A recent challenge was to see if the algorithm can be used to place spherical caps on the surface of a sphere. After a substantial effort it was concluded that the answer is yes. The algorithm runs smoothly with a maximum c comparable to that for circles. The image shows a projection of the spherical caps with c=1.43, N=6, 241 caps, 80% fill. Representation of a sphere on a flat surface is well known to be problematic, and this projection has much apparent distortion at the poles. The two large regions at top and bottom are caps which enclose the north and south pole. The algorithm was constructed such that trials and placements are not constrained by the details of spherical coordinates.
A much better way of visualizing the data is as a movie in which the sphere rotates. Paul Bourke has done this, with the result shown. The spherical caps are shown as cones with spherical bases. movie