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CS 418: Final Exam
May 11, 2005
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General Directions
- Make sure your name is on every page.
- Make sure that you answer all the questions.
- Remember to write clearly and legibly. Unreadable answers will receive 0 credit.
- Unless explicitly stated otherwise, you may leave complex functions such as sin θ, cross product u×v, matrix product A·B, matrix inverse A−^1 , etc. unevaluated.
- When asked to write code, you do not need to produce 100% syntactically correct C++.
- Remember to time yourself. You’ll have 180 minutes to complete 100 points worth of questions. So you should only be spending roughly 25 minutes on a 15 point question.
Question Points Out of
Extra 1
Total 100
- (20 points) Selected Topics
(a) Indicate which of the following visual phenomena can not be simulated by the classical radiosity algorithm discussed in class.
- mirror reflection
- color bleeding
- caustics
- diffuse inter-reflection
- soft shadows
- specular highlights
- participating media
(b) In the standard radiosity equation:
BiAi = EiAi + ρi
j
FjiBj Aj
ρi is the reflectance of patch i. The reflectance of a patch is constant precisely because of the fundamental assumption made by the radiosity algorithm: that all surfaces are perfectly diffuse. Explain why this implies that the reflectance ρi is a constant.
- (20 points) We have a CRT monitor whose color primaries are R 1 , G 1 , B 1 and a projection system whose color primaries are R 2 , G 2 , B 2. Suppose that each primary of the projector can be written as an affine combination of the CRT primaries. For example R 2 = αr R 1 + αg G 1 + αbB 1 where αr + αg + αb = 1 and αr , αg , αb ≥ 0.
(a) What is meant by the gamut of the CRT monitor?
(b) The color space defined by the primaries R 1 , G 1 , B 1 is not perceptually uniform. Explain what this means.
(c) Are there colors which can be displayed on the CRT monitor that cannot be displayed on the projector? Are there colors which can be displayed on the projector that cannot be displayed on the CRT? Explain your answer.
(d) In contrast to red/green/blue, cyan/magenta/yellow are referred to as subtractive primaries. Ex- plain what this means.
(c) Given a light source L, describe how to build a shadow map for this light.
(d) Suppose that we’re trying to shade pixel (i, j). Describe how to find the corresponding point in the shadow map. Your answer should provide a specific mathematical procedure for performing this computation.
(e) Assume that we’ve found the point in the shadow map that corresponds to pixel (i, j). Describe the test you would need to perform to decide whether the pixel (i, j) under consideration is in shadow with respect to the light L.
- (20 points) Ray tracing
(a) Consider the surface of an infinite cylinder of radius 1, centered along the z axis, as shown in the figure below. Give the implicit equation for this surface.
z
y
r { = 1
x
(b) Suppose you are given a ray p + td. Using your implicit equation above, derive an equation for the value(s) of t at which the ray may intersect this cylinder.
(e) Suppose that you are given the value of t at which the ray intersects the cylinder. Furthermore, suppose that there is a single point light source located at the point q. Give an expression for the shadow ray that we would use to determine whether the point on the cylinder is in shadow with respect to the point light at q.
(f) A basic (non-recursive) ray caster loops over every pixel (i, j) and computes a color for that pixel, thus producing an output image. Briefly outline the process by which it would compute this color.
- (20 points) Texturing
(a) Briefly describe the construction of an image pyramid and its primary use.
(b) Recall that normal mapping is a variant of texture mapping where the texture is used to encode unit surface normals. Standard texture minification involves averaging together all texels covered by a particular pixel sample. Explain why this produces incorrect results on normal maps.
- (1 point) Extra Credit. The following computer graphics luminaries all received their Ph.D. degrees from the same Computer Science Department. Name the school. - Ed Catmull (founded Pixar) - Jim Clark (founded SGI and Netscape) - John Warnock (founded Adobe) - Henri Gouraud (shading) - Bui Tuong-Phong (shading) - Jim Blinn (developed texture and environment mapping)
Note: No partial credit is awarded on extra credit questions.
