Quickfur's renders

Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.

Re: Quickfur's renders

Postby quickfur » Mon Feb 10, 2014 5:29 pm

wendy wrote:The renders look like stereo pairs. (sigh). I really can't see stereo images. But they're beautiful all the same.

They are cross-eyed stereo pairs. The nice thing about it, is that if you can't see stereo pairs, you can still look at them individually as non-stereo images. :)

But cross-eyed viewing is really not that hard. I avoided it for a long time because it sounded a bit scary, but once I decided to learn it, it took me only a day or two to get accustomed to it. And once you see the images in full 3D, you just don't wanna go back again. :P Especially with 4D projections, you really want to see the projections with 3D depth, it helps a lot to perceive what's going on in the projected image.
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Re: Quickfur's renders

Postby quickfur » Mon Feb 10, 2014 5:33 pm

Keiji wrote:Hmm, do they really affect it that badly? How long are the renders taking?

Well OK, technically it doesn't take that long, but with the smaller polytopes it just takes a few seconds from writing the script to seeing the image on screen, whereas with the omnitruncated 120-cell, it's taking minutes for every small change to the scripts. It sorta dampens the momentum a lot (imagine when you're writing code and it takes two hours after a 1-line change to see whether or not it worked -- you can still do it, it's just not very pleasant).

OTOH, I was just being a bit whiny... If I intersperse it with other things, it's really not that bad. So maybe that's what I'll do, work on CRF crown jewels while waiting for the renders to run. :P
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Re: Quickfur's renders

Postby quickfur » Mon Feb 17, 2014 9:16 pm

student91 wrote:
quickfur wrote:Sighh... one week in February has already rolled by, and barely any progress on the omnitruncated-120cell page. :( There are some O(n^2) algorithms in my polytope viewer that's really killing rendering times with the insane number of vertices/edges that the omnitruncated 120-cell has. :cry: :oops: Maybe the Polytope of the Month for March should be the J92 rhombochoron instead. :XP: Or the castellated prism. :D That should give me enough buffer to get the omni-120cell done at last. :lol:

I vote for the J92-rhombochoron!! I would love to undertand it's structure in more depth :D

I've been making good progress on the omnitruncated 120-cell projections in the past day or so, after finally finding a good coloring scheme for the "mugshot" perspective projection. So it seems likely that March's Polytope of the Month will be the omnitruncated 120-cell after all.

But don't worry, the CRF crown jewels are definitely on the list for after March. I just thought it would be nice to finally have some closure for the uniform polychoron renders that I started years ago. Judging by the number of CRFs we're discovering every week recently, I'm not going to run out of things to render anytime soon! (Not to mention, even the good ole regular polychora have many more rendering possibilities that I just haven't had the time to visit yet. Like the vertex-first projections of the 120-cell, or, respectively, the cell-first projections of the 600-cell, which may indirectly lead to more CRF possibilities. And I'd like to render the 12 Hopf fibration rings of the 120-cell some time, too. So even within the uniform polychora alone, there's still a ton of stuff that can be done.)
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Re: Quickfur's renders

Postby quickfur » Wed Feb 19, 2014 9:33 pm

quickfur wrote:[...]
But don't worry, the CRF crown jewels are definitely on the list for after March.
[...]

And in preparation for that, I've already posted renders of the pentagonal rotunda (J6), the metabidiminished icosahedron, the bilunabirotunda (J91), and the triangular hebesphenorotunda (J92). These are probably old news for you forumites, but I'm posting here because I'm particularly pleased with this diagram that I made that shows the relationship between J92 and the icosidodecahedron:

Image

As you can see, J92 is intimately connected with the icosidodecahedron; its hexagonal face is actually the 6 vertices of the icosidodecahedron lying on the bisected plane, scaled down by the Golden Ratio.

This diagram is also the precursor to the J92 rhombochoron: if we fold the two J92's into 4D around the grey plane until they make a 60° dichoral angle with each other, they would form half of the J92 rhombochoron (minus the 12 additional vertices needed to make this side of the polytope CRF).
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Re: Quickfur's renders

Postby quickfur » Sat Mar 01, 2014 8:35 am

Welp, here it is! The final (convex) uniform polychoron on my website!

Image

This one was quite a beast to render, due to its sheer number of surtopes. It exposed a lot of poorly-written algorithms in my polytope viewer program. :P

This is, of course, the omnitruncated 120-cell, aka the omnitruncated 600-cell. Some of my favorite images from this round of renders:

Image

Image

Image

Really beautiful, if I say so myself. :P :oops: :lol:

And now that I'm finally done with the uniform polychora, next month we're gonna start on the cool stuff, the CRFs... And perhaps some of the Catalans as well? We shall see!
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Re: Quickfur's renders

Postby Marek14 » Sat Mar 01, 2014 8:47 am

I'm looking at your polychoron pages, and I think I found a mistake -- on the 24-cell page you say:

In 3D and beyond, the only regular space-tiling polytopes are the hypercubes, with one exception: the 24-cell.

