Introductory Tiling Theory for Computer Graphics

Tiling theory is an elegant branch of mathematics that has applications in several areas of computer science. The most immediate application area is graphics, where tiling theory has been used in the contexts of texture generation, sampling theory, remeshing, and of course the generation of decorative patterns. The combination of a solid theoretical base (complete with tantalizing open problems), practical algorithmic techniques, and exciting applications make tiling theory a worthwhile area of study for practitioners and students in computer science. This synthesis lecture introduces the mathematical and algorithmic foundations of tiling theory to a computer graphics audience. The goal is primarily to introduce concepts and terminology, clear up common misconceptions, and state and apply important results. The book also describes some of the algorithms and data structures that allow several aspects of tiling theory to be used in practice. Table of Contents: Introduction / Tiling Basics / Symmetry / Tilings by Polygons / Isohedral Tilings / Nonperiodic and Aperiodic Tilings / Survey

Craig S. Kaplan is an associate professor in the David R. Cheriton School of Computer Science at the University of Waterloo. He is interested in applications of computer graphics in art, architecture and design, and makes occasional forays into human-computer interaction and computational geometry. Craig has a Bachelor’s degree in Pure Mathematics and Computer Science from the University of Waterloo and a PhD in Computer Science from the University of Washington. A native of Montreal, he lives in Waterloo, Ontario with his long-suffering wife, their daughter and son, and two cats. He enjoys solving puzzles, making paper airplanes for his children, and eating soup.