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.
Highlights
In the modern era, we are increasingly collecting vast amounts of information about the Earth; many zettabytes of data are already available, and more is being collected daily [1,2]
We develop an indexing scheme inspired by Atlas of Connectivity Maps (ACM) [16]
We show that our Discrete Global Grid System (DGGS) reduces the mean angular distortion by almost a factor of four while maintaining accurate and efficient queries and without significantly sacrificing desirable DGGS properties
Summary
We are increasingly collecting vast amounts of information about the Earth; many zettabytes of data are already available, and more is being collected daily [1,2]. The projection chosen should preserve the above properties for cells of the polyhedron and their spherical counterparts at all resolutions It should reduce the distortion created in the resulting planar cells as much as possible. An important challenge for DGGS research is to find new initial polyhedra and associated area-preserving projections that further reduce angle and shape distortion while maintaining fast and efficient DGGS operations. To address this challenge, we introduce a new DGGS that uses a Disdyakis Triacontahedron (DT) as the initial polyhedron (see Figure 1). The main contributions of this work are the creation of a novel DGGS system that preserves area and maintains fast queries while decreasing angular distortion
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