Titlebook: Introductory Tiling Theory for Computer Graphics; Craig S. Kaplan Book 2009 Springer Nature Switzerland AG 2009

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Tiling Basics,rovisionally formalize these notions by stating that a set . of shapes . the plane if the union of all shapes in . is the entire plane, and that an . is a non-empty intersection between two tiles (in which case . has no overlaps if it consists of pairwise disjoint sets). Under this definition, the t

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Symmetry,be surprising that there is a strong connection between symmetry and tilings—tilings of the plane typically feature some degree of repetition, and symmetry is a means of measuring that repetition. Planar symmetry groups have served as a powerful tool in understanding and classifying designs belongin

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Isohedral Tilings, every tile plays an equivalent role relative to the whole. Despite that constraint, they still permit a wide range of expression. Decorative tilings developed without explicit mathematical knowledge are frequently isohedral. M.C. Escher developed his own “layman’s theory” for his regular divisions

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Tiling Basics,t, worthwhile mathematical objects. I will deliberately add more constraints than are strictly necessary mathematically, in order to arrive at a definition suitable for the kinds of tilings that we encounter in computer graphics. After formulating a practical definition, I explore some of the basic

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