Message #11

From: David Vanderschel <DvdS@Austin.RR.com>
Subject: Fwd: Re: [MC4D] Re: phew, at last… [4^4 solution]
Date: Fri, 01 Aug 2003 19:36:17 -0000

Date: Tue Apr 9, 2002 11:53 am

— In MC4D@yahoogroups.com, "Christian Lundkvist"
<christian.lundkvist@t…> wrote:

Hi again Daniel!

It was pretty late when I wrote the letter, so maybe I didn’t make
myself clear. We seem to agree that a completely accurate 4d
projection would be very surreal and probably unusable for puzzling.
The way to go is with the "unfolding box" projection that the MC4D
uses. Think about the 3D -> 2D analogy again. What I meant was a lot
like your suggestion of putting a mirror "inside" the box. The image
that you would have seen if there had been a mirror inside the box
would be placed off to the side, so it wouldn’t be completely
correct. You would still see the bottom of the box, but off to the
side is the image that would have been in the center had there been a
mirror there. I’m not sure if this would be much help making it
easier to solve the cube, but it was nice thinking about how the
mirrored image would move when you move the cube.

About how the correct representation would look like: You would
probably need to separate the stickers as is done with the "box"-
projection. Then you would have to make the stickers on the
other "side" invisible too so as to not obscure the image. It would
be quite fun to play around with it since it would be distorted when
you rotate it without twisting, like the 3D image in your posting
would be distorted in 2D when you rotate the cube… Maybe it could
be implemented as a choice in some future version of MC4D, for
the "hardcore" cubers! :-)

/Christian

—– Original Message —–
From: dgreen@s…
To: MC4D@yahoogroups.com
Sent: Tuesday, April 09, 2002 3:18 AM
Subject: Re: [MC4D] Re: phew, at last… [4^4 solution]

hello christian,

i assume you’re asking me rather than don.
yes, i wanted a completely accurate projection of a 4d cube+mirror
scene
using 4d viewpoint and direction that "sees" both objects such that
the
mirror mostly includes a 4d "reflected" view of the missing face.
The
view you described may not be complete. i think it also wouldn’t be
correct since the current display is of a 4d viewpoint in a direct
line
from the center of the object through both the closest and furthest
faces. a single mirror somewhat off to that line would not display
an
axis-oriented view

that said, i just realized i may not be making the correct 3d
analogy. i
keep forgetting that our 4d projection is really analogous to
taking the
lid off a box and looking in so that the bottom of the box is a
small
square in the center, and the sides appear foreshortened arrayed
around
that furthest face. i suppose it would make some sense to think of
putting a mirror inside the box so that you can look back at the
inside
of the lid, but that suggests that the mirror would necessarily
obscure
part of the normal view of the puzzle.

it occurs to me that i don’t really know what the "correct" view of
the
puzzle from the outside would look like. the only thing that seems
obvious is that you could never see more than half of the faces just
like in 3d which, while perhaps more accurate, would be harder to
operate on. though perhaps the addition of a true 4d mirror would
ameliorate that problem, especially if we allowed users to click on
hidden faces "through the mirror".

i’m not sure what you’re getting at with "lines between stickers"
but i
can say that we never experimented with 4d mirrors but we did
experiment
with faithful projections of the invisible face both normally and in
wireframe, but the results were clearly unhelpful.

don, you want to jump in here and tell us what this all means and
what
would be possible or helpful?

-daniel
— End forwarded message —