Planar decomposition for quadtree data structure

The quadtree data structure is extensively used in representing 2dimensional data in many applications like image processing, cartographic data processing. VLSI embedding, graphics, computer animation, computer-aided architecture, etc. The data structure employs the divideand-conquer technique to recursively decompose the planar region. This paper addresses the problem of planar tessellation which yields the quadtree data structure. Arbitrary triangles and parallelograms have been used as basic cells and hyper-cellular structures corresponding to lower order k-gons have been shown to represent such data structures. Different tessellation schemes have been discussed using the notion of tessellation matrix. The performances of different tessellation schemes have been compared, introducing the concept of the neighborhood graph.