Craig S . Kaplan

Craig is a professor of computer science at the University of Waterloo who wrote his doctoral thesis on the tesselations (tiling patterns) in Islamic art. Here he shows off a wooden Islamic star pattern that he programmed a computer to cut out.

A man, a plan, a canal, Craig!

Craig S. Kaplan

Associate Professor		[private]
Computer Graphics Lab		[people] [private]
The David R. Cheriton
School of Computer Science		[faculty] [staff] [talks]
University of Waterloo		[schedule] [dates]
Waterloo, Ontario, Canada

Office: DC2110
Voice: (519) 888 4567 x34589
email: csk@uwaterloo.ca

Research

I'm a member of the Computer Graphics Lab, where I study the use of computer graphics in art, ornament, and design. My interests extend from there into nonphotorealistic rendering. I also dabble in human-computer interaction, computational geometry and programming languages.

Pages devoted to specific research projects
Complete list of publications
A separate page about my doctoral dissertation, Computer Graphics and Geometric Ornamental Design
Current students: Kate Kinnear, Zheng Qin, Jie Xu
Former students: Paul Church, Alex Kalaidjian, Celine Latulipe, Michael Wasilewski, Dmitry Chechik, Roman Karatchinski, Frank Liu, Richard Moore, Justin Ng, Ken Rose, Kostas Sakellis

Teaching

Fall 2008:		CS 115 -- Introduction to Computer Science 1

Winter 2009:		CS 115 -- Introduction to Computer Science 1

Previous terms

Other Activities

In July 2007, I led a one-week workshop on geometric sculpture for high school students participating in the Shad Valley summer program.

I'm one of the associate editors for the Journal of Mathematics and the Arts, a new journal by Taylor & Francis that began publishing in 2007.

I'm co-organizing the Bridges 2009 conference, which will be held in Banff, Alberta.

Bridges 2008 -- 24-29 July 2008

Bridges 2008 took place in late July in Leeuwarden, the capital of the northern Dutch province of Friesland. The conference included excursions to art exhibits in local churches and an activity day in the centre of town, right in front of the house where Escher was born.

SIGGRAPH 2008 -- 11-15 August 2008

This year, I had a couple of pieces in one of the SIGGRAPH art galleries, a curated exhibit entitled Design & Computation. With the help of the curator I managed to procure a press pass, which allowed me to capture many photos of the exhibit without falling afoul of the vigilant volunteers trying to stop people from photographing the work.

Computer Graphics and Geometric Ornamental Design

Craig S. Kaplan. PhD thesis, 2002

Inspired by the wonderful page Robert Glenn Scharein has dedicated to his PhD thesis Interactive Topological Drawing, I decided to give my own thesis a happy little home on the internet. Like Robert, I wanted to include some of the figures from the thesis with which I was particularly pleased. From this page, you can download my thesis in a couple of different formats suitable for on-screen viewing or printing. You can also sample some of my favourite pages.

If you enjoy looking at pretty thesis pages, I also recommend the finely illustrated work of Sascha Rogmann: Wachstumsfunktionen von Pflasterungen. Sadly, I can't read German.

Abstract

Throughout history, geometric patterns have formed an important part of art and ornamental design. Today we have unprecedented ability to understand ornamental styles of the past, to recreate traditional designs, and to innovate with new interpretations of old styles and with new styles altogether.

The power to further the study and practice of ornament stems from three sources. We have new mathematical tools: a modern conception of geometry that enables us to describe with precision what designers of the past could only hint at. We have new algorithmic tools: computers and the abstract mathematical processing they enable allow us to perform calculations that were intractable in previous generations. Finally, we have technological tools: manufacturing devices that can turn a synthetic description provided by a computer into a real-world artifact. Taken together, these three sets of tools provide new opportunities for the application of computers to the analysis and creation of ornament.

In this dissertation, I present my research in the area of computer-generated geometric art and ornament. I focus on two projects in particular. First I develop a collection of tools and methods for producing traditional Islamic star patterns. Then I examine the tessellations of M.C. Escher, developing an “Escherization” algorithm that can derive novel Escher-like tessellations of the plane from arbitrary user-supplied shapes. Throughout, I show how modern mathematics, algorithms, and technology can be applied to the study of these ornamental styles.

Favourite Figures

I enjoy creating expository diagrams. My thesis already had a great deal of graphics by virtue of being in the field of computer graphics, but I wanted to use graphics as much as possible to explain concepts, or failing that to help clarify the writing. What follows are some of my favourite figures from the thesis. These aren't the results, they're just the pretty diagrams. Click on each one for a full-size version and some occasional commentary.