# encoding: utf-8 # module fontTools.misc.bezierTools # from C:\Programs\Python\Python313\Lib\site-packages\fontTools\misc\bezierTools.cp313-win_amd64.pyd # by generator 1.147 """ fontTools.misc.bezierTools.py -- tools for working with Bezier path segments. """ # imports import builtins as __builtins__ # import math as math # from math import acos, cos, sqrt # Variables with simple values COMPILED = True EPSILON = 1e-09 epsilon = 1e-10 epsilonDigits = 6 pi = 3.141592653589793 # functions def approximateCubicArcLength(pt1, pt2, pt3, pt4): # real signature unknown; restored from __doc__ """ 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 """ pass def approximateCubicArcLengthC(double_complex_pt1, double_complex_pt2, double_complex_pt3, double_complex_pt4): # real signature unknown; restored from __doc__ """ 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. """ pass def approximateQuadraticArcLength(pt1, pt2, pt3): # real signature unknown; restored from __doc__ """ approximateQuadraticArcLength(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. """ pass def approximateQuadraticArcLengthC(double_complex_pt1, double_complex_pt2, double_complex_pt3): # real signature unknown; restored from __doc__ """ 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. """ pass def calcBounds(array): # reliably restored by inspect """ Calculate the bounding rectangle of a 2D points array. Args: array: A sequence of 2D tuples. Returns: A four-item tuple representing the bounding rectangle ``(xMin, yMin, xMax, yMax)``. """ pass def calcCubicArcLength(pt1, pt2, pt3, pt4, tolerance=0.005): # real signature unknown; restored from __doc__ """ calcCubicArcLength(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. """ pass def calcCubicArcLengthC(double_complex_pt1, double_complex_pt2, double_complex_pt3, double_complex_pt4, double_tolerance=0.005): # real signature unknown; restored from __doc__ """ calcCubicArcLengthC(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. """ pass def calcCubicBounds(pt1, pt2, pt3, pt4): # real signature unknown; restored from __doc__ """ 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 """ pass def calcCubicParameters(pt1, pt2, pt3, pt4): # real signature unknown; restored from __doc__ """ calcCubicParameters(pt1, pt2, pt3, pt4) """ pass def calcCubicPoints(a, b, c, d): # real signature unknown; restored from __doc__ """ calcCubicPoints(a, b, c, d) """ pass def calcQuadraticArcLength(pt1, pt2, pt3): # real signature unknown; restored from __doc__ """ calcQuadraticArcLength(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 """ pass def calcQuadraticArcLengthC(double_complex_pt1, double_complex_pt2, double_complex_pt3): # real signature unknown; restored from __doc__ """ calcQuadraticArcLengthC(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. """ pass def calcQuadraticBounds(pt1, pt2, pt3): # real signature unknown; restored from __doc__ """ 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) """ pass def calcQuadraticParameters(pt1, pt2, pt3): # real signature unknown; restored from __doc__ """ calcQuadraticParameters(pt1, pt2, pt3) """ pass def calcQuadraticPoints(a, b, c): # real signature unknown; restored from __doc__ """ calcQuadraticPoints(a, b, c) """ pass def cubicPointAtT(pt1, pt2, pt3, pt4, t): # real signature unknown; restored from __doc__ """ cubicPointAtT(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. """ pass def cubicPointAtTC(double_complex_pt1, double_complex_pt2, double_complex_pt3, double_complex_pt4, double_t): # real signature unknown; restored from __doc__ """ cubicPointAtTC(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. """ pass def curveCurveIntersections(curve1, curve2): # real signature unknown; restored from __doc__ """ curveCurveIntersections(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) """ pass def curveLineIntersections(curve, line): # real signature unknown; restored from __doc__ """ curveLineIntersections(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) """ pass def lineLineIntersections(s1, e1, s2, e2): # real signature unknown; restored from __doc__ """ lineLineIntersections(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) """ pass def linePointAtT(pt1, pt2, t): # real signature unknown; restored from __doc__ """ linePointAtT(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. """ pass def namedtuple(typename, field_names, *, rename=False, defaults=None, module=None): # reliably restored by inspect """ Returns a new subclass of tuple with named fields. >>> Point = namedtuple('Point', ['x', 'y']) >>> Point.__doc__ # docstring for the new class 'Point(x, y)' >>> p = Point(11, y=22) # instantiate with positional args or keywords >>> p[0] + p[1] # indexable like a plain tuple 33 >>> x, y = p # unpack like a regular tuple >>> x, y (11, 22) >>> p.x + p.y # fields also accessible by name 33 >>> d = p._asdict() # convert to a dictionary >>> d['x'] 11 >>> Point(**d) # convert from a dictionary Point(x=11, y=22) >>> p._replace(x=100) # _replace() is like str.replace() but targets named fields Point(x=100, y=22) """ pass def printSegments(segments): # real signature unknown; restored from __doc__ """ printSegments(segments) Helper for the doctests, displaying each segment in a list of segments on a single line as a tuple. """ pass def quadraticPointAtT(pt1, pt2, pt3, t): # real signature unknown; restored from __doc__ """ quadraticPointAtT(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. """ pass def rectArea(rect): # reliably restored by inspect """ Determine rectangle area. Args: rect: Bounding rectangle, expressed as tuples ``(xMin, yMin, xMax, yMax)``. Returns: The area of the rectangle. """ pass def sectRect(rect1, rect2): # reliably restored by inspect """ Test for rectangle-rectangle intersection. Args: rect1: First bounding rectangle, expressed as tuples ``(xMin, yMin, xMax, yMax)``. rect2: Second bounding rectangle. Returns: A boolean and a rectangle. If the input rectangles intersect, returns ``True`` and the intersecting rectangle. Returns ``False`` and ``(0, 0, 0, 0)`` if the input rectangles don't intersect. """ pass def segmentPointAtT(seg, t): # real signature unknown; restored from __doc__ """ segmentPointAtT(seg, t) """ pass def segmentSegmentIntersections(seg1, seg2): # real signature unknown; restored from __doc__ """ segmentSegmentIntersections(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) """ pass def solveCubic(a, b, c, d): # real signature unknown; restored from __doc__ """ 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 """ pass def solveQuadratic(a, b, c, sqrt=None): # real signature unknown; restored from __doc__ """ solveQuadratic(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! """ pass def splitCubic(pt1, pt2, pt3, pt4, where, isHorizontal): # real signature unknown; restored from __doc__ """ 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)) """ pass def splitCubicAtT(pt1, pt2, pt3, pt4, *ts): # real signature unknown; restored from __doc__ """ splitCubicAtT(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)) """ pass def splitCubicAtTC(double_complex_pt1, double_complex_pt2, double_complex_pt3, double_complex_pt4, *ts): # real