I have to deal with a concrete problem that is: Given a 3d object I want to select N directions with N integer and N>=3 for projection that would maximize the information I gain and thus my ability to reconstruct the 3d object from 1d projections
I think (but I am not sure) that this can be translated to a simpler mathematical problem, that I poorly state here as: In 3d euclidean space, chosen an integer N, I want to find the N versor(unitary vector) maximizing the distance between them.
The 2D equivalent would have solutions expressed in angles for simplicity is: N=2 -> 0˚, 90˚ N=3 -> 0˚, 60˚, 120˚ N=4 -> 0˚, 45˚, 90˚, 135˚
Suggestions to solve this problem?
If I understand correctly, the Thomson problem should be quite related.
But since you want to restrict yourself to a half sphere, this might be something to have a look at: http://www.mathworks.com/matlabcentral/fileexchange/44515-generate-non-parallel-axes