On the Optimal Representation of Vector Location using Fixed-Width Multi-Precision Quantizers

Abstract. Current generation geospatial applications primarily rely on location representations that were developed for the manipulation and display of planar maps of portions of the earth’s surface. The next generation of digital earth applications will require fundamentally new technological approaches to location representation. Improvements in the efficiency of the representation of vector location can result in substantial performance increases. We examine the advantages and limitations of the most common current approach: as tuples of fixed-width floating point representations of real numbers, and identify a list of desirable design features for an optimal replacement system. These include the use of explicitly discrete integer indexes, the use of an optimal quantification scheme, and the ability to represent point locations at multiple precisions, including the capability to exactly represent key point locations, and the ability to encode multi-precision quantizations. We describe a class of planar systems that meet these criteria, which we call Central Place Indexing (CPI) systems. We then extend these systems to the sphere to provide a class of optimal known fixed-width geospatial vector location representation systems we call CPI43 systems.