## What is a Discrete Global Grid (DGG)?

A **Discrete Global Grid** (**DGG**) consists of a set of regions that form a partition of the Earth’s surface, where each region has a single point contained in the region associated with it. Each region/point combination is a called a *cell*. Depending on the application, data objects or values may be associated with the regions, points, or cells of a **DGG**. A **Discrete Global Grid System** (**DGGS**) is a series of discrete global grids, usually consisting of increasingly finer resolution grids (though the term **DGG** is often used interchangeably with the term **DGGS**).

## Defining a Discrete Global Grid System (DGGS)

Regular **DGGS**s are often built using an underlying regular polyhedron. Such **DGGS**s can be fully described by specifying four design choices [Sahr, White, and Kimerling, 2003]. These are given below, along with the design options that are currently supported by our **DGG** software program **DGGRID:**

**Base Polyhedron:****DGGRID**allows the creation of**DGGS**s based on the icosahedron.**Orientation of the Base Polyhedron relative to the Earth:**Three common orientations for icosahedral**DGGS**s are illustrated**here.****DGGRID**allows the user to specify an arbitrary icosahedral orientation.**Transformation from spherical to planar face:****DGGRID**allows the user to choose between the Icosahedral Snyder Equal Area (**ISEA**) projection [Snyder, 1992], and the icosahedral Dymaxion projection of R. Buckminster Fuller [1975] (as developed analytically in [Gray, 1995] and [Crider, 2008]]).**Hierarchical spatial partitioning method:**This consists of choosing a cell region shape and specifying how the cell region area changes between successive resolutions of a**DGGS**. The change in resolution is often specified as an*aperture*, defined as the ratio of areas between cells in a given**DGG**resolution and the next coarser resolution.**DGGRID**allows the user to specify triangle and diamond grids with an aperture of 4, or hexagon grids with apertures of 3, 4, or a mixed sequence of apertures 3 and 4.**Assignment of points to cell regions**:**DGGRID**allows the user to choose between using either the cell centroids or a random point within each cell region.

## Additional Information

- Briefing slides discussing the role of DGGs in the future of geospatial computing
- Three common orientations for
**DGGS**s based on the icosahedron - Animated gifs that illustrate mulitple resolutions of some common DGGSs
- Foldable Images of the ISEA3H DGGS

## References

Crider, JE. 2008. “Exact equations for Fuller’s map projection and inverse,” *Cartographica* 43(1): 67-72.

Fuller, RB. 1975. *Synergetics*. New York: MacMillan.

Gray, RW. 1995. “Exact transformation equations for Fuller’s world map,” *Cartography and
Geographic Information Systems* 32:243-246.

Sahr K, White D, Kimerling AJ. 2003. “Geodesic discrete global grid systems,”* Cartography and
Geographic Information Science* 30(2):121-134.

Snyder, J.P. (1992), “An equal-area map projection for polyhedral globes,” *Cartographica* 29(1):10-21.