Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 GeodesicGridPoints

Source Notebook

Generate points on a geodesic grid

Contributed by: Jan Mangaldan

ResourceFunction["GeodesicGridPoints"][n]

attempts to arrange n points in a geodesic grid on a unit sphere centered at the origin.

Details and Options

A geodesic grid is also known as the icosahedral-hexagonal grid.
A geodesic grid subdivides a sphere according to the vertices of a geodesic polyhedron.
ResourceFunction["GeodesicGridPoints"] returns 10m2+2 points, where m=Ceiling[Sqrt[(n-2)/10]].
The points returned by ResourceFunction["GeodesicGridPoints"] are arranged to have the symmetries of an icosahedron.
ResourceFunction["GeodesicGridPoints"][n,WorkingPrecision→p] gives a result with entries of precision p.

Examples

Basic Examples (1) 

Generate 162 geodesic grid points:

In[1]:=
Graphics3D[Point[ResourceFunction["GeodesicGridPoints"][162]]]
Out[1]=

Options (2) 

WorkingPrecision (2) 

Generate machine-precision geodesic grid points:

In[2]:=
ResourceFunction["GeodesicGridPoints"][12]
Out[2]=

Generate geodesic grid points with 24-digit precision:

In[3]:=
ResourceFunction["GeodesicGridPoints"][12, WorkingPrecision -> 24]
Out[3]=

Applications (1) 

Use a Delaunay mesh to make an approximation to a sphere:

In[4]:=
DelaunayMesh[ResourceFunction["GeodesicGridPoints"][252]]
Out[4]=

Neat Examples (1) 

Visualize the spherical Voronoi diagram of a set of geodesic grid points:

In[5]:=
ResourceFunction["SphericalVoronoiDiagram"][ ResourceFunction["GeodesicGridPoints"][252], "ShowOriginalPoints" -> True]
Out[5]=

Version History

  • 1.0.0 – 14 June 2021

Source Metadata

  • Citation:
    • Bauer, R., "Distribution of Points on a Sphere with Application to Star Catalogs." Journal of Guidance, Control, and Dynamics, vol. 23, no. 1, 130-137, 2000. DOI: 10.2514/2.4497
    • Sadourny, R., Arakawa, A., Mintz, Y., "Integration of the non-divergent barotropic vorticity equation with an icosahedral-hexagonal grid for the sphere." Monthly Weather Review, vol. 96, no. 6, 351-356, 1968. DOI: 10.1175/1520-0493(1968)096<0351:IOTNBV>2.0.CO;2
    • Williamson, D.L., "Integration of the barotropic vorticity equation on a spherical geodesic grid." Tellus, vol. 20, no. 4, 642-653, 1968. DOI: 10.1111/j.2153-3490.1968.tb00406.x

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