[danwills]

I think it can be done that way yeah but in order to yield a uniform-density of points on the surface of the sphere there's some pre-correction (maybe a sqrt or something? I can't remember) that's needed before feeding the 'uv' values to the trig functions to make 3D positions. Otherwise points will 'bunch up' and be more dense at the poles I think.

[srean]

Indeed.

One way to fix the problem is to sample uniformly not on the latitude x longitude rectangle but the sin (latitude) x longitude rectangle.

The reason this works is because the area of a infinitesimal lat long patch on the sphere is dlong x lat x cosine (lat). Now, if we sample on the long x sin(lat) rectangle, an infinitesimal rectangle also has area dlong x dlat x d/dlat sin(lat) = dlong x dlat cos (lat).

Unfortunately, these simple fixes do not generalize to arbitrary dimensions. For that those that exploit rotational symmetry of L2 norm works best.

[murkle]

Yes, see https://news.ycombinator.com/item?id=45001593

[egorfine]

Generating two random 1..360 numbers and converting them to xyz would bunch up at the poles?

[danwills]

Yeah @srean gives the example of the different areas of strips at different lattitude, that's a good one - and I think if you imagine wrapping the unit square (2 values randomly between 0 and 1) to a sphere in a lat-long way, the whole top and bottom edges of the square get contracted to single points at the top and bottom latitude locations (respectively) on the sphere.. so if the point density was uniform going into that then it surely won't be afterwards ;)

[egorfine]

See @srean's explanation above.