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Server: Apache/2.4.46 (Win64) OpenSSL/1.1.1j PHP/8.4.25
System: Windows NT DESKTOP-4TAV2RJ 10.0 build 19045 (Windows 10) AMD64
User: fred (0)
PHP: 8.4.25
Disabled: NONE
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File: C:/Users/fred/anaconda3/Lib/site-packages/fontTools/misc/bezierTools.cp312-win_amd64.pyd
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�"�0�F�\�l�x�������ʈ���� �.�B�P�`�x���������Ή�����.�B�T�j�x�������Ȋ����&�6�F�Z�r���������̋���؅*�:�N�`�|�����Ȍڌ�����J�f���������ʍލ����6�J�\�p�������֎���.�>�P�b�r�������ʏޏ����&�:�P�b�v�������ʐڐ����"�4�H�f�|���ą����l�T�@�(����؄Ƅ������h�T�D�0�����ڃƃކĆ������l�X�>�$���&�������x��p�������Lib/fontTools/misc/bezierTools.cLib\\fontTools\\misc\\bezierTools.pycalcCubicArcLengthfontTools.misc.bezierTools.calcCubicArcLength_split_cubic_into_twofontTools.misc.bezierTools._split_cubic_into_two_calcCubicArcLengthCRecursefontTools.misc.bezierTools._calcCubicArcLengthCRecursecalcCubicArcLengthCfontTools.misc.bezierTools.calcCubicArcLengthCfontTools.misc.bezierTools._intSecAtancalcQuadraticArcLengthfontTools.misc.bezierTools.calcQuadraticArcLengthcalcQuadraticArcLengthCfontTools.misc.bezierTools.calcQuadraticArcLengthCfloat divisionapproximateQuadraticArcLengthfontTools.misc.bezierTools.approximateQuadraticArcLengthapproximateQuadraticArcLengthCfontTools.misc.bezierTools.approximateQuadraticArcLengthCcalcQuadraticBoundsfontTools.misc.bezierTools.calcQuadraticBoundsapproximateCubicArcLengthfontTools.misc.bezierTools.approximateCubicArcLengthapproximateCubicArcLengthCfontTools.misc.bezierTools.approximateCubicArcLengthCcalcCubicBoundsfontTools.misc.bezierTools.calcCubicBoundssplitLinefontTools.misc.bezierTools.splitLinesplitQuadraticfontTools.misc.bezierTools.splitQuadraticfontTools.misc.bezierTools.splitQuadratic.genexpr.0genexprsplitCubicfontTools.misc.bezierTools.splitCubicfontTools.misc.bezierTools.splitCubic.genexprsplitQuadraticAtTfontTools.misc.bezierTools.splitQuadraticAtTsplitCubicAtTfontTools.misc.bezierTools.splitCubicAtTsplitCubicAtTCfontTools.misc.bezierTools.splitCubicAtTCsplitCubicIntoTwoAtTCfontTools.misc.bezierTools.splitCubicIntoTwoAtTC_splitQuadraticAtTfontTools.misc.bezierTools._splitQuadraticAtT_splitCubicAtTfontTools.misc.bezierTools._splitCubicAtT_splitCubicAtTCfontTools.misc.bezierTools._splitCubicAtTCfontTools.misc.bezierTools.__defaults__solveQuadraticfontTools.misc.bezierTools.solveQuadraticsolveCubicfontTools.misc.bezierTools.solveCubiccalcQuadraticParametersfontTools.misc.bezierTools.calcQuadraticParameterscalcCubicParametersfontTools.misc.bezierTools.calcCubicParametersfontTools.misc.bezierTools.calcCubicParametersCcalcQuadraticPointsfontTools.misc.bezierTools.calcQuadraticPointscalcCubicPointsfontTools.misc.bezierTools.calcCubicPointsfontTools.misc.bezierTools.calcCubicPointsClinePointAtTfontTools.misc.bezierTools.linePointAtTquadraticPointAtTfontTools.misc.bezierTools.quadraticPointAtTcubicPointAtTfontTools.misc.bezierTools.cubicPointAtTcubicPointAtTCfontTools.misc.bezierTools.cubicPointAtTCsegmentPointAtTfontTools.misc.bezierTools.segmentPointAtT_line_t_of_ptfontTools.misc.bezierTools._line_t_of_pt_both_points_are_on_same_side_of_originfontTools.misc.bezierTools._both_points_are_on_same_side_of_originlineLineIntersectionsfontTools.misc.bezierTools.lineLineIntersections_alignment_transformationfontTools.misc.bezierTools._alignment_transformation_curve_line_intersections_tfontTools.misc.bezierTools._curve_line_intersections_tfontTools.misc.bezierTools._curve_line_intersections_t.genexprcurveLineIntersectionsfontTools.misc.bezierTools.curveLineIntersections_curve_boundsfontTools.misc.bezierTools._curve_bounds_split_segment_at_tfontTools.misc.bezierTools._split_segment_at_t_curve_curve_intersections_tfontTools.misc.bezierTools._curve_curve_intersections_tmidpointfontTools.misc.bezierTools._curve_curve_intersections_t.midpointlambda3fontTools.misc.bezierTools._curve_curve_intersections_t.lambda3precision_is_linelikefontTools.misc.bezierTools._is_linelikefontTools.misc.bezierTools._is_linelike.genexprcurveCurveIntersectionsfontTools.misc.bezierTools.curveCurveIntersectionssegmentSegmentIntersectionsfontTools.misc.bezierTools.segmentSegmentIntersections_segmentreprfontTools.misc.bezierTools._segmentreprfontTools.misc.bezierTools._segmentrepr.genexprprintSegmentsfontTools.misc.bezierTools.printSegmentsfontTools.misc.bezierTools.__pyx_scope_struct__genexprfontTools.misc.bezierTools.__pyx_scope_struct_1_genexprfontTools.misc.bezierTools.__pyx_scope_struct_2_splitCubicAtTCfontTools.misc.bezierTools.__pyx_scope_struct_3__splitCubicAtTCfontTools.misc.bezierTools.__pyx_scope_struct_4_genexprfontTools.misc.bezierTools.__pyx_scope_struct_5__curve_curve_intersections_tfontTools.misc.bezierTools.__pyx_scope_struct_6_genexprfontTools.misc.bezierTools.__pyx_scope_struct_7_genexprbezierToolsInterpreter change detected - this module can only be loaded into one interpreter per process.name__loader__loader__file__origin__package__parent__path__submodule_search_locationsModule 'bezierTools' has already been imported. Re-initialisation is not supported.builtinscython_runtime__builtins__fontTools.misc.bezierToolsinit fontTools.misc.bezierToolsname '%U' is not definedat leastat mostexactlys%.200s() takes %.8s %zd positional argument%.1s (%zd given)%s() got multiple values for keyword argument '%U'%.200s() keywords must be strings%s() got an unexpected keyword argument '%U' while calling a Python objectNULL result without error in PyObject_Calltoo many values to unpack (expected %zd)need more than %zd value%.1s to unpackcannot fit '%.200s' into an index-sized integer'%.200s' object is not subscriptablelocal variable '%s' referenced before assignmentgenerator raised StopIteration_cython_3_0_10Shared Cython type %.200s is not a type objectShared Cython type %.200s has the wrong size, try recompilingraise: arg 3 must be a traceback or Noneinstance exception may not have a separate valuecalling %R should have returned an instance of BaseException, not %Rraise: exception class must be a subclass of BaseExceptiongenerator already executingcan't send non-None value to a just-started generatorgenerator ignored GeneratorExitthrow__name__ must be set to a string object__qualname__ must be set to a string object_cython_coroutine_type_cython_generator_type_moduleCython module failed to patch module with custom typeif _cython_generator_type is not None:
    try: Generator = _module.Generator
    except AttributeError: pass
    else: Generator.register(_cython_generator_type)
if _cython_coroutine_type is not None:
    try: Coroutine = _module.Coroutine
    except AttributeError: pass
    else: Coroutine.register(_cython_coroutine_type)
collections.abcCython module failed to register with collections.abc modulebackports_abcsendsend(arg) -> send 'arg' into generator,
return next yielded value or raise StopIteration.throw(typ[,val[,tb]]) -> raise exception in generator,
return next yielded value or raise StopIteration.closeclose() -> raise GeneratorExit inside generator.gi_runninggi_yieldfromobject being iterated by 'yield from', or Nonegi_code__module____name__name of the generator__qualname__qualified name of the generatorgi_frameFrame of the generator_cython_3_0_10.generatoriter() returned non-iterator of type '%.200s'free variable '%s' referenced before assignment in enclosing scopekeywords must be stringsfunction's dictionary may not be deletedsetting function's dictionary to a non-dict__defaults__ must be set to a tuple objectchanges to cyfunction.__defaults__ will not currently affect the values used in function calls__kwdefaults__ must be set to a dict objectchanges to cyfunction.__kwdefaults__ will not currently affect the values used in function calls__annotations__ must be set to a dict objectfunc_doc__doc__func_namefunc_dict__dict__func_globals__globals__func_closure__closure__func_code__code__func_defaults__defaults____kwdefaults____annotations___is_coroutine__reduce__Bad call flags for CyFunction<cyfunction %U at %p>%.200s() takes no arguments (%zd given)%.200s() takes exactly one argument (%zd given)%.200s() takes no keyword argumentsunbound method %.200S() needs an argument%.200s() needs an argument_cython_3_0_10.cython_function_or_methodbase class '%.200s' is not a heap typeextension type '%.200s' has no __dict__ slot, but base type '%.200s' has: either add 'cdef dict __dict__' to the extension type or add '__slots__ = [...]' to the base typecannot import name %S%s (%s:%d)does not matchcompile time Python version %d.%d of module '%.100s' %s runtime version %d.%ddelta_3ycalcQuadraticBounds (line 298)calcCubicBoundssplitLinerDDfontTools.misc.transformv1_2_t_1_tt2_segmentreprcurveCurveIntersections(curve1, curve2)
Finds intersections between a curve and a curve.

