A novel identifier scheme for the ISEA Aperture 3 Hexagon Discrete Global Grid System

ABSTRACT

Geospatial data is often spatially aggregated by the use of Discrete Global Grid Systems. References to grid cells are needed for the communication of such data, and different identifier schemes have accordingly been introduced in literature. These schemes suffer, however, from being hard to understand for non-experts, and the geometry of a cell cannot be inferred from its identifier without complex computations. In this article, a novel identifier scheme that encodes the geographic coordinates of the centroid of a cell is proposed, which comes at the cost of potentially being ambiguous in case of a very fine-grained grid. We reason and computationally demonstrate that ambiguity does though not occur for real-world applications. The novel identifier scheme minimizes the amount of data to be communicated, for example, between a server and a client application, and it allows to infer approximate geometries of the cells only by their identifiers.

KEYWORDS:

• Discrete Global Grid System (DGGS)
• Inverse Snyder Equal-Area Projection (ISEA)
• ISEA Aperture 3 Hexagon Discrete Global Grid System (ISEA3H)
• grid
• indexing
• identifier
• performance

Acknowledgments

The author is grateful to Rafael Troilo for his technical support in running software on a high-performance server.

Disclosure statement

The author declares that he has no competing interests.

Notes

1. If a sphere would be tessellated by $n$ hexagons, there would be $2n$ vertices (each hexagon has six vertices, which are shared among three hexagons), and $3n$ edges (each hexagon has six edges, which are shared among two hexagons). The Euler characteristics of the grid is thus $2n-3n+n=0$, which contradicts the Euler characteristics of a sphere being $2$.

2. http://github.com/giscience/geogrid.

3. http://github.com/giscience/geogrid.

Additional information

Funding

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) project “A framework for measuring the fitness for purpose of OpenStreetMap data based on intrinsic quality indicators” [Grant Number FA 1189/3-1].