o i@srdZddlmZmZmZddlmZddlZddlm Z zddl Z Wne e fy3ddl m Z Ynwe jZdZe dgd Zgd Zdd d ZddZe e je je je je je jde je je je jdddZe e je je je je je jde je je jddddZdZdZe je je e je je je jdddZe je je e je je jdddZ d d!Z!e e je je je je je je je je jd"e je je je je je je je jd#d$d%Z"d&d'Z#e e je je je je jd(e je je je jd)d*d+Z$d,d-Z%d.d/Z&e e je je je je je jde je je je je je jd0d1d2Z'd3d4Z(d5d6Z)d7d8Z*d9d:Z+d;d<Z,d=d>Z-e je je je je je je je je jd?d@dAZ.e e je je je je je je je je je jdBe je je je je jdCdDdEZ/dFdGZ0dHdIZ1e je je je je je je je je je je je je je jdJ dKdLZ2ddMlm3Z3m4Z4m5Z5m6Z6e3fdNdOZ7dPdQZ8dRdSZ9dTdUZ:e je je je je je je je je je jdVdWdXZ;dYdZZd`daZ?dbdcZ@dddeZAe e je je je je je je jdfe je je je jdgdhdiZBdjdkZCdldmZDdndoZEdpdqZFdrdsZGdtduZHdvdwZIdxdyZJdzd{ZK dd}d~ZLddZMddZNddZOddZPddZQeRdkrddlSZSddlTZTeSUeTVjWdSdS)zNfontTools.misc.bezierTools.py -- tools for working with Bezier path segments. ) calcBoundssectRectrectArea)IdentityN) namedtuple)cythong& .> Intersectionptt1t2)approximateCubicArcLengthapproximateCubicArcLengthCapproximateQuadraticArcLengthapproximateQuadraticArcLengthCcalcCubicArcLengthcalcCubicArcLengthCcalcQuadraticArcLengthcalcQuadraticArcLengthCcalcCubicBoundscalcQuadraticBounds splitLinesplitQuadratic splitCubicsplitQuadraticAtT splitCubicAtTsplitCubicAtTCsplitCubicIntoTwoAtTCsolveQuadratic solveCubicquadraticPointAtT cubicPointAtTcubicPointAtTC linePointAtTsegmentPointAtTlineLineIntersectionscurveLineIntersectionscurveCurveIntersectionssegmentSegmentIntersections{Gzt?cCs tt|t|t|t||S)aCalculates 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. )rcomplex)pt1pt2pt3pt4 tolerancer0i/var/www/html/eduruby.in/lip-sync/lip-sync-env/lib/python3.10/site-packages/fontTools/misc/bezierTools.pyr8srcCs\|d|||d}||||d}|||d|||f|||||d|ffS)Ng??r0)p0p1p2p3midZderiv3r0r0r1_split_cubic_into_twoKs r9)r4r5r6r7)multarchboxc Cs~t||}t||t||t||}||t|kr&||dSt||||\}}t|g|Rt|g|RSNr3)absEPSILONr9_calcCubicArcLengthCRecurse) r:r4r5r6r7r;r<onetwor0r0r1r@Ts $  r@r+r,r-r.)r/r:cCsdd|}t|||||S)zCalculates 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. ?g?)r@)r+r,r-r.r/r:r0r0r1rhs rg|=v1v2cCs||jSN) conjugaterealrFr0r0r1_dotsrLxcCs(|t|dddt|dS)N)mathsqrtasinhrMr0r0r1 _intSecAtans(rTcCtt|t|t|S)aCalculates 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 )rr*r+r,r-r0r0r1rs r)r+r,r-d0d1dn)scaleorigDistabx0x1LencCs||}||}||}|d}t|}|dkrt||St||}t|tkrKt||dkr6t||St|t|} } | | | | | | St|||} t|||} tdt| t| ||| | } | S)a$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. y?rrO)r>rLepsilonrT)r+r,r-rWrXrYrZr[r\r]r^r_r`rar0r0r1rs"     (rcCrU)aCalculates 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. )rr*rVr0r0r1rsrrV)v0rGrHcCsTtd|d|d|}t||d}td|d|d|}|||S)aCalculates 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. g̔xb߿gb?gFVW?gqq?gFVWg̔xb?r>)r+r,r-rdrGrHr0r0r1rs! rcst|||\\\\d}d}g}|dkr%| ||dkr1| |fdd|D||g}t|S)aCalculates 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) @rcsTg|]&}d|krdkrnn||||||fqSrrPr0.0taxaybxbycxcyr0r1 