This is, however, not true -- the 16-cell is also a regular space-tiling polytope; the 16-cell tiling is the dual of the 24-cell one (24-cell tiling is 3-4-3-3, the 16-cell is 3-3-4-3).

EDIT: Another minor bug - the grand antiprism page says:

In the same way, all the pentagonal prisms are identical in 4D, but the ones nearer the ends of the tube appear flattened because of the projection.

Should be "pentagonal antiprisms".
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Re: Quickfur's renders

Postby quickfur » Sat Mar 01, 2014 3:21 pm

Thanks for the corrections!! Sad to say, they were long-standing mistakes. :( :oops:
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Re: Quickfur's renders

Postby quickfur » Thu Apr 03, 2014 5:18 am

Alright, here it is: the long-awaited renders of the J92 rhombochoron.

Image

Well? What are you waiting for? :lol: Go to the J92 rhombochoron page and look at them. ;) This month you guys get a bonus: I did renders of the J92 rhombochoron from two different 4D viewpoints! (Arguably the J92 rhombochoron deserves more than that, but it's already April and I don't have enough time to work on this all day. :glare: They can always be added later. :mrgreen: )

Some of my favorite renders this time round:

Image

Image

Image

Image

Image

This last one should ring bells among you Johnson solid fans. It's the tetrahedron + triangular prism (and 3 square pyramids) + tetrahedron sequence, serving an analogous role in 4D as the triangular + square + triangle sequence serves in 3D! I've a strong feeling that we haven't begun seeing all that this flexible cell combo can do just yet. They could be the key to making CRFs out of CVP 3 Johnson solids, by acting as a kind of macro-strut that is far more flexible in configurability than tetrahedra alone could ever hope to be.
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Re: Quickfur's renders

Postby quickfur » Thu May 01, 2014 2:46 pm

It's that time of the month again! (Sigh... that line is getting old.) This time we have some nice renders of the castellated rhombicosidodecahedral prism, the crown jewel that started CRFebruary:

Image

The parallel projection centered on a rhombicosidodecahedron is an actual rhombic triacontahedron, with J91's serving as phi-rhombuses! Check it out:

Image

Incidentally, it also shows an interesting way of inscribing a rhombicosidodecahedron inside a rhombic triacontahedron. ;)
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Re: Quickfur's renders

Postby Klitzing » Thu May 01, 2014 4:38 pm

quickfur wrote:Image
Incidentally, it also shows an interesting way of inscribing a rhombicosidodecahedron inside a rhombic triacontahedron. ;)


In fact, this is how the rhombicosidodecahedron got its name:
  • the squares are in the planes of a circumscribing rhombohedron,
  • the triangles are in the planes of a circumscribing icosahedron, and
  • the pentagons are in the planes of a circumscribing dodecahedron
--- rk
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Re: Quickfur's renders

Postby quickfur » Thu May 01, 2014 4:56 pm

:o Wow. I didn't know this before. Now the name makes a lot more sense. Thanks for sharing this tidbit! :)
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Re: Quickfur's renders

Postby Keiji » Thu Sep 04, 2014 9:23 pm

No PotM since May? :(
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Re: Quickfur's renders

Postby ICN5D » Tue Sep 09, 2014 1:26 am

No, quickfur hasn't been around since May. That's probably his last post since then! Nice to see you back around here, Keiji.
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Re: Quickfur's renders

Postby quickfur » Wed Sep 10, 2014 5:24 pm

I apologize for the lack of updates... :( :oops: :cry: I was halfway through the renderings of spidrox, but got busy with other things and didn't have a chance to finish it. Unfortunately, I also made the mistake of working directly on the main branch of my website's version control repository for the spidrox renderings, so it would require additional effort to revert those changes and put them in a branch, and replace it with a simpler PotM, and only post spidrox when it's ready.

(Yeah my website is outdated -- it's still maintained by Subversion whereas most of my code projects are now on git, which is far more flexible in situations like this and would have been trivial to make this branch change. I just haven't had the time to work on 4D-related stuff at all, much less spend the time to migrate everything over to git -- it's not just the migration itself, but I also need to update a variety of scripts and stuff that I use for website maintenance; those would need some effort to update to use git instead of svn.)

I don't know when I'll get back to 4D stuff, but I'm hoping to, some day -- hopefully not too far into the future! :]
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