Assignment 2

# Assignment 2 - Assignment 2(Non-Programming Programming...

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1 Assignment 2 (Non-Programming & Programming) Worth: 5 points Due Date and Time: Before class begins at 12:20 pm on 06/12/2007. Copy zipped programming submission to CS250 web page. Place your stapled non-programming submission in CS250 submission box in front office. Topics Introduction to Graphics Pipe Transforms: Scaling, Rotation, Translation, and View Non-Programming Section: Statement (Worth 50 points) Part 1: First, solve all three parts of exercise 5.15 from the text. The first part of exercise 5.15 is to derive the transformation matrix that rotates by an angle θ about u ˆ . The matrix is to be derived by composing the matrix that rotates u ˆ into the Z axis (call this M ) with a rotation transform ( ) z R , then composing this result with 1 M . The resultant matrix is written as: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + + + + + + 1 0 0 0 0 1 cos sin cos 1 sin cos 1 0 sin cos 1 1 cos sin cos 1 0 sin cos 1 sin cos 1 1 cos 2 2 2 2 2 2 z z x z y y x z x z y y y z y x y x z z y x x x u u u u u u u u u u u u u u u u u u u u u u u u The second part is to verify that, if u ˆ is a principal axis, the matrix reduces to x R , y R , or z R . Finally, explain why negating u ˆ and leaves the result unchanged. Part 2: Assume that we wish to align p ˆ to q ˆ by rotation in a plane containing both. As explained in class, alignment from

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Assignment 2 - Assignment 2(Non-Programming Programming...

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