<`A ddlZn#e$r ddlmZYnwxYwddlZddlmZmZddgZdZ e dZ ej rd Z nd Z ejejejejejejej d Zejejejejejejej ejejejejejdZejejejejejejejejejejejej dZejejejejejejdZejejejejejejejejejejej ejejejejejejejejejejdZejejejejejejejejdZejejejejejejejejejejejd;dZejejejejejejejejejejejdZejejejejejejej ejejejejej d!Zejejejejejejejejej"ejejejd#Zejejejej$ejejejejejej%dN)cython)ErrorApproxNotFoundErrorcurve_to_quadraticcurves_to_quadraticdNaNTFv1v2c:||zjS)zReturn the dot product of two vectors. Args: v1 (complex): First vector. v2 (complex): Second vector. Returns: double: Dot product. ) conjugaterealr s 5lib/python3.11/site-packages/fontTools/cu2qu/cu2qu.pydotr,s   %%)abcd)_1_2_3_4cN|}|dz |z}||zdz |z}||z|z|z}||||fSN@)rrrrrrrrs rcalc_cubic_pointsr =sG B c'QB a%3 B QQB r2r>r)p0p1p2p3cN||z dz}||z dz|z }|}||z |z |z }||||fSrr)r!r"r#r$rrrrs rcalc_cubic_parametersr&IsG bCA bC!A A Q QA aA:rc|dkrtt||||S|dkrtt||||S|dkr5t||||\}}tt|t|zS|dkr5t||||\}}tt|t|zSt|||||S)aSplit a cubic Bezier into n equal parts. Splits the curve into `n` equal parts by curve time. (t=0..1/n, t=1/n..2/n, ...) Args: p0 (complex): Start point of curve. p1 (complex): First handle of curve. p2 (complex): Second handle of curve. p3 (complex): End point of curve. Returns: An iterator yielding the control points (four complex values) of the subcurves. )itersplit_cubic_into_twosplit_cubic_into_three_split_cubic_into_n_gen)r!r"r#r$nrrs rsplit_cubic_into_n_iterr1Us& Avv(RR88999Avv*2r2r::;;;Avv#BB331(!,/CQ/GGHHHAvv#BB331*A.1G1KKLLL "2bBq 1 11r)r!r"r#r$r0)dtdelta_2delta_3i)a1b1c1d1c#8Kt||||\}}}}d|z } | | z} | | z} t|D]a} | | z} | | z}|| z}d|z| z|z| z}d|z| z|zd|z|zz| z}|| z|z||zz|| zz|z}t||||VbdS)Nrr)r()r&ranger )r!r"r#r$r0rrrrr2r3r4r5t1t1_2r6r7r8r9s rr/r/vs 'r2r266JAq!Q QB2gG7lG 1XX00 VBw [c"fqjG #c"fqj1Q3t8#r ) rT$Y4 !B$ & *BB//////00r)midderiv3c||d||zzz|zdz}||z|z |z dz}|||zdz||z |f|||z||zdz|ffS)aSplit 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#r$r>r?s rr-r-sq" R"W  "d *C2glR4 'F "r'Rvs 3 #,bB 3 55r)r!r"r#r$_27)mid1deriv1mid2deriv2h/?cd|zd|zzd|zz|z|z}|d|zzd|zz |z}|d|zzd|zzd|zz|z}d|zd|zz |z |z}|d|z|zdz ||z |f|||z||z |f|||z|d|zzdz |ffS)aSplit 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+r)r*r(rr) r!r"r#r$rCrDrErFrGs rr.r.s& bD2b5L1R4 " $ +D1R4i!B$# %F 2I2 " $ +DdQrTkB# %F !B$)s"D6M4 8 4&=$- 6 4&=2"9"3R 8 ::r)tr!r"r#r$)_p1_p2cD|||z dzz}|||z dzz}|||z |zzS)axApproximate a cubic Bezier using a quadratic one. Args: t (double): Position of control point. p0 (complex): Start point of curve. p1 (complex): First handle of curve. p2 (complex): Second handle of curve. p3 (complex): End point of curve. Returns: complex: Location of candidate control point on quadratic curve. g?r)rLr!r"r#r$rMrNs rcubic_approx_controlrPs; R3 C R3 C #)q  r)abcdphc||z }||z }|dz} t|||z t||z }n*#t$rtttcYSwxYw|||zzS)ayCalculate 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?)rZeroDivisionErrorcomplexNAN)rrrrrQrRrSrTs rcalc_intersectrYs QB QB RA! 1q5MMC2JJ & !!!sC     ! rAv:s$6$AA) tolerancer!r"r#r$c*t||krt||krdS|d||zzz|zdz}t||krdS||z|z |z dz}t|||zdz||z ||ot|||z||zdz||S)aCheck if a cubic Bezier lies within a given distance of the origin. "Origin" means *the* origin (0,0), not the start of the curve. Note that no checks are made on the start and end positions of the curve; this function only checks the inside of the curve. Args: p0 (complex): Start point of curve. p1 (complex): First handle of curve. p2 (complex): Second handle of curve. p3 (complex): End point of curve. tolerance (double): Distance from origin. Returns: bool: True if the cubic Bezier ``p`` entirely lies within a distance ``tolerance`` of the