Wikipedia:WikiProject Mathematics/Graphics/Torus

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Old discussion[edit]

copied from Wikipedia talk:WikiProject Mathematics/Graphics:

...make a better image of transformation from coffee mug to doughnut for the topology page. The current image there is unsatsifactory for two reasons: 1) the handle mysteriously switches sides when it would be better to keep it on the same side 2) one more picture between each stage illustrated would make things much more clearer. An animation would be nice here. --C S (Talk) 01:11, 15 April 2006 (UTC)

Such a thing can be done; but it's nontrivial. Animating a 3D deformation is an order of magnitude trickier than, say, animating a 3D translation. Any 3D animation is more complex than a similar static 3D rendering and much more complex than a 2D animation; on this scale a static 2D rendering is beneath notice. I work for free here but just to give you an idea: the coffeecup-into-doughnut trick is roughly a $1000 job -- done on the cheap... John Reid 19:43, 15 April 2006 (UTC)

Well, I did it. I must admit, I wouldn't mind getting $1000 for it! ☢ Ҡiff 06:18, 2 October 2006 (UTC)


I've been thinking about this task. I might do it with claymation. Interested? John Reid 07:56, 14 June 2006 (UTC)

Hi John, I didn't notice this until now. I guess things have just been busier and busier. Unfortunately, I'm g oing to be spending even less time now on Wikipedia. A claymation would be fantastic and beyond what I had originally hoped for: just a series of images. Feel free to email me, as I will not be checking here that often; I will try and provide a reasonably quick response. --C S (Talk) 14:38, 22 July 2006 (UTC)

I've been working for the last several weeks on this claymation. I'm not sure it will ever be practical, due to large file size, but it's too late now to fail to complete anyway. John Reid 11:06, 12 September 2006 (UTC)

Your effort is appreciated, John. It looks like Kieff's animation is the way to go though. --C S (Talk) 06:29, 6 October 2006 (UTC)

New discussion[edit]


Well, here ya go. The image you see here is terribly jerky, for reference only. The "good" image weighs in at a whopping 1.6 Mb and still looks jerky. I don't even want to display that on this page; you can follow the link if you want to see it.

Now, I think animated GIF is a wholly impractical format for this work. I can produce some sort of video and it will come in with a much smaller file size, a larger frame size, and a much better "look", as well as smoother animation. However I can only export standard video formats such as MPEG, not any weirdo open-source free format.

Somebody who actually goes for this kind of thing might want to team up on this. As it stands, I think this is a bust. John Reid 02:43, 13 September 2006 (UTC)

A couple of thoughts, shadows are a bit heavy, composition not spot on it all seems to be slightly too the right. Do we need the spoon? I'm having a go at installing FFmpeg which look like it can deal with the Theora codec. --Salix alba (talk) 07:28, 13 September 2006 (UTC)

The shadows, the composition, the overall quality of the action -- all suck. Okay? I knocked this out way too quickly and spent way too much time rotoscoping the model in order to get any kind of visual contrast. That's all pretty much irrelevant; this work will serve a good purpose if it shows us what not to do.

I hope I don't have to argue the spoon; it is a graphic design requirement, not a mathematical one. I'm not entirely sure that mathematicians who lack a graphic arts background are ever going to perceive the need; sorry. Trust me; it helps.

Salix, if you think you can process suitable video, tell me what kind of format you need as input. You can work with series 3 until we have a process figured out; then I'll reshoot. John Reid 03:34, 14 September 2006 (UTC)

I've converted the animated gif to ogg:
. I think my conversion prog can handle most video formats, mpeg is probaly prefered.
As too spoon, I think I understand why spoon should be there. Maybe a bit more white space between spoon and cup. No wanting to teach my grandmother to suck eggs. --Salix alba (talk) 08:14, 14 September 2006 (UTC)

You've converted the crummy for-ref only image. Can you work with the full-length version, Image:Clay-torus-3a.gif? I strongly suggest you don't display this image on the image description page of your upload (or anywhere else). John Reid 10:59, 14 September 2006 (UTC)

OK done, same image page. --Salix alba (talk) 11:16, 14 September 2006 (UTC)

If that truly is a conversion of Clay-torus-3a.gif, you might like to change the description link. I see nothing in any case except an iconic speaker. I don't know if there's any way for me to view an OGG with my system -- and let's not get sidetracked into a discussion of that. You do seem to have gotten an impressive compression ratio.

