If we are solving an ik problem to place the tip of

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Unformatted text preview: al Exam CS 184: Foundations of Computer Graphics Fall 2008 Prof. James O’Brien page 12 of 15 19. Consider this diagram showing a three-joint arm in 2D where each joint is a simple pin joint and the base is fixed in space. If we are solving an IK problem to place the tip of the arm (the black dot) at a particular location, what is the size of the Jacobian matrix we will be working with? 3 points Draw any one configuration of the arm where the rows of the Jacobian will not be linearly independent. 5 points Draw any one configuration of the arm where the columns of the Jacobian will not be linearly independent. 5 points Important: You may not draw the same configuration twice! Final Exam CS 184: Foundations of Computer Graphics Fall 2008 Prof. James O’Brien page 13 of 15 20. Name two types of useful image effects that would require shooting more than one ray per pixel in a ray-tracer. 4 points 21. The “Painter’s algorithm” sorts polygons by the depth of their center of gravity, and draws the furthest polygon first. Sketch one example where this algorithm fails. 3 points 22. Consider the two diagrams below. All four surfaces are identical ideal diffuse reflectors. In each diagram circle the surface that will appear brighter to the observer. 4 points Diagram #1 Diagram #2 Final Exam CS 184: Foundations of Computer Graphics Fall 2008 Prof. James O’Brien EXTRA CREDIT page 14 of 15 5 points Given a line and a sphere: Parametric Line: l(t) = a + t b Implicit Sphere: s(x) = ||c − x|| − r = 0 Write out an e...
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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 University of California, Berkeley.

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