U Dv fR@ @s\zddlZejZWn(eefk r:ddlmZdZYnXddlZddlmZ m Z ddgZ dZ e d Zejejeejejejejd d d Zejejejejejejejd ejejejejejdddZejejejejejejejdejejejejejd ddZejejejejejejejdddZejejejejejejdejejejejejd ejejejejejdejejejejejdddZejejejejejejejdejejejdddZejejejejejejejdejejejejejddd Zejejeejejejejejejejd!ejejejd"d#d$Zejejeejejejejejejd ejejejejejd%d&d'Zejeejejejejejejejd(ejejejdd)d*Zejejejejd+ejejejejejejd,d-d.Z ejejejejd/ejejd0ejejd1ejejejejejd2ejejejejejejd3d4d5Z!ejejd6ejejd7ejejd1dN)cythonF)ErrorApproxNotFoundErrorcurve_to_quadraticcurves_to_quadraticdNaNZv1Zv2cCs||jS)zReturn the dot product of two vectors. Args: v1 (complex): First vector. v2 (complex): Second vector. Returns: double: Dot product. ) conjugaterealr r 9/tmp/pip-unpacked-wheel-qlge9rch/fontTools/cu2qu/cu2qu.pydot(sr)abcd)_1_2_3_4cCs<|}|d|}||d|}||||}||||fSN@r )rrrrrrrrr r rcalc_cubic_points9s  r)p0p1p2p3cCs<||d}||d|}|}||||}||||fSrr )rrrrrrrrr r rcalc_cubic_parametersGs  rcCs|dkrtt||||S|dkr4tt||||S|dkrt||||\}}tt|d|d|d|dt|d|d|d|dS|dkrt||||\}}tt|d|d|d|dt|d|d|d|dSt|||||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. rr)itersplit_cubic_into_twosplit_cubic_into_three_split_cubic_into_n_gen)rrrrnrrr r rsplit_cubic_into_n_iterUs&r))rrrrr()dtdelta_2delta_3i)a1b1c1d1ccst||||\}}}}d|} | | } | | } t|D]} | | } | | }|| }d|| || }d|| |d||| }|| ||||| |}t||||Vq6dS)Nrr!r )rranger)rrrrr(rrrrr*r+r,r-t1Zt1_2r.r/r0r1r r rr's   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 )rrrrr4r5r r rr%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 rr )rrrrr8r9r:r;r r rr&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?r@r r rcubic_approx_controlsrA)abcdphcCs`||}||}|d}zt|||t||}Wntk rRtttYSX|||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)rrrrrBrCrDrEr r rcalc_intersectsrI) tolerancerrrrcCst||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!r6Fr7)abscubic_farthest_fit_inside)rrrrrJr4r5r r rrLs  rL)rJ)q1c0r0c2c3cCst|d|d|d|d}t|jr.dS|d}|d}|||d}|||d}td||d||dd|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. rrr r!NUUUUUU?)rImathisnanimagrL)cubicrJrMrNrPr0rOr r rcubic_approx_quadraticEs  rV)r(rJ)r-) all_quadratic)rNr0rOrP)q0rMnext_q1q2r1cCsd|dkrt||S|dkr&|dkr&|St|d|d|d|d|}t|}td|d|d|d|d}|d}d}|d|g} td|dD]} |\} } } }|}|}| |krt|}t| |d|d|d|d|d}| |||d}n|}|}||}t||ksJt||||d| |||d| ||sd Sq| |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!yr7rQN)rVr)nextrAr2appendrKrL)rUr(rJrWZcubicsZ next_cubicrYrZr1spliner-rNr0rOrPrXrMZd0r r rcubic_approx_splineisX      r^)max_err)r(TcCsVdd|D}tdtdD],}t||||}|dk rdd|DSqt|dS)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). cSsg|] }t|qSr rG.0rDr r r sz&curve_to_quadratic..rNcSsg|]}|j|jfqSr r rTrbsr r rrcs)r2MAX_Nr^r)curver_rWr(r]r r rrs )llast_ir-c Csdd|D}t|t|ks"tt|}dg|}d}}d}t||||||}|dkrv|tkrhq|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. 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. cSsg|]}dd|DqS)cSsg|] }t|qSr r`rar r rrcs2curves_to_quadratic...r )rbrhr r rrcsz'curves_to_quadratic..NrrcSsg|]}dd|DqS)cSsg|]}|j|jfqSr rdrer r rrcsrkr )rbr]r r rrcs)lenAssertionErrorr^rgr) ZcurvesZ max_errorsrWriZsplinesrjr-r(r]r r rrs$'  )T)T)$rZcompiledZCOMPILEDAttributeError ImportErrorZfontTools.miscrRerrorsrZ Cu2QuErrorr__all__rgfloatrHZcfuncinlineZreturnsdoublelocalsrGrrrr)intr'r%r&rArIrLrVr^rrr r r rs6     %       @