Anyway, if you feel comfortable working in OGG, we might want to get together on a for-show version. I really would like, in addition to the OGG, a version suitable for display right on the article page. I don't know if extremely hard pushing can get a decent ani-GIF down to a reasonable size, though.

It seems worth asking at this point if anyone else has the slightest interest in this effort. Claymation is ungodly labor-intensive; I wouldn't consider it at all if I weren't sure that digital 3D animation of a full-object deformation would be so much worse. John Reid 21:10, 16 September 2006 (UTC)

From what I can tell the only way to have animations appear directly in wikipedia pages is by using animated gifs. Ogg videos are the only type which can be uploaded but these will only appear as a link like you saw. Wikipedia:Media discusses the different media allowed and Wikipedia:Media help (Ogg) discusses the different players with which you could view an ogg video. --Salix alba (talk) 09:49, 17 September 2006 (UTC)

Well, this just reinforces my opinion that OGG is a mistake. This is another case of fanatic adherence to doctrine in the face of unpleasant reality. Reality is that the vast majority of desktop and laptop users have some flavor of Windows installed and most of the rest of us run Macintosh. Linux, Unix, and variants thereof may be more politically pure but the userbase is just not there -- gaining ground all the time, but still, just not there. Yet here we are pushing this unrealistic *nix video standard. Why? Sorry, but I'm deaf to all strident calls for everything to be "free". I just want stuff to work -- and especially when I'm asking the public to look at my stuff, I want them to be able to do so.

I have followed many links and searched hard for a Theora-OGG player -- in vain. (I may not like it, but at least I'm willing to install another piece of software for this one website.) So I'll just have to take your word for it that you've got the conversion figured out. I'll repeat, it's an impressive compression ratio.

I'd like to see what you can do with the much larger JPGs I have of this work. (Image:Clay-torus-3c-frame169.jpg &c.) Well there I go again; I want to see. Also, I don't want to upload all the individual frames to WP; that's just nuts.

Howabout can we agree on a common workfile exchange area? I'll stuff a set of JPGs into a single archive for you to assemble into a video. But I have to ask you to output both the WP-required OGG and something the rest of us can see, preferably MPEG. Can you do both? You can put the MPEG back on the exchange site and the OGG on WP. Deal? John Reid 07:40, 20 September 2006 (UTC)

3D animation[edit]

Mug and Torus morph.gif

I just found this page today and decided to give it a shot using POV-Ray. You can see the result at the right. I hope it pleases everyone. :)

I had to divide the process into two parts, though. The first consists in transforming the concave coffee mug into a similar, convex shape. The second is the actual morphing. I did this because I couldn't find a way to map the concave surface of the mug into the convex one of a torus directly. By dividing the two tasks I was able to use a simpler approach to the problem, and it worked reasonably well.

It was pretty fun to do this, especially because I had to figure the function that describes a coffee mug in 3D space. Isn't mathematics just great? :D ☢ Ҡiff 06:15, 2 October 2006 (UTC)

Nice. Strangly it didn't display until I added 300px to the image tag. --Salix alba (talk) 08:04, 2 October 2006 (UTC)
That is so ridiculously cool. I don't have any objection to the two-step; it makes me think of drinking the coffee. I'd rather see some sort of background, preferably with a teaspoon for scale; I'd like the handle to have more bulk at the mug-extreme; I wish the thing had some surface texture. But it is vastly superior to the claymation. It does however tip the scales at over half a Mb. That's the price you pay for smooth animation. John Reid 04:12, 6 October 2006 (UTC)
The file size is big because I didn't really optimize the colors and it has too much contrast to it. A new version will be in order as soon as I get some free time again this week. Been busy with work. Thanks for the feedback. ☢ Ҡiff 08:27, 10 October 2006 (UTC)
Wow, this is a great conception, Kieff. --C S (Talk) 06:25, 6 October 2006 (UTC)

This animation has been nominated for featured status: Wikipedia:Featured picture candidates/Homeomorphism. I opposed the promotion for the following reasons:

  • the image is a better illustration of homotopy than homeomorphism (see also the comment from SurDin on Talk:Homeomorphism),
  • and more importantly, the transformation that is suggested by the animation is not actually an homeomorphism.
By this I meant the transformation between the first and the last frame of the animation --Bernard 01:46, 13 March 2007 (UTC)

Your comments are welcome (though the nomination will probably be closed soon). --Bernard 02:01, 12 March 2007 (UTC)