Assignment Group 2 (Week 3 Feb3-7)

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The second week of assignments focus on one of the most important ideas in computer graphics: transformations. The idea is that geometry is much easier to think about/work with if we do it in a convenient coordinate system - so we make sure to describe things in convenient coorinate systems, and use transformations to move between those coordinate systems. We’ll explore the use of transformations in 2D (trust me, it is better to understand it in 2D and then we’ll see that things work in 3D).

In the regular class we divide this into two weeks/workbooks: first, we motivate transformations and try to use them; and then, we look under the hood at the math that makes them work. Both are important. Traditionally, computer graphics is taught math first, but I’ve found it’s better to appreciate why you need to know this and to get the intuitions - once you do, the math falls into place.

In addition to the workbooks and lectures, you will need to look at some extra resources. You’ll need something to show you some of the mathematical specifics (I’ll give you a book chapter, but you might find something else). And, you might want to brush up on your linear algebra (or, to get the intuitions behind all that stuff you should have learned in linear algebra).

A warning: it’s tempting to skip over the math of transformations. The APIs implement for you. But it really is essential for understanding what is going on, and using it effectively.

Learning Goals

I am hoping if I am clear about what I want you to learn from the assignments, you can do better at structuring your work to make sure you learn it.

  • Understand (and apply) the concepts of coordinate systems and transformations
  • Understand (and apply) the idea of hierarchical modeling
  • The idea of building complex transformations and hierarchies from simple pieces
  • Use composition effectively to create useful transformations from basic pieces
  • Be able to implement hierarchical modeling with a “stack” (in an immediate mode API)
  • Use retained-mode APIs to explicitly model hierarchies
  • Write SVG by hand to appreciate it, and how retained mode (scene graph) representations represent hierarchical models
  • Understand how we implement transformations with linear operators and composition
  • Understand homogeneous coordinates
  • Be aware of the possibilities for applying more linear algebra ideas to transformations (more than the basics of multiplication for composition)
  • Understand how the APIs deal with transformations internally

One way to think about this… in a week or two, we will ask you to write programs to demonstrate your knowledge. The things your programs will need to demonstrate:

  • That you can make a picture using SVG that shows instancing and hierarchical modeling (this is a “make a picture assignment” in WB4)
  • That you can create an articulated (hierarchical) object and animate it (the quadcopter in WB3)
  • That you can write programs that manage many objects all moving at the same time and interacting with each other (the boids from WB4)

Unfortunately, it’s hard to check your understanding of the math through programming.

Book Caveat

In the regular class, we would explain the textbooks a bit. But most students ignored them. I am trying to move away from using textbooks for class - but this is a case where there are some details that you will want to see written out.

The main textbook I refer to is “Fundamentals of Computer Graphics” by Peter Shirley, and others (including me). Do not buy this book for class. We won’t use much of it, and it is available online through the library (Fundamentals of Computer Graphics 4e (official access at ProQuest)). I have PDFs of chapters from old versions of the book in Canvas (Canvas Directory).

Assignment

Required Reading List (complete Content Survey 2: 2D Transformations (due Mon, Feb 03) to be ready for class discussion):

  • My tutorial CS559 Tutorial: Points, Vectors, Coordinate Systems (you should have read the ones on color, and raster vs. object)
  • Workbook 3 (link on Canvas)
  • Workbook 4 (links on Canvas)
  • Week 3 Lectures Week 3 (2/6 - 2/10)
  • Week 4 Lectures Week 4 (2/13 - 2/17) Most of the readings are referred to in the workbooks.
  • Chapter 6 of “Fundamentals of Computer Graphics” (which I refer to as FCG or Shirley) covers the math which is not described in the workbooks. Read the workbooks first to motivate the math, then read Shirley Chapter 6 (Skip 6.2 about 3D for now). In the regular class, I say that 6.1.6 and 6.5 are optional - but I think they are good for the honors class as they will help you connect with the linear algebra math).
  • The tutorials on SVG - mine cover enough of the basics.
  • The Steve Seitz videos (from the other UW) - to get a different take on it all, and they are short. (Affine Transformations in 5 Minutes and Hierarchical Modeling in 5 Minutes). If you want to understand the philosophy of these, you might want to watch the first video (Graphics in 5 Minutes).
  • If you need a refresher on linear algebra to help you connect the math to the geometric intuitions, see the resources at CS559 Tutorial: Linear Algebra for CS559

The relevant assignments (on Canvas):

What to do with the workbooks (for Workbook Drafts 2: (WB3 and WB4) (due Wed, Feb 05)):

  • Take the time to play with the demos (especially the transform toy) as it makes some of the hard concepts visible.
  • The workbooks are full of little problems and checks (little math things). Make sure you understand how to do them - if nothing else, they make for great exam questions.
  • There are 3 “bigger things”
    • Quadcopter - this is to show that you can create and animate a hierarchical model. Make a basic one - and then you can make a cooler one for your portfolio (or some other hierarchical thing).
    • SVG Picture - this is to show that you understand SVG, and how it uses hierarchy. Make something simple - you can do something fancier for your portfolio
    • Boids (page 5, now it’s called “Lots of Walking Objects”) - this is good for your portfolio, but it is only partially connected to the workbook. Don’t worry about it for now.

Optional Materials: