o:i,BSrSSKJr SSKJr SSKrSSKrSr\4Sjr \ \ 4Sjr Sr S rS rS rS rS rSrSrSrSrSrSrSrSSjr"SS\5rSSjrSr\S:Xa4SSKrSSKr\R@"\RB"5RD5 gg)zTRoutines for calculating bounding boxes, point in rectangle calculations and so on. )otRound)VectorNcU(dgUVVs/sHupUPM nnnUVVs/sHupUPM nnn[U5[U5[U5[U54$s snnfs snnf)zCalculate the bounding rectangle of a 2D points array. Args: array: A sequence of 2D tuples. Returns: A four-item tuple representing the bounding rectangle ``(xMin, yMin, xMax, yMax)``. rrrrminmax)arrayxyxsyss \/srv/projetos/modelo_ml_acdoc/venv/lib/python3.13/site-packages/fontTools/misc/arrayTools.py calcBoundsr s]  !B  !B  r7CGSWc"g --  s AA%c@^[U4Sj[U555$)aCalculate the integer bounding rectangle of a 2D points array. Values are rounded to closest integer towards ``+Infinity`` using the :func:`fontTools.misc.fixedTools.otRound` function by default, unless an optional ``round`` function is passed. Args: array: A sequence of 2D tuples. round: A rounding function of type ``f(x: float) -> int``. Returns: A four-item tuple of integers representing the bounding rectangle: ``(xMin, yMin, xMax, yMax)``. c34># UH nT"U5v M g7f)N).0vrounds r calcIntBounds..*s5#4aq#4s)tupler)r rs `r calcIntBoundsrs 5:e#45 55c^UupEUcXEXE4$UupgpU"Xd5U"Xu5U"X5U"X54$)a?Add a point to a bounding rectangle. Args: bounds: A bounding rectangle expressed as a tuple ``(xMin, yMin, xMax, yMax), or None``. p: A 2D tuple representing a point. min,max: functions to compute the minimum and maximum. Returns: The updated bounding rectangle ``(xMin, yMin, xMax, yMax)``. r) boundsprr r r xMinyMinxMaxyMaxs r updateBoundsr#-sCFQ ~Qz#D t<Ts4|S\ AArcrUup#UupEpgXBs=:*=(a U:*Os =(a XSs=:*=(a U:*$s $)a Test if a point is inside a bounding rectangle. Args: p: A 2D tuple representing a point. rect: A bounding rectangle expressed as a tuple ``(xMin, yMin, xMax, yMax)``. Returns: ``True`` if the point is inside the rectangle, ``False`` otherwise. r)rrectr r rr r!r"s r pointInRectr&@s<FQ!D     6D$5$5$56$56rc[U5S:a/$Uup#pEUVVs/sH4upgX&s=:*=(a U:*Os =(a X7s=:*=(a U:*Os PM6 snn$s snnf)zDetermine which points are inside a bounding rectangle. Args: array: A sequence of 2D tuples. rect: A bounding rectangle expressed as a tuple ``(xMin, yMin, xMax, yMax)``. Returns: A list containing the points inside the rectangle. )len)r r%rr r!r"r r s r pointsInRectr*PsV 5zA~ !DDI JEDAT  $  7T%6%6$%6 7E JJ Js;AcHUup[R"US-US--5$)z{Calculate the length of the given vector. Args: vector: A 2D tuple. Returns: The Euclidean length of the vector. )mathsqrt)vectorr r s r vectorLengthr0as& DA 99QTAqD[ !!rc rUVs/sH%n[[R"US-55PM' sn$s snf)zRound a list of floats to 16-bit signed integers. Args: array: List of float values. Returns: A list of rounded integers. g?)intr-floor)r is rasInt16r5ns./4 4eC 1s7# $e 44 4s,4c`Uupp4[X5[X$5[X5[X$54$)a,Normalize a bounding box rectangle. This function "turns the rectangle the right way up", so that the following holds:: xMin <= xMax and yMin <= yMax Args: rect: A bounding rectangle expressed as