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Date: Tue, 30 Mar 1999 21:57:43 -0500 (EST)
From: Nichael Cramer <ncramer@bbn.com>
To: Norman Richards <orb@cs.utexas.edu>
Cc: "Cube Lovers (E-mail)" <Cube-Lovers@ai.mit.edu>
Subject: Re: Keyboard cube [was: Re: Wrist pains]
In-Reply-To: <199903302344.SAA11205@life.ai.mit.edu>

Norman Richards wrote:
>   Oddly enough, I have been thinking about a method to manipulate a
> cube by use of the numeric keypad.  It seems most moves can be
> completed rather naturally, but I do not know if it works in practice.
>
>   Anyways, take a keypad like this:
>
> 7 8 9
> 4 5 6
> 1 2 3
>
>   This corresponds to a face of a cube quite nicely.  Suppose you
> wanted to rotate the right face clockwise.  One could enter 36 or 69,
> for example, which you could conceptually think of as the direction
> your hand would move to rotate the right face clockwise.  Counter
> clockwise would be the other direction.  (96 or 63 or even 93) The
> same technique could be applied to the left face or top face or bottom
> face.  The middle slices could be rotated just as easil: 52 would rotate
> the middle vertical slice down.

Or a extension of your scheme might be to combine arrow keys with the
keypad, in a two-handed approach.

I.e. 6^ or 6v rather than 36 or 69; no order dependence this way.
(Likewise, I find the arrow keys more mnemomic.)  The model is that you're
"grabbing" the specified cubie and rotating it in the specified direction.

In its most natural form, this assumes that the numeric key-pad and the
arrow keys are separate (as they are on my keyboard), although one could
certainly use some other set of "directional" keys aside from the standard
arrow keys.

And as I say, this also assumes --most naturally, although not
necessarily-- a two-handed approach.

>   The question is how to effect rotating the front and rear faces.
> For me, 19 and 91 seem natural for F and F' because they basically
> mimic the twisting motion.  The rear is more troublesome, but perhaps
> for symetry 73 and 37 might be used?

For completeness, too, there is also the slice between the front and back
face.

Rather than muddy the paradigm, perhaps other (non-assigned) keys should
be used.

The handy "0" key might make a natural candidate for the front face.

On the other hand since the back face and middle slice are rather
"pathological" cases in this paradigm, might it perhaps make sense to use
keys "outside" the model?  For example "R" and "M".  (Or, less
mnemonically --and depending on the set-up of your keyboard-- "/" or "*"
or ".", which on my keyboard are right beside the numeric keypad keys.)

(For these last cases, perhaps on the <- and -> keys should by
operational.  The up and down arrows being less meaningful here.)

>   Anyways, that could take care the turns, Cube rotations could be as
> simple as a shift followed by a direction. [...]

This seems like a good scheme.

N