o l^Ufæ9ã@s´dZddlZddlmZddlmZgd¢ZdZdeZdeZ d d „Z Gd d „d eƒZ e ƒZ dd d„Z ddd„ZeGdd„dƒƒZedkrXddlZddlZe e ¡j¡dSdS)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)] >>> éN)Ú NamedTuple)Ú dataclass)Ú TransformÚIdentityÚOffsetÚScaleÚDecomposedTransformgV瞯Ò<ééÿÿÿÿcCs4t|ƒtkr d}|S|tkrd}|S|tkrd}|S)Nrr r )ÚabsÚ_EPSILONÚ _ONE_EPSILONÚ_MINUS_ONE_EPSILON)Úv©rú8lib/python3.10/site-packages/fontTools/misc/transform.pyÚ _normSinCosDs üþrc@sÚeZdZUdZdZeed<dZeed<dZeed<dZ eed<dZ eed<dZ eed <d d „Z d d „Z dd„Zdd„Zd+dd„Zd,dd„Zdd„Zd+dd„Zdd„Zdd„Zdd „Zd!d"„Zd-d%d&„Zd'd(„Zd)d*„ZdS).raœ 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 ÚxxrÚxyÚyxÚyyÚdxÚdyc Cs@|\}}|\}}}}}} |||||||||| fS)zÍTransform a point. :Example: >>> t = Transform() >>> t = t.scale(2.5, 5.5) >>> t.transformPoint((100, 100)) (250.0, 550.0) r) ÚselfÚpÚxÚyrrrrrrrrrÚtransformPoint¤s (zTransform.transformPointcs,|\‰‰‰‰‰‰‡‡‡‡‡‡fdd„|DƒS)zùTransform 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)] >>> cs8g|]\}}ˆ|ˆ|ˆˆ|ˆ|ˆf‘qSrr)Ú.0rr©rrrrrrrrÚ ½s8z-Transform.transformPoints..r)rZpointsrrrÚtransformPoints²s zTransform.transformPointscCs<|\}}|dd…\}}}}||||||||fS)zéTransform an (dx, dy) vector, treating translation as zero. :Example: >>> t = Transform(2, 0, 0, 2, 10, 20) >>> t.transformVector((3, -4)) (6, -8) >>> Nér)rrrrrrrrrrrÚtransformVector¿s  zTransform.transformVectorcs,|dd…\‰‰‰‰‡‡‡‡fdd„|DƒS)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"cs0g|]\}}ˆ|ˆ|ˆ|ˆ|f‘qSrr)rrr©rrrrrrr ×s0z.Transform.transformVectors..r)rZvectorsrr$rÚtransformVectorsÍs zTransform.transformVectorscCs| dddd||f¡S)záReturn a new transformation, translated (offset) by x, y. :Example: >>> t = Transform() >>> t.translate(20, 30) >>> r r©Ú transform©rrrrrrÚ translateÙs zTransform.translateNcCs"|dur|}| |dd|ddf¡S)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) >>> Nrr&r(rrrÚscaleäs zTransform.scalecCs<ddl}t| |¡ƒ}t| |¡ƒ}| ||| |ddf¡S)aReturn a new transformation, rotated by 'angle' (radians). :Example: >>> import math >>> t = Transform() >>> t.rotate(math.pi / 2) >>> rN)ÚmathrZcosZsinr')rZangler+ÚcÚsrrrÚrotateôs zTransform.rotatecCs*ddl}| d| |¡| |¡dddf¡S)zõReturn a new transformation, skewed by x and y. :Example: >>> import math >>> t = Transform() >>> t.skew(math.pi / 4) >>> rNr )r+r'Ztan)rrrr+rrrÚskews "zTransform.skewc Cs„|\}}}}}}|\}} } } } } | |||| || || |||| || || ||| || | || || ¡S)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)) >>> ©Ú __class__©rÚotherZxx1Zxy1Zyx1Zyy1Zdx1Zdy1Zxx2Zxy2Zyx2Zyy2Zdx2Zdy2rrrr's úzTransform.transformc Cs„|\}}}}}}|\}} } } } } | |||| || || |||| || || ||| || | || || ¡S)aíReturn 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)) >>> r0r2rrrÚreverseTransform's úzTransform.reverseTransformcCsŽ|tkr|S|\}}}}}}||||}||| || |||f\}}}}| |||| |||}}| ||||||¡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) >>> )rr1)rrrrrrrZdetrrrÚinverse?s (&zTransform.inversecCsd|S)zÎReturn 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]r©rrrrÚtoPSSs zTransform.toPSÚreturnrcCs t |¡S)z%Decompose into a DecomposedTransform.)rÚ fromTransformr6rrrÚ toDecomposed_s zTransform.toDecomposedcCs|tkS)aëReturns 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 )rr6rrrÚ__bool__cszTransform.__bool__cCsd|jjf|S)Nz<%s [%g %g %g %g %g %g]>)r1Ú__name__r6rrrÚ__repr__yszTransform.__repr__©rr)r N)r8r)r<Ú __module__Ú __qualname__Ú__doc__rÚfloatÚ__annotations__rrrrrrr!r#r%r)r*r.r/r'r4r5r7r:r;r=rrrrrNs.  N          rcCstdddd||ƒS)z™Return the identity transformation offset by x, y. :Example: >>> Offset(2, 3) >>> r r©r©rrrrrr€srcCs|dur|}t|dd|ddƒS)zêReturn 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) >>> NrrDrErrrr‹s rc@sšeZdZUdZdZeed<dZeed<dZeed<dZ eed<dZ eed<dZ eed <dZ eed <dZ eed <dZeed <d d„Zedd„ƒZdd„ZdS)rz˜The DecomposedTransform class implements a transformation with separate translate, rotation, scale, skew, and transformation-center components. rÚ translateXÚ translateYÚrotationr ÚscaleXÚscaleYÚskewXÚskewYÚtCenterXÚtCenterYcCsZ|jdkp,|jdkp,|jdkp,|jdkp,|jdkp,|jdkp,|jdkp,|jdkp,|jdkS)Nrr ) rFrGrHrIrJrKrLrMrNr6rrrr;©s" ÿþýüûúù÷zDecomposedTransform.__bool__c Cs˜|\}}}}}}t d|¡}|dkr||9}||9}||||} d} d} } d} }|dks4|dkrlt ||||¡}|dkrJt ||¡nt ||¡ } || |} } t ||||||¡d} }nG|dkst|dkr²t ||||¡}tjd|dkrt | |¡nt ||¡ } | ||} } dt ||||||¡} }n t||t | ¡| || t | ¡|t |¡ddƒ S)Nr ré)r+ZcopysignZsqrtZacosZatanZpirZdegrees)rr'ÚaÚbr,ÚdrrZsxZdeltarHrIrJrKrLÚrr-rrrr9¶sB &&&ÿ& ÷z!DecomposedTransform.fromTransformcCsxtƒ}| |j|j|j|j¡}| t |j ¡¡}|  |j |j ¡}|  t |j¡t |j¡¡}| |j |j ¡}|S)zÝReturn the Transform() equivalent of this transformation. :Example: >>> DecomposedTransform(scaleX=2, scaleY=2).toTransform() >>> )rr)rFrMrGrNr.r+ZradiansrHr*rIrJr/rKrL)rÚtrrrÚ toTransformäsÿzDecomposedTransform.toTransformN)r<r?r@rArFrBrCrGrHrIrJrKrLrMrNr;Ú classmethodr9rUrrrrr™s            -rÚ__main__r>)N)rAr+ÚtypingrZ dataclassesrÚ__all__r r rrrrrrrr<ÚsysZdoctestÚexitZtestmodZfailedrrrrÚs,6   1  ]ü