1. Chad Fox Author

    @Numberphile  Thanks for this. I work in 3D Animation and have been wondering about the math behind Subdivision and limit surfaces for quite some time.

    On a side note, you asked Tony if everything comes out blobized, but in this vid, it doesnt seem like he answered the question the way you were expecting. The answer is no. In the 2d example, if we wanted one corner to be sharper than the others we add 1 or more vertices near the corner vert. The result is the averaging and splitting is tighter where we've added more vertex density resulting in a sharper smoothed corner

  2. cbbuntz Author

    Interesting observations:
    Each row of pascals triangle is generated by the convolution of the row above it by 1 1.

    Each progressive row becomes closer and closer to approximating a perfect gaussian curve [or e^(-x^2) ]

  3. TheGeekiestWoman Author

    I really enjoyed this one, but I do have a background in math, programming AND graphic design (since the 60s), so it made my skin … twitch.

  4. dfsfklsj Author

    Fun fact about Toy Story- the character of Andy was allegedly named after Andy Van Dam, a Brown University professor who mentored many people on the animation team. In one scene, you can find Andy Van Dam's book about computer animation on a bookshelf.

  5. LotharioCassanova Author

    Can someone tell me, what is the application used in the video, where the guy introduced as the Pascal's Triangle. Where the buttons Split, Average, and the Subdivide.

  6. Manolito Mystique Author

    Quality material as usual. But please, check your microphone levels. This is not the first time that the sound is clipping a whole lot. You did show us that you are checking your sound by asking what your interviewees had for breakfast. So maybe it’s a post processing issue?

    Anyway great job, but please do something about the sound issues.

  7. Mckenna Cisler Author

    So when they say 1,2,1 weights it means that B's x and y coordinates are weighed 4 times as much than both A's and C's coordinates, and the average of all those coordinates is the new value? In that case, how can you use something like 1,3,3,1 when operating on 3 points?

  8. Arikyo-kun Author

    I have been researching into catcall-clark subdivision surface and it's very difficult to find the connection between Pascal's triangle weight to how the dots move. My brain is burnt 0____0

  9. Dinkle berg Author

    going to hopefully be doing Computer Visualisation and Animation at Bournemouth Uni, the artistic side of computer animation is awesome but the Maths side is so damn interesting, really glad that were going to be looking at the Maths, not sure whether this'll be covered but hope so, seems really interesting:3

  10. david lewis Author

    Watched this like 3 times for some reason. Learned something useful about all rendering. Weird this is unknown by many who use this. tried to explain this to friends in AutoCAD/Image Design and ended up just showing this video.

  11. Christopher Rogers Author

    I've always been intrigued by this material. I have a double major in Sec. Math. Ed. and Mathematics with a minor in physics. I love/know my math and I know html, python, and C++. I'm currently looking for employment and I would love some experience in programming. Does anyone know what I would be qualified for?

  12. morgengabe1 Author

    Does anyone know what software he uses?
    Also, I'm interested in constructing time graphs. I don't know any programming, but I've been working on some maths i'd like to model. Could any one recommend languages/techniques/programs to use?
    I've got a mac, so xCode's obviously an option. But I want something with a graphical interface like his one so that I can generate active graphs. Would I just have to get that going from zero?

    Would appreciate any help anyone can give!

  13. Soulsphere001 Author

    The first three minutes of this video is extremely informative. I've always wondered about how to convert a square to a circle, and it seems like this might be the way to do it.

    I also wonder if they explain this in "Pixar in a Box".

  14. Xan the Dragon Author

    Huh. I had no prior education to 3D modelling when I got started – I taught myself everything up to what I know today. It's interesting to know that what I do after making my low-poly representation to turn it into a higher detail model is a trick used by this guy as well.

  15. Ella Skultinas Author

    Thank the lords I found this video. I had to pick a job that uses science and mathematics for an essay and I chose animating. I only found small things in other videos, but I got so many notes in this video. THANK THE LORDS.

  16. Tracy Roese Author

    We watched this in my Geometry class. Students bet me that I could not give them any examples of using geometry in real life and this was PERFECT! Thanks for helping me win my bet! 🙂

  17. jlinkels Author

    Why the irritating and distracting background sound sequence? I don't think I hard it before on Numberphile. Once I noticed it, the 8 eternally repeating notes it almost drove me insane.

  18. anon ymous Author

    seems like you could just have a playbook of curves… no reason to model them with this splitting-subdivision technique. This whole thing could be instantly streamlined to relatively simple geometry functions


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