Reading assignment 2: Hierarchical modeling and introduction to 3D transforms

by Eftychios Sifakis on February 3, 2016

Due: Friday, Feb 5th (Note slightly extended deadline)

Synopsis: We will cover the concepts related to hierarchical modeling, initially focusing on 2D examples. Then we’ll move into 3D, which means reviewing a bit about how linear algebra works in 3D and seeing how transformations happen. In addition to the readings, there will be a quiz again to help you confirm that you’re getting (at least) the basic ideas.

Learning Objectives: Become comfortable with composition of transforms, the concept of a transform stack, and hierarchical modeling. Understand 3D Transforms and Linear Algebra well enough to follow the lectures and use them in a program.

Evaluation: Check/No Check (based on passing the Quiz). You may re-try the quiz until you pass it (everyone should be able to).

Handin: Quiz on Canvas [LINK]


As we move to 3D, transformations become a little bit more complicated. We also need to review the mathematical foundations on which they are built. (review, since you should have seen this in either calculus or linear algebra).

After you’ve done the reading, take the online quiz (link coming) to make sure you’ve understood what you’ve read. If you get something wrong, go back and try again.

The Required Reading List

  • Chapter 6 of Hart’s Big Fun Computer Graphics Book (Link)
  • Chapter 7 of Hart’s Big Fun Computer Graphics Book (Link). This also touches on the topic of hierarchical modeling (including 3D), although in class we covered this primarily from a 2D perspective. The concepts are entirely similar.
  • Chapter 6 of Shirley et. Al Foundations of Computer Graphics (Link)

The Optional Readings

If you haven’t seen the 3D linear math stuff before, it might be harder to get. Seeing it presented a different way is helpful.

  • Chapters 1,2, 4 are a good linear algebra refresher from Practical Linear Algebra (Link, Link, Link)
  • Chapter 8-10 are where PLA gets to 3D (Link, Link, Link)
  • Section 2.4 of Foundations of Computer Graphics is a helpful review of linear algebra as well (Link)
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