Efficient Calculation of Distance Transform on Discrete Global Grid Systems and Its Application in Automatic Soil Sampling Site Selection

Geospatial data analysis often requires the computing of a distance transform (DT) for a given vector feature. For instance, in wildfire management, it is helpful to find the distance of all points in an area from the wildfire’s boundary. Computing a distance transform on traditional Geographic Information Systems (GIS) is usually adopted from image processing methods, albeit prone to distortion resulting from flat maps. Discrete Global Grid Systems (DGGS) are relatively new low-distortion globe-based GIS that discretize the Earth into highly regular cells using multiresolution grids. In this thesis, we introduce an efficient DT algorithm for DGGS. Our novel algorithm heavily exploits the hierarchy of a DGGS and its mathematical properties and applies to many different DGGSs. We evaluate our method by comparing its distortion with the DT methods used in traditional GIS and its speed with the application of general 3D mesh DT algorithms on the DGGS grid. We demonstrate that our method is efficient and has lower distortion. To evaluate our DT algorithm further, we have used a real-world case study of selecting soil test points within agricultural fields. Multiple criteria including the distance of soil test points to different features should be considered to select representative points in a field. We show that DT can help to automate the process of selecting test points, by allowing us to efficiently calculate objectives for a representative test point. DT also allows for efficient calculation of buffers from certain features such as farm headlands and underground pipelines, to avoid certain regions when selecting the test points

Disdyakis Triacontahedron Discrete Global Grid System

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 to store all of the information about the Earth in a convenient format such that one can easily use it to solve a wide variety of problems. In this thesis, we explore the idea of creating 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 also 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, neighborhood 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