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Student Name: Class Account Username: Instructions: Read them carefully! The exam begins at 12:40pm and ends at 3:30pm. You must turn your exam in when time is an- nounced or risk not having it accepted. Make sure you fill in your name and the above information, and that you sign below. Anonymous tests will not be graded. Write legibly. If the person grading the test cannot read something, he/she will simply assume that you meant the illegible portion as a note to yourself and they will ignore it. If you lose points because part of your answer could not be read, you will not be given the opportunity to explain what it says. Be clear and concise. The answers to most questions should be short. If you find yourself writing an excessively long response, you may want to think more carefully about the question. Long rambling answers generally get fewer points that short ones do because there are more opportunities to mark something wrong. You may use two pages of notes while taking the exam. You may not ask questions of other students, look at another studentās exam, use a textbook, use a phone or calculator, or seek any other form of assistance. In summary: do not cheat. Persons caught cheating will be subject to disciplinary action. Do not ask questions during the exam. Most questions are unnecessary and they disturb other stu- dents. Figuring out what the exam question is asking is part of the test. If you think you have to make some unusual assumption to answer a problem, note what that assumption is on the test. I have read these instructions, I understand them, and I will follow them. _Your Signature: ____________________________________ Date: ____________________________________ Student ID: ____________________________________ Total Points: 133 + 10 You Scored: ________ + Extra _________ CS 184: Foundations of Computer Graphics page 1 of 12 Spring 2008 Prof. James OāBrien
1. Answer the following questions with True (T) or False (F) 1 point each ______ Cloth can be modeled reasonably well using a collection of particles attached by springs. ______ Particle systems have become obsolete and are seldom used in modern applications. ______ All types of numerical integration are basically the same and there is no strong reason to prefer one method over another. ______ Active optical motion capture systems are make use of multiple cameras to determine the location of retroactive markers. ______ Magnetic motion capture systems use trackers that return orientation and position infor- mation. ______ The pseudo inverse of a matrix can be computed using the Singular Value Decomposition (SVD) algorithm. ______ It is impossible to write a robust IK solver and as a result people typically use motion cap- ture algorithms. ______ Standard kinematic algorithms assume that articulated structures will have a ring topology. ______ In 2D all IK problems have simple closed-form solutions. ______ In 3D all IK problems have simple closed-form solutions. ______ The Jacobian of a valid kinematic system will never be invertible. ______ When representing directions in 3D using homogenized coordinates, the fourth coordinate ( i.e. āwā) will be zero. ______ Overly large time-steps can cause a spring and mass simulation to go unstable. ______ Motion capture data is often used in video games. ______ Animations lacking motion blur may suffer from unnatural looking artifacts. ______ The rendering equation discussed in class does not account for atmospheric scattering. CS 184: Foundations of Computer Graphics page 2 of 12 Spring 2008 Prof. James OāBrien
2. Write the regular expression that concisely describes the light paths captured by the given rendering method. (L = Light, D = Diffuse, S = Specular, E = Eye) 8 points The real world _____________________ Local illumination _____________________ Basic raytracing _____________________ **Radiosity _____________________
- Imagine that you have a RGB monitor where the wires have been swapped so that the red,** green, and blue outputs from the computer have been respectively attached to the green, blue, and red inputs on the monitor. When one attempts to display the following colors, what colors will actually appear on the screen? 8 points ! Red!! _______________________ ! Green!! _______________________ ! Blue!! _______________________ ! Cyan!! _______________________ ! Magenta! _______________________ ! Yellow!! _______________________ ! Black!! _______________________ ! White!! _______________________ 4. If a surface is defined implicitly by the function f^ (x) =^0 , write out the equation you would use to compute the surfaceās normal at some point****. (Assume that negative values are inside the surface.) 4 points 5. If a surface is defined explicitly by the function x^ =^ f^ (u,^ v)^ , write out the equation you would use to compute the surfaceās normal at some point****. 4 points CS 184: Foundations of Computer Graphics page 4 of 12 Spring 2008 Prof. James OāBrien
