Thread: "Visualizing Hyperbolic Honeycombs"

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Thanks Melinda! I didn't know about Shapeways supporting voxel format -
that's great. It's been two years since we focused on the physical models,
but we are planning some more and this is really good to know.

Since you like the catacombs, I bet you'll like this...

1. Download this hires equirectangular projection:
https://www.dropbox.com/s/ftl5fdatkzed01e/373_catacombs_equi.png?dl=3D0
2. Go to this link: http://hawksley.github.io/eleVR-Picture-Player/
3. Use the folder icon at the bottom right to open the downloaded file.
You might have to try twice (I did).
4. Voil=C3=A0, the catacombs in immersive 3D :D Have a look around with=
the
A,S,D,W keys.

Henry, Vi Hart, and I were playing with that one evening, and started to
make an immersive video too, but haven't finished. A fun goal in this
direction is an immersive experience with hyperbolic transformations of the
catacombs, rather than only traversing them in a euclidean fashion. That
would result in all sorts of bizarre warping of the ceiling and red
creatures.

seeya,
Roice


On Wed, Nov 11, 2015 at 3:56 PM, Melinda Green melinda@superliminal.com
[4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:

>
>
> From honeycombs to catacombs. How cool is that? That's an incredible piec=
e
> of work, Roice! I'm really happy that you and Henry did such a huge piece
> of work, are publishing the results, and are sharing them with us. I can'=
t
> claim to understand more than a small fraction of it, but it's more than
> pertinent to anyone interested in creating or solving puzzles based on
> hyperbolic tilings. The images alone are incredible, and your 3D printed
> models are especially helpful and intriguing. I appreciate your attention
> to geometric accuracy with your "banana" edges.
>
> Brandon pointed out to me that Shapeways now supports a voxel format, so
> you will no longer need to perform the conversion back to polygons if you
> don't want to. I've been printing some fractal models of mine this way wi=
th
> excellent results. Here's one example:
> https://www.shapeways.com/product/AY8964AT9/zr-0 Just note that the
> documentation is thin and even wrong in parts but it should get better an=
d
> I can help if needed.
>
> Your 3D Schlafli symbol map is amazing. Your image grids give wonderful
> surveys of the mathematical landscapes, and your hyperbolic catacombs ima=
ge
> continues to fascinate me. Incredible job, guys!
>
>
> On 11/10/2015 5:56 PM, Roice Nelson roice3@gmail.com [4D_Cubing] wrote:
>
> Hello again,
>
> I wanted to share a new paper that Henry Segerman and I have been working
> on in the background for the last few years, which we just submitted it t=
o
> the Journal of Mathematics and the Arts.
>
> Why share with this group? Because the paper was born right here with th=
e
> following thread started by Nan!
>
> https://groups.yahoo.com/neo/groups/4D_Cubing/conversations/topics/2291
>
> It's an exciting thread in my opinion, and a nice record of an unfolding
> mathematical investigation. In the paper, we give a shout out to Nan and
> Don, and reference that initial thread.
>
> We were able to extend upper half space boundary images to all {p,q,r}
> honeycombs, even {=E2=88=9E,=E2=88=9E,=E2=88=9E}. Will someone figure ou=
t how to make a
> permutation puzzle out of that honeycomb?!? Believe it or not, I suspect
> it is possible.
>
> I hope some of you will enjoy reading the paper, or looking at the many
> images it contains. The preprint is here:
>
> http://arxiv.org/abs/1511.02851
>
> Best,
> Roice
>
>
>
>
>=20
>

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Welcome Vladimir!

Great to hear from you in this forum. Everyone, Vladimir is a very=20
prolific geometer who has developed many interesting and beautiful=20
things. He wrote the VRML tiler that I used to explore my=20
pseudo-platonic polyhedra (what I'd been calling infinite regular=20
polyhedra), which have since been incorporated into Magic Tile. I was=20
very glad to learn that he has joined Shapeways where I'm sure he will=20
do wonderful things.

Even though you convert to polygons on the back end, it's still a huge=20
help to users in many ways. First is because it's not at all easy for=20
most users to do that conversion, and second because bitmapped images=20
compress so well. It's tricky to set up a workflow that results in files=20
that Shapeways will accept, largely because we get almost no clues what=20
is wrong when a file is rejected, but since I've been able to do that,=20
I've found that your system is very tolerant of all sorts of=20
degeneracies in the data. My models often have lots of tiny floating=20
bits that I don't care about, and in general I get exactly what I want.=20
I would indeed love to print voxels directly when you are ready. Please=20
just let us know when and how to do that. In the meantime, I highly=20
suggest people start fooling around with SVX printing. I just now made=20
my model below downloadable as it can really help to start from a=20
non-trivial working example.

-Melinda

On 11/11/2015 4:47 PM, Vladimir Bulatov vladimir.bulatov@gmail.com=20
[4D_Cubing] wrote:
>
>
> Congratulations to Roice and Henry on thins very nice paper.
>
> I would like to comment on the voxel format support.
> Yes, we develop and support SVX voxel format in attempt to make more=20
> convenient and compact
> file format for 3D printing of very complex models. The notoriously=20
> detailed hyperbolic models are the ideal candidate for using SVX.
> However in the back end we are still converting SVX into triangles=20
> using abfab3d.
> It is because not all components of the 3D printing workflow can work=20
> directly with voxels yet.
> So, your voxel model needs to be reasonable good for conversion into=20
> triangle mesh.
>
> On Wed, Nov 11, 2015 at 4:26 PM, Roice Nelson roice3@gmail.com=20
> [4D_Cubing] <4D_Cubing@yahoogroups.com=20
> > wrote:
>
> Thanks Melinda! I didn't know about Shapeways supporting voxel
> format - that's great. It's been two years since we focused on
> the physical models, but we are planning some more and this is
> really good to know.
>
>
>
>
> --=20
> Vladimir Bulatov
> 3D graphics researcher
> Shapeways
> http://bulatov.org/
>
>
>=20


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">


Welcome Vladimir!



Great to hear from you in this forum. Everyone, Vladimir is a very
prolific geometer who has developed many interesting and beautiful
things. He wrote the VRML tiler that I used to explore my
pseudo-platonic polyhedra (what I'd been calling infinite regular
polyhedra), which have since been incorporated into Magic Tile. I
was very glad to learn that he has joined Shapeways where I'm sure
he will do wonderful things.



Even though you convert to polygons on the back end, it's still a
huge help to users in many ways. First is because it's not at all
easy for most users to do that conversion, and second because
bitmapped images compress so well. It's tricky to set up a workflow
that results in files that Shapeways will accept, largely because we
get almost no clues what is wrong when a file is rejected, but since
I've been able to do that, I've found that your system is very
tolerant of all sorts of degeneracies in the data. My models often
have lots of tiny floating bits that I don't care about, and in
general I get exactly what I want. I would indeed love to print
voxels directly when you are ready. Please just let us know when and
how to do that. In the meantime, I highly suggest people start
fooling around with SVX printing. I just now made my model below
downloadable as it can really help to start from a non-trivial
working example.



-Melinda