15, December 2006
Name __________________
CS445 Final Exam
Fall 2006
1. (max = 14) 7. 2. (max = 10) 8. 3. (max = 17) 9. Final Score _____________(max=95)
(max = 25) (max = 9) (max = 20)
1. (7 pts each, 14 pts total) 3D Transforms in homogeneous coordinates: Write down the 4x4 matrix transform (or sequence of matrix transforms) needed to perform each of the following transformations. If more than one matrix is needed, make sure the order of multiplication is clear. You do not need to multiply the matrices out. You also do not need to numerically evaluate any trig functions. a. Rotate about the y-axis by 25 degrees. Also give the inverse.
b. Scale by 2 along a direction defined by the points (0,0,0) and (1,1,0). Also give the inverse.
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2. (5 pts each, 10 pts total) What is a 3x3 convolution filter for: a. Blurring an image
b. Detecting only vertical lines.
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3. (17 pts total) Bitmaps can be used for masking images. Suppose you want to write code to generate a bitmap that will mask a 128x48 image. The bitmap will be vertical stripes where each stripe is 4 pixels wide. a. (3 pts) How many bits are required to mask a single pixel? ____________ b. (4 pts) If you store this mask in a 2D byte array:
byte[][] stripes = new byte[row][col];
then what is the value of row? ____________ what is the value of col? ____________
c. (10 pts) Write a for-loop that will set the values of the stripes array:
3
4. pts (25 total) Suppose you want to write a program that models and controls the movement for the upper body of a person consisting of a torso, upper and lower arms, head, and hands. The head can turn back and forth, the arms can rotate at the shoulders and elbows, and the hands can rotate at the wrists. One should also be able to move the entire body together. a. (20 pts) What is the scene graph for this body? Assume that you use only transformed spheres and cube shapes as shown in the picture below. You should indicate the type of transformation or node: R = rotate, S = scale, T = translate, G=group node, C = cube, Sp=sphere. You do not need to indicate the size of the transformation or specific angles or axes involved. Label the parts of the scene graph which correspond to the different body parts.
4
b. (5 pts) Pivot p...