@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

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.

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.

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.

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?

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

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

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.

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?

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?

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".

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.

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.

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! 🙂

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.

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

Fuck that was interesting! 😀 More videos about this 1,1;1,2,1 Pyramid series thing, please 😀

@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

I wonder if this links to how large rubiks cubes are smoothed? Anyone else see a similarity to the cube when it is smoothed?

Thanks brady for bringing so much cool science stuff in a lot of different fields, kudos to you

love the A113 double easter egg at the end!!

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) ]

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.

i dont understand nothing

Whew, I thought they weren't going to use the brown paper.

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.

If you heard of the goldbach conjecture, look at my video, i found a nice pattern.

What are you a smart guy or something?

Is the Geri's Game guy ythe same guy who cleans Woody in Toy Story 2?

Absolutely brilliant

Then he put in a limit of -1/12 and the computer imploded!

Wow!! Never realised there was so much maths in animation and art. Fantastic stuff!

This is way cool.

What program is used?

21

CATMULL CLARK!!!

What program is that?

Is this software available to mess around with? If not, I might try to program a simple version in C++.

9:22 is the blue dot the last stadium or what happens when you do the SPLIT once again? It remains the same?

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.

I want to see him explain the derivation of the (A+4B+C)/6 expression!!

When is the second video coming????

I was really hoping he was going to discuss the mathematics behind radiosity!

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.

When should we expect the 2nd video in this series? Awesome stuff! Thanks!

Does anybody know what is the name of the software used in the video?

Just so cool!

Is this used in Anti-Aliasing in games?

what does it mean 2 parts of this point and 1 part to the one of the left and right ? what is he calculating?

Amazing video, please keep making more of these.

He looks a lot like Willem Dafoe.

5:00 : this is not an emergent property, he pretty much described a spline

answers so much to me, listen for the

where did the 1, 4, 1 come from?..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?

Amusing mathematical methods to create smooth animated works of art.

Great video and use of STEM in film…also a great example of how to use Calculus and Geometry in animation!

I thought B(infinity) would just be at the center of the polygon lol

So amazing… I wanna work in this area 🙂

Wow I couldn't believe that 1,4,1 could make you laugh, sad, cry, and be entertained!

Americans are just the best, for sure!

I thought it was all done through magic. PFFT!

I hat this video ok do not play this video im serius all right

Can I get the program for the 2d curves in the video?

Great video, thanks.

as a 3d modeler, this was really awesome to watch. Much thanks!

you could totally 3d print Geris hand from a digital model now n_n

Am I the only one to see the basic shapes of the Brazilian flag at 5:49? (Well, maybe because I am Brazilian… :-))

what site is that

Is there a program I can download to do this? I would love to play with this program.

Is that a toll booth in front of PIXAR Animation studios so you can pay to go in or something?

"Where did you get 1, 4, 1 again?

"From by back pocket."

"Okay!, look here smart ass." Interviewer probably

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

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

This is really interesting 🙂

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.

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?

6:45 Looks like a sharingan.

So they're basically taking derivatives and integrating.

Wait. I'm a bit confused. Is this kind of math only exclusive to 3D animation, or is it used for 2D too?

Another special video, Haran!

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!

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".

Is maths is necessary to be an Animator?? Plz reply plz 🙂

behold trigonometry

what if your terrible at math but can still do animation? if that makes any sense.

Why he divide the expressions by six?

I won't have to do much math as an animator.

HALLELUJAH

huh =.= oh my

wow

Beautifully done!

Dank material

looks like Piet Heins superellipse and egg

TO B INFINITY AND BEYOND !!!

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.

A lot of this applies to video game rendering too, 😛 just on a much, simpler, smaller scale

is pascal's tetrahedron a thing?

Are they Beziere curves ? To smoothing out objects PieXAR 🙂

please fix your audio. the clipping is really unpleasant

omg where can i get the 2D software used in this, i really want to mess around with the weights

I love Pixar

sir which software he used while explaining

cool math

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.

What is the benefit of an eigenanalysis versus a Ritz analysis?

is the 1 4 1 not just the square of the 1 2 1 he used?

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! 🙂

Pretty cool.

Willem Dafoe was awesome here!

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.

He looks so much like Desmond Doss!! 😱

The lips especially!

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

My Dream .

I am using blender and observed it too

Which software is he using? to subdivide

Quit a few years ogo

Nope not even close