    Args:
        curve1: List of coordinates of the first curve segment as 2D tuples.
        curve2: List of coordinates of the second curve segment as 2D tuples.

    Returns:
        A list of ``Intersection`` objects, each object having ``pt``, ``t1``
        and ``t2`` attributes containing the intersection point, time on first
        segment and time on second segment respectively.

    Examples::
        >>> curve1 = [ (10,100), (90,30), (40,140), (220,220) ]
        >>> curve2 = [ (5,150), (180,20), (80,250), (210,190) ]
        >>> intersections = curveCurveIntersections(curve1, curve2)
        >>> len(intersections)
        3
        >>> intersections[0].pt
        (81.7831487395506, 109.88904552375288)
    R2testmodLib\fontTools\misc\bezierTools.pyslope34Finds intersections between a curve and a line.

    Args:
        curve: List of coordinates of the curve segment as 2D tuples.
        line: List of coordinates of the line segment as 2D tuples.

    Returns:
        A list of ``Intersection`` objects, each object having ``pt``, ``t1``
        and ``t2`` attributes containing the intersection point, time on first
        segment and time on second segment respectively.

    Examples::
        >>> curve = [ (100, 240), (30, 60), (210, 230), (160, 30) ]
        >>> line  = [ (25, 260), (230, 20) ]
        >>> intersections = curveLineIntersections(curve, line)
        >>> len(intersections)
        3
        >>> intersections[0].pt
        (84.9000930760723, 189.87306176459828)
    close_dxrv3calcBoundsonetoleranceseg1t1_2enabled0splitCubiccline_in_tracebacksolveQuadratic(a, b, c, sqrt=sqrt)
Solve a quadratic equation.

    Solves *a*x*x + b*x + c = 0* where a, b and c are real.

