Location coding on icosahedral aperture 3 hexagon discrete global grids

Abstract

Discrete global grid systems (DGGSs) represent a relatively new, but increasingly popular, approach to the problem of representing geospatial location on computer systems. Despite growing interest amongst potential users in icosahedral aperture 3 hexagon DGGSs, the practical use of such systems has been hindered by a lack of efficient spatial indexing methods. In this paper we discuss the two primary approaches to developing multi-resolution location coding systems for DGGSs: pyramid addressing and path addressing. We then describe an efficient pyramid addressing system for icosahedral aperture 3 hexagon DGGSs, the quadrilateral 2-dimensional integer system. After reviewing the problems inherent in developing path addressing systems for hexagon-based DGGSs we describe a class of path-based location coding solutions for icosahedral aperture 3 hexagon DGGSs called modified generalized balanced ternary, and show how this system can be used to index vector data. We then discuss a subset of this system, the icosahedral aperture 3 hexagon tree, which can be used to index raster and bucket data structures. Conversion algorithms to/from geodetic coordinates are discussed.