lecture-07-2d-transformations-part-i

# Lecture-07-2d-transf - 2DTransformations PartI Translation,Scaling&Rotation Basic transformations Translation Scaling Rotation Purposes To move the

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2D Transformations Part I Translation, Scaling & Rotation

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Geometric Transformations Basic transformations: Translation Scaling Rotation Purposes: To move the position of objects To alter the shape / size of objects To change the orientation of objects
Translation P’ = P + T x t x x + = ' y t y y + = ' P’ P

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Translation In matrix form: = = = y x t t T y x P y x P , , ' ' ' + = y x t t y x y x ' '
Scaling P’ = S.P In matrix form: x s x x = ' y s y y = ' = y x s s y x y x 0 0 ' '

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Rotation P’ = R(θ).P In matrix form: θ sin cos ' y x x - = cos sin ' y x y + = - = y x y x cos sin sin cos ' ' r r Ф (x,y) (x’,y’) θ
Basics of Trigonometry  sin A = a/c = cos A= b/c = tan A = a/b = 2 1 √3 3 1 2 3 2 1

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## This note was uploaded on 04/05/2010 for the course COMPUTER S 876 taught by Professor Ch during the Spring '10 term at Amirkabir University of Technology.

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Lecture-07-2d-transf - 2DTransformations PartI Translation,Scaling&Rotation Basic transformations Translation Scaling Rotation Purposes To move the

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