signature unknown; restored from __doc__ """ splitCubicAtTC(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). """ pass def splitCubicIntoTwoAtTC(double_complex_pt1, double_complex_pt2, double_complex_pt3, double_complex_pt4, double_t): # real signature unknown; restored from __doc__ """ 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). """ pass def splitLine(pt1, pt2, where, isHorizontal): # real signature unknown; restored from __doc__ """ 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)) """ pass def splitQuadratic(pt1, pt2, pt3, where, isHorizontal): # real signature unknown; restored from __doc__ """ splitQuadratic(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)) """ pass def splitQuadraticAtT(pt1, pt2, pt3, *ts): # real signature unknown; restored from __doc__ """ splitQuadraticAtT(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)) """ pass def _alignment_transformation(segment): # real signature unknown; restored from __doc__ """ _alignment_transformation(segment) """ pass def _both_points_are_on_same_side_of_origin(a, b, origin): # real signature unknown; restored from __doc__ """ _both_points_are_on_same_side_of_origin(a, b, origin) """ pass def _calcCubicArcLengthCRecurse(double_mult, double_complex_p0, double_complex_p1, double_complex_p2, double_complex_p3): # real signature unknown; restored from __doc__ """ _calcCubicArcLengthCRecurse(double mult, double complex p0, double complex p1, double complex p2, double complex p3) """ pass def _curve_bounds(c): # real signature unknown; restored from __doc__ """ _curve_bounds(c) """ pass def _curve_curve_intersections_t(curve1, curve2, precision=1, *args, **kwargs): # real signature unknown; NOTE: unreliably restored from __doc__ """ _curve_curve_intersections_t(curve1, curve2, precision=1e-3, range1=None, range2=None) """ pass def _curve_line_intersections_t(curve, line): # real signature unknown; restored from __doc__ """ _curve_line_intersections_t(curve, line) """ pass def _is_linelike(segment): # real signature unknown; restored from __doc__ """ _is_linelike(segment) """ pass def _line_t_of_pt(s, e, pt): # real signature unknown; restored from __doc__ """ _line_t_of_pt(s, e, pt) """ pass def _segmentrepr(obj): # real signature unknown; restored from __doc__ """ _segmentrepr(obj) >>> _segmentrepr([1, [2, 3], [], [[2, [3, 4], [0.1, 2.2]]]]) '(1, (2, 3), (), ((2, (3, 4), (0.1, 2.2))))' """ pass def _splitCubicAtT(a, b, c, d, *ts): # real signature unknown; restored from __doc__ """ _splitCubicAtT(a, b, c, d, *ts) """ pass def _splitCubicAtTC(double_complex_a, double_complex_b, double_complex_c, double_complex_d, *ts): # real signature unknown; restored from __doc__ """ _splitCubicAtTC(double complex a, double complex b, double complex c, double complex d, *ts) """ pass def _splitQuadraticAtT(a, b, c, *ts): # real signature unknown; restored from __doc__ """ _splitQuadraticAtT(a, b, c, *ts) """ pass def _split_cubic_into_two(p0, p1, p2, p3): # real signature unknown; restored from __doc__ """ _split_cubic_into_two(p0, p1, p2, p3) """ pass def _split_segment_at_t(c, t): # real signature unknown; restored from __doc__ """ _split_segment_at_t(c, t) """ pass # classes class Intersection(tuple): """ Intersection(pt, t1, t2) """ def _asdict(self): # reliably restored by inspect """ Return a new dict which maps field names to their values. """ pass @classmethod def _make(cls, *args, **kwargs): # real signature unknown """ Make a new Intersection object from a sequence or iterable """ pass def _replace(self, **kwds): # reliably