Message #1451

From: Andrey <andreyastrelin@yahoo.com>
Subject: Re: [MC4D] Social dream
Date: Wed, 23 Feb 2011 07:31:13 -0000

Roice,
We don’t need to calculate axis set for each polytope. The list that I presented in the first message is complete for non-prismatic bodies. For prisms there will be 5 or so more axes sets, but we can include them in log structure description with the coordinate system (and axis ordering) for every set.
Initial camera position may be different for different bodies, but I think that it’ll be enough to keep camera position in the program-specific section of log (that will be read by the program that created log file and ignored by other programs).
Twist definition by two axes is good only for 4D polytopes with axes passing through the body center. For 5D and more we shold return to the restricted set of elementary twists (and I’m not sure that 3 axes will give definition of the twist - take for example 5D simplex with its 3-cycles of cells. What axis goes where?). For flats we should have separate enumeration of rotation centers (and use center instead of the first axis) - not a big deal, log structure will be almost the same, but… there is infinite number of centers and we must describe periodic pattern that gives finite centers set (and enumeration will depend on this pattern). And in hyperbolic spaces we have no vectors at all - so there will be something very different for sticker-free twist definitions.

Andrey

— In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@…> wrote:
>
> I like it :)
>
> It would be good if we could come up with a way to specify the initial
> orientation of the polytopes used to generate the axis set in a generic
> manner, such that it didn’t have to be considered for each polytope. I’d
> even prefer this if the chosen coordinate systems were not very natural for
> some of the shapes. Like you say, difficult for human, but easy for the
> program.
>
> I also like Melinda’s suggestion to try to ensure everything is general if
> possible. It feels like your thoughts extend perfectly well to 5D and other
> dimensions. I’m not yet sure how to apply them to the hyperbolic puzzles of
> MagicTile, but perhaps you already have thought about that and know how it
> might go for MHT633?
>
> Roice
>
>
> On Tue, Feb 22, 2011 at 12:56 PM, Andrey <andreyastrelin@…> wrote:
>
> > Okay, let’s write fractions of full turn: 1/2,2/3,2/5,37/100 etc. It’s
> > universal (in 4D puzzles) and not a big problem for programs.
> >
> > So twist record will look like 15:23:2/3:8 .
> >
> > To enumerate axes of the set we can select some coordinate system (that is
> > natural for tesseract, 24-cell and duoprisms, and we can select something
> > for 5-cell and 120-cell), get vectors of length 1 in directions of all axes,
> > sort them in by w coordinate, then by z, by y and at last by x, and select
> > the last (maximal) vector as 0, next as 1 and so on (for vectors greater
> > than (0,0,0,0)). It may be difficult for human, but easy for the program.
> >
> > Andrey
> >
> > — In 4D_Cubing@yahoogroups.com, "Andrey" <andreyastrelin@> wrote:
> > >
> > > I thought about usage of degrees (72, 120, 90,…) but it will not work
> > for douprisms. Actually I want to have rational number there, but it’s more
> > easy to write their common denominator is the head (near the set
> > description) and show only numerators of the angle in all twists. We may
> > write D=360 for all puzzles other than douprisms.
> > > Or you want to write denominators only? Then again we’ll need two records
> > for 144-deg rotation… Not good when we can select format with one record
> > for every twist of the cell/face/edge/vertex…
> > >
> > > Andrey
> > >
> > > >
> > > > But if I’m reading right, you are suggesting a 180-degree rotation on
> > the
> > > > 120-cell puzzle would be angle=30 (60/2). So the nature of the puzzle
> > does
> > > > seem to affect how the same twist angle is recorded. It feels like
> > it’d be
> > > > nicer if the recording of angles did not have this kind of dependency.
> > > >
> > > > seeya,
> > > > Roice
> > > >
> > >
> >
> >
> >
> >
> > ————————————
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
>