Make sure and whose root link is attached to ground

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Unformatted text preview: indicate the goal point. 3 points diagram is clear. Use an X to indicate the goal point. 9. 4 points Concisely describe what “foot skate” is and why it is a problem. 2 points 18. Suppose you have a color C = (c,m,y) in the CMY subtractive color space. How would you express this color in the RGB additive color space? 4 points r= g= b 10. On= the spring diagram below, draw the springs that should be added for the structure to resist shear. 3 points 19. Write out a parametric equation for a sphere. 4 points 20. Write out an implicit equation for a line in 3D. 3 points -6- Final Exam CS 184: Foundations of Computer Graphics Spring 2008 Prof. James O’Brien page 11 of 12 21. 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￿￿ 15 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 ￿ ￿￿ ￿ ￿￿ Final Exam CS 184: Foundations of Computer Graphics Spring 2008 Prof. James O’Brien EXTRA CREDIT page 12 of 12 10 points Given two planes in R3 described by the implicit equations: n1 · x − f1 = 0 Plane 1: n2 · x − f2 = 0 Plane 2: one can generally write the parametric equation for their line of intersection as: Line of intersection: x = a + td Write out equations for computing both a and d . Note any situations where your equations would not have a solution. Your answer must be neat and clear. No points will be awarded for imprecise answers that do not fit in the boxes. Do not attempt this question until you have completed the rest of the exam! d= 3 points a= 6 points Fails when: 1 point...
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