a g0@s,z ddlZWn"eefy.ddlmZYn0ejZddlmZddlm Z ddl Z ddl m Z m Z mZdgZejeejejejejejejejdejejejdd d Zejejejejejd d d Zejejejejejejejejejejejejejd ddZejejejejejejejdddZee eefefZejejejdd"e e eeee e edfdddZe dgdZejejejejejejejejejejejejejejejejejejejejejejdd#ddZdd Z e!d!kr(e dS)$N)cython)splitCubicAtTC) namedtuple)ListTupleUnionquadratic_to_curves) tolerancep0p1p2p3)midderiv3cCst||krt||krdS|d|||d}t||krDdS||||d}t|||d||||ot|||||d||S)aCheck if a cubic Bezier lies within a given distance of the origin. "Origin" means *the* origin (0,0), not the start of the curve. Note that no checks are made on the start and end positions of the curve; this function only checks the inside of the curve. Args: p0 (complex): Start point of curve. p1 (complex): First handle of curve. p2 (complex): Second handle of curve. p3 (complex): End point of curve. tolerance (double): Distance from origin. Returns: bool: True if the cubic Bezier ``p`` entirely lies within a distance ``tolerance`` of the origin, False otherwise. Tg?F?)abscubic_farthest_fit_inside)r r r r r rrrN/var/www/sistema_ama/venv/lib/python3.9/site-packages/fontTools/qu2cu/qu2cu.pyr(s rr r r Zp1_2_3cCs$|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]v}|||}|||d}|d|dksLJt|d|dt|d|d}||9}|7|qfdd|dd D}||d} ||d} |||dd} |||dd} | | | |r|dnd} | | | |r d|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 z 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}||d|||d7}q"|S)Nrr rr)listlenr&insert)pqr,r-r.r/r0r1rrradd_implicit_on_curvess    r7)cost is_complexrF.)quadsmax_err all_cubicreturnc Cst|ddtu}|s&dd|D}|ddg}dg}d}|D]~}|d|dksZJtt|dD] }|d7}||||qjt|dd} ||| |d7}||qBt||||} |sdd| D} | S) aConverts a connecting list of quadratic splines to a list of quadratic and cubic curves. 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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 rcSsg|]}dd|DqS)cSsg|]\}}t||qSr)complex)r!xyrrrr#r$z2quadratic_to_curves...r)r!r5rrrr#r$z'quadratic_to_curves..rr%r NcSsg|]}tdd|DqS)css|]}|j|jfVqdSN)realimag)r!crrr r$z1quadratic_to_curves...)tuple)r!r*rrrr#r$) typer>r&r3r'r7popextendspline_to_curves) r:r;r<r9r6costsr8r5r.Zqqr(rrrrs*#    Solution) num_pointserror start_indexis_cubic)r.jrr i_sol_count j_sol_countZthis_sol_countr errrN i_sol_error j_sol_errorr<rPr,r r r r vuc$ stdksJdfddtdtddD}t}tdt|D]^}||dd}||d}||d} t||t| ||t| |krJ||qJtddddg} tt|ddddd} d} tdt|dD]}| } t| |D]}| |j| |j}}|sx|d|d|d|d}||}|}t||||d}|| krl|} |dkrxqzt||||\}}Wnt yYqYn0t g||R}g}d}t |D]N\}}|||}t|d|d}t ||}||krq| |q||kr(qt |D]V\}}|||}td d t||D\}}} }t||| ||s0|d}qq0||krq|d}t ||}t||||d }|| kr|} |dkrqq| | ||vr|} qg}g} t| d}|r>| |j| |j}!}"| || |"||!8}qg}#d}ttt|| D]`\}}"|"r|# t||||dn0t||D]$}|# |d|ddq|}qX|#S) aF q: quadratic spline with alternating on-curve / off-curve points. costs: cumulative list of encoding cost of q in terms of number of points that need to be encoded. Implied on-curve points do not contribute to the cost. If all points need to be encoded, then costs will be range(1, len(q)+1). rz+quadratic spline requires at least 3 pointscs g|]}t||dqS)r)r)r!r.r6rrr#sz$spline_to_curves..rr rFcss|]\}}||VqdSrAr)r!rWrXrrrrETr$z#spline_to_curves..T)r3r&setraddrLrMrNr+ZeroDivisionErrorr enumeratemaxr'rFziprrOrPreversedr2)$r6rKr r<Zelevated_quadraticsZforcedr.r r r ZsolsZ impossiblerZbest_solrQrSrVZ this_countrRrUZi_solr*r)Zreconstructed_iterZ reconstructedrNrZreconstorigrTr splitsZcubicr,rPr(rrYrrJs!   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