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Student Name: Class Account Username: Instructions: Read them carefully! The exam begins at 5:10pm and ends at 8:00pm. You must turn your exam in when time is announced 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 student’s 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: 223 + 5 You Scored: ________ + Extra _________ CS 184: Foundations of Computer Graphics page 1 of 16 Fall 2009 Prof. James O’Brien
1. Please fill in each of the blanks with an appropriate answer. 2 points each blank, 68 total The Euler integration scheme tends to cause simulations to “blow up.” The implicit version of this
scheme, known as _________________, is much more stable but has a tendency to damp
motions artificially.
Explicit integration schemes make use of the accelerations at the ____________ of each simu-
lation timestep. Inverse kinematics algorithms we discussed in class involve numerical root finding for a set of non-
linear equations and can be solved using _____________________________.
________________ colors consist of light at a single wavelengh.
________________ motion capture systems record the position and orientation of the sensors
on the subject.
The ________________ of a matrix can be computed using the singular value decomposition
algorithm. The tangent vectors of an parametric surface generally can be used to compute the surface
________________.
When representing __________________ in 3D using homogenized coordinates, the fourth
coordinate (i.e. “w”) will be one.
Temporal anti-aliasing is often called _____________________.
The __________________ method operates from the assumption that all surfaces in a scene
act like diffuse reflectors.
The final gather often is the most time consuming step of the _____________________
rendering method. Computing form factors is between patches often is the most time consuming step of the
_____________________ rendering method.
CS 184: Foundations of Computer Graphics page 2 of 16 Fall 2009 Prof. James O’Brien
The “B” in BSP-Tree stands for __________________.
__________________ is a special case of a point light source where the viewer is infinitely
far away. In the context of a scan-line renderer, Z-buffers are used for ________________________.
A bump map is used to change the __________________ vectors when shading an object.
When two curve segments join at a point and both curves approach that point with non-zero parallel
tangent vectors from opposite directions, the joining is said to be ______ continuous.
When two curve segments join at a point and both curves approach that point with non-parallel tan-
gent vectors, the joining is said to be ______ continuous.
NURBS are b-splines that use ________________________ for control points.
Steradians are the dimensionless units used to measure __________________.
When the view point used to generate a radiosity solution changes, updating the solution for the
new viewpoint recomputing __________________.
2. Answer the following questions with True (T) or False (F) 2 points each, 46 total ______ Cloth can be modeled reasonably well using a collection of particles attached by springs. ______ The pseudo inverse of a matrix can be computed using the Singular Value Decomposition (SVD) algorithm. ______ The Jacobian of a valid kinematic system will always be invertible. ______ Polished metallic surfaces typically have bright white specularities. ______ Radiance grows with distance along a straight line. ______ The implicit representation of a given geometric entity is unique. CS 184: Foundations of Computer Graphics page 4 of 16 Fall 2009 Prof. James O’Brien
______ The rods in the human eye have a flat spectral response function. ______ Under linear perspective projection, squares always appear as a square. ______ Under linear perspective projection, triangles always appear as a triangle. ______ Under orthographic projection, all sets of parallel lines will remain parallel. ______ Quaternions represent rotations as points in 4D space on the surface of a hypersphere. ______ Any set of non-intersecting polygons can be sorted in front-to-back order. ______ Ink-based color printers could be designed to use other colors besides cyan, magenta, and yellow. ______ Shining an ultraviolet light on scorpions induces a chemical response that causes them to glow green and become paralyzed, thus making them easy to find and safe to handle. ______ The force exerted by a spring with zero rest length is given by a function that is linear in terms of the endpoint locations. ______ Cubic Bézier curves will always be C 2 across segment boundaries. ______ Light fields are (ideally) records of the light passing through all points in a region of space in all directions. ______ In a kinematic skeleton, every body must have exactly one inboard joint. ______ Modern LCD displays have a dynamic range approximately twice that of the human eye. ______ A rotation matrix always has determinant of +/- π. ______ Pasteurized coordinates facilitate representing perspective and translation using matrices. ______ Ambient occlusion tends to enhance the appearance of surface detail. ______ The sky is blue because water vapor scatters red light. CS 184: Foundations of Computer Graphics page 5 of 16 Fall 2009 Prof. James O’Brien
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 8. Briefly state why interpolating transformation matrices by linearly interpolating the matrix components is a bad idea. 4 points CS 184: Foundations of Computer Graphics page 7 of 16 Fall 2009 Prof. James O’Brien
