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Source Code: Optimal orientations of discrete global grids

Title of Manuscript: Optimal orientations of discrete global grids

Authors: Richard Barnes

Corresponding Author: Richard Barnes (

DOI Number of Manuscript TODO

Code Repositories

This repository contains the algorithms and program described in the manuscript above, along with information on acquiring the various datasets used, and code to perform correctness tests. OpenMP is used to parallelize the code.


Spatial analyses involving binning require that every bin have the same area, but this is impossible using a rectangular grid laid over the Earth or over any projection of the Earth. Discrete global grids use hexagons, triangles, and diamonds to overcome this issue, overlaying the Earth with equally-sized bins. Such discrete global grids are formed by tiling the faces of a polyhedron. However, the orientations of these polyhedra have been chosen to satisfy only simple criteria such as equatorial symmetry or minimizing the number of vertices intersecting landmasses. Here, efficient algorithms are used to optimize the orientation of polyhedra with respect to a number of quantities of interest. The optimized orientations are used to reenvision Fuller's Dymaxion map.


Clone this repo using

git clone

You must also obtain certain prerequisites:

sudo apt install TODO gdal geographiclib boost-geometry

Anaconda3 was used to install the aforementioned libraries on XSEDE. The file Makefile.xsede should provide useful hints for getting everything working; however, given the uniqueness of potential target environments for the code, I do not give details here. While I am happy to provide support for my code, it is best to work with your supercomputer's help staff to get this compiled on your machine of choice.

To compile the program for production run:

mkdir build
cd build
cmake -DCMAKE_BUILD_TYPE=Release ..

The result of either compilation is a program called dgfinder.exe.

Running this program will either run extensive code tests or perform the optimal orientation search.

Converting the ADD data

The ADD high-res data can be acquired from here:

The exact dataset used is here:

It must be converted into a WGS84 projection and appropriate datasets selected, as follows:

ogr2ogr -progress -t_srs '+proj=longlat +datum=WGS84 +no_defs' -where "surface='ice coastline' OR surface='grounding line'" -f "ESRI Shapefile" add_ice_coast_and_grounding_line.shp add_coastline_high_res_line_v7.3.shp


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