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Wang tiles have been used for procedural synthesis of textures, heightfields, and other large and nonrepeating bi-dimensional data sets; a small set of precomputed or hand-made source tiles can be assembled very cheaply without too obvious repetitions and periodicity. In this case, traditional aperiodic tilings would show their very regular ...
A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art , especially in textiles , tiles , and wallpaper .
If a geometric shape can be used as a prototile to create a tessellation, the shape is said to tessellate or to tile the plane. The Conway criterion is a sufficient, but not necessary, set of rules for deciding whether a given shape tiles the plane periodically without reflections: some tiles fail the criterion, but still tile the plane. [19]
In computer graphics, a texel, texture element, or texture pixel is the fundamental unit of a texture map. [1] Textures are represented by arrays of texels representing the texture space, just as other images are represented by arrays of pixels. Texels can also be described by image regions that are obtained through simple procedures such as ...
[22] [23] Moroccan geometric woodwork from the 14th to 19th centuries makes use of only 5 wallpaper groups, mainly p4mm and c2mm, with p6mm and p2mm occasionally and p4gm rarely; it is claimed that the "Hasba" (measure) method of construction, which starts with n-fold rosettes, can however generate all 17 groups. [24] Methods of construction
Covering a flat surface ("the plane") with some pattern of geometric shapes ("tiles"), with no overlaps or gaps, is called a tiling. The most familiar tilings, such as covering a floor with squares meeting edge-to-edge, are examples of periodic tilings. If a square tiling is shifted by the width of a tile, parallel to the sides of the tile, the ...
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