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lecture-08-2d-transformations-part-ii

# lecture-08-2d-transformations-part-ii - 2DTransformations...

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2D Transformations Part II Composite & Other Transformations

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Composite Translation P t t T t t T P y x y x = ) , ( ) , ( ' 1 1 2 2 P t t t t T y y x x + + = ) , ( 2 1 2 1 = 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 ' ' 1 1 2 2 y x t t t t y x y x y x + + = 1 1 0 0 1 0 0 1 1 ' ' 2 1 2 1 y x t t t t y x y y x x
Composite Scaling P s s S s s S P y x y x = ) , ( ) , ( ' 1 1 2 2 P s s s s S y y x x = ) , ( 2 1 2 1 = 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ' ' 1 1 2 2 y x s s s s y x y x y x = 1 1 0 0 0 0 0 0 1 ' ' 2 1 2 1 y x s s s s y x y y x x

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Composite Rotation P R P R R P + = = ) ( ) ( ) ( ' 2 1 1 2 θ θ θ θ
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