Quadtree-based indexing of hierarchical diamond subdivisions of the global

In recent years a method of recursive subdivisions of the triangular faces of the octahedron or icosahedron has been developed for approximating to the surface of the Earth. But the triangle-based discrete grids produced by this method are complicated in geometry structure, and is difficult to make such geographical operations as neighbor-finding, spatial searches and so on. We conceive the surface of the octahedron as composed of pairs of adjacent triangles, or diamonds, that tessellate the surface, and thus create nested diamond subdivision of the surface of the globe by quadtree recursive partitioning. The quadtree Morton coding system is used as the index for addressing the diamonds and for linearizing storage that preserves a high degree of spatial locality. A method of finding neighbor, ancestors and descendants also is developed. Based on this we further develop an index for addressing the triangle and a neighbor-finding method. The addressing system exhibits a high degree of regularity that makes it possible to develop very efficient algorithms for common spatial database and geometric operations.