Continuous indexing of hierarchical subdivisions of the globe

We describe how to create a continuous global index of the surface of the Earth. The index is based on a hierarchical subdivision of the surface into triangular regions in which each region is assigned a numerical label according to a spacefilling curve, Sequential labels are assigned to adjacent regions, so labels can be sorted to create a continuous one-dimensional index. Benefits of continuity include the implicit preservation of adjacency information, and the ability to vary resolution at different locations. Previously suggested schemes based on similar models produce indices that are discontinuous. Unfortunately, discontinuities degrade the usefulness of an index, as we show by comparing continuous and discontinuous schemes based on performance criteria such as the ability to preserve spatial adjacency. The best index appears to be the continuous one based on the Sierpinski spacefilling curve.