a tuple ``(xMin, yMin, xMax, yMax)``. Returns: A normalized bounding rectangle. rr%rr r!r"s rnormRectr8zs- $T t?COS_c$o MMrc(Uup4pVX1-XB-XQ-Xb-4$)aScale a bounding box rectangle. Args: rect: A bounding rectangle expressed as a tuple ``(xMin, yMin, xMax, yMax)``. x: Factor to scale the rectangle along the X axis. Y: Factor to scale the rectangle along the Y axis. Returns: A scaled bounding rectangle. r)r%r r rr r!r"s r scaleRectr:s% $T 8TXtx 11rc(Uup4pVX1-XB-XQ-Xb-4$)a Offset a bounding box rectangle. Args: rect: A bounding rectangle expressed as a tuple ``(xMin, yMin, xMax, yMax)``. dx: Amount to offset the rectangle along the X axis. dY: Amount to offset the rectangle along the Y axis. Returns: An offset bounding rectangle. rr%dxdyrr r!r"s r offsetRectr?% $T 9diDI 55rc(Uup4pVX1-XB-XQ- Xb- 4$)a)Inset a bounding box rectangle on all sides. Args: rect: A bounding rectangle expressed as a tuple ``(xMin, yMin, xMax, yMax)``. dx: Amount to inset the rectangle along the X axis. dY: Amount to inset the rectangle along the Y axis. Returns: An inset bounding rectangle. rr<s r insetRectrBr@rcUup#pEUupgp[X&5[X75[XH5[XY54uppX:dX:agSXX44$)aTest for rectangle-rectangle intersection. Args: rect1: First bounding rectangle, expressed as tuples ``(xMin, yMin, xMax, yMax)``. rect2: Second bounding rectangle. Returns: A boolean and a rectangle. If the input rectangles intersect, returns ``True`` and the intersecting rectangle. Returns ``False`` and ``(0, 0, 0, 0)`` if the input rectangles don't intersect. )FrT)r rrect1rect2xMin1yMin1xMax1yMax1xMin2yMin2xMax2yMax2rr r!r"s rsectRectrOsb$) U5#( U5 E E E E D  |t|" $d) ))rcxUup#pEUupgp[X&5[X75[XH5[XY54uppXX4$)aDetermine union of bounding rectangles. Args: rect1: First bounding rectangle, expressed as tuples ``(xMin, yMin, xMax, yMax)``. rect2: Second bounding rectangle. Returns: The smallest rectangle in which both input rectangles are fully enclosed. rrDs r unionRectrQsQ$) U5#( U5 E E E E D  ##rc(Uupp4X-S- X$-S- 4$)zDetermine rectangle center. Args: rect: Bounding rectangle, expressed as tuples ``(xMin, yMin, xMax, yMax)``. Returns: A 2D tuple representing the point at the center of the rectangle. r,rr7s r rectCenterrSs' $T K1 t{a/ //rcUupp4XB- X1- -$)zDetermine rectangle area. Args: rect: Bounding rectangle, expressed as tuples ``(xMin, yMin, xMax, yMax)``. Returns: The area of the rectangle. rr7s rrectArearUs $T KDK ((rc Uupp4[[R"U55n[[R"U55n[[R"U55n[[R"U55nXX44$)zRound a rectangle to integer values. Guarantees that the resulting rectangle is NOT smaller than the original. Args: rect: Bounding rectangle, expressed as tuples ``(xMin, yMin, xMax, yMax)``. Returns: A rounded bounding rectangle. )r2r-r3ceilr7s rintRectrX sc $T tzz$ D tzz$ D tyy D tyy D  ##rc dUS:a[SU<35e[U5up#pE[[R"X!- 5U-5[[R"X1- 5U-5[[R "XA- 5U-5[[R "XQ- 5U-54$)z >>> bounds = (72.3, -218.4, 1201.3, 919.1) >>> quantizeRect(bounds) (72, -219, 1202, 920) >>> quantizeRect(bounds, factor=10) (70, -220, 1210, 920) >>> quantizeRect(bounds, factor=100) (0, -300, 1300, 1000) r(z*Expected quantization factor >= 1, found: ) ValueErrorr8r2r-r3rW)r%factorrr r!r"s r quantizeRectr\szEfZPQQ%d^D DJJt} % ./ DJJt} % ./ DIIdm $v -. DIIdm $v -.  