![]() To reduce the number of irregular panels that may form during the tessellation process, this paper presents an algorithmic approach to restructuring the surface tessellation by investigating irregular boundary conditions. These tessellations are irregular because they include different shapes. Other quadrants have to be split further. For example, irregularly shaped panels form at the trimmed edges. So here are examples of regular and irregular polygons: Regular and. After the first split, the southeast quadrant is entirely green, and this is indicated by a green square at level two of the tree. To construct a quadtree, the field is successively split into four quadrants until all parts have only a single value. Figure: An 8 x8, three value raster (here, three colours) and its representation as a region quadtree. Therefore, a quadtree provides a nested tessellation: quadrants are only split if they have two or more different values. When a conglomerate of cells has the same value, they are represented together in the quadtree, provided their boundaries coincide with the predefined quadrant boundaries. Quadtrees are adaptive because they apply Tobler’s law. The links between them are pointers, i.e. a programming technique to address (or to point to) other records. Examples range from the simple hexagonal pattern of the bees honeycomb or a tiled floor to the intricate decorations used by the Moors in thirteenth century. ![]() In the computer’s main memory, the nodes of a quadtree (both circles and squares in the Figure) are represented as records. Tessellations can also be made from more than one shape, as long as they fit together with no gaps. So squares form a tessellation (a rectangular grid ), but circles do not. The procedure produces an upside-down, tree-like structure, hence the name “quadtree”. A pattern of shapes that fit together without any gaps is called a tessellation. This procedure stops when all the cells in a quadrant have the same field value. Regular tessellations provide simple structures with straightforward algorithms that are, however, not adaptive to the phenomena they represent. The quadtree that represents this raster is constructed by repeatedly splitting up the area into four quadrants, which are called NW, NE, SE, SW for obvious reasons. Irregular tessellations are more complex than regular ones, but they are also more adaptive, which typically leads to a reduction in the amount of computer memory needed to store the data. It shows a small 8×8 raster with three possible field values: white, green and blue. A simple illustration is provided in the Figure above. Irregular Tessellation are partitions of space into mutually distinct cells, but now the cells may vary in size and shape, allowing them to adapt to the spatial. It is based on a regular tessellation of square cells, but takes advantage of cases where neighbouring cells have the same field value, so that they can be represented together as one bigger cell. A well-known data structure in this family - upon which many more variations have been based - is the region quadtree.
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