a EbA @s\z ddlZWney*ddlmZYn0ddlZddlmZmZddgZdZ e dZ ej rdd Z nd Z ejejeejejejejd d d ZejejejejejejejdejejejejejdddZejejejejejejejdejejejejejdddZejejejejejejdddZejejejejejejdejejejejejdejejejejejdejejejejejdddZejejejejejdejejejdddZejejejejejejdejejejejejd dLd"d#Zeejejejejejejejd$ejejejd%d&d'Zeejejejejejejdejejejejejd(d)d*Zejeejejejejejejejd+ejejejdd,d-Zejejejejd.ejejejejejejd/dMd1d2Zejejejejejd3ejejd4ejejejejejd5ejejejejejejd6dNd7d8Z ejejd9ejejd:d;dZ!ejejejejd<d=dZ"e#d>krXddl$Z$ddl%Z%d?Z&d@dAZ'dBdCZ(dDdEZ)dOdHdIZ*dJdKZ+e$,de+dS)PN)cython)ErrorApproxNotFoundErrorcurve_to_quadraticcurves_to_quadraticdNaNTFv1v2cCs||jS)zReturn the dot product of two vectors. Args: v1 (complex): First vector. v2 (complex): Second vector. Returns: double: Dot product. ) conjugaterealr rU/home/ja/django-apps/lartica_env/lib/python3.9/site-packages/fontTools/cu2qu/cu2qu.pydot,sr)abcd)_1_2_3_4cCs<|}|d|}||d|}||||}||||fSN@r)rrrrrrrrrrrcalc_cubic_points=s  r)p0p1p2p3cCs<||d}||d|}|}||||}||||fSrr)rrrr rrrrrrrcalc_cubic_parametersIs  r!cCs|dkrtt||||S|dkr4tt||||S|dkrbt||||\}}tt|t|S|dkrt||||\}}tt|t|St|||||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)rrrr nrrrrrsplit_cubic_into_n_iterUsr+)rrrr r*)dtdelta_2delta_3i)a1b1c1d1ccst||||\}}}}d|} | | } | | } t|D]} | | } | | }|| }d|| || }d|| |d||| }|| ||||| |}t||||Vq6dS)Nrr#r")r!ranger)rrrr r*rrrrr,r-r.r/t1Zt1_2r0r1r2r3rrrr)vs   r))midderiv3cCs\|d|||d}||||d}|||d|||f|||||d|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)rrrr r6r7rrrr's r')rrrr _27)mid1deriv1mid2deriv2h/?c Csd|d|d|||}|d|d||}|d|d|d||}d|d|||}|d||d|||f||||||f||||d|d|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) rrrr r:r;r<r=r>rrrr(s  r()trrrr )_p1_p2cCs0|||d}|||d}||||S)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)rBrrrr rCrDrrrcubic_approx_controlsrE)abcdphcCs^||}||}|d}zt|||t||}WntyPtttYS0|||S)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)rrrrrFrGrHrIrrrcalc_intersects rM) tolerancerrrr cCst||krt||krdS|d|||d}t||krDdS||||d}t|||d||||ot|||||d||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#r8Fr9)abscubic_farthest_fit_inside)rrrr rNr6r7rrrrPs rP)rN_2_3)q1c0r2c2c3UUUUUU?cCsvt|}t|jrdS|d}|d}||||}||||}td||d||dd|sldS|||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")rMmathisnanimagrP)cubicrNrQrRrSrUr2rTrrrcubic_approx_quadratics   r[)r*rNrQ)r/)rSr2rTrU)q0rRnext_q1q2r3cCs0|dkrt||St|d|d|d|d|}t|}tdg|R}|d}d}|d|g} td|dD]} |\} } } }|}|}| |krt|}t| |dg|R}| |||d}n|}|}||}t||kst|||||| ||||| ||spdSqp| |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#yr9N)r[r+nextrEr4appendrOrP)rZr*rNrQZcubicsZ next_cubicr]r^r3spliner/rSr2rTrUr\rRZd0rrrcubic_approx_spline1s>     rb)max_err)r*cCsTdd|D}tdtdD]*}t|||}|durdd|DSqt|dS)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. cSsg|] }t|qSrrK.0rHrrr z&curve_to_quadratic..rNcSsg|]}|j|jfqSrrrYrfsrrrrgrh)r4MAX_Nrbr)curvercr*rarrrrrs  )llast_ir/cCsdd|D}t|t|ks"Jt|}dg|}d}}d}t|||||}|durt|tkrfq|d7}|}q@|||<|d|}||kr@dd|DSq@t|dS)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. cSsg|]}dd|DqS)cSsg|] }t|qSrrdrerrrrgrh2curves_to_quadratic...rrfrmrrrrgrhz'curves_to_quadratic..NrrcSsg|]}dd|DqS)cSsg|]}|j|jfqSrrirjrrrrgrhrpr)rfrarrrrgrh)lenrbrlr)ZcurvesZ max_errorsrnZsplinesror/r*rarrrrs$  __main__cCsddtdDS)NcSs"g|]}tddtdDqS)css|]}ttddVqdS)riN)floatrandomrandint)rfZcoordrrr rhz,generate_curve...r")tupler4)rfpointrrrrgsz"generate_curve..r$)r4rrrrgenerate_curvesr{cCs ttfSN)r{MAX_ERRrrrrsetup_curve_to_quadraticsr~cCs d}ddt|Dtg|fS)Nr#cSsg|] }tqSr)r{rqrrrrgrhz-setup_curves_to_quadratic..)r4r})Z num_curvesrrrsetup_curves_to_quadraticsrc Csxd|}|r.td||fdd|d|7}ntd|dddd}tj|||||d }td t|d |dS) NZsetup_z %s with %s:r)end_z%s:cs&ttfdd}|S)Ncs Sr|rrfunction setup_funcrrwrappedsz/run_benchmark..wrapper..wrapped)globals)rrrrrrwrappers  zrun_benchmark..wrapper)repeatnumberz %5.1fusg.A)printtimeitrmin) Zbenchmark_modulemodulerZ setup_suffixrrrrresultsrrr run_benchmarksrcCstdddtddddS)Nzcu2qu.benchmarkZcu2qurr)rrrrrmains r)r?)rV)rV)rrtr)-r ImportErrorZfontTools.miscrWerrorsrZ Cu2QuErrorr__all__rlrurLcompiledZCOMPILEDZcfuncinlinereturnsdoublelocalsrKrrr!r+intr)r'r(rErMrPr[rbrr__name__rvrr}r{r~rrrseedrrrrs          <    6