Generating Fixed-Size Hexagonal Grids On A Globe With QGIS, R And Terra

Creating a polygonal grid of hexagons around the globe with a fixed size for each hexagon presents a fascinating challenge in geospatial analysis. This article delves into the intricacies of generating such grids, particularly focusing on achieving a custom size for each hexagon, specifically 40,000 km². We'll explore the complexities involved in projecting hexagonal grids onto a sphere and discuss various approaches using tools like QGIS, R, and other geospatial libraries. Understanding the nuances of spherical geometry, map projections, and grid generation algorithms is crucial for tackling this problem effectively. This comprehensive guide aims to provide a thorough understanding of the concepts and techniques required to generate fixed-size hexagonal grids on a spherical globe.

The Challenge of Hexagonal Grids on a Sphere

The inherent challenge lies in the fact that a sphere's surface cannot be perfectly divided into regular hexagons. Unlike a flat plane where hexagons can tessellate seamlessly, a sphere's curvature introduces distortions. Think of a soccer ball – it's made of pentagons and hexagons, a necessary compromise to cover the spherical surface. When we attempt to project a regular hexagonal grid onto a sphere, we encounter distortions in shape and area, especially as we move away from the projection's center. To maintain a consistent area for each hexagon, we need to employ sophisticated techniques that account for these distortions.

Spherical geometry dictates that the angles and distances on a sphere are calculated differently than on a flat plane. This difference is crucial when we aim for equal-area hexagons. We need to consider the geodesic distances, which are the shortest paths between two points on a sphere, rather than simple Euclidean distances. Furthermore, map projections, which transform the sphere's surface onto a 2D plane, introduce their own distortions. Selecting an appropriate projection is paramount to minimizing area distortions and ensuring the generated hexagons are as close to the desired size as possible. The choice of projection will significantly impact the final grid, and a careful evaluation of different projections is necessary for optimal results.

Tools and Techniques for Hexagonal Grid Generation

Several tools and techniques can be employed to tackle the challenge of generating fixed-size hexagonal grids on a sphere. QGIS, a powerful open-source Geographic Information System, offers a range of functionalities for grid generation and geospatial analysis. R, a programming language and environment for statistical computing and graphics, provides extensive libraries for geospatial data manipulation and analysis, including the sf and geos packages. Other geospatial libraries and tools, such as Terra, can also be leveraged for this task. Let's explore some of these approaches in detail:

QGIS

QGIS provides a user-friendly interface for creating grids, but generating truly equal-area hexagons on a sphere requires careful consideration of the Coordinate Reference System (CRS). One approach is to generate a hexagonal grid in a projected CRS that minimizes area distortion for the region of interest. For global grids, equal-area projections like the Hammer projection or Mollweide projection are suitable choices. However, even with these projections, the hexagons won't be perfectly equal in area due to the inherent distortions. The key is to choose a projection that minimizes these distortions across the globe. Once the grid is generated, QGIS's geoprocessing tools can be used to calculate the area of each hexagon and adjust the grid parameters iteratively to achieve the desired size.

Another approach within QGIS involves using the **