8. Consider the transformation below: Before ty After 5 +X 5 +x -y Write down a

Question

8. Consider the transformation below: Before ty After 5 +X 5 +x -y Write down a sequence of three transformations that when applied to each point of the "Before" shape results in the illustrated "After" shape. Numer your transformations 1,2 and 3 to show which order they should be applied in. Use R(degrees), T(x,y) and S(x,y) to denote rotate, translate and scale transforms respectively. You don't necessarily have to use one of each to solve this problem. a. b. Write down the actual matrices for your three transforms from part a (3x3 matrices for 2-dimensional homogeneous coordinates) at the bottom of the space below. Pay attention to the order of your matrices (notice how the transformed vector [x, y', W] is being computed from the original vector [x, y, w]). You can use sines/cosines/tangents in your answer without computing their numerical values). tw

Explanation / Answer

a.

1 : S(2-x,y)

2 : T(x+1,y)

3. R(45)

b.

[2-x 0 0; y 0 0; w 0 0]*[x+1 0 0 ; y 0 0 ; w 0 0]*[xcos45 0 0 ; ycos45 0 0 ; w 0 0]

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