Message #809

From: David Smith <>
Subject: Re: [MC4D] 5D interface
Date: Thu, 31 Dec 2009 06:38:34 -0800

Hi everyone,

I thought I would give my own brief thoughts on the concept of a 1-click twist user
interface for MC5D and higher-dimensional cubes.  In order to define a unique
twist of a 4-dimensional face in MC5D, we need to specify two different coordinates
relative to the center sticker of that face, so that we have two axes, or a "plane of
rotation" about which a 90-degree rotation could be defined.  Let us consider an
interface analogous to the tesseract in MC4D, in which a 2-dimensional face of
the 3-dimensional face of stickers is selected (by clicking a 2-colored piece sticker),
and then rotated either clockwise or counter-clockwise.  In MC5D, we would have
to select a 3-dimensional face of stickers, of which there are eight, and then
specify one of six axes to rotate that
3-dimensional face around, which defines
the rotation of the 4-dimensional face completely.  In the 3^5 cube, I do not believe
a natural twist with a single click exists because if we were to click a 2-colored piece
sticker, that would not provide enough information to define a twist (we would have
specified a 3-dimensional face, but not how to rotate it).  If we click a 3, 4, or 5-colored
piece, the problem is that each of these pieces belongs to multiple 3-dimensional
faces, so we have not defined a unique 4-dimensional rotation.

On 5^5 cubes and larger 5-dimensional cubes it would be possible, because we can
click 2-colored piece stickers which define both the 3-dimensional face and the axis
around which to rotate it.  However, using a single click is, in my opinion, a bit
too unnatural and complex.  It would be much simpler to use two clicks, and I believe
Roice’s solution to this is better than the
analogous one from MC4D I described above,
as in 5 dimensions it would be difficult to predict how the face would rotate around
the two axes, while as MC5D is set up, one can see where the pieces are going to
move to.

Considering higher-dimensional cubes, we would need more axes of rotation, so that
the method analogous to MC4D I described above would use three clicks for a
6-dimensional cube, four clicks for a 7-dimensional cube, etc.  In theory a 1-click
solution might be possible for many sizes and dimensions, but only by using an
unnatural and abstract method.

All the best,

— On Thu, 12/31/09, Melinda Green <> wrote:

From: Melinda Green <>
Subject: Re: [MC4D] 5D interface
Date: Thursday, December 31,
2009, 2:27 AM


I don’t have a full answer to this question but I feel like I might be

able to put some constraints on its answer. I think that what we’re

hoping for is a 1-click UI that performs a natural twist, and ideally

one that extends to N-dimensions. I also don’t think that we want a UI

similar to the TouchCube because that seems particularly awkward to me.

People seem to like the MC4D twisting UI and I think that a goal should

be for the basic MC4D twist UI to fall out of an N-D definition. Given a

basic twist, I bet that we can find appropriate modifier keys and other

variations on it to let us reach all positions and face reorientations,

but that goal should be secondary to finding a good basic twist UI


The constraint that I suggest that we work with is that a twisting click

on a sticker should always identify two special N-D points: The center

of the cubie containing the clicked sticker, and the center of the face

containing the sticker. The twist should define a rotation that leaves

these two points unmoved while rotating the selected face (plus one

slice of all neighboring faces) in a direction controlled by which mouse

button was clicked, such that the twisting stops at the first point

where the geometry of the puzzle is identical to when it started. IOW,

when the face first snaps into a new legal position. Any stickers that

can not provide any such rotation that changes the state of the puzzle

would not identify a "grip".

What I don’t know is how many different kinds of rotations will satisfy

these constraints in N-dimensions. The above may not provide enough

constraints in that some stickers might be capable of identifying more

than one grip, but I feel as if looking at the problem this way might

give us a start on finding a natural and usable N-D 1-click twist UI



Roice Nelson wrote:



> Hi Kyle,


> By "Change it so that clicking a face alters the cubies in that face",

> I figure you mean "Change it so that clicking a face alters the

> */stickers/ *in that face". This is an interesting idea. It might be

> good to use Rubik’s TouchCube

> < com/watch? v=waY_evu6D_ Y> for analogies. There,

> you can drag your finger along a row of stickers in a face to define a

> twist of an adjacent face (one that your fingers did not touch). As

> you’re pointing out, this is in contrast with MC5D, where you "drag"

> the sticker of one 2C piece to the sticker of another 2C piece,

> twisting the face containing the stickers.


> So I definitely think there is "some there there" in your suggestion,

> but I also think it is not close to clearly defined yet, and a lot

> would need to be worked out to make it viable. The main issue is that

> there are so many possible twists to choose from, and a single twist

> needs to be fully specified by what the user clicks (this was a

> difficult aspect in coming up with the current workable interface).

> Without having really thought it through, here are some off the cuff

> questions which might help direct ideas:


> (1) Which type of cubie(s) will the user need to click? Right now in

> MC5D, it is only 2C cubies. In the TouchCube, it is a corner/edge/ corner.

> (2) How many cubies does the user need to click? MC5D: 2, TouchCube: 3.

> (3) How to define which face to twist? Currently, it is the face

> containing the clicked stickers. In the TouchCube, it is the only

> other face sharing all the specified cubies.

> (4) Can this be done such that the complete set of twists are

> available? We need the coordinate-axis- aligned twists at a minimum,

> and there are 12 of these per face.


> I think a good goal is to keep the number of clicks to a minimum. My

> guess is that a new approach along the lines of this suggestion could

> likely require 3 or even 4 clicks, but I’m not sure. If so, that is a

> big downside in my opinion to the 2 clicks we have now. I still

> occasionally wonder if there might be some magical way to specify a

> twist with one click, and I’d love it if someone could figure out

> how. The specification is much more difficult than the coding!


> Take Care,

> Roice


> P.S. A relevant historical post on this is here

> <http://games. com/group/ 4D_Cubing/ message/234>. Scroll

> down to the section titled "User Interface for the Twists"…



> On 12/30/09, *kygron* <kygron@yahoo. com <mailto:kygron@yahoo. com>> wrote:


> Hi,


> I said a while ago that I would critic the 5D interface,

> apparently I wanted to do more than I am willing, so I’m writing

> the quick form here and you can ask questions if I’m unclear.


> My problem is one of attention. There’s too many things on screen

> to attend to all of them at once. (I know, that’s the point,

> but…) There IS a way to change the interface to help with this,

> while still maintaining the essence of the puzzle.


> When I started the puzzle, I picked a (5)face, got a picture in my

> mind of how it looked, clicked a few cubies, and…. nothing

> happened! Sure, the thing rotated, but all the cubies stayed in

> the same relative positions to each other. I would have had to

> look elsewhere to see the manipulations I caused.


> Change it so that clicking a face alters the cubies in that face

> and you’ll get alot more people able to enjoy manipulating your

> puzzle.


> Hope that helps




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