How to Distribute N Points on the Surface of a Sphere ?


This java-Applet compares different construction methods.

For optimization, select how to evaluate the given point set and press "poly" or "type".
The number above a point-set is its evaluation value, the data below are the Euler-vector of its combinatorial type.
  • In the first case, the applet optimizes the point-set only and leaves the combinatorial type of the initial point-set is untouched.
  • In the second case, the applet tries to find also the best combinatorial type of the point-set for given N.
  • It first optimizes the point-set according to the given combinatorial type.
  • Then one edge is crossed and the point-set with the new combinatorial type is optimized.
    If the second point-set is better than the first, the point-set is kept; otherwise it shall be removed.
  • This crossing-edge routine continues until no better point-set had been found after all edges of a point-set had been tested.