An adaptive block decomposition of a three-dimensional spatial domain is illustrated in Figure 3. A three-dimensional adaptive block decomposition. In contrast to adaptive blocks, Figure 4 illustrates a quadtree decomposition. In this cell-based tree decomposition, when a cell is subdivided, the child cells are created and the parent remains, so that the region of the original cell now has two representations. Leaves are shown in green.
Lines indicate parent-child links.
In the adaptive block data structure, inter-block connectivity is defined using pointers. Thus neighbor information is maintained explicitly. This is similar to the explicit maintenance of neighbor information in unstructured grids. In contrast, quadtree and octree data structures explicitly maintain only parent-child information and neighbor information must be obtained by a tree traversal. Note that a block may have many neighbors along a given face, depending on the number of times refinement has occurred among the neighbors.