by on October 3, 2014

The topic for this week is curves. I’d like to talk about shape modeling more broadly, but there’s nothing to read about that.

For curve readings… Last week, I gave you the readings and told you we’d get to them in the future. Well, the future is here.

(1) The primary reading is my notes on curves. This is a preliminary version that became a chapter of the Shirley Fundamentals of Computer Graphics book. If you have the 2nd or 3rd edition of FCG, you can read the chapter in that. In the notes (the chapter numbering is different, and the content is a little bit improved) you are responsible for:

1. Section 1 (definition of curves)
2. Section 2 (properties of curves, continuity)
3. Section 3 (piecewise polynomials) – note: the way things are written, there is an over-emphasis on deriving the basis matrices. You don’t need to know the derivations, but you should get an idea of the concepts and the types of curves.
4. Section 4 is a long-winded way of getting at some things that should be obvious.
5. Section 5 – what is important is to understand the different types of cubics (particularly cardinals and Hermites)
6. Section 6 & 6.1 – The treatment of Bezier curves has all the important parts, but will come at them differently than we will in lecture.
7. Section 6.2 – BSplines. I am not sure if we will have time to discuss these in class. We almost certainly won’t get to non-uniform B-Splines (unless there is extra time at the end of the class)

The basic parts of these will be similar to how we introduce things in class. For the polynomials, we won’t spend much time on the derivations (I used to make students do those a lot). We’ll come at Bezier Curves from a different direction (but you’ll see how they come together)

(2) I’d also like you to read through the Real-Time Rendering Book, Chapter 13 Section 1, that describes the details of lots of different kinds of curves. You can skip 13.1.2. Section 13.1.5 is something we’ll only touch on briefly in class (and we’ll call them “tension-continuity-bias” splines (TCB).

(3) John Hart’s book Chapter 19 (up to and including 19.5, but not 19.6) is very similar – and somewhat redundant to the first 2 readings. Section 19.5 will help you see how uniform cubic B-Splines work, and his section on Hermite curves will show you a different derivation that my notes do (but you don’t have to worry about the derivation). His section on interpolating polynomials has more detail than mine, but the message is the same: just because you can, doesn’t mean you should.

I will also (hopefully) provide some tutorial information about Bezier Algorithms. You’ll need that for Assignment 5, and it isn’t well covered in the reading.

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