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 DGGSs are often built using an underlying regular polyhedron. Such DGGSs 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 DGGSs based on the icosahedron.
- Orientation of the Base Polyhedron relative to the Earth: Three common orientations for icosahedral DGGSs 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 DGGSs 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.