Uniform Geodesic Grid

Overview

uniform-geodesic-grid is a Node.js command-line tool for generating a homogeneous hexagonal geodesic grid, specifically designed for geostatistical applications. The tool produces well-behaved grids that maintain uniform spacing across the globe (~20% variance in cell area), based on the algorithm developed by Philippe Rivière. For more details on the algorithm, please refer to Rivière's notebook on Observable.

The tool outputs a GeoJSON FeatureCollection containing the grid cell geometries. Included cell properties are

• gid, the unique cell id
• lon and lat, the coordinates of the cell centroid
• neighbors, the list of adjacent cell ids
• icosahedron_placement, one of "vertex", "edge", or "face", depending on where the cell is located with respect to the geodesic icosahedron used to project the points

Installation

To install the tool, use npm to install directly from the GitHub repository:

npm install -g https://github.com/tzakharko/uniform-geodesic-grid

Usage

After installation, the tool can be used via the command line. Below are the basic usage instructions:

Basic Command

uniform-geodesic-grid [options]

Options

• --cell-spacing <km>: Specifies the desired spacing between points (cell centroids) in kilometers. This corresponds to the radius of the instribed circle for each hexagonal cell.

• --cell-area <km>: Specifies the desired area per cell in kilometers squared.

• --k <subdivisions>: Sets the number of triangle edge subdivisions for grid generation.

• --pretty: Pretty-formats the JSON output for easier readability.

One of the options --cell-spacing, --cell-area, or --k should be specified. These options are mutually exclusive. Note that the resulting grid properties are not guaranteed to be an exact fit with the specified parameters, in practice the difference is less than 5%.

Examples

1. Generate a grid with a specific cell spacing:

   uniform-geodesic-grid --cell-spacing 100

   This command aims to generate a grid with a hexagonal cell diameter of 100km. The actual returned grid has cells ranging in size between 90.3km and 108km, with median cell diameter of 100km.

2. Generate a grid with a specific number of subdivisions:

   uniform-geodesic-grid --k 20

   This command generates a grid using 20 subdivisions of triangle edges.

3. Generate a grid with pretty-formatted JSON output:

   uniform-geodesic-grid --cell-spacing 100 --pretty

   This command generates the grid and outputs the GeoJSON in a more readable format.

Algorithm Description

The tool generates a geodesic grid by first placing equally spaced points on the faces of a planar icosahedron. These points are then backprojected onto a spherical surface to form a geodesic icosahedron. The grid cells are created by constructing a Voronoi diagram of these backprojected points, resulting in a homogeneous hexagonal grid. This method ensures uniform spacing and consistent cell shapes, making it ideal for geostatistical applications.

The algorithm follows the approach outlined by Philippe Rivière, utilizing the Gray-Fuller projection to maintain geometric accuracy during the transformation from the plane to the sphere.

Acknowledgments

This tool is based on and reproduces the work of Philippe Rivière. For a more in-depth understanding of the algorithm and its mathematical foundations, please visit his Observable notebook.