2.7soln - Solutions to even problems from section 2.7 4...

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Unformatted text preview: Solutions to even problems from section 2.7 4. Find the 3 × 3 matrix that produces the following composite 2D transformation using homo- geneous coordinates: Translate by (- 2 , 3), and then scale the x-coordinate by . 8 and the y-coordinate by 1 . 2. Solution: The 3 × 3 matrix for translating by (- 2 , 3) is 1 0- 2 0 1 3 0 0 1 whereas the 3 × 3 matrix for scaling the x-coordinate by . 8 and the y-coordinate by 1 . 2 is . 8 0 0 0 1 . 2 0 0 1 . Thus the 3 × 3 matrix for the composite 2D transformation is found by multiplying the matrices together (in the correct order): . 8 0 0 0 1 . 2 0 0 1 1 0- 2 0 1 3 0 0 1 = . 8- 1 . 6 0 1 . 2 3 . 6 1 8. Find the 3 × 3 matrix that produces the following composite 2D transformation using homo- geneous coordinates: Rotate points 45 ◦ about the point (3 , 7). Solution: To rotate 45 ◦ about the point (3 , 7) we first translate by (- 3 ,- 7), then we rotate 45 ◦ about the origin, and finally we translate by (3...
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This note was uploaded on 01/28/2010 for the course MATH 307 taught by Professor Axenovich during the Fall '08 term at Iowa State.

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2.7soln - Solutions to even problems from section 2.7 4...

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