Quadtree based SBFEM analysis

Two different types of quadtree decompositons are considered. The first type, which expects pictures as input, is related to image decompositions and compression algorithms, whereas the second type, which expects geometric features and primatives as input, allows for a CAD-like description of the structure. 

Image based quadtree decomposition

The user supplies a grayscale image as input. It is then padded until it is square and the pixels align with powers of 2. Subsequently, it is divided into four equal parts (hence "quad") by bisecting its height and width. If any of these four resulting blocks contain pixels whose grayscale values vary by more than a user defined value, then that block is again divided into four equally sized blocks. This procedure is continued until every block contains only uniform grayscale values. The well known issue of hanging nodes between adjacent blocks of different size does not affect SBFEM, since at its core it is a polygon based method. In fact, this is heavy exploited in SBFEM to increase computational efficiency: By balancing the quadtree, only a limited amount of possible polygon orientations exist, which can be easily precomputed and retrieved as necessary.