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A Computer Technique for Displaying N-Dimensional Hyperobjects (1967) [pdf]
- kingcharles 5y agoI liked the ending: "At first it was thought that the computer-generated movies of the four-dimensional hyperobjects might result in some "feeling" or insight for the visualization of a fourth spatial dimension. In particular, perhaps some visualization of a solid four-dimensional hyperobjeet would be gained from the distortions in the three-dimensional perspective projection. Unfortunately, this did not happen, and we are still as puzzled as the inhabitants of Flatland in attempting to visualize a higher spatial dimension." When I wrote my first 3D engine as a kid, I immediately extended it to 4D because I was a nerd and I thought the same thing - maybe I'll be able to train my brain to understand 4D objects. No. Your brain remains confused. Perhaps if you did it from birth. Like they did with those kittens that never saw horizontal and vertical lines. This would be a totally unethical experiment to carry out on a human child though :)
- vba616 5y agoMaybe it's only possible to project/fake one additional dimension and not two? So if we had a 3D display, holographic or something, then a projected 4-D object might make more sense.
- newswasboring 5y agoSounds like an awesome VR project to me
- mettamage 5y agoYou’re right! Now I have an extra reason to learn math.
- r2_pilot 5y agohttps://store.steampowered.com/app/619210/4D_Toys/ https://store.steampowered.com/app/619210/4D_Toys/ 4d VR simulator
- kingcharles 5y agoNow live inside this app exclusively for a year and see if 3D is weird for you when you come back...
- hypertele-Xii 5y agohttp://eusebeia.dyndns.org/4d/vis/01-intro http://eusebeia.dyndns.org/4d/vis/01-intro
- tehsauce 5y agoshamelessly sharing my UI for viewing 4D objects (works with touch screen or mouse) https://transdimensional.xyz/ https://transdimensional.xyz/
- jcun4128 5y agoCanvas is amazing Also the trick is to try and return to your starting position ha
- mateo1 5y agoYeah that's one hell of a Rubik's cube. OP should add a "shuffle" button and make a game where you win if you return to the original (or a specific) shape within some error.
- lukasb 5y agothis is great
- hoseja 5y agoWould be cool if the individual rotation columns responded to the mousewheel.
- bruce343434 5y agoInteresting, firefox says "gah, your tab just crashed".
- Spare_account 5y agoFWIW I'm on Firefox 96.0.3 (64-bit), on Windows 10 64 bit and it works fine. My brain can't handle it but my browser can :-)
- cgufus 5y agoCool, Thanks. To me, 4-D rotation is completely “unpredictable” or “contraintuitive”, or both. I wonder, you as a developer of that visualization, did you get an intuition for it? do you know in advance how the projection changes when you apply one or the other rotation?
- magpi3 5y agoFlatland, referenced in this paper, is a wonderful and thought-provoking little story. EDIT: I removed the link because I was worried about the server I linked to. But you can find the PDF of flatland if you just google "flatland pdf"
- bb88 5y agoI was curious how they did the typesetting of the computer generated graphics back then. Printers weren't really a thing.
- 2bitlobster 5y agohttps://houseind.com/hi/photolettering https://houseind.com/hi/photolettering
- mateo1 5y agoIt could be just a high contrast photograph. I know that at some point they used to wait for all the vectors to be drawn on a CRT with a "permanent"-resettable phosphor and then take a photo with everything on it, clear the screen, and start drawing the next frame. Fun stuff.
- bb88 5y agoYour thought intrigued me and I wanted to look further. https://piratefsh.github.io/2019/01/07/computer-art-history-part-1.html https://piratefsh.github.io/2019/01/07/computer-art-history-... https://piratefsh.github.io/2019/01/07/computer-art-history-part-2.html https://piratefsh.github.io/2019/01/07/computer-art-history-... So there were plotters, which would need to be photographed, like you were talking about, but there's also this: > And then they were the electronic or microfilm plotters. It works in a similar way as the mechanical plotter, but instead of a pen, it uses an electron beam and instead of paper, it “draws” on microfilm. The idea is that it plots an electron beam in a cathode ray tube, runs it through a camera lens system, which records these beams onto microfilm. I think of it like how a CRT display works, but it also exposes light onto film. The microfilm can then be viewed via a microfilm reader, printed or even animated."
- tgvaughan 5y agoI remember encountering this approach in A. K. Dewdney's Computer Recreations column of the April 1986 issue of Scientific American: "A program for rotating hypercubes induces four-dimensional dementia". It included enough pseudo-code for my young self to get something working in qbasic, even adding support for red-blue cellophane glasses so that the hypercubes could be seen in 3d. Great memories!
- ArtWomb 5y agoGenius! I've seen the animation on youtube a hundred times, but never a write-up. Supposedly, the basis for a non-euclidean sculpting robot ;)
- pizza 5y agoCould you link the video? Sounds cool
- jcun4128 5y agoNot OP, is it the 4D Hypercube? https://www.youtube.com/watch?v=q5Qh2XpoCsY https://www.youtube.com/watch?v=q5Qh2XpoCsY side note it is a mind f (to me) to do point rotations in graphics case, just trying to make a rotating cube in WebGL wow.
- leonry 5y agoMaybe this blog entry is another good starting point: https://ciechanow.ski/tesseract/ https://ciechanow.ski/tesseract/ and references therein (at the end). It has been discussed on HN a while ago.