Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 KoayPoints

Source Notebook

Generate Koay's uniformly distributed points on a sphere

Contributed by: Jan Mangaldan

ResourceFunction["KoayPoints"][n]

gives the positions of n uniformly distributed points on the surface of a unit sphere using Koay's method.

Details and Options

ResourceFunction["KoayPoints"] places points so they are approximately equally spaced.
ResourceFunction["KoayPoints"][n,WorkingPrecision→p] gives a result with entries of precision p.

Examples

Basic Examples (1) 

200 uniformly distributed points on a sphere:

In[1]:=
Graphics3D[Point[ResourceFunction["KoayPoints"][200]]]
Out[1]=

Options (2) 

WorkingPrecision (2) 

Generate machine-precision points:

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

Generate geodesic grid points with 24-digit precision:

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

Applications (1) 

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

In[4]:=
DelaunayMesh[ResourceFunction["KoayPoints"][99]]
Out[4]=

Neat Examples (1) 

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

In[5]:=
ResourceFunction["SphericalVoronoiDiagram"][ ResourceFunction["KoayPoints"][88], "ShowOriginalPoints" -> True]
Out[5]=

Version History

  • 1.0.0 – 14 June 2021

Source Metadata

  • Citation:
    • Koay C.G., "Analytically exact spiral scheme for generating uniformly distributed points on the unit sphere." Journal of Computational Science, vol. 2, no. 1, 88–91, 2011. DOI: 10.1016/j.jocs.2010.12.003

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