restored by inspect """ Return a new Intersection object replacing specified fields with new values """ pass def __getnewargs__(self): # reliably restored by inspect """ Return self as a plain tuple. Used by copy and pickle. """ pass def __init__(self, pt, t1, t2): # real signature unknown; restored from __doc__ pass @staticmethod # known case of __new__ def __new__(_cls, pt, t1, t2): # reliably restored by inspect """ Create new instance of Intersection(pt, t1, t2) """ pass def __replace__(self, **kwds): # reliably restored by inspect """ Return a new Intersection object replacing specified fields with new values """ pass def __repr__(self): # reliably restored by inspect """ Return a nicely formatted representation string """ pass pt = _tuplegetter(0, 'Alias for field number 0') t1 = _tuplegetter(1, 'Alias for field number 1') t2 = _tuplegetter(2, 'Alias for field number 2') _fields = ( 'pt', 't1', 't2', ) _field_defaults = {} __match_args__ = ( 'pt', 't1', 't2', ) __slots__ = () # variables with complex values Identity = ( 1, 0, 0, 1, 0, 0, ) __all__ = [ 'approximateCubicArcLength', 'approximateCubicArcLengthC', 'approximateQuadraticArcLength', 'approximateQuadraticArcLengthC', 'calcCubicArcLength', 'calcCubicArcLengthC', 'calcQuadraticArcLength', 'calcQuadraticArcLengthC', 'calcCubicBounds', 'calcQuadraticBounds', 'splitLine', 'splitQuadratic', 'splitCubic', 'splitQuadraticAtT', 'splitCubicAtT', 'splitCubicAtTC', 'splitCubicIntoTwoAtTC', 'solveQuadratic', 'solveCubic', 'quadraticPointAtT', 'cubicPointAtT', 'cubicPointAtTC', 'linePointAtT', 'segmentPointAtT', 'lineLineIntersections', 'curveLineIntersections', 'curveCurveIntersections', 'segmentSegmentIntersections', ] __loader__ = None # (!) real value is '<_frozen_importlib_external.ExtensionFileLoader object at 0x00000217D22A9AE0>' __spec__ = None # (!) real value is "ModuleSpec(name='fontTools.misc.bezierTools', loader=<_frozen_importlib_external.ExtensionFileLoader object at 0x00000217D22A9AE0>, origin='C:\\\\Programs\\\\Python\\\\Python313\\\\Lib\\\\site-packages\\\\fontTools\\\\misc\\\\bezierTools.cp313-win_amd64.pyd')" __test__ = { '_segmentrepr (line 1472)': "\n >>> _segmentrepr([1, [2, 3], [], [[2, [3, 4], [0.1, 2.2]]]])\n '(1, (2, 3), (), ((2, (3, 4), (0.1, 2.2))))'\n ", 'approximateCubicArcLength (line 332)': 'Approximates the arc length for a cubic Bezier segment.\n\n Uses Gauss-Lobatto quadrature with n=5 points to approximate arc length.\n See :func:`calcCubicArcLength` for a slower but more accurate result.\n\n Args:\n pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.\n\n Returns:\n Arc length value.\n\n Example::\n\n >>> approximateCubicArcLength((0, 0), (25, 100), (75, 100), (100, 0))\n 190.04332968932817\n >>> approximateCubicArcLength((0, 0), (50, 0), (100, 50), (100, 100))\n 154.8852074945903\n >>> approximateCubicArcLength((0, 0), (50, 0), (100, 0), (150, 0)) # line; exact result should be 150.\n 149.99999999999991\n >>> approximateCubicArcLength((0, 0), (50, 0), (100, 0), (-50, 0)) # cusp; exact result should be 150.\n 136.9267662156362\n >>> approximateCubicArcLength((0, 0), (50, 0), (100, -50), (-50, 0)) # cusp\n 154.80848416537057\n ', 'calcCubicBounds (line 412)': 'Calculates the bounding rectangle for a quadratic Bezier segment.\n\n Args:\n pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.\n\n Returns:\n A four-item tuple representing the bounding rectangle ``(xMin, yMin, xMax, yMax)``.