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Unformatted text preview: CSE 152 Homework 1 solution Question 1 a. In Euclidean coordinates, denote the line as y = ax + b, we have 1 = a + b pass through (1,1) 2 = 3a + b pass through (3,2) => a = 1/2, b = 1/2 => y = x/2 + 1/2 => x + 2y 1 = 0 b. In homogeneous coordinates, the line connecting (1,1) and (3,2) is (1,1,1) (3,2,1) = (1,2,1) => line equation: x + 2y 1 = 0 c. Four corners: A=(1,3), B=(2,4), C=(5,2), D=(2,1) => 4 edges AB: (1,3,1) (2,4,1) = (1,1,2) => x +y 2 = 0 BC: (2,4,1) (5,2,1) = (2,3,16) => 2x + 3y 16 = 0 CD: (5,2,1) (2,1,1) = (1,3,1) => x 3y +1 = 0 DA: (2,1,1) (1,3,1) = (2,1,5) => 2x y + 5 = 0 Two vanishing points AB CD = (1,1,2) (1,3,1) = (5,1,2) => (5/2, 1/2) in Euclidean BC DA = (2,3,16) (2,1,5) = (1,22,4) => (1/4, 22/4) in Euclidean Question 3 Homogeneous coordinates of the rectangle (4 corners): P 1 = (6, 3, 6, 1) T , P 2 = (3, 3, 6, 1) T , P 3 = (3, 3, 9, 1) T , P 4 = (6, 3, 9, 1) T a....
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This note was uploaded on 08/05/2011 for the course CSE 152 taught by Professor Staff during the Spring '08 term at UCSD.
 Spring '08
 staff

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