    Args:
        a: coefficient of *x²*
        b: coefficient of *x*
        c: constant term

    Returns:
        A list of roots. Note that the returned list is neither guaranteed to
        be sorted nor to contain unique values!
    _curve_curve_intersections_t(curve1, curve2, precision=1e-3, range1=None, range2=None)calcCubicArcLengtha1delta_2splitCubic.<locals>.genexprd1_is_linelike.<locals>.genexprrange1(��bx2cubicPointAtT(pt1, pt2, pt3, pt4, t)
Finds the point at time `t` on a cubic curve.

    Args:
        pt1, pt2, pt3, pt4: Coordinates of the curve as 2D tuples.
        t: The time along the curve.

    Returns:
        A 2D tuple with the coordinates of the point.
    splitCubicAtTCoff1itFinds intersections between a curve and a curve.

    Args:
        curve1: List of coordinates of the first curve segment as 2D tuples.
        curve2: List of coordinates of the second curve segment as 2D tuples.

    Returns:
        A list of ``Intersection`` objects, each object having ``pt``, ``t1``
        and ``t2`` attributes containing the intersection point, time on first
        segment and time on second segment respectively.

    Examples::
        >>> curve1 = [ (10,100), (90,30), (40,140), (220,220) ]
        >>> curve2 = [ (5,150), (180,20), (80,250), (210,190) ]
        >>> intersections = curveCurveIntersections(curve1, curve2)
        >>> len(intersections)
        3
        >>> intersections[0].pt
        (81.7831487395506, 109.88904552375288)
    ax2c1xv4line2fontTools.misc.bezierTools.py -- tools for working with Bezier path segments.
splitCubic(pt1, pt2, pt3, pt4, where, isHorizontal)
Split a cubic Bezier curve at a given coordinate.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.
        where: Position at which to split the curve.
        isHorizontal: Direction of the ray splitting the curve. If true,
            ``where`` is interpreted as a Y coordinate; if false, then
            ``where`` is interpreted as an X coordinate.

    Returns:
        A list of two curve segments (each curve segment being four 2D tuples)
        if the curve was successfully split, or a list containing the original
        curve.

    Example::

        >>> printSegments(splitCubic((0, 0), (25, 100), (75, 100), (100, 0), 150, False))
        ((0, 0), (25, 100), (75, 100), (100, 0))
        >>> printSegments(splitCubic((0, 0), (25, 100), (75, 100), (100, 0), 50, False))
        ((0, 0), (12.5, 50), (31.25, 75), (50, 75))
        ((50, 75), (68.75, 75), (87.5, 50), (100, 0))
        >>> printSegments(splitCubic((0, 0), (25, 100), (75, 100), (100, 0), 25, True))
        ((0, 0), (2.29379, 9.17517), (4.79804, 17.5085), (7.47414, 25))
        ((7.47414, 25), (31.2886, 91.6667), (68.7114, 91.6667), (92.5259, 25))
        ((92.5259, 25), (95.202, 17.5085), (97.7062, 9.17517), (100, 1.77636e-15))
    x0bounds1cubicPointAtTCsplitCubicAtTcalcQuadraticArcLengthCsplitQuadraticAtT
    >>> _segmentrepr([1, [2, 3], [], [[2, [3, 4], [0.1, 2.2]]]])
    '(1, (2, 3), (), ((2, (3, 4), (0.1, 2.2))))'
    segmentSegmentIntersectionsamaybelinet1_3rootspointsv0isHorizontalFinds intersections between two line segments.

    Args:
        s1, e1: Coordinates of the first line as 2D tuples.
        s2, e2: Coordinates of the second line as 2D tuples.

    Returns:
        A list of ``Intersection`` objects, each object having ``pt``, ``t1``
        and ``t2`` attributes containing the intersection point, time on first
        segment and time on second segment respectively.

    Examples::

        >>> a = lineLineIntersections( (310,389), (453, 222), (289, 251), (447, 367))
        >>> len(a)
        1
        >>> intersection = a[0]
        >>> intersection.pt
        (374.44882952482897, 313.73458370177315)
        >>> (intersection.t1, intersection.t2)
        (0.45069111555824465, 0.5408153767394238)
    swappedarchImportErrorseenc22_range_both_points_are_on_same_side_of_origin(a, b, origin)_segmentrepr(obj)

    >>> _segmentrepr([1, [2, 3], [], [[2, [3, 4], [0.1, 2.2]]]])
    '(1, (2, 3), (), ((2, (3, 4), (0.1, 2.2))))'
    line_split_cubic_into_twosplitCubicAtTC(double complex pt1, double complex pt2, double complex pt3, double complex pt4, *ts)
Split a cubic Bezier curve at one or more values of t.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as complex numbers..
        *ts: Positions at which to split the curve.

    Yields:
        Curve segments (each curve segment being four complex numbers).
    solveCubic(a, b, c, d)
Solve a cubic equation.

    Solves *a*x*x*x + b*x*x + c*x + d = 0* where a, b, c and d are real.

    Args:
        a: coefficient of *x³*
        b: coefficient of *x²*
        c: coefficient of *x*
        d: constant term

    Returns:
        A list of roots. Note that the returned list is neither guaranteed to
        be sorted nor to contain unique values!

    Examples::

        >>> solveCubic(1, 1, -6, 0)
        [-3.0, -0.0, 2.0]
        >>> solveCubic(-10.0, -9.0, 48.0, -29.0)
        [-2.9, 1.0, 1.0]
        >>> solveCubic(-9.875, -9.0, 47.625, -28.75)
        [-2.911392, 1.0, 1.0]
        >>> solveCubic(1.0, -4.5, 6.75, -3.375)
        [1.5, 1.5, 1.5]
        >>> solveCubic(-12.0, 18.0, -9.0, 1.50023651123)
        [0.5, 0.5, 0.5]
        >>> solveCubic(
        ...     9.0, 0.0, 0.0, -7.62939453125e-05
        ... ) == [-0.0, -0.0, -0.0]
        True
    approximateQuadraticArcLengthC(double complex pt1, double complex pt2, double complex pt3)
Calculates the arc length for a quadratic Bezier segment.

    Uses Gauss-Legendre quadrature for a branch-free approximation.
    See :func:`calcQuadraticArcLength` for a slower but more accurate result.

