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Unformatted text preview: CS221 Midterm: Question 7 supplement solution 1 CS 221, Fall 2009 Practice Midterm Solutions: Question 7 Supplement Computer vision question: Your kiteflying robot needs to know which direction the wind is blowing and has fortuitously found a weathervane with its arrow at known height Y . The robot identifies a point P at the back of the arrow and a point P ′ at the front of the arrow, both at height Y. Their coordinates as projected onto the robot’s image plane are ( x, y ) and ( x ′ , y ′ ), respectively. The robot is facing due east with the Zaxis of its camera perfectly horizontal and at height 0. The Xaxis is pointing due north. The focal length of the camera is known to be f . The length of the vane is unknown. In what direction is the wind blowing? (Assume that the wind is blowing in the direction from P to P ′ .) Report your answer as an expression for the angle between due east and the wind. I.e., report the angle t as pictured in the diagram below, as a function of x, y, x ′ , y ′ , Y and f . ( Hint: Because the height Y of the vane is known, you should be able to find the 3D coordinates of points P and P ′ .) E N S W P P’ t X Z (Yaxis coming out of plane of paper) CS221 Midterm: Question 7 supplement solution...
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 Fall '09
 KOLLER,NG
 Euclidean geometry, Polar coordinate system, Right angle

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