Thread: "Presenting 3D Cube looking from inside out"

From: David Vanderschel <DvdS@Austin.RR.com>
Date: 27 Mar 2005 12:20:45 -0600
Subject: Presenting 3D Cube looking from inside out



I am wondering if anyone can provide the reference for
a way of presenting 3D Rubik's in 2D by regarding it
as an empty box and displaying the view looking inside
with one face removed. (I recall that the method has
been mentioned on this list previously, but without
much elaboration.)

I know that I have seen a thorough presentation using
that method of showing the state of the Cube. I have
done some fairly exhaustive Web-searching on the
subject, and I have not come up with anything. So I
am inclined to suspect that I probably saw it in a
magazine. My best bet is that it was in one of
Douglas Hofstadter's Metamagical Themas columns in
Scientific American. If that is the case, I probably
have the old issue still lying about if someone could
just tell me which one. (Yes, I have them going back
to the '70s.) Of course, something on the Web would be
even better.

More detail on the presentation method: Think of the
Cube as an empty box with 9 transparent stickers stuck
on each of 6 transparent faces to the Cube. Looking
down from the top, remove the Up face and set it to
the side of the box with the same orientation. Now,
for the 2D viewing projection, the vertical sides of
the box (and the stickers on them) project as
trapezoids; but, looking from the inside out this way,
it is easy to see which stickers are adjacent to any
given one. It is not even difficult to imagine how
the stickers on the set-aside 'lid' relate to those in
the top rows of the vertical faces. This solves the
problem that a normal projection of the 3D Cube will
leave at least three faces unobservable, so additional
mechanisms for 'looking around' are needed with these
normal projections.

What I was really hoping for was a software simulation
of Rubik's Cube based on this looking-from-the-inside
model. It would be far simpler to implement than
MagicCube4D. A big advantage of having such a
simulation is that this way of looking at the 3D Cube
is much more nearly analogous to the way MagicCube4D
presents the 4D Cube. I think folks might catch on to
MagicCube4D's way more quickly if they could first
play with a 3D Cube presented in the 'lid off' manner.

Regards,
David V.




From: David Barr <david20708@gmail.com>
Date: Sun, 27 Mar 2005 13:55:06 -0500
Subject: Re: [MC4D] Presenting 3D Cube looking from inside out



Two Java applets come to mind. I wrote the first one:

http://www.puzzlingaddiction.com/Cube/applet/
http://www.geocities.com/jaapsch/puzzles/cubie.htm




From: David Barr <david20708@gmail.com>
Date: 28 Mar 2005 15:01:04 -0600
Subject: Re: [MC4D] Presenting 3D Cube looking from inside out



On Sunday, March 27, "David Barr" wrote:
>Two Java applets come to mind. I wrote the first one:

>http://www.puzzlingaddiction.com/Cube/applet/
>http://www.geocities.com/jaapsch/puzzles/cubie.htm

I had not found those. The second one has some the
more impressive elaborations I have seen in any of the
Rubik's Cube simulators. David's comes closest to
simulating what I recall. The main difference is that
what I was looking for displayed the top face with it
set aside (to the right, as I recall; and as opposed
to just tilted up and out), as viewed from the outside
(exception for this one face), and with correct aspect
ratio (square). I think that displaying the top
(only) as viewed from the outside makes it easier to
visualize how its stickers lay relative to those in
the top rows of the vertical faces.

I may try diddling David's code to make it do what I
want - that is if I can figure out how it works. ;-)

I am becoming more confident that the original thing I
saw was a magazine article; and, if anyone knows the
details of the reference, I would still be interested
to learn about it.

Regards,
David V.





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