graphics3d - how to get $n$ equidistributed points on the unit sphere

We can get $n$ equidistributed points in the unit circle using CirclePoints. But how do you get $n$ equidistributed points on the unit sphere(surface of a ball)? The preliminary idea is to suppose that the points are some electric charges with same electric quantity on a sphere. And they have the same effective working area. I think their position is what I want. This is my current solution:

point = RandomPoint[Sphere[], 10^6];
Graphics3D[{Sphere[], Blue, PointSize[.02], 
  Point[Union[point,SameTest -> (EuclideanDistance[#1, #2] < 0.4 &)]]}, 
 Boxed -> False]

points

But this solution cannot draw the specified number of points, and the space is not very equidistributed in some places.

Answer

Aha~ I suppose this question is created while solving this. Am I correct @yode :P

So here's an easy solution, simple, elegant, and may I say even quite fast after some optimization?

pt = With[{p = 
     Table[{x[i], y[i], z[i]}, {i, 80(*number of charges*)}]}, 
   p /. Last@
     NMinimize[
      Total[1/Norm[Normalize[#1] - Normalize[#2]] & @@@ 
        Subsets[p, {2}]], Flatten[p, 1]]];
Graphics3D[{Opacity@.3, Darker@Green, Sphere[], Opacity@1, 
  PointSize@Large, Darker@Blue, Point@*Normalize /@ pt}]

The result is quite good:

the setting of the minimization variable is crucial, or the point will not be on surface. But fortunately, our 'kindergarten physics' taught us that when charges are freely scattering in a sphere, they'll always be on surface evenly! Thus this must be some sort of 'most even' form of scattering as it follows physical laws.

Comments

plotting - Plot 4D data with color as 4th dimension

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I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1....

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