6. Here is a piece of mesh. Draw the result of applying one iteration of Catmull-Clark subdivi- sion. Then circle all vertices (both original and the new ones you added) that are extraordi- nary. Note: I am only interested in the topology of your answer. 7 points 7. Name a phenomenon that can be modeled easily using radiosity but that cannot be modeled with a basic ray-tracing algorithm. Give an example. 3 points CS 184: Foundations of Computer Graphics page 5 of 12 Spring 2008 Prof. James OāBrien
10. The diagram below is the control polygon for a Bezier curve segment. Draw the curve and show how de Casteljauās algorithm can be used to subdivide the curve into two halves. Make sure your drawing is geometrically reasonable and shows correct curve tangents for the the beginning, middle, and end of each segment. 5 points 11. Given a 3x3 matrix that encodes a 3D transformation, how does singular value decomposi- tion separate the matrix into scale and rotation components? 4 points CS 184: Foundations of Computer Graphics page 7 of 12 Spring 2008 Prof. James OāBrien
12. There are 8 functions plotted below. Neatly cross out the ones that are not part of the cubic Hermite basis set. Next to the remaining plots write what feature of the curve that basis con- trols. 6 points 0.2 0.4 0.6 0.8 1
1 0.2 0.4 0.6 0.8 1
1 0.2 0.4 0.6 0.8 1
0.2 0.4 0.6 0.8 1 -0. -0. -0. -0. -0. -0. -0. 0.2 0.4 0.6 0.8 1
1
2 0.2 0.4 0.6 0.8 1
1 0.2 0.4 0.6 0.8 1
1 0.2 0.4 0.6 0.8 1
1 A B C D E F G H For those that are NOT Hermite basis functions write a single short sentence that explains why they could not be. Your reason should be simple. Note: āIt isnāt what I have in my notes,ā āit wonāt fit,ā āit doesnāt solve the equations,ā or other generic answers will not be accepted. 4 points Letter Reason _____ __________________________________________________ _____ __________________________________________________ _____ __________________________________________________ _____ __________________________________________________ CS 184: Foundations of Computer Graphics page 8 of 12 Spring 2008 Prof. James OāBrien
17. In the context of doing inverse kinematics, draw an example configuration for a two-link arm that results in a singular Jacobian. Your example arm should have links that are connected by a rotation joint and whose root link is attached to ground with a rotation joint. Make sure your diagram is clear. Use an X to indicate the goal point. 3 points - 6 -
- In the context of doing inverse kinematics problems, when is the Jacobian singular? Draw an example using a two-link arm whose links are connected by a rotation joint and whose root link is attached to ground with a rotation joint. Make sure your diagram is clear. Use an X to indicate the goal point. 4 points
- Concisely describe what āfoot skateā is and why it is a problem. 2 points
- On the spring diagram below, draw the springs that should be added for the structure to resist shear. 3 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 =
- Write out a parametric equation for a sphere.** 4 points 20. Write out an implicit equation for a line in 3D. 3 points CS 184: Foundations of Computer Graphics page 10 of 12 Spring 2008 Prof. James OāBrien
21. Consider the following equation and diagram:
Ls ( x , x
) = Ī“( x , x
)
ļææ E ( x , x
) +
Z
S
Ļ x ļææ( x , x
) Ls ( x
, x
)
cos(Īø
) cos(Īø
)
|| x
ā x
d x
n Ėļææ n Ėļææļææ x ļææļææ x ļææ x !ļææ !ļææļææ Explain what effects each of the following is responsible for. 15 points
x , x
) = !( x , x
)
ļææ E ( x , x
Z
S
" x ļææ( x , x
) Ls ( x
, x
)
cos(#
) cos(#
)
|| x
ā x
d x
________________________________
!( x , x
)
ļææ E ( x , x
Z
S
" x ļææ( x , x
) Ls ( x
, x
)
cos(#
) cos(#
)
|| x
ā x
d x
________________________________
x
, x
)
cos(#
) cos(#
)
|| x
ā x
d x
________________________________
s ( x
, x
)
cos(#
) cos(#
)
|| x
ā x
d x
________________________________
, x
Z
S
" x ļææ( x , x
) Ls ( x
, x
)
cos(#
) cos(#
)
|| x
ā x
d x
________________________________ CS 184: Foundations of Computer Graphics page 11 of 12 Spring 2008 Prof. James OāBrien
