<`h!dZddlmZgdZdZdez ZdezZdZGdd eZeZ dd Z dd Z e d kr,dd l Z dd lZe jejjd Sd S)aAffine 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 Examples: >>> 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)] >>> ) NamedTuple) TransformIdentityOffsetScalegV瞯<crt|tkrd}n|tkrd}n |tkrd}|S)Nrrr )abs_EPSILON _ONE_EPSILON_MINUS_ONE_EPSILON)vs 8lib/python3.11/site-packages/fontTools/misc/transform.py _normSinCosr;sBFFX!!,!! ! ceZdZUdZdZeed<dZeed<dZeed<dZ eed<dZ eed<dZ eed <d Z d Z dd ZddZdZddZdZdZdZdZdZdZd S)raw2x2 transformation matrix plus offset, a.k.a. Affine transform. Transform instances are immutable: all transforming methods, eg. rotate(), return a new Transform instance. Examples: >>> 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: rxxrxyyxyydxdycV|\}}|\}}}}}} ||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.transformPointsL &1a"b"b"b Q$A+ BqD2a4K", --rcF|\fd|DS)zTransform a list of points. Example: >>> t = Scale(2, 3) >>> t.transformPoints([(0, 0), (0, 100), (100, 100), (100, 0)]) [(0, 0), (0, 300), (200, 300), (200, 0)] >>> cNg|]!\}}|z|zzz|z|zzzf"Srr) .0rrrrrrrrs r z-Transform.transformPoints..sD B B B41a2a4"Q$; RTBqD[2- . B B Brr)rpointsrrrrrrs @@@@@@rtransformPointszTransform.transformPointssE "b"b"b B B B B B B B B B6 B B BBrc8|dddd||fS)zReturn a new transformation, translated (offset) by x, y. Example: >>> t = Transform() >>> t.translate(20, 30) >>> rr transformrrrs r translatezTransform.translates# Aq!Q* + ++rNc@||}||dd|ddfS)a Return 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*s rscalezTransform.scales-Y1 Aq!Q* + ++rcddl}t||}t||}|||| |ddfS)zReturn a new transformation, rotated by 'angle' (radians). Example: >>> import math >>> t = Transform() >>> t.rotate(math.pi / 2) >>> rN)mathrcossinr))rangler/css rrotatezTransform.rotates\+++$((5//""!$((5//""! Ar1a+ , ,,rcddl}|d||||dddfS)zReturn a new transformation, skewed by x and y. Example: >>> import math >>> t = Transform() >>> t.skew(math.pi / 4) >>> rNr)r/r)tan)rrrr/s rskewzTransform.skews@+++ DHHQKK!aA> ? ??rc |\}}}}}}|\}} } } } } |||z|| zz|| z|| zz||z|| zz|| z|| zz||z| |zz| z| |z| |zz| zS)zReturn 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"'#sCc3!%#sCc3 Gc#gGc#gGc#gGc#gGc#gGc#g   rc |\}}}}}}|\}} } } } } |||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:r<s rreverseTransformzTransform.reverseTransforms"&#sCc3!&#sCc3 Gc#gGc#gGc#gGc#gGc#gGc#g   rc|tkr|S|\}}}}}}||z||zz }||z | |z | |z ||z f\}}}}| |z||zz | |z||zz }}|||||||S)zReturn 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.inverses X ;"b"b"b 22 #c6B3s7RCGRV3."b"b 3r6BrE>B3r6BrE>b" BBB / //rc d|zS)zReturn a PostScript representation: >>> 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.toPS$s  %%rc|tkS)aReturns True if transform is not identity, False otherwise. >>> 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 )rrPs r__bool__zTransform.__bool__-s"  rc(d|jjf|zzS)Nz<%s [%g %g %g %g %g %g]>)r;__name__rPs r__repr__zTransform.__repr__@s #(?'AD'H IIrrr)rN)rU __module__ __qualname____doc__rfloat__annotations__rrrrrr r&r+r-r5r8r)rKrNrQrSrVrrrrrEsBEENU U U U U U . . . C C C , , , ,,,,, - - - @ @ @ @(.000(&&&&JJJJJrrc*tdddd||S)ztReturn the identity transformation offset by x, y. Example: >>> Offset(2, 3) >>> rrrrrs rrrFs !Q1a###rNc2||}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) >>> Nrr^r_s rrrPs&I!!Q1a###r__main__rW)N)rZtypingr__all__r r rrrrrrrUsysdoctestexittestmodfailedrrrris--^ 7 6 6 8| (]   |J|J|J|J|J |J|J|J~ 9;;$$$$ $ $ $ $ z  /'/   "#####r