\n\n Example::\n\n >>> calcCubicBounds((0, 0), (25, 100), (75, 100), (100, 0))\n (0, 0, 100, 75.0)\n >>> calcCubicBounds((0, 0), (50, 0), (100, 50), (100, 100))\n (0.0, 0.0, 100, 100)\n >>> print("%f %f %f %f" % calcCubicBounds((50, 0), (0, 100), (100, 100), (50, 0)))\n 35.566243 0.000000 64.433757 75.000000\n ', 'calcQuadraticArcLength (line 151)': 'Calculates the arc length for a quadratic Bezier segment.\n\n Args:\n pt1: Start point of the Bezier as 2D tuple.\n pt2: Handle point of the Bezier as 2D tuple.\n pt3: End point of the Bezier as 2D tuple.\n\n Returns:\n Arc length value.\n\n Example::\n\n >>> calcQuadraticArcLength((0, 0), (0, 0), (0, 0)) # empty segment\n 0.0\n >>> calcQuadraticArcLength((0, 0), (50, 0), (80, 0)) # collinear points\n 80.0\n >>> calcQuadraticArcLength((0, 0), (0, 50), (0, 80)) # collinear points vertical\n 80.0\n >>> calcQuadraticArcLength((0, 0), (50, 20), (100, 40)) # collinear points\n 107.70329614269008\n >>> calcQuadraticArcLength((0, 0), (0, 100), (100, 0))\n 154.02976155645263\n >>> calcQuadraticArcLength((0, 0), (0, 50), (100, 0))\n 120.21581243984076\n >>> calcQuadraticArcLength((0, 0), (50, -10), (80, 50))\n 102.53273816445825\n >>> calcQuadraticArcLength((0, 0), (40, 0), (-40, 0)) # collinear points, control point outside\n 66.66666666666667\n >>> calcQuadraticArcLength((0, 0), (40, 0), (0, 0)) # collinear points, looping back\n 40.0\n ', 'calcQuadraticBounds (line 298)': 'Calculates the bounding rectangle for a quadratic Bezier segment.\n\n Args:\n pt1: Start point of the Bezier as a 2D tuple.\n pt2: Handle point of the Bezier as a 2D tuple.\n pt3: End point of the Bezier as a 2D tuple.\n\n Returns:\n A four-item tuple representing the bounding rectangle ``(xMin, yMin, xMax, yMax)``.\n\n Example::\n\n >>> calcQuadraticBounds((0, 0), (50, 100), (100, 0))\n (0, 0, 100, 50.0)\n >>> calcQuadraticBounds((0, 0), (100, 0), (100, 100))\n (0.0, 0.0, 100, 100)\n ', 'curveCurveIntersections (line 1385)': 'Finds intersections between a curve and a curve.\n\n Args:\n curve1: List of coordinates of the first curve segment as 2D tuples.\n curve2: List of coordinates of the second curve segment as 2D tuples.\n\n Returns:\n A list of ``Intersection`` objects, each object having ``pt``, ``t1``\n and ``t2`` attributes containing the intersection point, time on first\n segment and time on second segment respectively.\n\n Examples::\n >>> curve1 = [ (10,100), (90,30), (40,140), (220,220) ]\n >>> curve2 = [ (5,150), (180,20), (80,250), (210,190) ]\n >>> intersections = curveCurveIntersections(curve1, curve2)\n >>> len(intersections)\n 3\n >>> intersections[0].pt\n (81.7831487395506, 109.88904552375288)\n ', 'curveLineIntersections (line 1255)': 'Finds intersections between a curve and a line.\n\n Args:\n curve: List of coordinates of the curve segment as 2D tuples.\n line: List of coordinates of the line segment as 2D tuples.\n\n Returns:\n A list of ``Intersection`` objects, each object having ``pt``, ``t1``\n and ``t2`` attributes containing the intersection point, time on first\n segment and time on second segment respectively.\n\n Examples::\n >>> curve = [ (100, 240), (30, 60), (210, 230), (160, 30) ]\n >>> line = [ (25, 260), (230, 20) ]\n >>> intersections = curveLineIntersections(curve, line)\n >>> len(intersections)\n 3\n >>> intersections[0].pt\n (84.9000930760723, 189.87306176459828)\n ', 'lineLineIntersections (line 1154)': 'Finds intersections between two line segments.\n\n Args:\n s1, e1: Coordinates of the first line as 2D tuples.\n s2, e2: Coordinates of the second line as 2D tuples.\n\n Returns:\n A list of ``Intersection`` objects, each object having ``pt``, ``t1``\n and ``t2`` attributes containing the intersection point, time on first\n segment and time on second segment respectively.