rc\rSrSrSrSrg)ri4c:[R"S[5 g)NzffontTools.misc.arrayTools.Vector has been deprecated, please use fontTools.misc.vector.Vector instead.)warningswarnDeprecationWarning)selfargskwargss r__init__Vector.__init__5s  4  rrN)__name__ __module__ __qualname____firstlineno__re__static_attributes__rrrrr4s rrc## U(dgU(a [U5nO [U5n[US5nUnUH nXE4v UnM XC4v g7f)a]Iterate over current and next items in iterable. Args: iterable: An iterable reverse: If true, iterate in reverse order. Returns: A iterable yielding two elements per iteration. Example: >>> tuple(pairwise([])) () >>> tuple(pairwise([], reverse=True)) () >>> tuple(pairwise([0])) ((0, 0),) >>> tuple(pairwise([0], reverse=True)) ((0, 0),) >>> tuple(pairwise([0, 1])) ((0, 1), (1, 0)) >>> tuple(pairwise([0, 1], reverse=True)) ((1, 0), (0, 1)) >>> tuple(pairwise([0, 1, 2])) ((0, 1), (1, 2), (2, 0)) >>> tuple(pairwise([0, 1, 2], reverse=True)) ((2, 1), (1, 0), (0, 2)) >>> tuple(pairwise(['a', 'b', 'c', 'd'])) (('a', 'b'), ('b', 'c'), ('c', 'd'), ('d', 'a')) >>> tuple(pairwise(['a', 'b', 'c', 'd'], reverse=True)) (('d', 'c'), ('c', 'b'), ('b', 'a'), ('a', 'd')) N)reversediternext)iterablereverseitfirstabs rpairwiserv=sTB  h  (^ TNE A f  *sA A cg)aM >>> import math >>> calcBounds([]) (0, 0, 0, 0) >>> calcBounds([(0, 40), (0, 100), (50, 50), (80, 10)]) (0, 10, 80, 100) >>> updateBounds((0, 0, 0, 0), (100, 100)) (0, 0, 100, 100) >>> pointInRect((50, 50), (0, 0, 100, 100)) True >>> pointInRect((0, 0), (0, 0, 100, 100)) True >>> pointInRect((100, 100), (0, 0, 100, 100)) True >>> not pointInRect((101, 100), (0, 0, 100, 100)) True >>> list(pointsInRect([(50, 50), (0, 0), (100, 100), (101, 100)], (0, 0, 100, 100))) [True, True, True, False] >>> vectorLength((3, 4)) 5.0 >>> vectorLength((1, 1)) == math.sqrt(2) True >>> list(asInt16([0, 0.1, 0.5, 0.9])) [0, 0, 1, 1] >>> normRect((0, 10, 100, 200)) (0, 10, 100, 200) >>> normRect((100, 200, 0, 10)) (0, 10, 100, 200) >>> scaleRect((10, 20, 50, 150), 1.5, 2) (15.0, 40, 75.0, 300) >>> offsetRect((10, 20, 30, 40), 5, 6) (15, 26, 35, 46) >>> insetRect((10, 20, 50, 60), 5, 10) (15, 30, 45, 50) >>> insetRect((10, 20, 50, 60), -5, -10) (5, 10, 55, 70) >>> intersects, rect = sectRect((0, 10, 20, 30), (0, 40, 20, 50)) >>> not intersects True >>> intersects, rect = sectRect((0, 10, 20, 30), (5, 20, 35, 50)) >>> intersects 1 >>> rect (5, 20, 20, 30) >>> unionRect((0, 10, 20, 30), (0, 40, 20, 50)) (0, 10, 20, 50) >>> rectCenter((0, 0, 100, 200)) (50.0, 100.0) >>> rectCenter((0, 0, 100, 199.0)) (50.0, 99.5) >>> intRect((0.9, 2.9, 3.1, 4.1)) (0, 2, 4, 5) Nrrrr_testrxlsr__main__)r()F)#__doc__fontTools.misc.roundToolsrfontTools.misc.vectorr_Vectorr-r_rrrr r#r&r*r0r5r8r:r?rBrOrQrSrUrXr\rvrxrgsysdoctestexittestmodfailedrrrrs.3  . '6$!$B& 7 K" " 5N& 2 6 6 *6$. 0 )$(* W ,^5p zHHW__  % %& r