Thin Shells for Computer Graphics: A Short Course

History

Thin shells, like their close relations thin plates, are objects that are thin in one dimension compared to the other two. Thin plates are, by definition, flat when they are undeformed, but thin shells can have curvature while undeformed. Common examples of thin plates include pieces of window glass or unfolded paper, while common examples of thin shells include glass bottles and egg shells. Shells are much more common than plates outside introductory physics texts.

I studied methods for simulating the physics of thin shells with Denis Zorin with the aim of creating new techniques for the computer graphics industry. In particular, I did a lot of reading in geometry, in physics, about computational models and about adaptive methods for my depth exam, which is NYU Computer Science's exam at the end of the third year of their PhD program. As an exercise as I studied, I wrote what was to become a short course in thin shells for computer graphics. This short course was not completed (my schedule got tighter and tighter before the exam), but it should form a good introduction for anyone wanting to learn more about thin shells. The last chapter consists of a set of further readings in more advanced topics.

The course is available in HTML for web viewing or as a PDF document for printing. The mathematical figures are also more comprehensible in the PDF version.