Sphere Packing

I woke up at 3:00am the other morning thinking about using shapes to fill a volume.

I wondered about using spheres to fill space. The reason I was thinking about spheres was because they are symmetric in space and their moment of inertia is independent of orientation (assuming homogeneous density).

Anyways!

But how well do spheres cover a space?

Turns out that it is an interesting problem. In 1611, Kepler proposed that at best spheres could cover about 74% of space. I actually worked through it that night and came up with 78% and thought of Nitrogen... but that has little to do with anything.

From what I read, there is still no verified proof that Kepler's solution is correct (although I read elsewhere it is proven).

Anyways, here is the wikipedia article if you are interested.

It answered my other question which was, "How about random packing, like BB's in one of those tubes?"

BTW, I think that uniform dense cubes are symmetric in terms of moment of inertia, and cover space well... but not sure.

I better shut up... but I thought it was neat that this problem is an entire field of research, I suppose under computational geometry or Finite Element Analysis... and is applicable for simulating equations of motion for models described as polygonal meshes.

Then there is collision detection!