I would expect the energy minimization approach to perform better than anything else, for vectors distributed uniformly on the surface of the N-sphere. Why go with the Fibonacci sphere instead?
def fibonacci_sphere_point(idx, num_points):
i = idx + 0.5
phi = math.acos(1 - 2 * i / num_points)
golden_ratio = (1 + 5 ** 0.5) / 2
theta = 2 * math.pi * i / golden_ratio
sin_phi = math.sin(phi)
cos_phi = math.cos(phi)
sin_theta = math.sin(theta)
cos_theta = math.cos(theta)
return (
cos_theta * sin_phi,
sin_theta * sin_phi,
cos_phi,
)
As I describe in the article, different methods produce similar but slightly different solutions. An optimal solution for one objective function, may not be the optimal for a different objective function. I then give details about how the solution that optimizes volume of the convex hull is different to the solution that optimizes for packing distance, etc.
If you just want N in a certain range, we can use the triangle-based polyhedron and successively quadruple or triple the number of faces. Then use the face normals as points. This gives visually appealing distributions without any real oddities.