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From: Matt J on 6 Apr 2010 14:49
ImageAnalyst <imageanalyst(a)mailinator.com> wrote in message <b26db047-bf86-46eb-a23d-f1ce4d045d21(a)11g2000yqr.googlegroups.com>...
> That may be true but Ruslan never did really answer Matt's question of
> whether they're allowed to have random orientation or not. If you're
> just dumping a bunch of sugar cubes into a bowl you won't have 100%
> packing efficiency. You'd pack them side to side if you wanted to
> maximize the number in the sphere but he didn't explicitly say that he
> needed to know the *maximum* number of cubes that can fit.
===============

Are we really sure that packing them side to side isn't a deceptive solution?

Packing side-to-side minimizes the separation between cube centers along some directions, i.e. directions parallel to the cube edges, but not along oblique directions. If you rotate some cubes 45% you can reduce the separation distance along these directions.

Are we sure this doesn't give rise to a trade-off in which the intuitive solution isn't the optimum one?
From: Mark Shore on 6 Apr 2010 15:17
>
> Are we sure this doesn't give rise to a trade-off in which the intuitive solution isn't the optimum one?

No, not _sure_ at all, which makes it kind of an interesting problem.
From: Ruslan on 6 Apr 2010 23:44
really sorry for my bad english :(..

I try to fit cubes in a way that they must be only vertical or horizontal, i.e their center must be in the same line with their neighbour horizontal and vertical lines. like cubic rubic :))

somehow there will be some error because of sphere, some part of some cubes will be outside of a sphere where cube and sphere intersects. for my case outside volume of any cube can be at most %25 - %30 of total volume of cube.

thank you
From: ImageAnalyst on 7 Apr 2010 06:15
OK, so did you try my strel() way?
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