9. Below are two 4x4 homogenized transformation matrices. What does the first one do? How does the effect produced by the second one differ from that produced by the first? 4 points €
The first one will: The second one will:
10. Draw the convex hull of the shapes shown below. 6 points 11. The diagram below is the control polygon for a Bezier curve segment. Draw the curve and show how de Casteljau’s 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 CS 184: Foundations of Computer Graphics page 8 of 16 Fall 2009 Prof. James O’Brien
16. Consider the following equation and diagram:
Ls ( x , x
) = δ( x , x
) E ( x , x
) + Z S ρ x ( x , x
) Ls ( x
, x
) cos(θ
) cos(θ
) || x
− x
||
d x
n ˆ n ˆ x x x ! ! Explain what effects each of the following is responsible for. 10 points x , x ) = !( x , x ) E ( x , x ) + Z S " x ( x , x ) Ls ( x , x ) cos(# ) cos(# ) || x − x || 2 d x ________________________________ !( x , x ) E ( x , x ) + Z S " x ( x , x ) Ls ( x , x ) cos(# ) cos(# ) || x − x || 2 d x ________________________________ x , x ) cos(# ) cos(# ) || x − x || 2 d x ________________________________ s ( x , x ) cos(# ) cos(# ) || x − x || 2 d x ________________________________ , x ) + Z S " x ( x , x ) Ls ( x , x ) cos(# ) cos(# ) || x − x || 2 d x ________________________________ CS 184: Foundations of Computer Graphics page 10 of 16 Fall 2009 Prof. James O’Brien
17. If a surface is defined explicitly by the function x^ =^ f^ (u,^ v)^ , write out the equation you would use to compute the surface’s normal at some point****. 4 points 18. Consider this diagram showing a four-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 loca- tion, what is the size of the Jacobian matrix we will be working with? 3 points Draw any one configuration of the arm where two columns of the Jacobian will be parallel vectors. 5 points In the drawing you made above, clearly show the direction of the parallel vectors. 3 points In the drawing you made, will the Jacobian have rank less than, greater than, or equal to two? 3 points When will the this system’s Jacobian be fully invertable? 3 points CS 184: Foundations of Computer Graphics page 11 of 16 Fall 2009 Prof. James O’Brien
22. The two images below show two 12 point versions of the letter “A” that have been signifi- cantly enlarged. Concisely explain the most likely difference between the two fonts used in the images. 4 points
Assignmen
Poin
23. The following equation describes how the radiosity at patch Pi is a function of the radiosity
of other patches. Circle the part(s) that are responsible for taking into account the visibility
of other patches when viewed from Pi. 3 points
Hi = Ei + ρ i ∑
j
Hj
Z
S j
δ i j
cos(θ i ) cos(θ j )
2 π|| c i − x ||
d x
24. The following are the response curves for the cones in the human eye. Which type of cone is most sensitive to red light? 2 point CS 184: Foundations of Computer Graphics page 13 of 16 Fall 2009 Prof. James O’Brien
25. Consider the diagram below. A location has been marked on the surface. Indicate a viewer position such that a viewer looking at the surface from that position would see a specular highlight on the surface at the marked location. 3 points - 8 -
- Consider the diagram below. A location has been marked on the surface. Indicate a viewer position such that a viewer looking at the surface from that position would see a specular highlight on the surface at the marked location. 3 points
- 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
- When clipping two arbitrarily oriented squares against each other to find their intersection (in 2 D), what is the maximum number of sides that the resulting shape may have? 2 points 26. Below is a diagram showing a bar that has been rotated 90 degrees about the point indicated with a circle. If intermediate positions were generated by linearly interpolating the transfor- mation matrices, how would the point indicated by the star move? Give your answer by drawing the path of the star. 4 points CS 184: Foundations of Computer Graphics page 14 of 16 Fall 2009 Prof. James O’Brien
Final project / Assignment 6 report submission instructions:
**- The report for your final project is due tomorrow (Friday the 18th) no later than 5pm.
- Reports should be posted as a webpage linked from your class home page.
- You may, and probably should, include images and videos.
- The names and login IDs for all project members should appear on your report.
- There is no leeway for accepting late submissions. Once I go home on Friday I will not be** **back on campus until after grades have been submitted.
- Submissions by e-mail will not be accepted. They will be deleted.
- Make sure your report accurately and fully describes your results. Your grade will be** **based entirely on this report.
- Use the submission system to turn in your code as if it were assignment 6 (even if you did** a project). We will spot check to make sure the code you submit matches the results shown in your report. CS 184: Foundations of Computer Graphics page 16 of 16 Fall 2009 Prof. James O’Brien
