Due Nov 1

- Find the matrix M, depending only on the vector a=(4,1,1), such that for all vectors p, Mp=a.p a.
- Find the matrix M, depending only on the vector a=(4,1,1), such that for all vectors p, Mp=a x p.
- Why can a rotation matrix never have an eigenvalue of 4?
- In our vector formula for rotating a point p about an axis a,
- Does p need to be normalized?
- Does a need to be normalized?

- 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.
- What 3-D coordinate system is used?
- What simplifying assumption was made to model the frontispiece image?

- Why does OpenGL not always use a 1/d
^{2}falloff for the intensity of light, as a function of the distance of the light? - 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?
- 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?
- 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:
- banks: It's a flight sim done in 1536 bytes of real code.
- buzzard: a maze in 31 lines.
- dodsond1: Othello game with the code looking like an Othello board.
- dodsond2: Go searching for the Wumpus in the Caverns of Doom! 55 LOC (Lines Of Code).
- eldby: flying spheres in 8 LOC.
- gavare: ray tracer, in 28 LOC, which are formatted to look like the eventual result
- natori: draw the current phase of the moon, in 3 LOC.
- schnitzi: Considering its input as a matrix of characters, it transposes it. Also, the source itself is symmetric, and only 52 LOC.
- vik1: road race
- williams: Missile Command, in 73 beautifully formatted LOC.

- 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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