    Args:
        pt1: Start point of the Bezier as a complex number.
        pt2: Handle point of the Bezier as a complex number.
        pt3: End point of the Bezier as a complex number.

    Returns:
        Approximate arc length value.
    theta__main__pxsegmentc1yroundFinds intersections between two segments.

    Args:
        seg1: List of coordinates of the first segment as 2D tuples.
        seg2: List of coordinates of the second segment as 2D tuples.

    Returns:
        A list of ``Intersection`` objects, each object having ``pt``, ``t1``
        and ``t2`` attributes containing the intersection point, time on first
        segment and time on second segment respectively.

    Examples::
        >>> curve1 = [ (10,100), (90,30), (40,140), (220,220) ]
        >>> curve2 = [ (5,150), (180,20), (80,250), (210,190) ]
        >>> intersections = segmentSegmentIntersections(curve1, curve2)
        >>> len(intersections)
        3
        >>> intersections[0].pt
        (81.7831487395506, 109.88904552375288)
        >>> curve3 = [ (100, 240), (30, 60), (210, 230), (160, 30) ]
        >>> line  = [ (25, 260), (230, 20) ]
        >>> intersections = segmentSegmentIntersections(curve3, line)
        >>> len(intersections)
        3
        >>> intersections[0].pt
        (84.9000930760723, 189.87306176459828)

    sxprint_split_cubic_into_two(p0, p1, p2, p3)%gex_splitQuadraticAtT(a, b, c, *ts)p0_split_segment_at_t(c, t)sqrts2y��_initializing_is_linelike(segment)approximateCubicArcLengthy2IdentitytwoValueErrors2atan2lineLineIntersections(s1, e1, s2, e2)
Finds intersections between two line segments.

    Args:
        s1, e1: Coordinates of the first line as 2D tuples.
        s2, e2: Coordinates of the second line as 2D tuples.

    Returns:
        A list of ``Intersection`` objects, each object having ``pt``, ``t1``
        and ``t2`` attributes containing the intersection point, time on first
        segment and time on second segment respectively.

    Examples::

        >>> a = lineLineIntersections( (310,389), (453, 222), (289, 251), (447, 367))
        >>> len(a)
        1
        >>> intersection = a[0]
        >>> intersection.pt
        (374.44882952482897, 313.73458370177315)
        >>> (intersection.t1, intersection.t2)
        (0.45069111555824465, 0.5408153767394238)
    c_calcCubicArcLengthCRecursept1Intersectionax3quadraticPointAtT(pt1, pt2, pt3, t)
Finds the point at time `t` on a quadratic curve.

    Args:
        pt1, pt2, pt3: Coordinates of the curve as 2D tuples.
        t: The time along the curve.

    Returns:
        A 2D tuple with the coordinates of the point.
    splitLine(pt1, pt2, where, isHorizontal)
Split a line at a given coordinate.

    Args:
        pt1: Start point of line as 2D tuple.
        pt2: End point of line as 2D tuple.
        where: Position at which to split the line.
        isHorizontal: Direction of the ray splitting the line. If true,
            ``where`` is interpreted as a Y coordinate; if false, then
            ``where`` is interpreted as an X coordinate.

    Returns:
        A list of two line segments (each line segment being two 2D tuples)
        if the line was successfully split, or a list containing the original
        line.

    Example::

        >>> printSegments(splitLine((0, 0), (100, 100), 50, True))
        ((0, 0), (50, 50))
        ((50, 50), (100, 100))
        >>> printSegments(splitLine((0, 0), (100, 100), 100, True))
        ((0, 0), (100, 100))
        >>> printSegments(splitLine((0, 0), (100, 100), 0, True))
        ((0, 0), (0, 0))
        ((0, 0), (100, 100))
        >>> printSegments(splitLine((0, 0), (100, 100), 0, False))
        ((0, 0), (0, 0))
        ((0, 0), (100, 100))
        >>> printSegments(splitLine((100, 0), (0, 0), 50, False))
        ((100, 0), (50, 0))
        ((50, 0), (0, 0))
        >>> printSegments(splitLine((0, 100), (0, 0), 50, True))
        ((0, 100), (0, 50))
        ((0, 50), (0, 0))
    a1y_calcCubicArcLengthCRecurse(double mult, double complex p0, double complex p1, double complex p2, double complex p3)x1approximateQuadraticArcLength(pt1, pt2, pt3)
Calculates the arc length for a quadratic Bezier segment.

    Uses Gauss-Legendre quadrature for a branch-free approximation.
    See :func:`calcQuadraticArcLength` for a slower but more accurate result.

    Args:
        pt1: Start point of the Bezier as 2D tuple.
        pt2: Handle point of the Bezier as 2D tuple.
        pt3: End point of the Bezier as 2D tuple.

    Returns:
        Approximate arc length value.
    p3range_splitCubicAtTCs1yQ3splitCubicAtT (line 613)Split a cubic Bezier curve at one or more values of t.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.
        *ts: Positions at which to split the curve.

    Returns:
        A list of curve segments (each curve segment being four 2D tuples).

    Examples::

        >>> printSegments(splitCubicAtT((0, 0), (25, 100), (75, 100), (100, 0), 0.5))
        ((0, 0), (12.5, 50), (31.25, 75), (50, 75))
        ((50, 75), (68.75, 75), (87.5, 50), (100, 0))
        >>> printSegments(splitCubicAtT((0, 0), (25, 100), (75, 100), (100, 0), 0.5, 0.75))
        ((0, 0), (12.5, 50), (31.25, 75), (50, 75))
        ((50, 75), (59.375, 75), (68.75, 68.75), (77.3438, 56.25))
        ((77.3438, 56.25), (85.9375, 43.75), (93.75, 25), (100, 0))
    mathcxnamedtuplerQ2AttributeErroryDiffapproximateQuadraticArcLengthc21_rangept2xcythone1y_is_coroutinesplitLine (line 450)approximateCubicArcLength(pt1, pt2, pt3, pt4)
Approximates the arc length for a cubic Bezier segment.

