Disdyakis Triacontahedron DGGS

Abstract

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.

Enabling geosimulations for global scale: Spherical geographic automata

“…Each discrete cell is assigned a unique identifier at each resolution and used as a data structure to represent its location (Sahr, 2008). Three techniques are primarily utilized to index cells in DGGSs: hierarchy‐based indexing, axis or coordinate‐based indexing, and space filling curve indexing (Hall et al, 2020). For hexagonal DGGS, hierarchy‐based indexing schemes are commonly used (Zhao et al, 2022).…”

Correlation Analysis and Reconstruction of the Geometric Evaluation Indicator System of the Discrete Global Grid

“…This paper selected a typical DGG model-QTM [33] (see Figure 6)-as an example to study the correlation of the quantitative indicators of the Goodchild Criteria. Because the spherical triangle is the most basic grid unit of many global discrete grid systems, it is simple and can be combined into other shapes of grid systems such as spherical diamonds, pentagons, and hexagons, depending on the needs [22,46]. QTM is a spherical triangular grid structure based on an octahedron.…”

“…DGGs have been widely used in large-scale spatial data management, decision making, and simulation analysis. For example, they have been used in the spatial data organization, indexing, analysis, and visualization [6][7][8][9]; global environmental and soil monitoring models [10,11]; atmospheric numerical simulations and visualizations [12]; ocean numerical simulations and visualizations [13]; place names management or gazetteers [14]; big Earth data observations [12,15]; modeling of offset regions around the locations of Internet of Things (IoT) devices [16]; cartographic generalization and pattern recognition for choropleth map-making [17]; the Unmanned Aerial Vehicle (UAV) data integration and sharing [18]; the Modifiable Areal Unit Problem (MAUP) [19]; especially in digital Earth [5,16,[20][21][22], and so on.…”

General Method for Extending Discrete Global Grid Systems to Three Dimensions

“…[49]. The input DGGS for this example uses a disdyakis triacontahedron as the initial polyhedron, a non-standard 1:4 triangle refinement, and the vertex oriented great circle slice and dice projection [48] to preserve area [50]. The 3D DGGS has a target aspect ratio of one, a radial mapping exponent of three to achieve perfect volume preservation (excluding the central layer), and a maximum radius of 1.33R (8495 km).…”