General Method for Extending Discrete Global Grid Systems to Three Dimensions

Abstract

Geospatial sensors are generating increasing amounts of three-dimensional (3D) data. While Discrete Global Grid Systems (DGGS) are a useful tool for integrating geospatial data, they provide no native support for 3D data. Several different 3D global grids have been proposed; however, these approaches are not consistent with state-of-the-art DGGSs. In this paper, we propose a general method that can extend any DGGS to the third dimension to operate as a 3D DGGS. This extension is done carefully to ensure any valid DGGS can be supported, including all refinement factors and non-congruent refinement. We define encoding, decoding, and indexing operations in a way that splits responsibility between the surface DGGS and the 3D component, which allows for easy transference of data between the 2D and 3D versions of a DGGS. As a part of this, we use radial mapping functions that serve a similar purpose as polyhedral projection in a conventional DGGS. We validate our method by creating three different 3D DGGSs tailored for three specific use cases. These use cases demonstrate our ability to quickly generate 3D global grids while achieving desired properties such as support for large ranges of altitudes, volume preservation between cells, and custom cell aspect ratio.

Efficient Calculation of Distance Transform on Discrete Global Grid Systems

“…Another interesting active branch of DGGS research is 3D DGGSs. There exist some works that aim to build a 3D DGGS or extend current 2D DGGSs to 3D DGGS [34,35]. For this work, we have assumed a 2D DGGS, but the same idea might be able to be reimplemented for a 3D DGGS.…”

Enabling geosimulations for global scale: Spherical geographic automata

“…presented in Figure 1. Polyhedrons with smaller and more faces provide a better representation of the Earth and cause less distortion when projecting between the base polyhedron and the corresponding spherical surface (Ulmer et al, 2020). The icosahedron has 20 faces which can easily be packed into hexagons and is thus a pop- After defining the preferred base polyhedron, a fixed orientation relative to the actual surface of the Earth must be specified.…”

“…There are five polyhedrons including tetrahedron, cube, octahedron, dodecahedron, and icosahedron which are commonly used as the initial sphere for DGGSs as presented in Figure 1. Polyhedrons with smaller and more faces provide a better representation of the Earth and cause less distortion when projecting between the base polyhedron and the corresponding spherical surface (Ulmer et al, 2020). The icosahedron has 20 faces which can easily be packed into hexagons and is thus a popular design choice for constructing spherical models.…”

QuadGridSIM: A quadrilateral grid‐based method for high‐performance and robust trajectory similarity analysis

“…The value of the geographic grid model has been recognized by previous research due to its advantageous features such as uniformity, discretization, multiresolution, and cell indexing (Gibb et al., 2022; Goodchild, 2018; Li & Stefanakis, 2020; Peterson, 2016; Yao et al., 2020). The geographic grid model can be defined as a system for representing a geographic entity using a series of discrete, regular cells according to some predefined rules (OGC, 2017; Ulmer et al., 2020; Zhou et al., 2010, 2023). Commonly used geographic grid geometries are triangle, quadrilateral, and hexagon (Hojati et al., 2021; OGC, 2017).…”