U Dv f8@sdZddlZddlmZddlmZddddd gZd Zd eZd eZ d dZ GdddeZ e Z dddZ dddZeGdd d ZedkrddlZddlZeejdS)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<cCs0t|tkrd}n|tkr d}n |tkr,d}|S)Nrr r )abs_EPSILON _ONE_EPSILON_MINUS_ONE_EPSILON)vr>> 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 xxrxyyxyydxdyc Cs@|\}}|\}}}}}} |||||||||| fS)zTransform a point. :Example: >>> t = Transform() >>> t = t.scale(2.5, 5.5) >>> t.transformPoint((100, 100)) (250.0, 550.0) r) selfpxyrrrrrrrrrtransformPoints zTransform.transformPointcs,|\fdd|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)] >>> cs8g|]0\}}||||fqSrr).0rrrrrrrrrr sz-Transform.transformPoints..r)rZpointsrrrtransformPointss zTransform.transformPointscCs<|\}}|dd\}}}}||||||||fS)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)rrrrrrrrrrrtransformVectors zTransform.transformVectorcs,|dd\fdd|DS)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|](\}}||||fqSrr)rrrrrrrrrr sz.Transform.transformVectors..r)rZvectorsrr$rtransformVectorss zTransform.transformVectorscCs|dddd||fS)zReturn a new transformation, translated (offset) by x, y. :Example: >>> t = Transform() >>> t.translate(20, 30) >>> r r transformrrrrrr translates zTransform.translateNcCs"|dkr |}||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) >>> Nrr&r(rrrscales zTransform.scalecCs<ddl}t||}t||}|||| |ddfS)aReturn a new transformation, rotated by 'angle' (radians). :Example: >>> import math >>> t = Transform() >>> t.rotate(math.pi / 2) >>> rN)mathrcossinr')rZangler+csrrrrotates zTransform.rotatecCs*ddl}|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+rrrskews 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)) >>>  __class__rotherZxx1Zxy1Zyx1Zyy1Zdx1Zdy1Zxx2Zxy2Zyx2Zyy2Zdx2Zdy2rrrr's zTransform.transformc Cs|\}}}}}}|\}} } } } } ||||| || || |||| || || ||| || | || || S)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)) >>> r3r5rrrreverseTransform's zTransform.reverseTransformcCs|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) >>> )rr4)rrrrrrrZdetrrrinverse?s (&zTransform.inversecCsd|S)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]rrrrrtoPSSs zTransform.toPSr)returncCs t|S)z%Decompose into a DecomposedTransform.)r fromTransformr9rrr toDecomposed_szTransform.toDecomposedcCs|tkS)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 )rr9rrr__bool__cszTransform.__bool__cCsd|jjf|S)Nz<%s [%g %g %g %g %g %g]>)r4__name__r9rrr__repr__yszTransform.__repr__)rr)r N)rr)r? __module__ __qualname____doc__rfloat__annotations__rrrrrrr!r#r%r)r*r0r2r'r7r8r:r=r>r@rrrrrNs, N          cCstdddd||S)zReturn the identity transformation offset by x, y. :Example: >>> Offset(2, 3) >>> r rrrrrrrrscCs|dkr |}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) >>> NrrFrGrrrrs c@seZdZUdZdZeed<dZeed<dZeed<dZ eed<dZ eed<dZ eed <dZ eed <dZ eed <dZeed <ed dZddZdS)rzThe DecomposedTransform class implements a transformation with separate translate, rotation, scale, skew, and transformation-center components. r translateX translateYrotationr scaleXscaleYskewXskewYtCenterXtCenterYc Cs|\}}}}}}td|}|dkr4||9}||9}||||} d} d} } d} }|dksh|dkrt||||}|dkrt||nt|| } || |} } t||||||d} }n|dks|dkrht||||}tjd|dkr"t| |nt|| } | ||} } dt||||||} }nt||t| | || t| |t|dd S)Nr r)r+copysignsqrtacosatanpirdegrees)rr'abr.drrZsxdeltarJrKrLrMrNrr/rrrr<s@ &&(& z!DecomposedTransform.fromTransformcCsxt}||j|j|j|j}|t|j }| |j |j }| t|jt|j}||j |j }|S)zReturn the Transform() equivalent of this transformation. :Example: >>> DecomposedTransform(scaleX=2, scaleY=2).toTransform() >>> )rr)rHrOrIrPr0r+radiansrJr*rKrLr2rMrN)rtrrr toTransforms zDecomposedTransform.toTransformN)r?rArBrCrHrDrErIrJrKrLrMrNrOrP classmethodr<r_rrrrrs           -__main__)rr)N)rCr+typingrZ dataclassesr__all__r r rrrrrrrr?sysdoctestexittestmodfailedrrrrs(6   1 P