Brief Contributions________________________________________________________________________________ On Spatial Orders and Location Codes

applications in matrix manipulation, graphic rendering, and data encryption. It is shown that these spatial orders are single examples of entire classes of spatial orders that can be defined in arbitrary numbers of dimensions and base values. Second, an algorithm is proposed that can be used to transform between these spatial orders and Cartesian coordinates. It is shown that the efficiency of the algorithm improves with a larger base value. By choosing a base value that corresponds to the available memory page size, the computational effort required to perform operations such as matrix multiplication can be optimized. Index Terms—Spatial order, location code, matrix multiplication, encryption, dilation, quadtree, octree. Ç