02-Xfmns_1

02-Xfmns_1 - Transformations Why use transformations? ! ! !...

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Transformations • Why use transformations? ! Create object in convenient coordinates ! Reuse basic shape multiple times ! Hierarchical modeling ! System independent ! Virtual cameras
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Translation z y x z y x t t t =+ z y x t t t T z y x ) , , ( z y x z y x t t t ' ' ' z y x
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Properties of Translation v = v ) 0 , 0 , 0 ( T = v ) , , ( ) , , ( z y x z y x t t t T s s s T = = v ) , , ( 1 z y x t t t T v ) , , ( ) , , ( z y x z y x t t t T s s s T v ) , , ( ) , , ( z y x z y x s s s T t t t T v ) , , ( z z y y x x t s t s t s T + + + v ) , , ( z y x t t t T
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Rotations (2D) φ sin cos r y r x = = θ cos ) ( ) cos ( ' ) ( cos ) cos ( ' r r y r r x + = = ) sin( ' ) cos( ' + = + = r y r x cos cos ) cos cos ) cos( + = + = + cos ' cos ' y x y y x x + = = y x , ' , ' y x x y
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Rotations 2D • So in matrix notation = y x y x θ cos sin cos ' '
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02-Xfmns_1 - Transformations Why use transformations? ! ! !...

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