    Uses Gauss-Lobatto quadrature with n=5 points to approximate arc length.
    See :func:`calcCubicArcLength` for a slower but more accurate result.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.

    Returns:
        Arc length value.

    Example::

        >>> approximateCubicArcLength((0, 0), (25, 100), (75, 100), (100, 0))
        190.04332968932817
        >>> approximateCubicArcLength((0, 0), (50, 0), (100, 50), (100, 100))
        154.8852074945903
        >>> approximateCubicArcLength((0, 0), (50, 0), (100, 0), (150, 0)) # line; exact result should be 150.
        149.99999999999991
        >>> approximateCubicArcLength((0, 0), (50, 0), (100, 0), (-50, 0)) # cusp; exact result should be 150.
        136.9267662156362
        >>> approximateCubicArcLength((0, 0), (50, 0), (100, -50), (-50, 0)) # cusp
        154.80848416537057
    __spec__calcCubicBounds(pt1, pt2, pt3, pt4)
Calculates the bounding rectangle for a quadratic Bezier segment.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.

    Returns:
        A four-item tuple representing the bounding rectangle ``(xMin, yMin, xMax, yMax)``.

    Example::

        >>> calcCubicBounds((0, 0), (25, 100), (75, 100), (100, 0))
        (0, 0, 100, 75.0)
        >>> calcCubicBounds((0, 0), (50, 0), (100, 50), (100, 100))
        (0.0, 0.0, 100, 100)
        >>> print("%f %f %f %f" % calcCubicBounds((50, 0), (0, 100), (100, 100), (50, 0)))
        35.566243 0.000000 64.433757 75.000000
    epsilons2xstartpi_is_linelike__all__calcCubicPointscurveLineIntersections(curve, line)
Finds intersections between a curve and a line.

    Args:
        curve: List of coordinates of the curve segment as 2D tuples.
        line: List of coordinates of the line segment as 2D tuples.

    Returns:
        A list of ``Intersection`` objects, each object having ``pt``, ``t1``
        and ``t2`` attributes containing the intersection point, time on first
        segment and time on second segment respectively.

    Examples::
        >>> curve = [ (100, 240), (30, 60), (210, 230), (160, 30) ]
        >>> line  = [ (25, 260), (230, 20) ]
        >>> intersections = curveLineIntersections(curve, line)
        >>> len(intersections)
        3
        >>> intersections[0].pt
        (84.9000930760723, 189.87306176459828)
    a3calcQuadraticPointscurveappendb1_curve_curve_intersections_tsegmentPointAtT(seg, t)cubicPointAtTcalcCubicParametersptunique_valuesb1ysplitQuadratic(pt1, pt2, pt3, where, isHorizontal)
Split a quadratic Bezier curve at a given coordinate.

    Args:
        pt1,pt2,pt3: Control points of the Bezier as 2D tuples.
        where: Position at which to split the curve.
        isHorizontal: Direction of the ray splitting the curve. If true,
            ``where`` is interpreted as a Y coordinate; if false, then
            ``where`` is interpreted as an X coordinate.

    Returns:
        A list of two curve segments (each curve segment being three 2D tuples)
        if the curve was successfully split, or a list containing the original
        curve.

    Example::

        >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 150, False))
        ((0, 0), (50, 100), (100, 0))
        >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 50, False))
        ((0, 0), (25, 50), (50, 50))
        ((50, 50), (75, 50), (100, 0))
        >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 25, False))
        ((0, 0), (12.5, 25), (25, 37.5))
        ((25, 37.5), (62.5, 75), (100, 0))
        >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 25, True))
        ((0, 0), (7.32233, 14.6447), (14.6447, 25))
        ((14.6447, 25), (50, 75), (85.3553, 25))
        ((85.3553, 25), (92.6777, 14.6447), (100, -7.10543e-15))
        >>> # XXX I'm not at all sure if the following behavior is desirable:
        >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 50, True))
        ((0, 0), (25, 50), (50, 50))
        ((50, 50), (50, 50), (50, 50))
        ((50, 50), (75, 50), (100, 0))
    xDiffax_curve_line_intersections_t(curve, line)y4__import__mult_1_tcoscollectionsgcdoctest_splitCubicAtT(a, b, c, d, *ts)calcQuadraticBoundsb1x_alignment_transformationinsertend__class_getitem__pt4lineLineIntersectionscurveCurveIntersections (line 1378)s1xcalcCubicParameters(pt1, pt2, pt3, pt4)transformPointscurveLineIntersections (line 1248)splitCubic (line 552)Solve a cubic equation.

    Solves *a*x*x*x + b*x*x + c*x + d = 0* where a, b, c and d are real.

    Args:
        a: coefficient of *x³*
        b: coefficient of *x²*
        c: coefficient of *x*
        d: constant term

    Returns:
        A list of roots. Note that the returned list is neither guaranteed to
        be sorted nor to contain unique values!

    Examples::

        >>> solveCubic(1, 1, -6, 0)
        [-3.0, -0.0, 2.0]
        >>> solveCubic(-10.0, -9.0, 48.0, -29.0)
        [-2.9, 1.0, 1.0]
        >>> solveCubic(-9.875, -9.0, 47.625, -28.75)
        [-2.911392, 1.0, 1.0]
        >>> solveCubic(1.0, -4.5, 6.75, -3.375)
        [1.5, 1.5, 1.5]
        >>> solveCubic(-12.0, 18.0, -9.0, 1.50023651123)
        [0.5, 0.5, 0.5]
        >>> solveCubic(
        ...     9.0, 0.0, 0.0, -7.62939453125e-05
        ... ) == [-0.0, -0.0, -0.0]
        True
    segmentspt1xCalculates the bounding rectangle for a quadratic Bezier segment.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.

    Returns:
        A four-item tuple representing the bounding rectangle ``(xMin, yMin, xMax, yMax)``.

