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A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics , tessellation can be generalized to higher dimensions and a variety of geometries.
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of {6,3} or t {3,6} (as a truncated triangular tiling).
The crease patterns of the Miura fold form a tessellation of the surface by parallelograms. In one direction, the creases lie along straight lines, with each parallelogram forming the mirror reflection of its neighbor across each crease.
A Pythagorean tiling Street Musicians at the Door, Jacob Ochtervelt, 1665.As observed by Nelsen [1] the floor tiles in this painting are set in the Pythagorean tiling. A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides.
The rhombic dodecahedral honeycomb (also dodecahedrille) is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoi diagram of the face-centered cubic sphere-packing, which has the densest possible packing of equal spheres in ordinary space (see Kepler conjecture ).
Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. [2] Cellular automata have found application in various areas, including physics , theoretical biology and microstructure modeling.
A simple tessellation pipeline rendering a smooth sphere from a crude cubic vertex set using a subdivision method. In computer graphics, tessellation is the dividing of datasets of polygons (sometimes called vertex sets) presenting objects in a scene into suitable structures for rendering.
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