Problem with 20b and 32b puzzles is fixed (at least they don't crash during=
initialization :) )
Roice,
by the way, there exists {infinity,3} tiling of the hyperbolic plane ;) W=
hat about including it in the 2D Magic Tiles program?
Andrey
--- In 4D_Cubing@yahoogroups.com, Roice Nelson
>
> Thanks for the explanations Andrey! They help a lot, and it's so cool th=
at
> the infinite cells are horospheres. Though they are spheres in the Poinc=
are
> model after all, at least I was right about them not living in a hyperbol=
ic
> plane, on sphere sections orthogonal to the model boundary :)
>=20
> You have really produced just about the ultimate analogue puzzle in my
> opinion. The fact that the "face" shape, the dimension, and the geometry
> are all three relaxed makes it such a lovely abstraction. I am quite
> excited to study and think about this more, and to actually spend a littl=
e
> time playing with the puzzle too!
>=20
> Cheers,
> Roice
> P.S. No pressure on the autorotation/autosliding of course (though I thin=
k
> it would be neat). I am able to get a good feel with the mouse alone.
>=20
> P.P.S. If it was not too difficult, it would be amazing if the puzzle co=
uld
> also be viewed in the Poincare model. I'm not sure how easy it would be =
to
> transform the mouse controls, or what other issues might arise. And in a=
ny
> case, it does feel like the half-space view is the best choice for ease o=
f
> working with the puzzle.
>=20
>=20
> On Wed, Oct 27, 2010 at 1:09 PM, Andrey
>=20
> > Roice,
> > Funny thing about the projection - that it's not the model! It's real =
view
> > of H3 from inside, central projections of points to the almost planar s=
ensor
> > of the small camera. So it was not me who selected the shape and angles=
of
> > infinite polyhedra, it's their real images (unless you use FishEye slid=
er).
> > I thought that we'll see more of the surface is we'll take a look from
> > large distance, but it looks like not the case. And I almost know why :=
)
> > In the Poincar=E9 models (both half-plane and disk) cells are going by
> > spheres that are tangent to the boundary plane/sphere of the model.
> >
> > Andrey
> >
> >
> >
> >
> > --- In 4D_Cubing@yahoogroups.com, Roice Nelson
> > >
> > > Andrey,
> > >
> > > I'm trying to understand how the infinite {6,3} cells appear to wrap
> > around
> > > on themselves. You did a really nice job making them look like conve=
x
> > > polyhedra...so much so, that when I first looked at the program, I
> > thought
> > > they were dodecahedra!
> > >
> > > Would you mind describing the projection to Euclidean space you're us=
ing?
> > > Beltrami-Klein model, Poincare disk model, something else? If you sh=
owed
> > > more of the {6,3} cells, would the projection cause these infinite ce=
lls
> > to
> > > visually intersect with themselves? (It appears like it would.) Mor=
e
> > > generally, I'd like to answer the question of what an entire cell wou=
ld
> > look
> > > like in your projection and in other models. (I think a cell does no=
t
> > live
> > > on a hyperbolic plane, so I'm betting a cell would not be a portion o=
f a
> > > sphere in the Poincare model). Thanks for any insight or references =
on
> > this
> > > topic you can provide!
> > >
> > > Take Care,
> > > Roice
> >
> >
> >
> >
> > ------------------------------------
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
>