General Method for Extending Discrete Global Grid Systems to Three Dimensions

Benjamin Ulmer,Faramarz Samavati,John Hall

doi:10.3390/ijgi9040233

Benjamin Ulmer, Faramarz Samavati + Show 1 more

Open Access

https://doi.org/10.3390/ijgi9040233

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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.

Highlights

IntroductionThe near-ubiquity of certain smart technologies (smartphones, LIDAR, autonomous vehicles, UAVs, drones) is leading to an increasing amount of spatial information and data being generated [1]
The near-ubiquity of certain smart technologies is leading to an increasing amount of spatial information and data being generated [1]
Geographic information systems (GIS) have traditionally been used for this task, where different datasets are represented as individual layers in a two-dimensional (2D)—or if altitude is represented a three-dimensional (3D)—coordinate system, which acts as a proxy for the Earth [2,3]

Summary

Introduction

The near-ubiquity of certain smart technologies (smartphones, LIDAR, autonomous vehicles, UAVs, drones) is leading to an increasing amount of spatial information and data being generated [1]. The development of technologies and tools for managing these types of data, along with other conventional geographic information, is more important than ever. Geographic information systems (GIS) have traditionally been used for this task, where different datasets are represented as individual layers in a two-dimensional (2D)—or if altitude is represented a three-dimensional (3D)—coordinate system, which acts as a proxy for the Earth [2,3]. A partitioning of the Earth into a set of non-overlapping cells allows information to be associated with the cell(s) that correspond with the appropriate region(s) of the Earth. Such partitionings are termed discrete global grids. Current state-of-the-art DGGSs make use of an approximating polyhedron as an initial discretization of the Earth’s surface [9,10,11], and are the class of DGGS this work will focus on

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