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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 kite-flying 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 Z-axis of its camera perfectly horizontal and at height 0. The X-axis 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 3-D coordinates of points P and P ′ .) E N S W P P’ t X Z (Y-axis coming out of plane of paper) CS221 Midterm: Question 7 supplement solution...
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- Fall '09
- Euclidean geometry, Polar coordinate system, Right angle