[AYBABTME]

Isn't the density distribution of values going to be higher along the directions pointing in the cube's corners? There's more volume between the sphere and nearby the corners than between the sphere and nearby the faces' centres.

[philipdloewen]

That’s why the method discards points outside the sphere, and returns a normalized point generated from an interior sample.

[joshka]

You can show the exact opposite of this in a degenerate fixed point situation. Say you have -1, 0, +1 in each dimension. The only valid coordinates are the 6 on each face. (+-1, 0, 0) (0, +-1, 0) (0, 0, +-1). Not sure if this is the only counter example. I'd guess that with floating point math and enough bits the bias would be very small and probably even out.