Message #1215

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] MHT633 v0.1 uploaded
Date: Wed, 27 Oct 2010 14:38:57 -0500

Interesting. That would be definitely be cool, though it might wreak havoc
on my code with special casing. E.g., the function that calculates the
rotation of a face based on the number of sides of the polygon would break
down. I think my simple algorithm to find the coloring pattern might too,
etc. I’ll add it to my running list of items to look into though. (I
haven’t worked on improving MagicTile as much as I hoped, but I have made
some changes towards supporting tilings of general {p,q} instead of just
{p,3}. Things still need further work though.)

By the way, please disregard the mistake at the end of my last email. When
I wrote "And in any case, it does feel like the half-space view is the best
choice for ease of working with the puzzle." I meant "*the real view you did
* is the best choice…". A half-space model representation would be cool
as well of course, in addition to a Poincare model view :)

seeya,
Roice

On Wed, Oct 27, 2010 at 2:24 PM, Andrey <andreyastrelin@yahoo.com> wrote:

> Roice,
> by the way, there exists {infinity,3} tiling of the hyperbolic plane ;)
> What about including it in the 2D Magic Tiles program?
>
> Andrey
>
>
> — In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@…> wrote:
> >
> > Thanks for the explanations Andrey! They help a lot, and it’s so cool
> that
> > the infinite cells are horospheres. Though they are spheres in the
> Poincare
> > model after all, at least I was right about them not living in a
> hyperbolic
> > plane, on sphere sections orthogonal to the model boundary :)
> >
> > 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
> little
> > time playing with the puzzle too!
> >
> > Cheers,
> > Roice
> > P.S. No pressure on the autorotation/autosliding of course (though I
> think
> > it would be neat). I am able to get a good feel with the mouse alone.
> >
> > P.P.S. If it was not too difficult, it would be amazing if the puzzle
> could
> > 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
> any
> > case, it does feel like the half-space view is the best choice for ease
> of
> > working with the puzzle.
> >
> >
> > On Wed, Oct 27, 2010 at 1:09 PM, Andrey <andreyastrelin@…> wrote:
> >
> > > 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
> sensor
> > > 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
> slider).
> > > 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 Poincaré 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 <roice3@> wrote:
> > > >
> > > > 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
> convex
> > > > 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
> using?
> > > > Beltrami-Klein model, Poincare disk model, something else? If you
> showed
> > > > more of the {6,3} cells, would the projection cause these infinite
> cells
> > > to
> > > > visually intersect with themselves? (It appears like it would.)
> More
> > > > generally, I’d like to answer the question of what an entire cell
> would
> > > look
> > > > like in your projection and in other models. (I think a cell does
> not
> > > live
> > > > on a hyperbolic plane, so I’m betting a cell would not be a portion
> of a
> > > > sphere in the Poincare model). Thanks for any insight or references
> on
> > > this
> > > > topic you can provide!
> > > >
> > > > Take Care,
> > > > Roice
> > >
> > >
> > >
> > >
> > > ————————————
> > >
> > > Yahoo! Groups Links
> > >
> > >
> > >
> > >
> >
>
>
>
>
> ————————————
>
> Yahoo! Groups Links
>
>
>
>