tile
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