#Vf8dZddlZddlmZddlmZgdZdZdez ZdezZ d Z Gd d eZ e Z dd Z dd ZeGddZedk(r4ddlZddlZej&ej(j*yy)a7Affine 2D transformation matrix class. The Transform class implements various transformation matrix operations, both on the matrix itself, as well as on 2D coordinates. Transform instances are effectively immutable: all methods that operate on the transformation itself always return a new instance. This has as the interesting side effect that Transform instances are hashable, ie. they can be used as dictionary keys. This module exports the following symbols: Transform this is the main class Identity Transform instance set to the identity transformation Offset Convenience function that returns a translating transformation Scale Convenience function that returns a scaling transformation The DecomposedTransform class implements a transformation with separate translate, rotation, scale, skew, and transformation-center components. :Example: >>> t = Transform(2, 0, 0, 3, 0, 0) >>> t.transformPoint((100, 100)) (200, 300) >>> t = Scale(2, 3) >>> t.transformPoint((100, 100)) (200, 300) >>> t.transformPoint((0, 0)) (0, 0) >>> t = Offset(2, 3) >>> t.transformPoint((100, 100)) (102, 103) >>> t.transformPoint((0, 0)) (2, 3) >>> t2 = t.scale(0.5) >>> t2.transformPoint((100, 100)) (52.0, 53.0) >>> import math >>> t3 = t2.rotate(math.pi / 2) >>> t3.transformPoint((0, 0)) (2.0, 3.0) >>> t3.transformPoint((100, 100)) (-48.0, 53.0) >>> t = Identity.scale(0.5).translate(100, 200).skew(0.1, 0.2) >>> t.transformPoints([(0, 0), (1, 1), (100, 100)]) [(50.0, 100.0), (50.550167336042726, 100.60135501775433), (105.01673360427253, 160.13550177543362)] >>> N) NamedTuple) dataclass) TransformIdentityOffsetScaleDecomposedTransformgV瞯<cbt|tkrd}|S|tkDrd}|S|tkrd}|S)Nrr r )abs_EPSILON _ONE_EPSILON_MINUS_ONE_EPSILON)vs a/var/www/html/software/conda/envs/catlas/lib/python3.12/site-packages/fontTools/misc/transform.py _normSinCosrDsE 1v  H \   H    HceZdZUdZdZeed<dZeed<dZeed<dZ eed<dZ eed<dZ eed <d Z d Z d Zd ZddZddZdZddZdZdZdZdZddZdZdZy)ra 2x2 transformation matrix plus offset, a.k.a. Affine transform. Transform instances are immutable: all transforming methods, eg. rotate(), return a new Transform instance. :Example: >>> t = Transform() >>> t >>> t.scale(2) >>> t.scale(2.5, 5.5) >>> >>> t.scale(2, 3).transformPoint((100, 100)) (200, 300) Transform's constructor takes six arguments, all of which are optional, and can be used as keyword arguments:: >>> Transform(12) >>> Transform(dx=12) >>> Transform(yx=12) Transform instances also behave like sequences of length 6:: >>> len(Identity) 6 >>> list(Identity) [1, 0, 0, 1, 0, 0] >>> tuple(Identity) (1, 0, 0, 1, 0, 0) Transform instances are comparable:: >>> t1 = Identity.scale(2, 3).translate(4, 6) >>> t2 = Identity.translate(8, 18).scale(2, 3) >>> t1 == t2 1 But beware of floating point rounding errors:: >>> t1 = Identity.scale(0.2, 0.3).translate(0.4, 0.6) >>> t2 = Identity.translate(0.08, 0.18).scale(0.2, 0.3) >>> t1 >>> t2 >>> t1 == t2 0 Transform instances are hashable, meaning you can use them as keys in dictionaries:: >>> d = {Scale(12, 13): None} >>> d {: None} But again, beware of floating point rounding errors:: >>> t1 = Identity.scale(0.2, 0.3).translate(0.4, 0.6) >>> t2 = Identity.translate(0.08, 0.18).scale(0.2, 0.3) >>> t1 >>> t2 >>> d = {t1: None} >>> d {: None} >>> d[t2] Traceback (most recent call last): File "", line 1, in ? KeyError: r xxrxyyxyydxdycV|\}}|\}}}}}} ||z||zz|z||z||zz| zfS)zTransform a point. :Example: >>> t = Transform() >>> t = t.scale(2.5, 5.5) >>> t.transformPoint((100, 100)) (250.0, 550.0) ) selfpxyrrrrrrs rtransformPointzTransform.transformPointsLA!%BBBQa"$b1frAvo&:;;rc~|\}}}}}}|D cgc]!\}} ||z|| zz|z||z|| zz|zf#c} }Scc} }w)zTransform a list of points. :Example: >>> t = Scale(2, 3) >>> t.transformPoints([(0, 0), (0, 100), (100, 100), (100, 0)]) [(0, 0), (0, 300), (200, 300), (200, 0)] >>> r) rpointsrrrrrrr r!s rtransformPointszTransform.transformPointssU"&BBBIOPAa"q&2%rAvQ';<PPPs&9cL|\}}|dd\}}}}||z||zz||z||zzfS)zTransform an (dx, dy) vector, treating translation as zero. :Example: >>> t = Transform(2, 0, 0, 2, 10, 20) >>> t.transformVector((3, -4)) (6, -8) >>> Nr)rrrrrrrrs rtransformVectorzTransform.transformVectorsERbqBBR"r'!27R"W#455rct|dd\}}}}|Dcgc]\}}||z||zz||z||zzfc}}Scc}}w)aTransform a list of (dx, dy) vector, treating translation as zero. :Example: >>> t = Transform(2, 0, 0, 2, 10, 20) >>> t.transformVectors([(3, -4), (5, -6)]) [(6, -8), (10, -12)] >>> Nr'r)rvectorsrrrrrrs rtransformVectorszTransform.transformVectorssNbqBBELM62rb27"BGb2g$56MMMs 4c0|jdddd||fS)zReturn a new transformation, translated (offset) by x, y. :Example: >>> t = Transform() >>> t.translate(20, 30) >>> r r transformrr r!s r translatezTransform.translates ~~q!Q1a011rNc8||}|j|dd|ddfS)akReturn a new transformation, scaled by x, y. The 'y' argument may be None, which implies to use the x value for y as well. :Example: >>> t = Transform() >>> t.scale(5) >>> t.scale(5, 6) >>> rr-r/s rscalezTransform.scales* 9A~~q!Q1a011rcddl}t|j|}t|j|}|j ||| |ddfS)aReturn a new transformation, rotated by 'angle' (radians). :Example: >>> import math >>> t = Transform() >>> t.rotate(math.pi / 2) >>> rN)mathrcossinr.)rangler4css rrotatezTransform.rotatesM   (  (~~q!aRAq122rcxddl}|jd|j||j|dddfS)zReturn a new transformation, skewed by x and y. :Example: >>> import math >>> t = Transform() >>> t.skew(math.pi / 4) >>> rNr )r4r.tan)rr r!r4s rskewzTransform.skews7 ~~q($((1+xtxx{Aq!DEErc |\}}}}}}|\}} } } } } |j||z|| zz|| z|| zz||z|| zz|| z|| zz||z| |zz| z| |z| |zz| zS)aReturn a new transformation, transformed by another transformation. :Example: >>> t = Transform(2, 0, 0, 3, 1, 6) >>> t.transform((4, 3, 2, 1, 5, 6)) >>>  __class__rotherxx1xy1yx1yy1dx1dy1xx2xy2yx2yy2dx2dy2s rr.zTransform.transforms(-$S#sC'+$S#sC~~ #Ic ! #Ic ! #Ic ! #Ic ! #Ic !C ' #Ic !C '   rc |\}}}}}}|\}} } } } } |j||z|| zz|| z|| zz||z|| zz|| z|| zz||z| |zz| z| |z| |zz| zS)aReturn a new transformation, which is the other transformation transformed by self. self.reverseTransform(other) is equivalent to other.transform(self). :Example: >>> t = Transform(2, 0, 0, 3, 1, 6) >>> t.reverseTransform((4, 3, 2, 