CS480 Problem Set 1

CS480 Problem Set 1 - CS480/CS680 Problem Set 1 Due in...

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CS480/CS680 Problem Set 1 Due in class Tuesday, February 12 at the beginning of lecture. Please prepare the answers to these questions, neatly written or typed, on separate paper. 1. (a) (3 points) Write a 4 × 4 homogeneous transform matrix M that when applied to a point ( x,y,z, 1) yields ( x 0 ,y 0 ,z 0 ,w 0 ) where x 0 = - 1 2 x - 1 2 z + a y 0 = - 2 y z 0 = 1 2 z - 1 2 x + a w 0 = 1 (b) (12 points)In words , what four basic computer graphics transforms occur when we apply M to a 3D point? Give a homogeneous transform matrix for each, and show the order in which they are multiplied. 2. (15 points) We have a unit cube centered at the point c = (1 . 5 , 0 . 5 , 2 . 5) . Derive the ho- mogeneous transformation matrix that will rotate the cube by angle θ around a vector in the direction v = (-1,0,-1). The pivot point for the rotation is the cube’s center c . 3. Use quaternions in your answers to the following. (5 points) Prove that in general two 3D rotations about different rotation axes do not
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