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INTRO TO TRANSFORMATIONS.ppt

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TRANSFORMATIONS Translation x’= x + tx y’= y + ty The translation distance pair (tx,ty) is called a translation vector or shift vector P = x1 P’= x1’ T = tx x2 x2’ ty This allows us to write the two dimensional translation equations in the matrix form P’ = P + T Translation Illustration P’ P Rotation 1 (x’,y’) r θ r (x,y) Ф The original coordinates of the point in Polar Coordinates are X= r cos (Ф) y = r sin (Ф) Rotation 2 ã x’ = r cos (Ф + θ) = r cos Ф cos θ – r sin Ф sin θ Y’ =
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  TRANSFORMATIONS  Translation x’= x + tx   y’= y + ty  The translation distance pair (tx,ty) is called a translation vector   or shift vector P = x1 P’= x1’ T = tx   x2 x2’ ty  This allows us to write the two dimensional translation equations in the matrix form P’ = P + T  Translation Illustration P’  P  Rotation 1 r r Ф   (x,y) (x’,y’)  The srcinal coordinates of the point in Polar Coordinates are X= r cos ( Ф ) y = r sin ( Ф ) θ  
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