UNIFORM DISTRIBUTION OF POINTS ON A SPHERE WITH APPLICATION IN AEROSPACE ENGINEERING

This work describes two distinct approaches to build uniform star catalogs. This is done by developing two distinct algorithms to distribute N points on a sphere, problem known as the seventh Smale's problem. The first algorithm provides quasi-uniform points by splitting Platonic solids into subsequent spherical triangles of identical areas. This method can be applied for discrete values of N = F 2s, where F is the number of triangles of the Platonic solid considered and s the number of divisions. The second approach works any value of N, by slicing the unit-sphere into a limited number depending on the decomposition of N into prime factors. The uniform star catalog is then built using two algorithms distributing the catalog stars into the quasi-uniform equal area bins.

UNIFORM DISTRIBUTION OF POINTS ON A SPHERE WITH APPLICATION IN AEROSPACE ENGINEERING Conference Paper