Rectangular Tiling

Abstract

Tilling starts with an iteration space and partitions the iteration space into uniform tiles of a given size and shape. The tiles can be any shapes such as triangles, squares, rectangles, parallelograms, hexagons or their higher-dimensional equivalents. In practice, however, squares, rectangles and parallelograms are common. As a result, two types of tiling techniques are distinguished in the literature: rectangular tiling and parallelepiped tiling. In the former case, all tiles are squares, rectangles or their higher-dimensional equivalents. In the latter case, the tiles can also be parallelepipeds (known as parallelograms in the 2-D space).