Final Exam 09

6 points 15 given two points a and b write out an

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Unformatted text preview: cover the sphere once. 6 points 15. Given two points, A and B, write out an implicit equation for the line in 3D that contains both points. You may assume A and B are distinct points. 4 points Final Exam CS 184: Foundations of Computer Graphics Fall 2009 Prof. James O’Brien page 10 of 16 16. Consider the following equation and diagram: ￿ ￿ Z cos(θ￿) cos(θ￿￿) ￿￿ Ls(x, x￿) = δ(x, x￿) E (x, x￿) + ρx￿(x, x￿￿)Ls(x￿, x￿￿) dx ||x￿ − x￿￿||2 S x ˆ n￿ !￿ x￿ Explain what effects each of the following is responsible for. x￿￿ !￿￿ ˆ n￿￿ 10 points ￿ ￿ Z ￿ ￿￿ ￿￿ ￿ ￿￿ cos(# ) cos(# ) ￿￿ ￿ ￿ ￿ ￿ (x, x )Ls(x , x ) x, x ) = !(x, x ) E (x_______________________________ , x ) + "x dx _ ||x￿ − x￿￿￿|2 | S ￿ Z cos(#￿) cos(#￿￿) ￿￿ "x￿(￿, x￿￿)Ls(x￿, x￿￿) x (x, x￿) E (x, x￿) + ________________________________ ￿ dx ||x − x￿￿||2 ￿ ￿￿S ￿ ￿￿ cos(# ) cos(# ) ￿￿ x ,x ) dx ￿ − x￿￿||2 ||x...
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