origin, False otherwise. Tr)rAFrB)abscubic_farthest_fit_inside)r!r"r#r$rZr>r?s rr]r]s. 2ww)B9 4 4t R"W  "d *C 3xx)u2glR4 'F %b2b5"*c&j#y Q Q R %c3v:2rz2y Q QSr)rZ_2_3)q1c0r8c2c3UUUUUU?ct|}tj|jrdS|d}|d}|||z |zz}|||z |zz}t d||dz ||dz d|sdS|||fS)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. Nrr)rr()rYmathisnanimagr])cubicrZr^r_r`rbr8ras rcubic_approx_quadraticris&  B z"'t qB qB rBw$ B rBw$ B $Q%'%(]%'%(]%&  3 3t r2:r)r0rZr^)r5)r`r8rarb)q0r_next_q1q2r9c|dkrt||St|d|d|d|d|}t|}tdg|R}|d}d}|d|g} t d|dzD]} |\} } } }|}|}| |kr@t|}t| |dz z g|R}| |||zdz}n|}|}||z }t ||ks+t||||z |zz| z |||z |zz| z ||sdS| |d| S)a'Approximate 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. rrr(r)yrBN)rir1nextrPr;appendr\r])rhr0rZr^cubics next_cubicrkrlr9spliner5r`r8rarbrjr_d0s rcubic_approx_splinert1s, Avv%eY777 $U1XuQxq58Q O OFfJ"12z222G qB BAh F 1ac]]$BB  q55fJ*1!9BzBBBG MM' " " "w,"$BBB "W GGi  )"*,R4/?*?"*D*,R4/?*?"*D*,*3 55 44  MM%( Mr)max_err)r0cd|D}tdtdzD]#}t|||}|d|DcS$t|)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. Returns: 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. c g|] }t| SrrW.0rSs r z&curve_to_quadratic..s ( ( (QWa[ ( ( (rrNc*g|]}|j|jfSrrrgrzss rr{z&curve_to_quadratic..s!555QVQV$555r)r;MAX_Nrtr)curverur0rrs rrrrsz ) (% ( ( (E 1eai 66$UAw77  55f555 5 5 5  e $ $$r)llast_ir5cZd|D}t|t|ksJt|}dg|z}dx}}d} t|||||}||tkrn(|dz }|}4|||<|dz|z}||kr d|DSSt|)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. 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: A list of splines, each spline being a list of 2D tuples. Raises: fontTools.cu2qu.Errors.ApproxNotFoundError: if no suitable approximation can be found for all curves with the given parameters. c&g|]}d|DS)c g|] }t| Srrxrys rr{z2curves_to_quadratic...s***qw{***rrrzrs rr{z'curves_to_quadratic..s' ? ? ?u**E*** ? ? ?rNrrTc&g|]}d|DS)c*g|]}|j|jfSrr}r~s rr{z2curves_to_quadratic...s!666!afaf%666rr)rzrrs rr{z'curves_to_quadratic..s'MMM666v666MMMr)lenrtrr)curves max_errorsrsplinesrr5r0rrs rrrs>@ ? ? ? ?F z??c&kk ) ) ) ) F AfqjGNFQ A N$VAY:a=AA >Ezz FAF  UaK ;;MMWMMM M N f % %%r__main__c4dtdDS)NcZg|](}tdtdD)S)c3ZK|]&}ttjddV'dS)riN)floatrandomrandint)rzcoords r z,generate_curve...s6GGU%q$//00GGGGGGrr()tupler;)rzpoints rr{z"generate_curve..sE### GGeAhhGGG G G###rr*)r;rrrgenerate_curvers)##q### #rc,ttfSN)rMAX_ERRrrrsetup_curve_to_quadraticrs((rcNd}dt|Dtg|zfS)Nr)c*g|]}tSr)rrs rr{z-setup_curves_to_quadratic..s = = =%^   = = =r)r;r) num_curvess rsetup_curves_to_quadraticrs4 = =5+<+< = = = I "$ $rcd|z}|r t|d|dd|d|zz }ntd|zdd}tj||||| }td t|d z|z zdS) Nsetup_z with :r)end_z%s:cfttfd}|S)NcSrr)function setup_funcsrwrappedz/run_benchmark..wrapper..wrappedsx..r)globals)rrrs`` rwrapperzrun_benchmark..wrappersCyy*H :.J / / / / / /Nr)repeatnumberz %5.1fusg.A)printtimeitrmin) benchmark_modulemoduler setup_suffixrrrrresultss r run_benchmarkrs(  , 888\\\: C C C C # , ,JJ %(" + + + +    -* = =fU[\\\ kS\\H4v=>?????rcJtdddtddddS)Nzcu2qu.benchmarkcu2qurr)rrrrmainrs0'2FGGG'2GHHHHHr)rH)rc)rrr)-r ImportErrorfontTools.miscreerrorsr Cu2QuErrorr__all__rrrXcompiledCOMPILEDcfuncinlinereturnsdoublelocalsrWrr r&r1intr/r-r.rPrYr]rirtrr__name__rrrrrrrrseedrrrrs$&MMMM&&&%%%%%%%%& <<<<<<<< !6 7  eEll ?HHH &.V^444 & &54 &6>V^v~VVV&.V^6>ZZZ[ZWV&.V^6>ZZZ6>V^v~VVVWV[Z&.V^6>ZZZ22[Z2>&.V^6>]c]ghhh6>V^v~VVV&- QWQ[\\\&.V^6>ZZZ 0 0[Z]\WVih 0 &.V^6>ZZZ6>&.99955:9[Z5*&.V^6>_e_lmmmFN6>W]Wefff:::gfnm:46>fn\b\jkkk6>v~666!!76lk !$6>V^v~VVV&.V^v~WWWXWWV . 6>fnQWQ_djdrsss6>&.999SS:9tsS>V];;;&.V^6>^d^lmmmnm<;>v}6=III&.V^6>ZZZ&.V^V^PVP^cicqrrr999sr[ZJI 9xv}%%%%%&%%4FJ&*===3&3&>=3&l zMMMMMMG### )))$$$SW@@@@$IIIFKNNNDFFFFFWs