At Pixar, we’re all about telling stories, but one story that hasn’t been told very much is the huge degree to which math is used in the production of our films. The math that you’re learning in middle school and high school is used all the time at Pixar. So, let’s start with a very simple example. Anybody recognize this guy? (Cheers) Yeah, so this is Woody from Toy Story, and let’s ask Woody to, say, walk across the stage from, say, left to right, just like that. So, believe it or not, you just saw a ton of mathematics. Where is it? Well, to explain that, it’s important to understand that artists and designers think in terms of shape and images but computers think in terms of numbers and equations. So, to bridge those two worlds we use a mathematical concept called coordinate geometry, right? That is, we lay down a coordinate system with x describing how far something is to the right and y describing how high something is. So, with these coordinates we can describe where Woody is at any instant in time. For instance, if we know the coordinates of the lower left corner of that image, then we know where the rest of the image is. And in that little sliding animation we saw a second ago, that motion we call translation, the x coordinate started with a value of one, and it ended with a value of about five. So, if we want to write that in mathematics, we see that the x at the end is four bigger than x at the start. So, in other words, the mathematics of translation is addition. Alright? How about scaling? That is making something bigger or smaller. Any guesses as to what the mathematics of scaling might be? Dilation, multiplication, exactly. If you’re going to make something twice as big, you need to mulitply the x and the y coordinates all by two. So, this shows us that the mathematics of scaling is mulitiplication. Okay? How about this one? How about rotation? Alright, spinning around. The mathematics of rotation is trigonometry. So, here’s an equation that expresses that. It looks a little scary at first. You’ll probably get this in eighth or ninth grade. If you find yourselves sitting in trigonometry class wondering when you’re ever going to need this stuff, just remember that any time you see anything rotate in one of our films, there’s trigonometry at work underneath. I first fell in love with mathematics in seventh grade. Any seventh graders? A few of you? Yeah. My seventh grade science teacher showed me how to use trigonometry to compute how high the rockets that I was building was going. I just thought that was amazing, and I’ve been enamored with math ever since. So, this is kind of old mathematics. Mathematics that’s been known and, you know, developed by the old dead Greek guys. And there’s a myth out there that all the interesting mathematics has already been figured out, in fact all of mathematics has been figured out. But the real story is that new mathematics is being created all the time. And some of it is being created at Pixar. So, I’d like to give you an example of that. So, here are some characters from some of our early films: Finding Nemo, Monsters Inc. and Toy Story 2. Anybody know who the blue character in the upper left is? It’s Dory. Okay, that was easy. Here’s a little harder one. Anybody know who’s the character in the lower right? Al McWhiggin from Al’s Toy Barn, exactly. The thing to notice about these characters is they’re really complicated. Those shapes are really complicated. In fact, the toy cleaner, I have an example, the toy cleaner there in the middle, here’s his hand. You can imagine how fun it was to bring this through airport security. His hand is a really complicated shape. It’s not just a bunch of spheres and cylinders stuck together, right? And not only is it complicated, but it has to move in complicated ways. So, I’d like to tell you how we do that, and to do that I need to tell you about midpoints. So, here’s a couple of points, A and B, and the line segment between them. We’re going to start out first in two dimensions. The midpoint, M, is the point that splits that line segment in the middle, right? So, that’s the geometry. To make equations and numbers, we again introduce a coordinate system, and if we know the coordinates of A and B, we can easily compute the coordinates of M just by averaging. You now know enough to work at Pixar. Let me show you. So, I’m going to do something slightly terrifying and move to a live demo here. So, what I have is a four-point polygon here, and it’s going to be my job to make a smooth curve out of this thing. And I’m going to do it just using the idea of midpoints. So, the first thing I’m going to do is an operation I’ll call split, which adds midpoints to all those edges. So, I went from four points to eight points, but it’s no smoother. I’m going to make it a little bit smoother by moving all of these points from where they are now to the midpoint of their clockwise neighbor. So, let me animate that for you. I’m going to call that the averaging step. So, now I’ve got eight points, they’re a little bit smoother, my job is to make a smooth curve, so what do I do? Do it again. Split and average. So, now I’ve got sixteen points. I’m going to put those two steps, split and average, together into something I’ll call subdivide, which just means split and then average. So, now I’ve got 32 points. If that’s not smooth enough, I’ll do more. I’ll get 64 points. Do you see a smooth curve appearing here from those original points? And that’s how we create the shapes of our charcters. But remember, I said a moment ago it’s not enough just to know the static shape, the fixed shape. We need to animate it. And to animate these curves, the cool thing about subdivision. Did you see the aliens in Toy Story? You know that sound they make, “Ooh”? Ready? So, the way we animate these curves is simply by animating the original four points. “Ooh.” Alright, I think that’s pretty cool, and if you don’t, the door is there, it doesn’t get any better than that, so. This idea of splitting and averaging also holds for surfaces. So, I’ll split, and I’ll average. I’ll split, and I’ll average. Put those together into subdivide, and this how we actually create the shapes of all of our surface characters in three dimensions. So, this idea of subdivision was first used in a short film in 1997 called Geri’s Game. And Geri actually made a cameo apperance in Toy Story 2 as the toy cleaner. Each of his hands was the first time we ever used subdivision. So, each hand was a subdivision surface, his face was a subdivision surface, so was his jacket. Here’s Geri’s hand before subdivision, and here’s Geri’s hand after subdivision, so subdivision just goes in and smooths out all those facets, and creates the beautiful surfaces that you see on the screen and in the theaters. Since that time, we’ve built all of our characters this way. So, here’s Merida, the lead character from Brave. Her dress was a subdivision surface, her hands, her face. The faces and hands of all the clansman were subdivision surfaces. Today we’ve seen how addition, multiplication, trigonometry and geometry play a roll in our films. Given a little more time, I could show you how linear algebra, differential calculus, integral calculus also play a roll. The main thing I want you to go away with today is to just remember that all the math that you’re learning in high school and actually up through sophomore college we use all the time, everyday, at Pixar. Thanks.