    Example::

        >>> calcCubicBounds((0, 0), (25, 100), (75, 100), (100, 0))
        (0, 0, 100, 75.0)
        >>> calcCubicBounds((0, 0), (50, 0), (100, 50), (100, 100))
        (0.0, 0.0, 100, 100)
        >>> print("%f %f %f %f" % calcCubicBounds((50, 0), (0, 100), (100, 100), (50, 0)))
        35.566243 0.000000 64.433757 75.000000
    deltan_both_points_are_on_same_side_of_originbounds2_splitQuadraticAtTpt1yy3epsilonDigitscalcQuadraticParameters(pt1, pt2, pt3)__name__*Split a quadratic Bezier curve at one or more values of t.

    Args:
        pt1,pt2,pt3: Control points of the Bezier as 2D tuples.
        *ts: Positions at which to split the curve.

    Returns:
        A list of curve segments (each curve segment being three 2D tuples).

    Examples::

        >>> printSegments(splitQuadraticAtT((0, 0), (50, 100), (100, 0), 0.5))
        ((0, 0), (25, 50), (50, 50))
        ((50, 50), (75, 50), (100, 0))
        >>> printSegments(splitQuadraticAtT((0, 0), (50, 100), (100, 0), 0.5, 0.75))
        ((0, 0), (25, 50), (50, 50))
        ((50, 50), (62.5, 50), (75, 37.5))
        ((75, 37.5), (87.5, 25), (100, 0))
    line_tQc21Unknown curve degreev2t1splitCubicIntoTwoAtTClinePointAtT(pt1, pt2, t)
Finds the point at time `t` on a line.

    Args:
        pt1, pt2: Coordinates of the line as 2D tuples.
        t: The time along the line.

    Returns:
        A 2D tuple with the coordinates of the point.
    p2aligned_curvetssplitCubicAtT(pt1, pt2, pt3, pt4, *ts)
Split a cubic Bezier curve at one or more values of t.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.
        *ts: Positions at which to split the curve.

    Returns:
        A list of curve segments (each curve segment being four 2D tuples).

    Examples::

        >>> printSegments(splitCubicAtT((0, 0), (25, 100), (75, 100), (100, 0), 0.5))
        ((0, 0), (12.5, 50), (31.25, 75), (50, 75))
        ((50, 75), (68.75, 75), (87.5, 50), (100, 0))
        >>> printSegments(splitCubicAtT((0, 0), (25, 100), (75, 100), (100, 0), 0.5, 0.75))
        ((0, 0), (12.5, 50), (31.25, 75), (50, 75))
        ((50, 75), (59.375, 75), (68.75, 68.75), (77.3438, 56.25))
        ((77.3438, 56.25), (85.9375, 43.75), (93.75, 25), (100, 0))
    e2sendLencalcCubicPoints(a, b, c, d)scaleSplit a cubic Bezier curve at a given coordinate.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.
        where: Position at which to split the curve.
        isHorizontal: Direction of the ray splitting the curve. If true,
            ``where`` is interpreted as a Y coordinate; if false, then
            ``where`` is interpreted as an X coordinate.

    Returns:
        A list of two curve segments (each curve segment being four 2D tuples)
        if the curve was successfully split, or a list containing the original
        curve.

    Example::

        >>> printSegments(splitCubic((0, 0), (25, 100), (75, 100), (100, 0), 150, False))
        ((0, 0), (25, 100), (75, 100), (100, 0))
        >>> printSegments(splitCubic((0, 0), (25, 100), (75, 100), (100, 0), 50, False))
        ((0, 0), (12.5, 50), (31.25, 75), (50, 75))
        ((50, 75), (68.75, 75), (87.5, 50), (100, 0))
        >>> printSegments(splitCubic((0, 0), (25, 100), (75, 100), (100, 0), 25, True))
        ((0, 0), (2.29379, 9.17517), (4.79804, 17.5085), (7.47414, 25))
        ((7.47414, 25), (31.2886, 91.6667), (68.7114, 91.6667), (92.5259, 25))
        ((92.5259, 25), (95.202, 17.5085), (97.7062, 9.17517), (100, 1.77636e-15))
    sectRectmidPtx_curve_line_intersections_t.<locals>.genexprpt3Calculates the arc length for a quadratic Bezier segment.

    Args:
        pt1: Start point of the Bezier as 2D tuple.
        pt2: Handle point of the Bezier as 2D tuple.
        pt3: End point of the Bezier as 2D tuple.

    Returns:
        Arc length value.

    Example::

        >>> calcQuadraticArcLength((0, 0), (0, 0), (0, 0)) # empty segment
        0.0
        >>> calcQuadraticArcLength((0, 0), (50, 0), (80, 0)) # collinear points
        80.0
        >>> calcQuadraticArcLength((0, 0), (0, 50), (0, 80)) # collinear points vertical
        80.0
        >>> calcQuadraticArcLength((0, 0), (50, 20), (100, 40)) # collinear points
        107.70329614269008
        >>> calcQuadraticArcLength((0, 0), (0, 100), (100, 0))
        154.02976155645263
        >>> calcQuadraticArcLength((0, 0), (0, 50), (100, 0))
        120.21581243984076
        >>> calcQuadraticArcLength((0, 0), (50, -10), (80, 50))
        102.53273816445825
        >>> calcQuadraticArcLength((0, 0), (40, 0), (-40, 0)) # collinear points, control point outside
        66.66666666666667
        >>> calcQuadraticArcLength((0, 0), (40, 0), (0, 0)) # collinear points, looping back
        40.0
    _segmentrepr (line 1465)dyintersectscalcQuadraticArcLengthC(double complex pt1, double complex pt2, double complex pt3)
Calculates the arc length for a quadratic Bezier segment.

    Args:
        pt1: Start point of the Bezier as a complex number.
        pt2: Handle point of the Bezier as a complex number.
        pt3: End point of the Bezier as a complex number.

    Returns:
        Arc length value.
    RcalcQuadraticPoints(a, b, c)pointFinderobjc12_range_1_t_2e1__test__xRootsmid_line_t_of_ptmidpointpt2yoriginx3fontTools.miscslope12_curve_curve_intersections_t.<locals>.<lambda>curve2isenabledcalcQuadraticArcLength(pt1, pt2, pt3)
Calculates the arc length for a quadratic Bezier segment.

