Message #1211

From: Andrey <andreyastrelin@yahoo.com>
Subject: Re: [MC4D] MHT633 v0.1 uploaded
Date: Wed, 27 Oct 2010 18:09:03 -0000

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