a
    w=ici<                     @   s  zd dl Z W n ey*   d dlm Z  Y n0 d dlZddlmZmZ ddgZdZ	e
dZe jrdd	Znd
Ze je je e je je je jddd Ze je je je je je je jde je je je je jddd Ze je je je je je je jde je je je je jddd Ze je je je je je jddd Ze je je je je je jde je je je je jde je je je je jde je je je je jddd Ze je je je je jde je je jddd Ze je je je je je jde je je je je jd d>d"d#Ze e je je je je je je jd$e je je jd%d&d' Ze e je je je je je jde je je je je jd(d)d* Ze je e je je je je je je jd+e je je jdd,d- Ze je je je jd.e je je je je je jd/d?d1d2Ze je je je je jd3e je jd4e je je je je jd5e je je je je je jd6d@d7d8Z e je jd9e je jd:d;d Z!e je je je jd<d=d Z"dS )A    N)cython   )ErrorApproxNotFoundErrorcurve_to_quadraticcurves_to_quadraticd   NaNTFv1v2c                 C   s   | |   jS )zReturn the dot product of two vectors.

    Args:
        v1 (complex): First vector.
        v2 (complex): Second vector.

    Returns:
        double: Dot product.
    )	conjugaterealr
    r   f/home/droni/.local/share/virtualenvs/DPS-5Je3_V2c/lib/python3.9/site-packages/fontTools/cu2qu/cu2qu.pydot,   s    r   )abcd)_1_2_3_4c                 C   s<   |}|d | }|| d | }| | | | }||||fS N      @r   )r   r   r   r   r   r   r   r   r   r   r   calc_cubic_points=   s
    r   )p0p1p2p3c                 C   s<   ||  d }|| d | }| }|| | | }||||fS r   r   )r   r   r   r    r   r   r   r   r   r   r   calc_cubic_parametersI   s
    r!   c                 C   s   |dkrt t| |||S |dkr4t t| |||S |dkrbt| |||\}}t t| t|  S |dkrt| |||\}}t t| t|  S t| ||||S )a  Split 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.
                )itersplit_cubic_into_twosplit_cubic_into_three_split_cubic_into_n_gen)r   r   r   r    nr   r   r   r   r   split_cubic_into_n_iterU   s    r+   )r   r   r   r    r*   )dtdelta_2delta_3i)a1b1c1d1c                 c   s   t | |||\}}}}d| }	|	|	 }
|	|
 }t|D ]}||	 }|| }|| }d| | | |
 }d| | | d| |  |	 }|| | ||  ||  | }t||||V  q6d S )Nr   r#   r"   )r!   ranger   )r   r   r   r    r*   r   r   r   r   r,   r-   r.   r/   t1Zt1_2r0   r1   r2   r3   r   r   r   r)   v   s      r)   )midderiv3c                 C   s\   | d||   | d }|| | |  d }| | | d || |f||| || d |ffS )a  Split 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   )r   r   r   r    r6   r7   r   r   r   r'      s
    r'   )r   r   r   r    _27)mid1deriv1mid2deriv2h/?c           	      C   s   d|  d|  d|  | | }|d|  d|   | }| d|  d|  d|  | }d| d|  |  | }| d|  | d || |f||| || |f||| |d|  d |ffS )a  Split 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%   r#   r$   r"   r   r   )	r   r   r   r    r:   r;   r<   r=   r>   r   r   r   r(      s      r(   )tr   r   r   r    )_p1_p2c                 C   s0   ||| d  }||| d  }||| |   S )ax  Approximate 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   )rB   r   r   r   r    rC   rD   r   r   r   cubic_approx_control   s    rE   )abcdphc                 C   s^   ||  }|| }|d }zt || | t || }W n tyP   ttt Y S 0 |||  S )ay  Calculate 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              ?)r   ZeroDivisionErrorcomplexNAN)r   r   r   r   rF   rG   rH   rI   r   r   r   calc_intersect   s    rM   )	tolerancer   r   r   r    c                 C   s   t ||krt ||krdS | d||   | d }t ||krDdS || | |  d }t| | | d || ||ot||| || d ||S )a  Check 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#   r8   Fr9   )abscubic_farthest_fit_inside)r   r   r   r    rN   r6   r7   r   r   r   rP      s    rP   )rN   _2_3)q1c0r2   c2c3UUUUUU?c                 C   sv   t |  }t|jrdS | d }| d }||| |  }||| |  }td|| d  || d  d|sldS |||fS )a  Approximate 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.
    Nr   r#   r   r"   )rM   mathisnanimagrP   )cubicrN   rQ   rR   rS   rU   r2   rT   r   r   r   cubic_approx_quadratic  s    

r[   )r*   rN   rQ   )r/   )rS   r2   rT   rU   )q0rR   next_q1q2r3   c                 C   s0  |dkrt | |S t| d | d | d | d |}t|}tdg|R  }| d }d}| d |g}	td|d D ]}
|\}}}}|}|}|
|k rt|}t|
|d  g|R  }|	| || d }n|}|}|| }t||kst|||| |  | ||| |  | ||sp dS qp|	| 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.
    r   r   r"   r#   y                r9   N)r[   r+   nextrE   r4   appendrO   rP   )rZ   r*   rN   rQ   ZcubicsZ
next_cubicr]   r^   r3   spliner/   rS   r2   rT   rU   r\   rR   Zd0r   r   r   cubic_approx_spline1  s>    
 
rb   )max_err)r*   c                 C   sT   dd | D } t dtd D ]*}t| ||}|durdd |D   S qt| dS )a  Approximate 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.

    Returns:
        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.
    c                 S   s   g | ]}t | qS r   rK   .0rH   r   r   r   
<listcomp>      z&curve_to_quadratic.<locals>.<listcomp>r   Nc                 S   s   g | ]}|j |jfqS r   r   rY   rf   sr   r   r   rg     rh   )r4   MAX_Nrb   r   )curverc   r*   ra   r   r   r   r   r  s    )llast_ir/   c                 C   s   dd | D } t |t | ks"J t | }dg| }d }}d}t| | ||| }|du rt|tkrfq|d7 }|}q@|||< |d | }||kr@dd |D S q@t| dS )a  Return 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.

    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:
        A list of splines, each spline being a list of 2D tuples.

    Raises:
        fontTools.cu2qu.Errors.ApproxNotFoundError: if no suitable approximation
        can be found for all curves with the given parameters.
    c                 S   s   g | ]}d d |D qS )c                 S   s   g | ]}t | qS r   rd   re   r   r   r   rg     rh   2curves_to_quadratic.<locals>.<listcomp>.<listcomp>r   )rf   rm   r   r   r   rg     rh   z'curves_to_quadratic.<locals>.<listcomp>Nr   r   c                 S   s   g | ]}d d |D qS )c                 S   s   g | ]}|j |jfqS r   ri   rj   r   r   r   rg     rh   rp   r   )rf   ra   r   r   r   rg     rh   )lenrb   rl   r   )ZcurvesZ
max_errorsrn   Zsplinesro   r/   r*   ra   r   r   r   r     s$    
)r?   )rV   )rV   )#r   ImportErrorZfontTools.miscrW   errorsr   Z
Cu2QuErrorr   __all__rl   floatrL   compiledZCOMPILEDZcfuncinlinereturnsdoublelocalsrK   r   r   r!   r+   intr)   r'   r(   rE   rM   rP   r[   rb   r   r   r   r   r   r   <module>   s   



<