The amount of information collected about the Earth has become extremely large. With this information comes the demand for integration, processing, visualization and distribution of this data so that it can be leveraged to solve real-world problems. To address this issue, a carefully designed information structure is needed that stores all of the information about the Earth in a convenient format such that it can be easily used to solve a wide variety of problems. The idea which we explore is to create a Discrete Global Grid System (DGGS) using a Disdyakis Triacontahedron (DT) as the initial polyhedron. We have adapted a simple, closed-form, equal-area projection to reduce distortion and speed up queries. We have derived an efficient, closed-form inverse for this projection that can be used in important DGGS queries. The resulting construction is indexed using an atlas of connectivity maps. Using some simple modular arithmetic, we can then address point to cell, neighbourhood and hierarchical queries on the grid, allowing for these queries to be performed in constant time. We have evaluated the angular distortion created by our DGGS by comparing it to a traditional icosahedron DGGS using a similar projection. We demonstrate that our grid reduces angular distortion while allowing for real-time rendering of data across the globe.

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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.

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