\n\n Examples::\n\n >>> a = lineLineIntersections( (310,389), (453, 222), (289, 251), (447, 367))\n >>> len(a)\n 1\n >>> intersection = a[0]\n >>> intersection.pt\n (374.44882952482897, 313.73458370177315)\n >>> (intersection.t1, intersection.t2)\n (0.45069111555824465, 0.5408153767394238)\n ', 'segmentSegmentIntersections (line 1424)': 'Finds intersections between two segments.\n\n Args:\n seg1: List of coordinates of the first segment as 2D tuples.\n seg2: List of coordinates of the second segment as 2D tuples.\n\n Returns:\n A list of ``Intersection`` objects, each object having ``pt``, ``t1``\n and ``t2`` attributes containing the intersection point, time on first\n segment and time on second segment respectively.\n\n Examples::\n >>> curve1 = [ (10,100), (90,30), (40,140), (220,220) ]\n >>> curve2 = [ (5,150), (180,20), (80,250), (210,190) ]\n >>> intersections = segmentSegmentIntersections(curve1, curve2)\n >>> len(intersections)\n 3\n >>> intersections[0].pt\n (81.7831487395506, 109.88904552375288)\n >>> curve3 = [ (100, 240), (30, 60), (210, 230), (160, 30) ]\n >>> line = [ (25, 260), (230, 20) ]\n >>> intersections = segmentSegmentIntersections(curve3, line)\n >>> len(intersections)\n 3\n >>> intersections[0].pt\n (84.9000930760723, 189.87306176459828)\n\n ', 'solveCubic (line 848)': 'Solve a cubic equation.\n\n Solves *a*x*x*x + b*x*x + c*x + d = 0* where a, b, c and d are real.\n\n Args:\n a: coefficient of *x³*\n b: coefficient of *x²*\n c: coefficient of *x*\n d: constant term\n\n Returns:\n A list of roots. Note that the returned list is neither guaranteed to\n be sorted nor to contain unique values!\n\n Examples::\n\n >>> solveCubic(1, 1, -6, 0)\n [-3.0, -0.0, 2.0]\n >>> solveCubic(-10.0, -9.0, 48.0, -29.0)\n [-2.9, 1.0, 1.0]\n >>> solveCubic(-9.875, -9.0, 47.625, -28.75)\n [-2.911392, 1.0, 1.0]\n >>> solveCubic(1.0, -4.5, 6.75, -3.375)\n [1.5, 1.5, 1.5]\n >>> solveCubic(-12.0, 18.0, -9.0, 1.50023651123)\n [0.5, 0.5, 0.5]\n >>> solveCubic(\n ... 9.0, 0.0, 0.0, -7.62939453125e-05\n ... ) == [-0.0, -0.0, -0.0]\n True\n ', 'splitCubic (line 552)': 'Split a cubic Bezier curve at a given coordinate.\n\n Args:\n pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.\n where: Position at which to split the curve.\n isHorizontal: Direction of the ray splitting the curve. If true,\n ``where`` is interpreted as a Y coordinate; if false, then\n ``where`` is interpreted as an X coordinate.\n\n Returns:\n A list of two curve segments (each curve segment being four 2D tuples)\n if the curve was successfully split, or a list containing the original\n curve.\n\n Example::\n\n >>> printSegments(splitCubic((0, 0), (25, 100), (75, 100), (100, 0), 150, False))\n ((0, 0), (25, 100), (75, 100), (100, 0))\n >>> printSegments(splitCubic((0, 0), (25, 100), (75, 100), (100, 0), 50, False))\n ((0, 0), (12.5, 50), (31.25, 75), (50, 75))\n ((50, 75), (68.75, 75), (87.5, 50), (100, 0))\n >>> printSegments(splitCubic((0, 0), (25, 100), (75, 100), (100, 0), 25, True))\n ((0, 0), (2.29379, 9.17517), (4.79804, 17.5085), (7.47414, 25))\n ((7.47414, 25), (31.2886, 91.6667), (68.7114, 91.6667), (92.5259, 25))\n ((92.5259, 25), (95.202, 17.5085), (97.7062, 9.17517), (100, 1.77636e-15))\n ', 'splitCubicAtT (line 613)': 'Split a cubic Bezier curve at one or more values of t.\n\n Args:\n pt1,pt2,pt3,pt4: Control points of the Bezier as 2D tuples.\n *ts: Positions at which to split the curve.\n\n Returns:\n A list of curve segments (each curve segment being four 2D tuples).