Ds .z'calcQuadraticBounds..)calcQuadraticParametersappendr)r+r,r-Zax2Zay2rootspointsr0rkr1r*srcCstt|t|t|t|S)aApproximates 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 )rr*rCr0r0r1r Lsr )rdrGrHv3v4c Cst||d}td|d|d|d|}t||||d}td|d|d|d|}t||d}|||||S) zApproximates 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. g333333?gc1g85$t?gu|Y?g#$?g?g#$gc1?re) r+r,r-r.rdrGrHrwrxr0r0r1rjs,rc st||||\\\\\d}d}d}d}ddt||D}ddt||D} || } fdd| D||g} t| S)aXCalculates 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 @rfcS(g|]}d|krdkrnn|qSrgr0rhr0r0r1rr(z#calcCubicBounds..cSrzrgr0rhr0r0r1rrr{cs\g|]*}||||||||||||fqSr0r0rhrlrmrnrorprqdxdyr0r1rrs &&)calcCubicParametersrr) r+r,r-r.Zax3Zay3Zbx2Zby2ZxRootsZyRootsrurvr0r|r1rs&rcCs|\}}|\}}||}||} |} |} || f|} | dkr#||fgS|| | f|| } d| kr7dkrMnn|| | | | | f}||f||fgS||fgS)a 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)) rrPr0)r+r,where isHorizontalZpt1xZpt1yZpt2xZpt2yrlrmrnror]rjZmidPtr0r0r1rs$   rc Csdt|||\}}}t|||||||}tdd|D}|s(|||fgSt|||g|RS)aSplit 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)) cs,|]}d|krdkrnn|VqdSrrPNr0rhr0r0r1 "*z!splitQuadratic..)rsrsorted_splitQuadraticAtT) r+r,r-rrr]r^c solutionsr0r0r1rs# rc Csrt||||\}}}} t||||||| ||} tdd| D} | s.||||fgSt|||| g| RS)aSplit 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)) csrrr0rhr0r0r1rGrzsplitCubic..)rrr_splitCubicAtT) r+r,r-r.rrr]r^rrYrr0r0r1r(srcGs&t|||\}}}t|||g|RS)aSplit 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)) )rsr)r+r,r-tsr]r^rr0r0r1rMsrc Gsjt||||\}}}}t||||g|R} |g| dddR| d<g| ddd|R| d<| S)aSplit 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)) rrPN)rr) r+r,r-r.rr]r^rrYsplitr0r0r1res r)r+r,r-r.r]r^rrYc gs8t||||\}}}}t||||g|REdHdS)aSplit 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). N)calcCubicParametersC_splitCubicAtTC) r+r,r-r.rr]r^rrYr0r0r1rs r)rjr+r,r-r.pointAtToff1off2)r _1_t_1_t_2_2_t_1_tc Cs||}d|}||}d||}|||d|||||||||} ||||||} ||||||} ||||}||||}||| | f| | ||ffS)aSplit 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). rPrOr2r0) r+r,r-r.rjr rrrrrrr0r0r1rs 2rcGst|}g}|dd|d|\}}|\}}|\} } tt|dD]_} || } || d} | | }||}||}||}d|| ||}d|| ||}| | }|||| | }|||| | }t||f||f||f\}}}||||fq%|S)NrrbrDrPrO)listinsertrtrangelencalcQuadraticPoints)r]r^rrsegmentsrlrmrnrorprqir r deltadelta_2a1xa1yb1xb1yt1_2c1xc1yr+r,r-r0r0r1rs,   rc"Gst|}|dd|dg}|\}}|\}} |\} } |\} } tt|dD]}||}||d}||}||}||}||}||}||}||}d||||}d||| |}d||| d|||}d| || d|||}||||| || }||| || || }t||f||f||f||f\}}} }!|||| |!fq)|SNrrbrDrPr2rO)rrrtrrcalcCubicPoints)"r]r^rrYrrrlrmrnrorprqr}r~rr r rrdelta_3rt1_3rrrrrrZd1xZd1yr+r,r-r.r0r0r1rs:      r) r]r^rrYr r rrra1b1c1rXcgst|}|dd|dtt|dD]^}||}||d}||}||} || } ||} || } || } d|||| }d|||d|| |}|| || |||}t| |||\}}}}||||fVqdSr)rrrtrrcalcCubicPointsC)r]r^rrYrrr r rrrrrrrrrXr+r,r-r.r0r0r1rs&    r)rRacoscospicCst|tkrt|tkrg}|S| |g}|S||d||}|dkr>||}| |d|| |d|g}|Sg}|S)uKSolve 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! @rbrfr>rc)r]r^rrRruZDDZrDDr0r0r1r/s    $rcCst|tkr t|||St|}||}||}||}||d|d}d|||d||d|d}||} |||} | tkrJdn| } t| tkrTdn| } | | } | dkro| dkrot| dt} | | | gS| tdkrttt|t | d d } d t |}|d}|t | d|}|t | dt d|}|t | d t d|}t |||g\}}}||tkr||tkrt|||dt}}}n>||tkrt||dt}}t|t}n'||tkr t|t}t||dt}}nt|t}t|t}t|t}|||gSt t | t|d } | || } |dkr6| } t| |dt} | gS)utSolve 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 ryg"@rfg;@gK@rrbr3rDggrUUUUUU?)r>rcrfloatround epsilonDigitsrmaxminrRrrrpow)r]r^rrYrZa2a3QRZR2ZQ3ZR2_Q3rNthetaZrQ2Za1_3r_r`x2r0r0r1rPsT & (             rc Cs^|\}}|\}}|\}}||d} ||d} ||| } ||| } | | f| | f||ffS)Nrfr0) r+r,r-ry2x3y3rprqrnrorlrmr0r0r1rss    rscCs|\}}|\}}|\}} |\} } || d} || d} ||d| }||d| }|| | |}| | | |}||f||f| | f| | ffSNryr0)r+r,r-r.rrrrx4y4r}r~rprqrnrorlrmr0r0r1rs  r)r+r,r-r.r]r^rcCs8||d}||d|}||||}||||fSrr0)r+r,r-r.rr^r]r0r0r1r  rcCsf|\}}|\}}|\}}|} |} |d|} |d|} |||} |||}| | f| | f| |ffSr=r0)r]r^rrlrmrnrorprqr`y1rrrrr0r0r1rs    rcCs|\}}|\}}|\}} |\} } | } | } |d| }| d| }||d|}|| d|}|| ||}|| | |}| | f||f||f||ffSrr0)r]r^rrYrlrmrnrorprqr}r~r`rrrrrrrr0r0r1rs  rr]r^rrYr6r7Zp4cCs8|d|}||d|}||||}||||fS)Nrr0rr0r0r1rrrcCs8|dd||d||dd||d|fS)zFinds 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. rrPr0)r+r,rjr0r0r1r#s8 r#cCsd|d||ddd|||d|||d}d|d||ddd|||d|||d}||fS)zFinds 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. rPrrOr0)r+r,r-rjrNyr0r0r1r s@ @r c Cs||}d|}||}|||dd|||d|||d|||d}|||dd|||d|||d|||d} || fS)zFinds 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. rPrr2r0) r+r,r-r.rjr rrrNrr0r0r1r!,s  ""r!)rjr+r,r-r.)r rrcCsL||}d|}||}|||d|||||||||S)zFinds 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. rPr2r0)r+r,r-r.rjr rrr0r0r1r"Fs4r"cCsbt|dkrtg||RSt|dkrtg||RSt|dkr-tg||RStdNrOr2Unknown curve degree)rr#r r! ValueError)segrjr0r0r1r$_s   r$c Cst|\}}|\}}|\}}t||tkrt||tkrdSt||t||kr2||||S||||S)Nrr) ser sxZsyexZeyZpxpyr0r0r1 _line_t_of_ptns rcCsR|d|d|d|d}|d|d|d|d}|dko'|dk S)NrrPrbr0)r]r^originZxDiffZyDiffr0r0r1'_both_points_are_on_same_side_of_origin|s  rcCs|\}}|\}}|\}} |\} } t|| r$t||r$t||s$gSt| | r8t||r8t|| s8gSt|| rFt| | rFgSt||rTt||rTgSt||r|} | | | |} | | || }| |f}t|t|||t|||dgSt|| r|} ||||}|| ||}| |f}t|t|||t|||dgS||||}| | | |} t|| rgS|||| || || } || ||}| |f}t|||rt|||rt|t|||t|||dgSgS)aFinds 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) r )rQiscloserrr)s1e1s2e2Zs1xZs1yZe1xZe1yZs2xZs2yZe2xZe2yrNZslope34rr Zslope12r0r0r1r%sr           r%cCsT|d}|d}t|d|d|d|d}t| |d |d S)NrrrP)rQatan2rrotate translate)segmentstartendZangler0r0r1_alignment_transformations$ rcCst||}t|dkr!t|\}}}t|d|d|d}n"t|dkr?t|\}}}}t|d|d|d|d}ntdtdd|DS)Nr2rPrrcss,|]}d|krdkrnn|VqdS)rbrPNr0rirr0r0r1rrz._curve_line_intersections_t..) rtransformPointsrrsrrrrr)curvelineZ aligned_curver]r^r intersectionsrYr0r0r1_curve_line_intersections_ts   rcCst|dkr t}n t|dkrt}ntdg}t||D]'}|g||R}tg||R}tg||R}|t|||dq|S)aFinds 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) r2rrr ) rr r!rrrr#rtr)rrZ pointFinderrrjr Zline_tr0r0r1r&s  