Dennis Clarke wrote:

> Any way, there are a number of Java applets that already do this with Java3D but
> I think that the cpu overhead is really massive.  You need a pile of Sun servers
> to render in any kind of reasonable time frame.
>

Applets doing Java3D???
Where?

Also, if the cpu overhead is for rendering, Java3D should have taken care of that
by using the hardware acceleration of the computer it's running on. So what does
take the cycles?

--
"My new computer's got the clocks, it rocks
But it was obsolete before I opened the box" - W.A.Y.

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Dennis Clarke wrote:

> > >The problem is how to place the spheres in the box to get the maximum
> > >numbers of spheres that can fit in the box. I think that this is not a
> > >trivial problem, but is there a complete analytic solution at all (using
> > >with, height, depth and radius as parameters)?
> > >
>
> A crystaline matrix that has the body-centered cubic lattice construction is the
> most efficient way to pack spheres.  Mother nature has proven this in many
> materials that we run into all the time.  There are arguments for the FCC ( face
> centered cubic lattice ) but those arguments are typically based on materials
> that are under stress and demonstrate any of a number of dislocations in order
> to achieve plastic deformation.  If you have a cubic box with three axi a,b,c of
> equal length and angles alpha, beta, and gamma ( between each pair of axi ) that
> are also equal then the lattice structure of Si or NaCl (salt) would be best.
> If you get into a triclinic system where all axi and angles are different then
> the problem gets ugly very fast and even mother nature has a fit.  The best
> material that would get close would be Al2SiO5 but again, like salt, we are
> dealing with spheres of different sizes.  Kepler suggested this problem about
> 400 years ago and suggested a solution that was correct, without the benefit of
> x-ray crystalography or modern numerical methods.  His solution was based on the
> simple observation that a man selling grape-fruit in the market will stack in a
> close packed haxagonal plane and then add another layer on top of that one
> slightly shifted to allow the next layer to sit in the crevass between three
> other touching grape-fruit on the lower layer.  Why?  Because it works.  The
> grape-fruit don't tumble over the edge and this seems to be a good arrangement.
> There is plenty of lost volume in this packing but such is life.  If the sphere
> radius is much smaller than the box dimensions then we have a solution.
>
> Dennis Clarke

I'm no math expert (high school sophomore) but I think this is right. Also, the most
efficient packing would depend on the ratio of the box size to the sphere size. For
example, if you have a 2x2x2 box and spheres of diameter one, obviously you could
pack at most eight spheres using a cube-type pattern. However, if the apheres are
much smaller, I believe the best arrangement is the hexagonal planes. The best way
to pack them is the way you would build a tetrahedron out of spheres, hexagonal
planes with each sphere resting on the three below it. There is a third way,
hexagonal planes where each sphere rests on two below it, so as to create hexagonal
tilings along the x-z plane and the x-y plane. I think this also depends on the
box-sphere ratio, but I'm pretty sure the tetrahedral stacking is best for
infinitessimal spheres.

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> GATTACA
> There is a little chemical joke in that movie title by the way.

I see that it looks like a sequence of DNA, but I don't get the joke... Could you
explain?

--
Anthony L. Bennett
http://welcome.to/TonyB

Non nova, sed nove.

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TonyB wrote:
> 
> > GATTACA
> > There is a little chemical joke in that movie title by the way.
> 
> I see that it looks like a sequence of DNA, but I don't get the joke... Could you
> explain?

... that particular nucleotide sequence can not happen.  At all. 

    Yeah .. I know .. a very little joke in a movie that had so much symbolism,
from the double helix staircase ( render that! ) that Jerome could not walk on
despite his genetic perfection to the Vincent Freeman ( free man ) last name. 
Why was his beautiful girlfriend named Irene Cassini?

Dennis Clarke

http://www.interlog.com/~dclarke/povray/povray.html

> 
> --
> Anthony L. Bennett
> http://welcome.to/TonyB
> 
> Non nova, sed nove.

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Dennis Clarke wrote in message <37CB1A84.3DD1D658@interlog.com>...
<snip>
>... that particular nucleotide sequence can not happen.  At all.

Why not?

<snip>
>Why was his beautiful girlfriend named Irene Cassini?

Something to do with a NASA mission currently on the way to Saturn?

On to another aspect of the film - did I miss something, or did that
incinerator have a switch on the inside?!

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Please don't post web pages to newsgroups!

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On Mon, 30 Aug 1999 19:36:04 -0400, Dennis Clarke <dcl### [at] interlogcom>
wrote:

> neomorphic.html

  Hi, Dennis. This looks like copyrighted material. It is probably in
everyone's best interests (including povray.org) to post the .url and let
interested parties read it for themselves.

  Thanks for your participation.

-- 
Alan
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Sorry all.  I guess that is a slight breech of news group etiquette.

Dennis Clarke

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Dennis Clarke wrote:

>   Sorry all.  I guess that is a slight breech of news group etiquette.
>
> Dennis Clarke

Nevertheless thank you, I enjoyed visiting the site and the information
it had to offer.

-earl

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