Message #1212

From: Roice Nelson <>
Subject: Re: [MC4D] MHT633 v0.1 uploaded
Date: Wed, 27 Oct 2010 13:56:07 -0500

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!

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 <> 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, 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
> ————————————
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