IMPROVED UNIFORM POINTS ON A SPHERE WITH APPLICATION TO ANY GEOGRAPHICAL DATA DISTRIBUTION

This paper describes improved algorithms based on equal-areas spherical subdivision to obtain approximated solutions to the problem of uniform distribution of points on a 2-dimensional sphere, known as Smale's seventh problem (Ref. 1). The algorithms provide quasi-uniform distribution points by splitting Platonic solids into subsequent spherical triangles of identical areas. Original equal-areas subdivision algorithm can be applied for a number of points N = f 2s, where f is based the number of triangles of the Platonic solid considered and s the number of divisions. The main feature of the improved algorithm is that adjacent triangles share common vertices that can be merged as well as to apply reshaping. If a side of the Platonic solid is split into p identical smaller triangles, then the improved method provides N = p f 2s points. The proposed algorithm is fast and efficient and, consequently, it is suitable for various applications requiring high value of N. The proposed algorithm is then applied to two geographical data distribution that are modeled by quasi-uniform distribution of weighted points.

IMPROVED UNIFORM POINTS ON A SPHERE WITH APPLICATION TO ANY GEOGRAPHICAL DATA DISTRIBUTION Conference Paper