His shirt is amazing

… I feel dumb, because im in 9th grade, and yet, im still in Algebra 1b… -3-

That was great! I'll show it to my students when we get back from spring break!

I do 3D modelling and animation and I don't remember doing any math… Especially not trigonometry!

If I can suggest something to kids is to learn HTML/Javascript… It is actually used in animation (Javascript) AND web design (HTML & Javascript)!

as much as i respect 3D animation, i really wish hand drawn 2D animation was still common today. The only 2D animation today is Adventure time or Regualr show, what has happened to the art style??!!

7th graders get to watch TED-Ed live? Lucky bastards!

and here I thought what I learnt back in school was useless. Well played, Pixar. Well played indeed.

пихарь

I love it 😉 but he's making this seem more complicated than it really is 🙂 the developers of these animations don't have to worry SO much about the math because of all the automated software they use to calculate all Of this for them,…

[email protected] the kids in the audience bored out of their minds – 1:43

He said you should've have learned this in the 8th or 9th grade (trigonometry) well my school system must be lacking like hell most students don't get the opportunity to take it here till their senior year.

Maths. That is all.

That was interesting

Interesting.

Graphics animator from world's largest studio and doesn't use vector image of Woody.

OK, SO THEY ARE SUB DIVIDING THAT IS PIXELATING …………

CAN BE UNDERSTOOD AS, WHEN YOU ZOOM TO A IMAGE WITH LESS PIXEL, IT WILL APPEAR LIKE JERRY'S HAND BEFORE SUB DIVIDING THE POINTS WHICH MAKE THE JERRY'S HAND SKIN. BUT WITH MORE SUB DIVISIONS LIKE MORE PIXEL IN A IMAGE IT APPEARS SMOOTH………………..

First thing Idk why anyone has to dislike this video its like he showing what he does for a living with mathematics. Umm but I swear if he never said anything about math mannnn… I wouldn't of thought it was useless … thanks pixar best thing ever I would love to make characters with these people one day if I learn it enough.

很好

hgujjhhgg

I remember making a game and adding a black hole with gravity. a^2+b^2=c^2 to figure how far away the player was. Trig to find the angle to the black hole. I love how much math helps.

I remember making a game and adding a black hole with gravity. a^2+b^2=c^2 to figure how far away the player was. Trig to find the angle to the black hole. I love how much math helps.

Haha, trigonometry in 8th or 9th grade? Where!? Most high school students don't ever touch it until 10th grade IF ever.

3:38 Awkward failed joke….

HANG IN THERE BRO. AT LEAST I GOT THE JOKE. CONCEAL, DONT FEEL

Yet you, the animator need to know none of the math required as even full 3d rendering suites are point, click, drag, tweak till fluid. I know, I do 3d artwork 😛 Sooo yeah feel free to ignore all of that math unless you want to actually make the 3d software.

Math we use all the time, every day, with preprogrammed commands in software we had someone else code and thus are doing absolutely no math, we are just using it.

Aww yeah, Tony DeRose!

"When will I ever use this??"

