Due Nov 1

1. Find the matrix M, depending only on the vector a=(4,1,1), such that for all vectors p, Mp=a.p a.
2. Find the matrix M, depending only on the vector a=(4,1,1), such that for all vectors p, Mp=a x p.
3. Why can a rotation matrix never have an eigenvalue of 4?
4. In our vector formula for rotating a point p about an axis a,
   1. Does p need to be normalized?
   2. Does a need to be normalized?
5. Look at this 1988 paper published in Communications of the ACM, the official publication of the ACM, the leading CS professional organization. The author is Paul Heckbert, a 3-D graphics architect for Nvidia, editor of the Graphics Gems books, researcher in realistic image synthesis, and former employee at Pixar.
   1. What 3-D coordinate system is used?
   2. What simplifying assumption was made to model the frontispiece image?
6. Why does OpenGL not always use a 1/d² falloff for the intensity of light, as a function of the distance of the light?
7. The Phong shading equation I discussed on Monday lets you give each light source an ambient, a diffuse, and also a specular color. How can some photons from the single light source reflect diffusely and other photons reflect specularly?
8. If the vector pointing to the light is l=(1,0,0) and the normal vector to the surface is n=(.6,0,.8), what is the perfect reflection vector, r?
9. To help you start to think about projects, take a look at some International Obfuscated C Code Contest (IOCCC) winners relating to graphics. I've cached some of them locally:
   1. banks: It's a flight sim done in 1536 bytes of real code.
   2. buzzard: a maze in 31 lines.
   3. dodsond1: Othello game with the code looking like an Othello board.
   4. dodsond2: Go searching for the Wumpus in the Caverns of Doom! 55 LOC (Lines Of Code).
   5. eldby: flying spheres in 8 LOC.
   6. gavare: ray tracer, in 28 LOC, which are formatted to look like the eventual result
   7. natori: draw the current phase of the moon, in 3 LOC.
   8. schnitzi: Considering its input as a matrix of characters, it transposes it. Also, the source itself is symmetric, and only 52 LOC.
   9. vik1: road race
   10. williams: Missile Command, in 73 beautifully formatted LOC.
   There's nothing to hand in for this question. Just play with these programs, and begin to understand why I can't answer the question, "How many lines of code should the project be?"
10. Email a term project proposal, with: title, up to 3 team members, 100 word description, to Lu. The term project should be a program doing something related to computer graphics, plus a video showing that it works and documentation on how to use it. You will demo your project in one of the last 2 labs.

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