Final Exam 1 08

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Unformatted text preview: 4 .ecafrus 15. When computing the boolean intersection of two arbitrarily oriented triangles (in 2D), what is the minimum and maximum number of sides that a resulting polygon could have? Draw an example of the minimum and maximum shapes. 3 points 16. Write out a implicit equation for a sphere. 4 points 17. Write out an parametric equation for a line in 3D. 3 points Final Exam CS 184: Foundations of Computer Graphics Fall 2008 Prof. James O’Brien page 11 of 15 18. 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 ________________________________ ￿ cos(# ) cos(________________________________ # ) ￿￿ dx s(x , x ) ￿ Z ||x￿ − x￿￿||2 ￿ ￿￿ cos(# ) cos(# ) x￿, x￿￿) , x￿) + "x￿(x, x￿￿)Ls(________________________________￿￿ dx ￿ − x￿￿||2 ||x S ￿ ￿￿ ￿ ￿￿ Fin...
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This note was uploaded on 01/24/2014 for the course CS 184 taught by Professor Staff during the Fall '08 term at Berkeley.

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