\n\n Examples::\n\n >>> printSegments(splitCubicAtT((0, 0), (25, 100), (75, 100), (100, 0), 0.5))\n ((0, 0), (12.5, 50), (31.25, 75), (50, 75))\n ((50, 75), (68.75, 75), (87.5, 50), (100, 0))\n >>> printSegments(splitCubicAtT((0, 0), (25, 100), (75, 100), (100, 0), 0.5, 0.75))\n ((0, 0), (12.5, 50), (31.25, 75), (50, 75))\n ((50, 75), (59.375, 75), (68.75, 68.75), (77.3438, 56.25))\n ((77.3438, 56.25), (85.9375, 43.75), (93.75, 25), (100, 0))\n ', 'splitLine (line 450)': 'Split a line at a given coordinate.\n\n Args:\n pt1: Start point of line as 2D tuple.\n pt2: End point of line as 2D tuple.\n where: Position at which to split the line.\n isHorizontal: Direction of the ray splitting the line. If true,\n ``where`` is interpreted as a Y coordinate; if false, then\n ``where`` is interpreted as an X coordinate.\n\n Returns:\n A list of two line segments (each line segment being two 2D tuples)\n if the line was successfully split, or a list containing the original\n line.\n\n Example::\n\n >>> printSegments(splitLine((0, 0), (100, 100), 50, True))\n ((0, 0), (50, 50))\n ((50, 50), (100, 100))\n >>> printSegments(splitLine((0, 0), (100, 100), 100, True))\n ((0, 0), (100, 100))\n >>> printSegments(splitLine((0, 0), (100, 100), 0, True))\n ((0, 0), (0, 0))\n ((0, 0), (100, 100))\n >>> printSegments(splitLine((0, 0), (100, 100), 0, False))\n ((0, 0), (0, 0))\n ((0, 0), (100, 100))\n >>> printSegments(splitLine((100, 0), (0, 0), 50, False))\n ((100, 0), (50, 0))\n ((50, 0), (0, 0))\n >>> printSegments(splitLine((0, 100), (0, 0), 50, True))\n ((0, 100), (0, 50))\n ((0, 50), (0, 0))\n ', 'splitQuadratic (line 507)': "Split a quadratic Bezier curve at a given coordinate.\n\n Args:\n pt1,pt2,pt3: Control points of the Bezier as 2D tuples.\n where: Position at which to split the curve.\n isHorizontal: Direction of the ray splitting the curve. If true,\n ``where`` is interpreted as a Y coordinate; if false, then\n ``where`` is interpreted as an X coordinate.\n\n Returns:\n A list of two curve segments (each curve segment being three 2D tuples)\n if the curve was successfully split, or a list containing the original\n curve.\n\n Example::\n\n >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 150, False))\n ((0, 0), (50, 100), (100, 0))\n >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 50, False))\n ((0, 0), (25, 50), (50, 50))\n ((50, 50), (75, 50), (100, 0))\n >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 25, False))\n ((0, 0), (12.5, 25), (25, 37.5))\n ((25, 37.5), (62.5, 75), (100, 0))\n >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 25, True))\n ((0, 0), (7.32233, 14.6447), (14.6447, 25))\n ((14.6447, 25), (50, 75), (85.3553, 25))\n ((85.3553, 25), (92.6777, 14.6447), (100, -7.10543e-15))\n >>> # XXX I'm not at all sure if the following behavior is desirable:\n >>> printSegments(splitQuadratic((0, 0), (50, 100), (100, 0), 50, True))\n ((0, 0), (25, 50), (50, 50))\n ((50, 50), (50, 50), (50, 50))\n ((50, 50), (75, 50), (100, 0))\n ", 'splitQuadraticAtT (line 589)': 'Split a quadratic Bezier curve at one or more values of t.\n\n Args:\n pt1,pt2,pt3: Control points of the Bezier as 2D tuples.\n *ts: Positions at which to split the curve.\n\n Returns:\n A list of curve segments (each curve segment being three 2D tuples).\n\n Examples::\n\n >>> printSegments(splitQuadraticAtT((0, 0), (50, 100), (100, 0), 0.5))\n ((0, 0), (25, 50), (50, 50))\n ((50, 50), (75, 50), (100, 0))\n >>> printSegments(splitQuadraticAtT((0, 0), (50, 100), (100, 0), 0.5, 0.75))\n ((0, 0), (25, 50), (50, 50))\n ((50, 50), (62.5, 50), (75, 37.5))\n ((75, 37.5), (87.5, 25), (100, 0))\n ', }