o iBF @szddlZWneefyddlmZYnwejZddlZddlmZ m Z ddgZ dZ e dZejejeejejejejejd d d Zejejejejd ejejejd ddZejejejejejejejdejejejejejdddZejejejejejejejdejejejejejdddZejejejejejejejdddZejejejejejejdejejejejejdejejejejejdejejejejejdddZejejejejejejejdejejejddd Zejejejejejejejdejejejejejd!d"d#Zejejeejejejejejejejd$ejejejd%d&d'Zejejeejejejejejejdejejejejejd(d)d*Zejeejejejejejejejd+ejejejdd,d-Z ejejejejd.ejejejejejejd/d0d1Z!ejejejejd2ejejd3ejejd4ejejejejejd5ejejejejejejd6d7d8Z"ejejd9ejejd:ejejd4d?ddZ$dS)@N)cython)ErrorApproxNotFoundErrorcurve_to_quadraticcurves_to_quadraticdNaNZv1Zv2resultcCs"||j}t|dkrd}|S)zReturn the dot product of two vectors. Args: v1 (complex): First vector. v2 (complex): Second vector. Returns: double: Dot product. gV瞯rrrr.s r.)mid1deriv1mid2deriv2cCsd|d|d||d}|d|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,gh/?r*r+r)r"r)r$r%r&r'rArBrCrDrrrr/s  r/)tr$r%r&r')_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)rGr$r%r&r'rHrIrrrcubic_approx_controlsrJ)abcdphcCs~||}||}|d}zt|||t||}Wnty8||kr1||ks-||kr1|YStttYSw|||S)ayCalculate the intersection of two lines. Args: a (complex): Start point of first line. b (complex): End point of first line. c (complex): Start point of second line. d (complex): End point of second line. Returns: complex: Location of intersection if one present, ``complex(NaN,NaN)`` if no intersection was found. y?)rZeroDivisionErrorrNAN)rrrrrKrLrMrNrrrcalc_intersects  rQ) tolerancer$r%r&r'cCst||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*r?Fr@)rcubic_farthest_fit_inside)r$r%r&r'rRr=r>rrrrS8s rS)rR)q1c0r9c2c3cCst|d|d|d|d}t|jrdS|d}|d}|||d}|||d}td||d||dd|sAdS|||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. rrr)r*NUUUUUU?)rQmathisnanrrS)cubicrRrTrUrWr9rVrrrcubic_approx_quadraticbs   r\)r1rR)r6) all_quadratic)rUr9rVrW)q0rTnext_q1q2r:cCsb|dkr t||S|dkr|dkr|St|d|d|d|d|}t|}td|d|d|d|d}|d}d}|d|g} td|dD]]} |\} } } }|}|}| |kr~t|}t| |d|d|d|d|d}| |||d}n|}|}||}t||kst||||d| |||d| ||sd SqJ| |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. rr)Frr*yr@rXN)r\r2nextrJr;appendrrS)r[r1rRr]ZcubicsZ next_cubicr_r`r:spliner6rUr9rVrWr^rTZd0rrrcubic_approx_splinesJ    " rd)max_err)r1TcCsRdd|D}tdtdD]}t||||}|dur$dd|DSqt|)a5Approximate 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). cSg|]}t|qSrr.0rMrrr z&curve_to_quadratic..rNcSg|]}|j|jfqSrr rrisrrrrj)r;MAX_Nrdr)curverer]r1rcrrrrs)llast_ir6c Csdd|D}t|t|ksJt|}dg|}d}}d} t||||||}|dur@|tkr9 t||d7}|}q |||<|d|}||krUdd|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. 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. cSg|] }dd|DqS)cSrfrrgrhrrrrjrk2curves_to_quadratic...r)rirrrrrrjz'curves_to_quadratic..NrrTcSru)cSrlrrmrnrrrrj1rprvr)rircrrrrj1rw)lenrdrqr) ZcurvesZ max_errorsr]rsZsplinesrtr6r1rcrrrrs('   )T)%rAttributeError ImportErrorZfontTools.misccompiledZCOMPILEDrYerrorsrZ Cu2QuErrorr__all__rqfloatrPZcfuncinlinereturnsdoublelocalsrrrr#r(r2intr0r.r/rJrQrSr\rdrrrrrrs  %        @