r&cCs0t|dkr t|St|dkrt|Std)Nr2rr)rrrr)rr0r0r1 _curve_bounds s  rcCstt|dkr|\}}t|||}||f||fgSt|dkr'tg||RSt|dkr6tg||RStdr)rr#rrr)rrjrrmidpointr0r0r1_split_segment_at_ts    rMbP?c srt|}t|}|s d}|sd}t||\}}|sgSdd} t|kr4t|kr4| || |fgSt|d\} } |d| |f} | ||df} t|d\}}|d| |f}| ||df}g}|t| || |d|t| || |d|t| || |d|t| || |dfdd }t}g}|D]}||}||vrq||||q|S) N)rbrDcSsd|d|dS)Nr3rrPr0)rr0r0r1r1sz._curve_curve_intersections_t..midpointr3rrP)range1range2cs t|dt|dfS)NrrP)int)r precisionr0r1V z._curve_curve_intersections_t..) rrrrextend_curve_curve_intersections_tsetaddrt)curve1curve2rrrZbounds1Zbounds2Z intersects_rZc11Zc12Z c11_rangeZ c12_rangeZc21Zc22Z c21_rangeZ c22_rangefoundZ unique_keyseenZ unique_valuesrkeyr0rr1r!sb       rcCs t||}tdd|DS)Ncss |] }t|ddVqdS)rPrbN)rQr)ripr0r0r1rfsz_is_linelike..)rrall)rZ maybeliner0r0r1 _is_linelikedsrcstr&ddf}t|r!|d|df}tg||RSt||St|r7|d|df}t|St|}fdd|DS)a 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) rrcs,g|]}tt|d|d|ddqS)rrPr )rr$)rirrr0r1rrsz+curveCurveIntersections..)rr%r&r)rrline1line2Zintersection_tsr0rr1r'is    r'cCsd}t|t|kr||}}d}t|dkr)t|dkr#t||}n t||}nt|dkr?t|dkr?tg||R}ntd|sG|Sdd|DS)a)Finds intersections between two segments. Args: seg1: List of coordinates of the first segment as 2D tuples. seg2: List of coordinates of the second segment as 2D tuples. Returns: A list of ``Intersection`` objects, each object having ``pt``, ``t1`` and ``t2`` attributes containing the intersection point, time on first segment and time on second segment respectively. Examples:: >>> curve1 = [ (10,100), (90,30), (40,140), (220,220) ] >>> curve2 = [ (5,150), (180,20), (80,250), (210,190) ] >>> intersections = segmentSegmentIntersections(curve1, curve2) >>> len(intersections) 3 >>> intersections[0].pt (81.7831487395506, 109.88904552375288) >>> curve3 = [ (100, 240), (30, 60), (210, 230), (160, 30) ] >>> line = [ (25, 260), (230, 20) ] >>> intersections = segmentSegmentIntersections(curve3, line) >>> len(intersections) 3 >>> intersections[0].pt (84.9000930760723, 189.87306176459828) FTrOz4Couldn't work out which intersection function to usecSs g|] }t|j|j|jdqS)r )rr r r rr0r0r1rrrz/segmentSegmentIntersections..)rr'r&r%r)Zseg1Zseg2Zswappedrr0r0r1r(s     r(cCs@zt|}Wn tyd|YSwdddd|DS)zw >>> _segmentrepr([1, [2, 3], [], [[2, [3, 4], [0.1, 2.2]]]]) '(1, (2, 3), (), ((2, (3, 4), (0.1, 2.2))))' z%gz(%s)z, css|]}t|VqdSrI) _segmentrepr)rirNr0r0r1rsz_segmentrepr..)iter TypeErrorjoin)objitr0r0r1rs    rcCs|D]}tt|qdS)zlHelper for the doctests, displaying each segment in a list of segments on a single line as a tuple. N)printr)rrr0r0r1 printSegmentssr __main__)r))rNN)X__doc__ZfontTools.misc.arrayToolsrrrZfontTools.misc.transformrrQ collectionsrrAttributeError ImportErrorZfontTools.misccompiledZCOMPILEDr?r__all__rr9returnsdoublelocalsr*r@rrrcZcfuncinlinerLrTrrrrrr rrrrrrrrrrrrrRrrrrrrsrrrrrr#r r!r"r$rrr%rrr&rrrrr'r(rr __name__sysdoctestexittestmodfailedr0r0r0r1s          #   !" $&9-%  #  !a       N  & C'0