic spline if it fits within the given tolerance, or ``None`` if no suitable spline could be calculated. FyrGNrb)rfr5nextrQr@appendrr\)rer4rZrgcubics next_cubicrirjr=spliner9r^r<r_r`rhr]d0s&&&& rcubic_approx_splinerrs: Av%e77Av-5( $U1XuQxq58Q OFfJ" :a=*Q-A 1 G qB BAh F 1a!e_#  5fJ*U Z]JqM:a=*UV-G MM' "w,#%BB W r7Y &?  "r'e$ $r ) "r'e$ $r )   ' ' 9: MM%( Mr)max_err)r4c VUu.uF p\V!NK pp\^\^,4F<p\WW4pVfKVUu.uFqfPVP 3NK upu# \ V4huupiuupi)aApproximate a cubic Bezier curve with a spline of n quadratics. Args: cubic (sequence): Four 2D tuples representing control points of the cubic Bezier curve. max_err (double): Permitted deviation from the original curve. all_quadratic (bool): If True (default) returned value is a quadratic spline. If False, it's either a single quadratic curve or a single cubic curve. Returns: If all_quadratic is True: A list of 2D tuples, representing control points of the quadratic spline if it fits within the given tolerance, or ``None`` if no suitable spline could be calculated. If all_quadratic is False: Either a quadratic curve (if length of output is 3), or a cubic curve (if length of output is 4). )rr@MAX_Nrrrrr)curversrgrTr4rpss&&& rrrsz0#( (%QWa[%E ( 1eai $UwF  .45fVVQVV$f5 5 ! e $$ ) 6s A; B)llast_ir9c VUUu.uFq3Uu.uF p\V!NK upNK ppp\V4\V48XgQh\V4pR.V,p^;rx^p \W,WV,V4p V fV \8XdMaV ^, p TpK8WV&V^,V,pW8XgKTVU U u.uF)qU u.uFqPV P 3NK up NK+ up p #\ V4huupiuuppiuup iuup p i)aReturn quadratic Bezier splines approximating the input cubic Beziers. Args: curves: A sequence of *n* curves, each curve being a sequence of four 2D tuples. max_errors: A sequence of *n* floats representing the maximum permissible deviation from each of the cubic Bezier curves. all_quadratic (bool): If True (default) returned values are a quadratic spline. If False, they are either a single quadratic curve or a single cubic curve. Example:: >>> curves_to_quadratic( [ ... [ (50,50), (100,100), (150,100), (200,50) ], ... [ (75,50), (120,100), (150,75), (200,60) ] ... ], [1,1] ) [[(50.0, 50.0), (75.0, 75.0), (125.0, 91.66666666666666), (175.0, 75.0), (200.0, 50.0)], [(75.0, 50.0), (97.5, 75.0), (135.41666666666666, 82.08333333333333), (175.0, 67.5), (200.0, 60.0)]] The returned splines have "implied oncurve points" suitable for use in TrueType ``glif`` outlines - i.e. in the first spline returned above, the first quadratic segment runs from (50,50) to ( (75 + 125)/2 , (120 + 91.666..)/2 ) = (100, 83.333...). Returns: If all_quadratic is True, a list of splines, each spline being a list of 2D tuples. If all_quadratic is False, a list of curves, each curve being a quadratic (length 3), or cubic (length 4). Raises: fontTools.cu2qu.Errors.ApproxNotFoundError: if no suitable approximation can be found for all curves with the given parameters. 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