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It would be my inclination to use triangles (or some polygon) for the snow.
In the real world falling snow can assume a variety of characteristics, but in
a snow globe the stuff seems to be composed of little white chips which are
generally flat. (I may be wrong here since I have not taken one of these things
in hand for some time.) Further, as has been mentioned, randomly oriented flat
surfaces (e.g. triangles) would help achieve the twinkling effect.
If the final rendering is to be a still image, filling a spherical space with
whatever objects randomly distributed should present no problem . However, if
it is to be an animation, I would agree with previous posts that the problem
becomes a little more complex - though being constrained to a sphere volume as
opposed to a box may be a good thing.
Abe
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