- 1 - CS 184: FOUNDATIONS OF COMPUTER GRAPHICS FALL 2005 PROF. JAMES O’BRIEN FINAL EXAM Your Name: ___________________________ Your Class Computer Account: cs184-_____ Room: _________ Your Student ID#: _______________________ 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. 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. Most questions are unnecessary and they disturb other students. 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. 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. Total Points: 116 You Scored: ________ Extra Credit Points: 10 You Scored: ________ I have read these instructions, I understand them, and I will follow them. Your Signature: ____________________________________- 2 - 1. Answer the following with true (T) or False(F) 1 point each _____ continuity does not always imply . _____ The Bezier basis functions are affine invariant. _____ The Hermite basis functions have local support. _____ Cubic spline surfaces can be ray-traced without first polygonizing them. _____ Key frame animation becomes trivially easy when inverse kinematics are used. _____ Animation of human characters rarely done using motion capture. _____ Generating high-quality animations requires either Arwen sampling or Aragorn filtering to remove motion blur. _____ Advanced methods for rendering arbitrary images in constant time exist, but we did not cover them in class. _____ The fully implicit version of Euler’s method (a.k.a. backwards Euler) is unconditionally stable. _____ The singular values of a rotation matrix are the amounts of rotation abut the X,Y, and Z axes. _____ The human eye is uniformly sensitive to all frequencies of visible light. _____ Perspective transformations distort straight lines into circles. _____ Radiosity methods are optimized for rendering scenes with diffuse surfaces. _____ Final gathering can be used with both photon mapping and radiosity. _____ Some motion capture systems use magnetic fields to determine the location and orientation of tracker objects. _____ Cubic B-Splines can be exactly converted to quartic B-splines.- 3 - 1. Answer the following with true (T) or False(F) 1 point each [Continued] _____ When applying transformations to a 3D scene, the transformation applied to normal vectors should have any translation part doubled. _____ Most useful cubic basis functions have both the interpolation and convex hull properties. _____ The human eye has three types of light receptor. _____ Pixel-based image representations have infinite resolution. _____ A good scan-conversion algorithm has the property that when given a set of non-overlapping polygons, every pixel “belongs” to at most one single polygon. _____ Non-zero winding number and parity testing will produce the same result for a polygon with non-self-intersecting boundary. _____ A series of transformations which are all 3D rotations can be permuted and the result will not change. _____ Bump-mapping will not change an object’s silhouette. _____ Tensor-product surfaces are built by letting the control points of a curve vary according to some other curves. _____ Catmull-Clark subdivision only works on regular meshes. _____ Cubic polynomial basis functions can be used to build interesting ! C5 curves. _____ Particle systems simulate objects such as waterfalls by modeling the interactions between individual molecules. _____ Particles can be used to render smoke. _____ Motion graphs are plots showing where joints are located in a figure. _____ The result of applying subdivision to a cubic curve is two quadratic curves. _____ Raytracing can be accelerated using BSP-Trees or K-D Trees.- 4 - 2. Imagine that you have an RGB monitor where the red and blue phospors have been swapped. When one attempts to display the following, what color will actually appear on the display? 4 points Red ___________________________ Green ___________________________ Blue ___________________________ Yellow ___________________________ Cyan ___________________________ Magenta ___________________________ Black ___________________________ White ___________________________ 3. The diagram below shows control points for a curve made by joining two cubic Bezier segments. However control point #5 has been removed. Indicate location(s) where #5 may be placed to achieve ! C1 continuity and where it may be placed to achieve ! G1 continuity. Clearly label your diagram. 5 points- 5 - 4. Give two examples of specific phenomena that cannot be computed with a local illumination method. For each, name an algorithm that could compute the phenomena. 4 points 5. When computing the Boolean intersection of two arbitrarily oriented squares (in 2D), what is the minimum and maximum number of sides that the resulting shape can have? Draw an example of the minimum and maximum shapes. 3 points 6. Concisely state how you should interpolate between two 3D transformation matrices. 4 points 7. When rendering a scene with a ray-tracing method, what part of the solution must be recomputed when the viewer moves? 2 points- 6 - 8. In the
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