Continuous indexing of hierarchical subdivisions of the globe

We describe how to create a continuous global index of the surface of the earth. The model is based on a hierarchical subdivision of the surface into triangular regions, in which each region is assigned a numerical label according to a space lling curve. Sequential labels are assigned to adjacent regions, so labels can be sorted to create a continuous one-dimensional index. Bene ts of this continuous model include the implicit preservation of adjacency information, and the ability to vary resolution at di erent locations. Previously suggested schemes based on similar models produce indices that are discontinuous. We demonstrate our method by showing how to create indices based on two space lling curves. We include procedures for labeling cells, converting between index values and surface coordinates, and nding cell neighbors. We also analyze the number and lengths of jumps in the discontinuous schemes. We discuss characteristics such as adjacency preservation, the ability to create paths and circuits, usability, and stability. We compare the total lengths of curves based on the continuous and discontinuous orderings discussed. We also compare Average Data File Storage Distance, a measure of adjacency preservation. The ordering based on the Sierpinski curve performs best overall, according to both measures.