    Args:
        pt1: Start point of the Bezier as 2D tuple.
        pt2: Handle point of the Bezier as 2D tuple.
        pt3: End point of the Bezier as 2D tuple.

    Returns:
        Arc length value.

    Example::

        >>> calcQuadraticArcLength((0, 0), (0, 0), (0, 0)) # empty segment
        0.0
        >>> calcQuadraticArcLength((0, 0), (50, 0), (80, 0)) # collinear points
        80.0
        >>> calcQuadraticArcLength((0, 0), (0, 50), (0, 80)) # collinear points vertical
        80.0
        >>> calcQuadraticArcLength((0, 0), (50, 20), (100, 40)) # collinear points
        107.70329614269008
        >>> calcQuadraticArcLength((0, 0), (0, 100), (100, 0))
        154.02976155645263
        >>> calcQuadraticArcLength((0, 0), (0, 50), (100, 0))
        120.21581243984076
        >>> calcQuadraticArcLength((0, 0), (50, -10), (80, 50))
        102.53273816445825
        >>> calcQuadraticArcLength((0, 0), (40, 0), (-40, 0)) # collinear points, control point outside
        66.66666666666667
        >>> calcQuadraticArcLength((0, 0), (40, 0), (0, 0)) # collinear points, looping back
        40.0
    R2_Q3calcCubicArcLength(pt1, pt2, pt3, pt4, tolerance=0.005)
Calculates the arc length for a cubic Bezier segment.

    Whereas :func:`approximateCubicArcLength` approximates the length, this
    function calculates it by "measuring", recursively dividing the curve
    until the divided segments are shorter than ``tolerance``.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.
        tolerance: Controls the precision of the calcuation.

    Returns:
        Arc length value.
    calcQuadraticBounds(pt1, pt2, pt3)
Calculates the bounding rectangle for a quadratic Bezier segment.

    Args:
        pt1: Start point of the Bezier as a 2D tuple.
        pt2: Handle point of the Bezier as a 2D tuple.
        pt3: End point of the Bezier as a 2D tuple.

    Returns:
        A four-item tuple representing the bounding rectangle ``(xMin, yMin, xMax, yMax)``.

    Example::

        >>> calcQuadraticBounds((0, 0), (50, 100), (100, 0))
        (0, 0, 100, 50.0)
        >>> calcQuadraticBounds((0, 0), (100, 0), (100, 100))
        (0.0, 0.0, 100, 100)
    linePointAtTx2Split a quadratic Bezier curve at a given coordinate.

    Args:
        pt1,pt2,pt3: Control points of the Bezier as 2D tuples.
        where: Position at which to split the curve.
        isHorizontal: Direction of the ray splitting the curve. If true,
            ``where`` is interpreted as a Y coordinate; if false, then
            ``where`` is interpreted as an X coordinate.

    Returns:
        A list of two curve segments (each curve segment being three 2D tuples)
        if the curve was successfully split, or a list containing the original
        curve.

    Example::

        >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 150, False))
        ((0, 0), (50, 100), (100, 0))
        >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 50, False))
        ((0, 0), (25, 50), (50, 50))
        ((50, 50), (75, 50), (100, 0))
        >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 25, False))
        ((0, 0), (12.5, 25), (25, 37.5))
        ((25, 37.5), (62.5, 75), (100, 0))
        >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 25, True))
        ((0, 0), (7.32233, 14.6447), (14.6447, 25))
        ((14.6447, 25), (50, 75), (85.3553, 25))
        ((85.3553, 25), (92.6777, 14.6447), (100, -7.10543e-15))
        >>> # XXX I'm not at all sure if the following behavior is desirable:
        >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 50, True))
        ((0, 0), (25, 50), (50, 50))
        ((50, 50), (50, 50), (50, 50))
        ((50, 50), (75, 50), (100, 0))
    c11_rangesysCOMPILEDept2keyintersectionsrange2genexprix4unique_keya2splitQuadratic (line 507)seglineLineIntersections (line 1147)asinhcurve1tsplitQuadraticapproximateCubicArcLength (line 332)_segmentrepr.<locals>.genexprd1ys1printSegmentsline1pointAtTfailedd1xderiv3Couldn't work out which intersection function to useseg2whereapproximateCubicArcLengthCDDsegmentPointAtTsplitQuadratic.<locals>.genexpr_curve_bounds(c)foundSplit a line at a given coordinate.

    Args:
        pt1: Start point of line as 2D tuple.
        pt2: End point of line as 2D tuple.
        where: Position at which to split the line.
        isHorizontal: Direction of the ray splitting the line. If true,
            ``where`` is interpreted as a Y coordinate; if false, then
            ``where`` is interpreted as an X coordinate.

    Returns:
        A list of two line segments (each line segment being two 2D tuples)
        if the line was successfully split, or a list containing the original
        line.

    Example::

        >>> printSegments(splitLine((0, 0), (100, 100), 50, True))
        ((0, 0), (50, 50))
        ((50, 50), (100, 100))
        >>> printSegments(splitLine((0, 0), (100, 100), 100, True))
        ((0, 0), (100, 100))
        >>> printSegments(splitLine((0, 0), (100, 100), 0, True))
        ((0, 0), (0, 0))
        ((0, 0), (100, 100))
        >>> printSegments(splitLine((0, 0), (100, 100), 0, False))
        ((0, 0), (0, 0))
        ((0, 0), (100, 100))
        >>> printSegments(splitLine((100, 0), (0, 0), 50, False))
        ((100, 0), (50, 0))
        ((50, 0), (0, 0))
        >>> printSegments(splitLine((0, 100), (0, 0), 50, True))
        ((0, 100), (0, 50))
        ((0, 50), (0, 0))
    splitCubicIntoTwoAtTC(double complex pt1, double complex pt2, double complex pt3, double complex pt4, double t)
Split a cubic Bezier curve at t.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as complex numbers.
        t: Position at which to split the curve.

