Wang Tiles In Computer Graphics
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Wang Tiles in Computer Graphics
Many complex signals in computer graphics, such as point distributions and textures, cannot be efficiently synthesized and stored. This book presents tile-based methods based on Wang tiles and corner tiles to solve both these problems. Instead of synthesizing a complex signal when needed, the signal is synthesized beforehand over a small set of Wang tiles or corner tiles. Arbitrary large amounts of that signal can then efficiently be generated when needed by generating a stochastic tiling, and storing only a small set of tiles reduces storage requirements. A tile-based method for generating a complex signal consists of a method for synthesizing the signal over a set of Wang tiles or corner tiles, and a method for generating a stochastic tiling using the set of tiles. The method for generating a stochastic tiling using the set of tiles is independent of the signal. This book covers scanline stochastic tiling algorithms and direct stochastic tiling algorithms for Wang tiles and corner tiles. The method for synthesizing the signal over a set of tiles is dependent on the signal. This book covers tile-based methods for texture synthesis and for generating Poisson disk distributions. This book also explores several applications such as tile-based texture mapping and procedural modeling and texturing. Although the methods for constructing a complex signal over a set of Wang tiles or corner tiles are dependent on the signal, the general idea behind these methods generalizes to other kinds of signals. The methods presented in this book therefore have the potential to make the generation and storage of almost any complex signal efficient. Table of Contents: Introduction / Wang Tiles and Corner Tiles / Tiling Algorithms for Wang Tiles and Corner Tiles / Tile-Based Methods for Texture Synthesis / Tile-Based Methods Generating Poisson Disk Distributions / Applications of Poisson Disk Distributions
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
Advances in Computer Graphics
Author: Tomoyuki Nishita
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-06-22
This is the refereed proceedings of the 24th Computer Graphics International Conference, CGI 2006. The 38 revised full papers and 37 revised short papers presented were carefully reviewed. The papers are organized in topical sections on rendering and texture, efficient modeling and deformation, digital geometry processing, shape matching and shape analysis, face, virtual reality, motion and image, as well as CAGD.