U md0@s6zddlZejZWn(eefk r:ddlmZdZYnXddlmZddlm Z ddl Z ddl m Z m Z mZdgZejeejejejejejejejdejejejd d d Zejejejejejd d dZejejejejejejejejejejejejejd ddZejejejejejejejdddZee eefefZejejejdd%e e eeee e edfdddZe dddddgZejejejejejejejejejejejejejejejejejejejejejejdd&d d!Zd"d#Z e!d$kr2e dS)'N)cythonF)splitCubicAtTC) namedtuple)ListTupleUnionquadratic_to_curves) tolerancep0p1p2p3)midderiv3cCst||krt||krdS|d|||d}t||krDdS||||d}t|||d||||ot|||||d||S)aCheck if a cubic Bezier lies within a given distance of the origin. "Origin" means *the* origin (0,0), not the start of the curve. Note that no checks are made on the start and end positions of the curve; this function only checks the inside of the curve. Args: p0 (complex): Start point of curve. p1 (complex): First handle of curve. p2 (complex): Second handle of curve. p3 (complex): End point of curve. tolerance (double): Distance from origin. Returns: bool: True if the cubic Bezier ``p`` entirely lies within a distance ``tolerance`` of the origin, False otherwise. Tg?F?)abscubic_farthest_fit_inside)r r r r r rrrN/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/fontTools/qu2cu/qu2cu.pyr+s  rr r r Zp1_2_3cCs$|d}||d||d||fS)zAGiven a quadratic bezier curve, return its degree-elevated cubic.gUUUUUU?gUUUUUU?rrrrrelevate_quadraticUs   r) startnk prod_ratio sum_ratioratiotr r r r cs<d}ddg}td|D]v}|||}|||d}|d|dksLtt|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 sz merge_curves..N)rangeAssertionErrorrappend)curvesrrrtsrZckZc_beforerr r r r curverr"r merge_curveshs( (   " 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_complexr.)quadsmax_err all_cubicreturnc Cst|ddtk}|s&dd|D}|ddg}dg}d}|D]~}|d|dksZttt|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#sz2quadratic_to_curves...r)r!r5rrrr#sz'quadratic_to_curves..rr$r NcSsg|]}tdd|DqS)css|]}|j|jfVqdSN)realimag)r!crrr sz1quadratic_to_curves...)tuple)r!r*rrrr#s) typer>r&r%r3r'r7popextendspline_to_curves) r:r;r<r9r6costsr8r5r.Zqqr(rrrrs*#    Solution num_pointserror start_indexis_cubic)r.jrr i_sol_count j_sol_countZthis_sol_countr errrN i_sol_error j_sol_errorr<rPr,r r r r vuc$ stdkstdfddtdtddD}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 k rYqYnXt ||}g}d}t |D]N\}}|||}t|d|d}t ||}||kr q||q||kr$qt |D]V\}}|||}td d t||D\}}} }t||| ||s,|d}qq,||krq|d}t ||}t||||d }|| kr|} |dkrqq| | ||kr|} qg}g} t| d}|r:| |j| |j}!}"||| |"||!8}qg}#d}ttt|| D]`\}}"|"r~|#t ||||dn0t||D]$}|#|d|ddq|}qT|#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. 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