    Returns:
        A tuple of two curve segments (each curve segment being four complex numbers).
    ay2_curve_curve_intersections_t.<locals>.midpointfontTools.misc.arrayToolsby2intersection_ts_curve_line_intersections_tb_alignment_transformation(segment)Approximates the arc length for a cubic Bezier segment.

    Uses Gauss-Lobatto quadrature with n=5 points to approximate arc length.
    See :func:`calcCubicArcLength` for a slower but more accurate result.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.

    Returns:
        Arc length value.

    Example::

        >>> approximateCubicArcLength((0, 0), (25, 100), (75, 100), (100, 0))
        190.04332968932817
        >>> approximateCubicArcLength((0, 0), (50, 0), (100, 50), (100, 100))
        154.8852074945903
        >>> approximateCubicArcLength((0, 0), (50, 0), (100, 0), (150, 0)) # line; exact result should be 150.
        149.99999999999991
        >>> approximateCubicArcLength((0, 0), (50, 0), (100, 0), (-50, 0)) # cusp; exact result should be 150.
        136.9267662156362
        >>> approximateCubicArcLength((0, 0), (50, 0), (100, -50), (-50, 0)) # cusp
        154.80848416537057
    TypeErrorcy_splitCubicAtTsegmentSegmentIntersections (line 1417)calcQuadraticArcLength (line 151)Calculates the bounding rectangle for a quadratic Bezier segment.

    Args:
        pt1: Start point of the Bezier as a 2D tuple.
        pt2: Handle point of the Bezier as a 2D tuple.
        pt3: End point of the Bezier as a 2D tuple.

    Returns:
        A four-item tuple representing the bounding rectangle ``(xMin, yMin, xMax, yMax)``.

    Example::

        >>> calcQuadraticBounds((0, 0), (50, 100), (100, 0))
        (0, 0, 100, 50.0)
        >>> calcQuadraticBounds((0, 0), (100, 0), (100, 100))
        (0.0, 0.0, 100, 100)
    solveCubicsegmentSegmentIntersections(seg1, seg2)
Finds intersections between two segments.

    Args:
        seg1: List of coordinates of the first segment as 2D tuples.
        seg2: List of coordinates of the second segment as 2D tuples.

    Returns:
        A list of ``Intersection`` objects, each object having ``pt``, ``t1``
        and ``t2`` attributes containing the intersection point, time on first
        segment and time on second segment respectively.

    Examples::
        >>> curve1 = [ (10,100), (90,30), (40,140), (220,220) ]
        >>> curve2 = [ (5,150), (180,20), (80,250), (210,190) ]
        >>> intersections = segmentSegmentIntersections(curve1, curve2)
        >>> len(intersections)
        3
        >>> intersections[0].pt
        (81.7831487395506, 109.88904552375288)
        >>> curve3 = [ (100, 240), (30, 60), (210, 230), (160, 30) ]
        >>> line  = [ (25, 260), (230, 20) ]
        >>> intersections = segmentSegmentIntersections(curve3, line)
        >>> len(intersections)
        3
        >>> intersections[0].pt
        (84.9000930760723, 189.87306176459828)

    a1xapproximateQuadraticArcLengthCacoscalcQuadraticArcLengthcalcQuadraticParametersargscalcCubicArcLengthCe1xcurveLineIntersectionsfontTools.misc.bezierToolsc1disable_split_segment_at_texity1bxeyboxcalcCubicArcLengthC(double complex pt1, double complex pt2, double complex pt3, double complex pt4, double tolerance=0.005)
Calculates the arc length for a cubic Bezier segment.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as complex numbers.
        tolerance: Controls the precision of the calcuation.

    Returns:
        Arc length value.
    ?splitQuadraticAtT (line 589).approximateCubicArcLengthC(double complex pt1, double complex pt2, double complex pt3, double complex pt4)
Approximates the arc length for a cubic Bezier segment.

    Args:
        pt1,pt2,pt3,pt4: Control points of the Bezier as complex numbers.

    Returns:
        Arc length value.
    _line_t_of_pt(s, e, pt)asyncio.coroutines_curve_boundsc12splitQuadraticAtT(pt1, pt2, pt3, *ts)
Split a quadratic Bezier curve at one or more values of t.

    Args:
        pt1,pt2,pt3: Control points of the Bezier as 2D tuples.
        *ts: Positions at which to split the curve.

    Returns:
        A list of curve segments (each curve segment being three 2D tuples).

    Examples::

        >>> printSegments(splitQuadraticAtT((0, 0), (50, 100), (100, 0), 0.5))
        ((0, 0), (25, 50), (50, 50))
        ((50, 50), (75, 50), (100, 0))
        >>> printSegments(splitQuadraticAtT((0, 0), (50, 100), (100, 0), 0.5, 0.75))
        ((0, 0), (25, 50), (50, 50))
        ((50, 50), (62.5, 50), (75, 37.5))
        ((75, 37.5), (87.5, 25), (100, 0))
    ssolutions, iscloseoff2rectAreap1translateyRootsay3solveQuadraticorigDistthrowcubicPointAtTC(double complex pt1, double complex pt2, double complex pt3, double complex pt4, double t)
Finds the point at time `t` on a cubic curve.

    Args:
        pt1, pt2, pt3, pt4: Coordinates of the curve as complex numbers.
        t: The time along the curve.

    Returns:
        A complex number with the coordinates of the point.
    _splitCubicAtTC(double complex a, double complex b, double complex c, double complex d, *ts)precisionc11anglea1_3rotatepye2xcurveCurveIntersectionsc22syby(%s)printSegments(segments)
Helper for the doctests, displaying each segment in a list of
    segments on a single line as a tuple.
    calcCubicBounds (line 412)dquadraticPointAtTaysolveCubic (line 841)e2y�����|�=����MbP?{�G�zt?��#$�?F�V�W�?�?333333�?u�|Y���?�?8�5$t��?UUUUUU�?��b���?�q�q�?̔x�b��?�?�c��1��?�?�?@@@"@;@K@����#$F�V�W��̔x�b�߿�c��1�������	

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