Computer Science 184 - Fall 1996 - Barsky - Midterm 1

# Computer Science 184 - Fall 1996 - Barsky - Midterm 1 - CS...

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CS 184, Midterm Exam #1, Fall 1996 CS 184, Fall 1996 Midterm #1 Professor: unknown Problem #1, Transformations (8pts) All questions assume a right handed coordinate system . Circle the correct answer: (2 pts each) a) In 3 space, two rotations about arbitrary axes can alaways be applied in either order to get the same result. True / False b) In 3-space, two rotations about principal axes can always be applied in either order to get the same result. True / False c) In 3-space, two uniform scalings (scaling with different scale factors in x, y, and z) can always be applied in either order to get the same result. True / False Short answer: (2 pts each) d) In a right handed coordinate system, in what direction does the positive y-axis point after a 90 degree rotation around the positive x-axis? Problem #2, Display Hardware (12 pts) Suppose we have a frame buffer with x x y pixels n bit planes for an index into the color table w bits for each of red, green, and blue in the color table 5 PM file:///C|/Documents%20and%20Settings/Jason%20Raft. ..-%20Fall%201996%20-%20Barsky%20-%20Midterm%201.htm (1 of 9)1/27/2007 5:24:0

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CS 184, Midterm Exam #1, Fall 1996 MAKE NO ASSUMPTIONS ABOUT THE RELATIVE MAGNITUDES OF x, y, n, AND w . a) How many colors can we choose from for our color table? b) What is the maximum number of different colors we can have in our color table at one time? c) What is the maximum number of different colors that can be displayed on our screem at one time? Problem #3, Vanishing Points (18 pts) In this problem, we use this perspective projection: The eye is at the point z=1 on the z-axis: COP = (0,0,1). The projection plane is at z=2: VRP = (0,0,2). The up vector is along the y-axis: VUP = (0,1,0). The view window is from (-1,-1) to (1,1). a) What is the vanishing point for the family of lines: p 0 + t (1,1,1)? b) Describe the set of lines whose vanishing point is ( x , y ,2. c) what is the 4x4 matrix that will compute this projection? (You may express this as a product of 4x4 matrices if you prefer.) Problem #4, is nonexistant Problem #5, Sample Point Algorithms for Scan Conversion (12 pts) 5 PM file:///C|/Documents%20and%20Settings/Jason%20Raft. ..-%20Fall%201996%20-%20Barsky%20-%20Midterm%201.htm (2 of 9)1/27/2007 5:24:0
CS 184, Midterm Exam #1, Fall 1996 The images on the left of this figure illustrate a sample point scan conversion algorithm that uses a sample point somewhere on the edge of a pixel. The thick lines indicate polygon boundaries. The shaded regions indicate pixels that were determined to be interior based on the algorithm. All of the vertices of polygons in this figure lie exactly on pixel grid lines or exactly halfway between pixel grid lines. a) What is the sample point for this algorithm? Draw a pixel and indicate the sample point.

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## This note was uploaded on 05/17/2009 for the course CS 184 taught by Professor Staff during the Spring '08 term at Berkeley.

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Computer Science 184 - Fall 1996 - Barsky - Midterm 1 - CS...

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