o `i=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 rrrS/home/ubuntu/SoloSpeech/.venv/lib/python3.10/site-packages/fontTools/qu2cu/qu2cu.pyr(s rr r r p1_2_3cCs$|d}||d||d||fS)zAGiven a quadratic bezier curve, return its degree-elevated cubic.gUUUUUU?gUUUUUU?rrrrrelevate_quadraticRs    r) startnk prod_ratio sum_ratioratiotr r r r cs:d}ddg}td|D];}|||}|||d}|d|dks&Jt|d|dt|d|d}||9}|7|q fdd|dd D}||d} ||d} |||dd} |||dd} | | | |r|dnd} | | | |rd|d nd} | | | | f} | |fS) zGive a cubic-Bezier spline, reconstruct one cubic-Bezier that has the same endpoints and tangents and approxmates the spline.g?rrcsg|]}|qSrr).0rrrr sz merge_curves..N)rangerappend)curvesrrrtsrckc_beforerr r r r curverr#r merge_curveses( (     r-)count num_offcurvesioff1off2oncCslt|}d}t|d}td|D]"}||}||d}|||d}||d|||d7}q|S)Nrr!r r)listlenr&insert)pqr.r/r0r1r2r3rrradd_implicit_on_curvess    r9cCstd|d|)Nz1Quadratic splines must connect end-to-start; got z then  ValueError)pointprevious_pointrrr_raise_incompatible_pointsr>cCst|dkr tddS)Nrz0Quadratic splines must contain at least 3 points)r5r;)splinerrr_validate_spline_lengths r@cCs|dkrtddS)Nrz!max_err must be greater than zeror:)max_errrrr_validate_positive_tolerancesrB)cost is_complexrFquadsrA all_cubicreturn.c Cs|sgSt||D]}t|q t|ddtu}|s$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$z2quadratic_to_curves...r)r"r7rrrr$rKz'quadratic_to_curves..r r%r!NcSsg|] }tdd|DqS)css|] }|j|jfVqdSN)realimag)r"crrr z1quadratic_to_curves...)tuple)r"r,rrrr$s) rBr@typerHr>r&r5r'r9popextendspline_to_curves) rErArFr?rDr8costsrCr7r0qqr(rrrrs6(     Solution) num_pointserror start_indexis_cubicr0jrr i_sol_count j_sol_countthis_sol_countr errr[ i_sol_error j_sol_errorr]r.r r r r vuc$ 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"r0r8rrr$2sz$spline_to_curves..rr!r Fcss|] \}}||VqdSrLr)r"rerfrrrrPprQz#spline_to_curves..T)r5r&setraddrYrZr[r-ZeroDivisionErrorr enumeratemaxr'rRziprr\r]reversedr4)$r8rWr rFelevated_quadraticsforcedr0r r r sols impossiblerbest_solr^r`rd this_countr_rci_solr,r)reconstructed_iter reconstructedr[rreconstorigrbr splitscubicr.r]r(rrgrrVs!   (                  "rVcCsddlm}ddlm}d}|d}|}|||}td||ftdt|t|g|}tdt|td |td |dS) Nr)generate_curve)curve_to_quadraticg?r z'cu2qu tolerance %g. qu2cu tolerance %g.z+One random cubic turned into %d quadratics.z-Those quadratics turned back into %d cubics. zOriginal curve:zReconstructed curve(s):)fontTools.cu2qu.benchmarkr|fontTools.cu2qur}printr5r)r|r}r reconstruct_tolerancer, quadraticsr(rrrmains      r__main__)rFr)%rAttributeError ImportErrorfontTools.misccompiledCOMPILEDfontTools.misc.bezierToolsr collectionsrmathtypingrrr__all__cfuncreturnsintlocalsdoublerHrrr-r9floatPointr>r@rBboolrrYrVr__name__rrrrs        '    E       y