CS798: Computer graphics, geometry, and ornamental design (Winter 2006)


Throughout history, geometric patterns have formed an important part of human expression. Ornament can even be found on artifacts dating back into prehistory.

It is only in the last century or two that we have developed the mathematical tools necessary to study the patterns we can created intuitively for millennia. Even more recently, we have computational tools that let us construct these patterns efficiently and painlessly, opening ever wider horizons of art and design.

This course is about the mathematical and computational tools that make it possible to analyze existing patterns and synthesize new ones. The focus is on ornamental design: abstract geometric patterns that adorn human artifacts.


Apr 11: By popular requests, Abram's photos of the polyhedral sculptures from Assignment 3.

Mar 30: I had seen pictures of this before, and went looking to find them again because of yesterday's discussion about architecture. Go look at pictures of the main stadium and aquatics centre for the 2008 summer games in Beijing. The architecture seems related to some of the topics we covered. The aquatic centre seems to be based on Voronoi diagrams, and I dimly recall reading that there's a connection between the lines that frame the stadium and Ammann bars (that's probably too good to be true).

Mar 21: Lecture notes now up-to-date as of the lecture of March 20th. There's a bit more coming on polyhedra.

Mar 20: Lecture notes now cover Islamic star patterns.

Mar 7: Lecture notes now cover Euclidean and non-Euclidean geometry.

Feb 27: Assignment 3 is now available in full.

Feb 25: The remaining notes on Penrose tilings are now available.

Feb 25: Implementation section of assignment 3 is now available. Math question(s) will follow shortly. It's due two weeks from Monday, on 13 March.

Feb 15: Lecture notes cover nonperiodic and aperiodic tilings (though I may have a bit more to say on the latter subject next week).

Feb 7: Suggested extensions and bonus question are now available for assignment 2.

Feb 7: Lecture notes now cover everything up to Lecture 9 (Metamorphoses and Deformations).

Feb 1: Assignment 2 is now available (modulo a couple of changes that will happen later). Still working on last week's worth of lecture notes.

Jan 24: Notes available for Lecture 6, polygonal tilings.

Jan 23: Some useful Postscript links, courtesy of Jonathan:

Jan 20: Lecture notes now cover lectures up to Jan 18.

Jan 20: Bruce Taylor in Fine Arts pointed me at interesting article relating symmetric ornament and "Chladni patterns" formed by small particles sitting on a membrane vibrating in response to sound. See Chladni's drawings in an online copy of his book Die Akustik. Other images here.

Course information



Assignment 1 18%
Assignment 2 18%
Assignment 3 18%
Project proposal 6%
Project content 16%
Project presentation 6%
Project write-up 8%
Participation 10%

Previous offerings

Although this course will generally remain in the field of nonphotorealistic rendering, I will make changes each time I teach it.
Craig S. Kaplan Last updated: