by on September 25, 2014

The topic in class will be curves – although we’ll do a little catch up to talk about rotations first.

For rotations,there’s no direct reading, you’ve seen a bunch in the prior readings on 3D transformations. If you have not looked at Chapter 6 of John Hart’s Big Fun Graphics Book, you should. It covers the main ideas of rotations pretty well. They are a little scattered about the chapter, so you’ll get some review material as well. 6.4 and 6.5 are the main resources on rotations for class, but 6.6 (and the cartoons explaining the process elsewhere in the chapter) may be useful if you want to construct the matrices yourself. If you really want to know about rotations, you can see the readings we used in the animation class 2 years ago.

For curves, I am not going to ask you to do the readings until AFTER we discuss things in class.

If you want to get ahead of things…

• The basic discussion of what a curve is comes from my notes. Especially sections 1 and 2. When we get to polynomial curves, there is too much about deriving basis matrices, which was the way I learned it – and not necessarily the best way for you to learn it. You’ll want to know about cubics, but the way they are explained is too much in the terminology of the derivations in Sections 3 and 4. (don’t worry – I won’t make you derive the basis functions as done in Section 4). Bezier curves (section 6.1) are really important, but the way they are introduced isn’t so great. It’s an OK reference for some of the algorithms. The explanation of B-Splines (6.2) is OK, but we probably won’t discuss them much in class.
• John Hart’s book Chapter 19 has a different way to get at the basics. It’s similar to mine. When he gets to blossoming, he goes off in a different direction. We probably won’t do blossoming in class. He thinks there a good way to understand splines.
• The Real-Time Rendering Book, Chapter 13 Section 1, describes the details of lots of different kinds of curves. This will be really useful once you’ve learned what the different kinds are and why.

But basically, I think the lectures will be the best way to get this material. So just pay attention in class. Then go look over these materials to get some of the details.

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