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Introductory tiling theory for computer graphics

By: Kaplan, Craig (Craig S.).
Material type: materialTypeLabelBookSeries: Synthesis lectures on computer graphics and animation: # 11.Publisher: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2009Description: 1 electronic text (x, 103 p. : ill.) : digital file.ISBN: 9781608450183 (electronic bk.).Uniform titles: Synthesis digital library of engineering and computer science. Subject(s): Tiling (Mathematics) | Computer graphics | Symmetry | Patterns | Tilings | Tessellations | Wallpaper groups | Isohedral tilings | Substitution tilings | Aperiodic tilings | Penrose tilingsDDC classification: 516 Online resources: Abstract with links to resource Also available in print.
Contents:
Introduction -- Organization -- Tiling basics -- Defining tilings -- Anatomy of a tiling -- Patches -- Tilings with congruent tiles -- Symmetry -- The set of symmetries -- Symmetry groups -- Factoring out repetition -- Periodic replication -- Symmetries of tilings -- Other forms of symmetry -- Colour symmetry -- Symmetry in other spaces -- Orbifolds -- Tilings by polygons -- Regular and uniform tilings -- Laves tilings -- Isohedral tilings -- Basic definitions -- Isohedral tiling types -- Parameterizing the isohedral tilings -- Edge shape parameterization -- Tiling vertex parameterization -- Data structures and algorithms for IH -- Representing tiling vertex parameterizations -- Computing transformation matrices -- Colourings -- Tiling edge shapes -- Isohedral templates and prototiles -- Beyond isohedral tilings -- Nonperiodic and aperiodic tilings -- Substitution tilings and rep-tiles -- Wang tiles and aperiodicity -- Penrose tilings -- Survey -- Drawing periodic tilings -- Drawing nonperiodic tilings -- Escher-like tilings -- Sampling -- Texture generation -- The isohedral tiling types.
Abstract: 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.
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E books E books PK Kelkar Library, IIT Kanpur
Available EBKE198
Total holds: 0

Mode of access: World Wide Web.

System requirements: Adobe Acrobat reader.

Part of: Synthesis digital library of engineering and computer science.

Series from website.

Includes bibliographical references (p. 99-102).

Introduction -- Organization -- Tiling basics -- Defining tilings -- Anatomy of a tiling -- Patches -- Tilings with congruent tiles -- Symmetry -- The set of symmetries -- Symmetry groups -- Factoring out repetition -- Periodic replication -- Symmetries of tilings -- Other forms of symmetry -- Colour symmetry -- Symmetry in other spaces -- Orbifolds -- Tilings by polygons -- Regular and uniform tilings -- Laves tilings -- Isohedral tilings -- Basic definitions -- Isohedral tiling types -- Parameterizing the isohedral tilings -- Edge shape parameterization -- Tiling vertex parameterization -- Data structures and algorithms for IH -- Representing tiling vertex parameterizations -- Computing transformation matrices -- Colourings -- Tiling edge shapes -- Isohedral templates and prototiles -- Beyond isohedral tilings -- Nonperiodic and aperiodic tilings -- Substitution tilings and rep-tiles -- Wang tiles and aperiodicity -- Penrose tilings -- Survey -- Drawing periodic tilings -- Drawing nonperiodic tilings -- Escher-like tilings -- Sampling -- Texture generation -- The isohedral tiling types.

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

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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.

Also available in print.

Title from PDF t.p. (viewed on August 9, 2009).

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