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From: Ruslan on 6 Apr 2010 05:22
if there is a package sometimes we'll need use that.

its not aim of my homework. actually little part of my thesis. I already coded for rectangular prism. but for more accurate results I need in sphere.

I can code it also. but it will be messy if I dont have really well algorithm,way to solution.

thanks
From: Matt J on 6 Apr 2010 10:53
Ruslan <akle(a)mynet.com> wrote in message <1841677921.509893.1270559287728.JavaMail.root(a)gallium.mathforum.org>...
> they are all the same identical. 1cm of side. it can also be smaller than 1cm, which will result in more accurate results but slower in time.
====

Sorry, that answer seemed ambiguous to me. "Identical" means they are not rotated with respect to one another?

If the cubes can have different orientation, then I believe there are more economical ways to pack the cubes. For example in 2D, assuming the cubes are square, I believe you can pack them into a hexagonal lattice. Not sure, though.
From: Mark Shore on 6 Apr 2010 11:25
> ====
>
> Sorry, that answer seemed ambiguous to me. "Identical" means they are not rotated with respect to one another?
>
> If the cubes can have different orientation, then I believe there are more economical ways to pack the cubes. For example in 2D, assuming the cubes are square, I believe you can pack them into a hexagonal lattice. Not sure, though.

I suspect not. The internal packing efficiency of cubes is 100%, so any unfilled volume will be between the sphere boundary and the outermost layers of cubes. Symmetry considerations suggest that rotation is irrelevant. Symmetry should also determine the centering appropriate for different number of layers of cubes, i.e. for an odd number the midpoint of a single central cube would lie at the center of the sphere, whereas for an even number the vertices of eight neighbouring cubes would. For non-central layers of cubes the same odd/cube-centered vs. even/four cube edges would apply to the 'axis' of the sphere.

Just my geometric intuition.
From: ImageAnalyst on 6 Apr 2010 14:10
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. He said "I
need many 1cm side cubes inside sphere as much as possible with their
location" which is not exactly unambiguous. Still not sure what that
means.
From: Mark Shore on 6 Apr 2010 14:28
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. He said "I
> need many 1cm side cubes inside sphere as much as possible with their
> location" which is not exactly unambiguous. Still not sure what that
> means.

True. My built-in English as a second language translator automatically changed "I need many 1cm side cubes inside sphere as much as possible with their location" to "I need to find as many 1 cm sided cubes as possible that will fit inside a 3 cm radius sphere, and their locations".

Which may or may not be the correct interpretation.

It actually looks like a moderately interesting problem if you allow the ratio of the cube edge length/sphere diameter to vary.
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