o aA @sbzddlZWneyddlmZYnwddlZddlmZmZddgZdZ e dZ ej r2d Z nd Z ejejeejejejejd d d ZejejejejejejejdejejejejejdddZejejejejejejejdejejejejejdddZejejejejejejdddZejejejejejejdejejejejejdejejejejejdejejejejejdddZejejejejejdejejejdddZejejejejejejdejejejejejd dLd"d#Zeejejejejejejejd$ejejejd%d&d'Zeejejejejejejdejejejejejd(d)d*Zejeejejejejejejejd+ejejejdd,d-Zejejejejd.ejejejejejejd/dMd1d2Zejejejejejd3ejejd4ejejejejejd5ejejejejejejd6dMd7d8Z ejejd9ejejd:d;dZ!ejejejejd<d=dZ"e#d>kr/ddl$Z$ddl%Z%d?Z&d@dAZ'dBdCZ(dDdEZ) GdNdHdIZ*dJdKZ+e$,de+dSdS)ON)cython)ErrorApproxNotFoundErrorcurve_to_quadraticcurves_to_quadraticdZNaNTFZv1Zv2cCs||jS)zReturn the dot product of two vectors. Args: v1 (complex): First vector. v2 (complex): Second vector. Returns: double: Dot product. ) conjugaterealr r 7/usr/lib/python3/dist-packages/fontTools/cu2qu/cu2qu.pydot,sr)abcd)_1_2_3_4cCs<|}|d|}||d|}||||}||||fSN@r )rrrrrrrrr r r calc_cubic_points=s   r)p0p1p2p3cCs<||d}||d|}|}||||}||||fSrr )rrrrrrrrr r r calc_cubic_parametersIs  rcCs|dkr tt||||S|dkrtt||||S|dkr1t||||\}}tt|t|S|dkrHt||||\}}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)rrrrnrrr r r split_cubic_into_n_iterUsr()rrrrr')dtdelta_2delta_3i)a1b1c1d1ccst||||\}}}}d|} | | } | | } t|D]@} | | } | | }|| }d|| || }d|| |d||| }|| ||||| |}t||||VqdS)Nrr r)rranger)rrrrr'rrrrr)r*r+r,t1Zt1_2r-r.r/r0r r r r&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 )rrrrr3r4r r r r$s r$)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!rrr ) rrrrr7r8r9r:r;r r r r%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 )r?rrrrr@rAr r r cubic_approx_controlsrB)abcdphcCs^||}||}|d}zt|||t||}Wnty(tttYSw|||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)rrrrrCrDrErFr r r calc_intersects  rJ) tolerancerrrrcCst||krt||krdS|d|||d}t||kr"dS||||d}t|||d||||oGt|||||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 r5Fr6)abscubic_farthest_fit_inside)rrrrrKr3r4r r r rMs rM)rK_2_3)q1c0r/c2c3UUUUUU?cCsvt|}t|jr dS|d}|d}||||}||||}td||d||dd|s6dS|||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)rJmathZisnanimagrM)cubicrKrNrOrPrRr/rQr r r cubic_approx_quadratics    rW)r'rKrN)r,)rPr/rQrR)q0rOnext_q1q2r0cCs.|dkr t||St|d|d|d|d|}t|}tdg|R}|d}d}|d|g} td|dD]U} |\} } } }|}|}| |krdt|}t| |dg|R}| |||d}n|}|}||}t||kst|||||| ||||| ||sdSq8| |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. rrrr yr6N)rWr(nextrBr1appendrLrM)rVr'rKrNZcubicsZ next_cubicrYrZr0spliner,rPr/rQrRrXrOZd0r r r cubic_approx_spline1s@      r^)max_err)r'cCsPdd|D}tdtdD]}t|||}|dur#dd|DSqt|)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. cSg|]}t|qSr rH.0rEr r r z&curve_to_quadratic..rNcSg|]}|j|jfqSr r rUrcsr r r rd)r1MAX_Nr^r)curver_r'r]r r r rrs )llast_ir,cCsdd|D}t|t|ksJt|}dg|}d}}d} t|||||}|dur?|tkr8 t||d7}|}q |||<|d|}||krTdd|DSq!)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. cSg|] }dd|DqS)cSr`r rarbr r r rdre2curves_to_quadratic...r rcrlr r r rdz'curves_to_quadratic..NrrTcSro)cSrfr rgrhr r r rdrjrpr )rcr]r r r rdrr)lenr^rkr)ZcurvesZ max_errorsrmZsplinesrnr,r'r]r r r rs(   __main__cCsddtdDS)NcSs"g|] }tddtdDqS)css |] }ttddVqdS)riN)floatrandomZrandint)rcZcoordr r r sz,generate_curve...r)tupler1)rcZpointr r r rdsz"generate_curve..r!)r1r r r r generate_curvesrzcCs ttfSN)rzMAX_ERRr r r r setup_curve_to_quadratic r}cCs d}ddt|Dtg|fS)Nr cSsg|]}tqSr )rzrqr r r rdsz-setup_curves_to_quadratic..)r1r|)Z num_curvesr r r setup_curves_to_quadraticsrc Csxd|}|rtd||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{r r function setup_funcr r wrappedr~z/run_benchmark..wrapper..wrapped)globals)rrrr rr wrappers  zrun_benchmark..wrapper)repeatnumberz %5.1fusg.A)printtimeitrmin) Zbenchmark_modulemodulerZ setup_suffixrrrrresultsr r r run_benchmarksrcCstdddtddddS)Nzcu2qu.benchmarkZcu2qurr)rr r r r mains r)r<)rS)rrur)-r ImportErrorZfontTools.miscrTerrorsrZ Cu2QuErrorr__all__rkrvrIZcompiledZCOMPILEDZcfuncZinlinereturnsZdoublelocalsrHrrrr(intr&r$r%rBrJrMrWr^rr__name__rwrr|rzr}rrrZseedr r r r s           <    6