Message #224

From: Roice Nelson <roice@gravitation3d.com>
Subject: Re: [MC4D] My gallery!
Date: Mon, 27 Mar 2006 17:54:41 -0600

Well I must eat my words, or at least admit to being a little ridiculous
because Remi’s enthusiasm gave me the bug again. I’ve relapsed slightly
into my obsessive compulsive rubik’s disorder by doing some hobby
programming this past week to create a MagicCube5D proof of concept. This
will allow 2^5 through 5^5, has some options to play with in terms of
projections, and allows overall cube (view) rotations. There is no twisting
yet, but it makes me believe such a puzzle is plenty possible. I’m not sure
yet if I want to do any more than this, but I did want to share what is
here with you guys.

I posted a couple screen shots and an install here if you are interested:

http://www.gravitation3d.com/magiccube5d/<http://www.gravitation3d.com/magiccube5d/>

A couple quick comments on it…

Left mouse dragging will rotate the view and right mouse dragging will zoom
(3D transformations only).

The full view rotations are done by selecting 2 axes and then pressing a
button. Using 2 axes is the proper extension to higher dimensions, and the
way to think about it is that a rotation transforms a set of points in a
plane. So for example, if this were a 3D puzzle and you wanted to do the
rotation you typically think of as about the z axis, you would select x and
y as your 2 axes to define the rotation plane. You could think of the
rotation axis as being the rotation plane normal vector, but in the case
of a 5D cube, there are 3 normal vectors to a given rotation plane.

I made the projection distance for 4D and 5D separately changeable to avoid
direct face overlapping problems if that is desired. Some of the other
options were just made in the effort to try and find out how to make enough
space for this puzzle.

Enjoy :)

Roice

On 3/17/06, Roice Nelson <roice@gravitation3d.com> wrote:
>
> Excellent point about us only needing to do 90 degree rotations. I
> spaced out on that 5D cube applet for a while and I agree it doesn’t help
> much, especially since the rotations aren’t restricted to 90 degrees. I
> think MagicCube5D cube will require 2 kinds of 4D rotations, those that
> change the view only and those that perform certain face twists. Note that
> 4D view rotations will be required because in Remi’s pictures, portions of
> each 4-cube face are not visible. So these rotations would be required to
> bring those portions of the faces into or out of view.
>
> Perhaps the 4D view (and the 90 degree 5D view) rotations could both use
> the control-click method. It doesn’t seem we would need to have
> control-shift-clicking for most 5D view rotations (more on this below)
> - differentiating a 4D or 5D view rotation would just depend on if you
> control-clicked a non-central 4-cube or a control-clicked a non-central
> sticker on the central 4-cube.
>
> Twisting, both 3D and 4D twists, could all be handled by single clicks as
> in MagicCube4D. A click on a 4D stickers not in the center of the 4-cube
> would result in a 4D twist. Single clicks in the center 3-cube of the
> 4-cube face would do 3D twist rotations just as in MagicCube4D. I have no
> idea if this is making sense. This new puzzle is difficult to talk about :)
>
>
> Remi’s cross-form idea has grown on me too. In the spirit of MagicCube4D,
> there could just be 3 hidden faces (the ones he has moved off to the
> sides). I guess that would be a lot of non-visible items to keep track of
> though. In regards to the 4-cubes that don’t seem to have a place, perhaps
> this is where a shift-control-click could come in. It could be used to
> rotate the puzzle such that these hidden faces move to the center and hence
> into the view. Say shift-control-left does one and shift-control-right does
> the other (the 3rd hidden face would behave more like the hidden face in the
> 4D puzzle).
>
> One thing I do not like about this projection however is that both the 4D
> and the 5D portions are being centrally projected, kind of like the
> attached image of a 5D cube. Since 2 dimensions are being projected along
> the same axis, information gets lost. This could be part of the trouble of
> fitting all the faces in. Maybe things could be improved if only the 5D
> axis was centrally projected, and the 4D axis was projected along another
> line. This sort of necessitates a 4D visualization portion with overlapping
> parts though, not as in MagicCube4D, so maybe having 4D and 5D both
> centrally projected is still the best despite the downsides. In any case,
> since space is such an issue, a couple of possible thoughts to help "make
> more space"…
>
> (1) Drawing in wireframe.
> (2) Drawing only colored dots at the centers of stickers - downside is
> that it won’t look cubelike.
> (3) Using alpha blending for translucency - I think that would be the
> most difficult).
>
> I have a few more thoughts on this puzzle, which I will mention in a
> response to Remi’s last email. But I hear you on volunteering for the code
> development, and the solving of this puzzle if it ever materialized. I sort
> of drew the line at the 4^4 and never tried the 5^4. I think it will be the
> same with the 3^5. At some point, it just gets a little ridiculous! I
> think we’ve all already safely secured super-geek status for ourselves
> anyway :)
>
> Roice
>
>
> On 3/15/06, Melinda Green <melinda@superliminal.com > wrote:
> >
> > I totally agree with everything you say about the problems of
> > representation, etc. Adjacent 4-cubes would "meet" at a common 3-cube,
> > and not just at their 2D faces but at every point in the 3-cube. I like
> > Remi’s idea of unfolding the 5-cube into a cross form. In such an
> > interface I am imagining that only the one (currently) central 4-cube
> > would be the workable one that you would interact with, but even with
> > allowing for overlapping 3-cubes we would need to recognize that the
> > central 3-cube in that central 4-cube would still need to be shown
> > somehow overlapping with a couple of other 4-cubes and I would have no
> > idea where to put them.
> >
> > Regarding your comment about playing with the rotations of a simple
> > 5-cube in order to understand the problem better, there is something
> > that looks like that here:
> > http://home.att.net/~numericana/answer/polyhedra.htm#polytopes but I
> > don’t see how that helps much. I mean that we’re not really looking for
> > a way to rotate a 5-cube but just a way to rotate one of its 4D
> > hyperfaces, right? Well MC4D already implements a way to rotate the 4D
> > cube by control-clicking a 3D hyperface to rotate it to the center. It
> > seems to me that this should be enough of an interface to specify a
> > twist in 5D. That would only allow 90 degree twists but some combination
> >
> > of these should be enough to specify any legal twist of a face of a
> > 5-cube. Now imagine operating on the central 4-cube in one of Remi’s
> > cross arrangements. The only other thing I expect would be needed to
> > solve the 5D cube would be some way to rotate other 4-cubes into the
> > center. The natural extension to the 4D puzzle would perhaps be to
> > shift-control-click on a 4-cube adjacent to the central one in order to
> > "rotate" that one into the center. Of course I still haven’t solved the
> > problem of where to place the missing couple of 4-cubes from the
> > previous paragraph, nor am I volunteering to do any of the development
> > of such a beast but I suspect it might just be possible. Good luck
> > solving it though!!
> >
> > -Melinda
> >
>