1, 5, 6)) >>> Transform(4, 3, 2, 1, 5, 6).transform((2, 0, 0, 3, 1, 6)) >>> r?rAs rreverseTransformzTransform.reverseTransform(s(,$S#sC',$S#sC~~ #Ic ! #Ic ! #Ic ! #Ic ! #Ic !C ' #Ic !C '   rc|tk(r|S|\}}}}}}||z||zz }||z | |z | |z ||z f\}}}}| |z||zz | |z||zz }}|j||||||S)aKReturn the inverse transformation. :Example: >>> t = Identity.translate(2, 3).scale(4, 5) >>> t.transformPoint((10, 20)) (42, 103) >>> it = t.inverse() >>> it.transformPoint((42, 103)) (10.0, 20.0) >>> )rr@)rrrrrrrdets rinversezTransform.inverse@s 8 K!%BBB2gRcB39rcCicABBrBG#bS2XR%7B~~b"b"b"55rc d|zS)zReturn a PostScript representation :Example: >>> t = Identity.scale(2, 3).translate(4, 5) >>> t.toPS() '[2 0 0 3 8 15]' >>> z[%s %s %s %s %s %s]rrs rtoPSzTransform.toPSTs%t++rc,tj|S)z%Decompose into a DecomposedTransform.)r fromTransformrUs r toDecomposedzTransform.toDecomposed`s"0066rc|tk7S)aReturns True if transform is not identity, False otherwise. :Example: >>> bool(Identity) False >>> bool(Transform()) False >>> bool(Scale(1.)) False >>> bool(Scale(2)) True >>> bool(Offset()) False >>> bool(Offset(0)) False >>> bool(Offset(2)) True )rrUs r__bool__zTransform.__bool__ds(xrc<d|jjf|zzS)Nz<%s [%g %g %g %g %g %g]>)r@__name__rUs r__repr__zTransform.__repr__zs)dnn.E.E-G$-NOOrrr)r N)returnr )r] __module__ __qualname____doc__rfloat__annotations__rrrrrr"r%r(r+r0r2r:r=r.rPrSrVrYr[r^rrrrrNsL\BMBMBMBMBMBM < Q 6 N 22 3 F * 06( ,7 ,Prrc"tdddd||S)zReturn the identity transformation offset by x, y. :Example: >>> Offset(2, 3) >>> r rrr r!s rrrs Q1aA &&rc*||}t|dd|ddS)zReturn the identity transformation scaled by x, y. The 'y' argument may be None, which implies to use the x value for y as well. :Example: >>> Scale(2, 3) >>> rrgrhs rrrs# y  Q1aA &&rceZdZUdZdZeed<dZeed<dZeed<dZ eed<dZ eed<dZ eed <dZ eed <dZ eed <dZeed <ed ZdZy)r zThe DecomposedTransform class implements a transformation with separate translate, rotation, scale, skew, and transformation-center components. r translateX translateYrotationr scaleXscaleYskewXskewYtCenterXtCenterYc |\}}}}}}tjd|}|dkr ||z}||z}||z||zz } d} dx} } dx} }|dk7s|dk7rtj||z||zz}|dk\rtj||z ntj||z  } || |z } } tj||z||zz||zz d}} n|dk7s|dk7rtj||z||zz}tj dz |dk\rtj| |z ntj||z  z } | |z |} } dtj||z||zz||zz }} n t ||tj| | |z| tj| |ztj|dd S)Nr r)r4copysignsqrtacosatanpir degrees)rr.abr8dr r!sxdeltarmrnrorprqrr9s rrXz!DecomposedTransform.fromTransforms%1aAq ]]1a  6 GA GAAA  6Q!V !a%!a%-(A+,6tyyQ' !a%8H7HHFF IIq1uq1u}Q&?@!5E !VqAv !a%!a%-(Aww{%&!V 1"q&!$))AE2B1BH$aiFFtyy!a%!a%-AE)BC5E " LL " RK  LL " $ LL    rc*t}|j|j|jz|j|j z}|j tj|j}|j|j|j}|jtj|jtj|j}|j|j |j }|S)zReturn the Transform() equivalent of this transformation. :Example: >>> DecomposedTransform(scaleX=2, scaleY=2).toTransform() >>> )rr0rkrrrlrsr:r4radiansrmr2rnror=rprq)rts r toTransformzDecomposedTransform.toTransforms K KK OOdmm +T__t}}-L  HHT\\$--0 1 GGDKK - FF4<< +T\\$**-E F KK 7rN)r]rarbrcrkrdrerlrmrnrorprqrrrs classmethodrXrrrrr r s{JJHeFEFEE5E5HeHe+ + Zrr __main__r_)N)rcr4typingr dataclassesr__all__rrrrrrrrr r]sysdoctestexittestmodfailedrrrrs4l ! N 8| (] mP mP` ;' ' MM M` z CHH_W__  % %& r