o j=3@szddlZWneefyddlmZYnwejZddlmZddlm Z ddl Z ddl m Z m Z mZdgZejeejejejejejejejdejejejdd d Zejejejejejd d d Zejejejejejejejejejejejejejd ddZejejejejejejejdddZee eefefZddZddZddZejejejd  d>de e ededed e e ed!ffd"dZ e d#gd$Z!ejd?id%ejd&ejd'ejd(ejd)ejd*ejd+ejd,ejd-ejd.ejd/ejd0ejdejd1ejd2ejd3ejd4ejd5ejd6ejd7ejd8ejd>d9d:Z"d;d<Z#e$d=krRe#dSdS)@N)cython)splitCubicAtTC) namedtuple)ListTupleUnionquadratic_to_curves) tolerancep0p1p2p3)midderiv3cCst||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. Tg?F?)abscubic_farthest_fit_inside)r r r r r rrrV/var/www/html/Deteccion_Ine/venv/lib/python3.10/site-packages/fontTools/qu2cu/qu2cu.pyr(s rr r r Zp1_2_3cCs$|d}||d||d||fS)zAGiven a quadratic bezier curve, return its degree-elevated cubic.gUUUUUU?gUUUUUU?rrrrrelevate_quadraticRs    r) startnk prod_ratio sum_ratioratiotr r r r cs:d}ddg}td|D];}|||}|||d}|d|dks&Jt|d|dt|d|d}||9}|7|q fdd|dd D}||d} ||d} |||dd} |||dd} | | | |r|dnd} | | | |rd|d nd} | | | | f} | |fS) zGive a cubic-Bezier spline, reconstruct one cubic-Bezier that has the same endpoints and tangents and approxmates the spline.g?rrcsg|]}|qSrr).0rrrr sz merge_curves..N)rangerappend)curvesrrrtsrZckZc_beforerr r r r curverr"r merge_curveses( (     r*)count num_offcurvesioff1off2oncCslt|}d}t|d}td|D]"}||}||d}|||d}||d|||d7}q|S)Nrr rr)listlenr%insert)pqr+r,r-r.r/r0rrradd_implicit_on_curvess    r6cCstd|d|)Nz1Quadratic splines must connect end-to-start; got z then  ValueError)pointZprevious_pointrrr_raise_incompatible_pointsr:cCst|dkr tddS)Nrz0Quadratic splines must contain at least 3 points)r2r8)splinerrr_validate_spline_lengths r<cCs|dkrtddS)Nrz!max_err must be greater than zeror7)max_errrrr_validate_positive_tolerancesr>)cost is_complexrFquadsr= all_cubicreturn.c Cs|sgSt||D]}t|q t|ddtu}|s$dd|D}|ddg}dg}d}|D]F}|d|dkrEt|d|dtt|dD]} |d7}||||qMt|dd} | | | |d7}||q2t ||||} |sdd| D} | S) aConverts a connecting list of quadratic splines to a list of quadratic and cubic curves. A quadratic spline is specified as a list of points. Either each point is a 2-tuple of X,Y coordinates, or each point is a complex number with real/imaginary components representing X,Y coordinates. The first and last points are on-curve points and the rest are off-curve points, with an implied on-curve point in the middle between every two consequtive off-curve points. Returns: The output is a list of tuples of points. Points are represented in the same format as the input, either as 2-tuples or complex numbers. If ``quads`` is empty, returns an empty list. Each tuple is either of length three, for a quadratic curve, or four, for a cubic curve. Each curve's last point is the same as the next curve's first point. Args: quads: quadratic splines max_err: absolute error tolerance; defaults to 0.5 all_cubic: if True, only cubic curves are generated; defaults to False Raises: ValueError: if an input spline has fewer than 3 points, or if adjacent splines do not connect end-to-start. rcSsg|] }dd|DqS)cSsg|] \}}t||qSr)complex)r!xyrrrr#z2quadratic_to_curves...r)r!r4rrrr#rGz'quadratic_to_curves..rr$r NcSsg|] }tdd|DqS)css|] }|j|jfVqdSN)realimag)r!crrr z1quadratic_to_curves...)tuple)r!r)rrrr#s) r>r<typerDr:r%r2r&r6popextendspline_to_curves) rAr=rBr;r@r5costsr?r4r-Zqqr'rrrrs6(     Solution) num_pointserror start_indexis_cubicr-jrr i_sol_count j_sol_countZthis_sol_countr errrV i_sol_error j_sol_errorrXr+r r r r vuc$ stdks JdfddtdtddD}t}tdt|D]/}||dd}||d}||d} t||t| ||t| |krT||q%tddddg} tt|ddddd} d} tdt|dD]}| } t| |D]}| |j| |j}}|s|d|d|d|d}||}|}t||||d}|| kr|} |dkrq~z t||||\}}Wn t yYq~wt g||R}g}d}t |D]$\}}|||}t|d|d}t ||}||krn| |q||kr q~t |D]*\}}|||}td d t||D\}}} }t||| ||s6|d}nq ||kr>q~|d}t ||}t||||d }|| krW|} |dkr^nq~| | ||vrk|} qug}g} t| d}|r| |j| |j}!}"| || |"||!8}|syg}#d}ttt|| D]0\}}"|"r|# t||||dnt||D]}|# |d|ddq|}q|#S) aF q: quadratic spline with alternating on-curve / off-curve points. costs: cumulative list of encoding cost of q in terms of number of points that need to be encoded. Implied on-curve points do not contribute to the cost. If all points need to be encoded, then costs will be range(1, len(q)+1). rz+quadratic spline requires at least 3 pointscs g|] }t||dqS)r)r)r!r-r5rrr#2sz$spline_to_curves..rr rFcss|] \}}||VqdSrHr)r!r_r`rrrrLprMz#spline_to_curves..T)r2r%setraddrTrUrVr*ZeroDivisionErrorr enumeratemaxr&rNziprrWrXreversedr1)$r5rSr rBZelevated_quadraticsZforcedr-r r r ZsolsZ impossiblerZbest_solrYr[r^Z this_countrZr]Zi_solr)r(Zreconstructed_iterZ reconstructedrVrZreconstorigr\r ZsplitsZcubicr+rXr'rrarrRs!   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