Fascinating !! Never felt better about Maths !! 🙂 🙂

This video is cool, but… Tone DeRose nearly dances on his ears to get these basic concepts into heads of those who just chill around twiddling their thumbs. It seems to me that they don't actually give a hang about his lecture.

Trigonometry in 8th grade? Holy shit I never even went through high school learning Trig.

I don't know how mathematics actually got in there because in 3D animation, everything is usually automated… Unless of course, these 3D guys code them manually.

Is it only me or does this guy looks like an older version of President Obama!!

True teaching

kewl! I bet math on rendering is extreemly complex calculating lighting, and shadows, and subsurface scattering!

The important thing is to know of the existence of calculus etc and not necessarily to know it by heart.

The when you hot a problem that needs solving you can remember that calculus can solve this sort of problem then look it up on the internet – there are some fantastic tutorials out there explaining quite complex mathematical problems.

reminds me of computer graphics course in be.

At some point he says: Trigonometry was invented by the old dead Greek guys. I guess he is another American idiot who has never travelled accross any borders. Go back to school pixar man and learn some geography, ignorant idiot.

07:21 boob clap

make smoother… why not use that on games… it would be a nice try with a talented animator in game industrie

They are sure great in creating movies, but they can't really make nice presentation 😀

I want his shirt !

Ew, I hate math.

It would be really cool if the knowledge contained in this video would actually qualify a 14year old to get a job at Pixar 🙂

The kids in 1:44 look bored to tears

Math is cool.

what program was he using I need to download it

what program was he using I need to download it

no brasil ia mostrar um mlk correndo com seu celular na tela

Interesting video.

Sure, it uses math, but the computers are the ones actually doing it

I'm so sad!!! I hate math but I want to work for pixar some day 🙁 I better learn to love it I guess…

when i was their age, i would've just snoozed out the whole presentation. ah well, i guess kids are smarter and more curious nowadays.

more about this at numberphile

hi if ms. lee directed you here

Its a trap. Animator just need to learn script

Tony DeRose has helped launch a series of math(s) tutorials on Khan Academy: https://www.khanacademy.org/partner-content/pixar

at 5:24 my blood pressure started to rise but at the "uuuu" I just had to laugh how easy that was 😀

The animators make such a great job with pixar films.

Thanks to all the genius creater and math makes it possible.

my teacher sent me this😂😂😂

Impressive concept!!!!! I liked the way math appears in movies!!

Um corredor matemático me trouxe aqui.

I don't think of rotation as a use of trigonometric functions, I think of it as a definition. For example, when you look at the standard definition that sin(x) is the length of the side opposite angle x divided by the length of the hypotenuse, it makes sense that asserting the hypotenuse to be equal to one makes the equation much simpler, that is, sin(x) is the length of the opposite side. Such a construction makes the hypotenuse a radius and the length of the opposite side becomes the y coordinate for angle x. The very process of describing the sine function also explains its relation to rotation, thus it is not trigonometry that describes rotation, but rotation that describes trigonometry.

Is it just me or does he look like Willem Dafoe

i wish i could watch this in my 7th grade….

I wish I could start doing maths again. I'm already a graduate. 😭😢😩😟 But I've immense desire to make animated films. I wish I could do that!

this is a similar concept to integration I mean the mid point idea, as the number of points increase the curve becomes more legitimate, meaning it's the limit to infinity.

I was surprised students in America learn trigonometry at junior high school .In Japan, it is at high school that students learn trigonometry.

pixar confirmed for kingdom hearts 3

I wish I had this kind of information when I was in school so I could relate all those abstract ugly graphs and equations with something "real". Kids these days are so lucky and I bet most of them don't realize it.

I love the enthusiasm

i never had trigonometry

I loved taking CAD and Geometry the same year in high school, and I loved ceramics years later. Funny because I asked the Ceramics teacher at which point do these two seemingly diverse professions meet. He said no at first, but then realized and replied that there is a special kind of clay people use in movies called polymer clay and that they take a laser and scan the hand-crafted object.

There is a time to craft an object using keyboard and mouse, and a time to craft an object with your fingers and wrists. Somehow, I feel as if the more organic designs such as an animal or a tree are better designed with fingers and wrists before being scanned with a laser while the more mechanical designs such as a car or a weapon are better designed with keyboard and mouse and can be printed on a 3D printer.

este men hizo encariñarme por las matemáticas mejor que el resto de maestros patéticos de secundaria y prepa.

I hadn't even heard of ted talks until halfway through my senior year of high school.

Nobody escapes math

this sound more like a silly maths class about how some 2d animation software for stick man works

i dont like math but thanks anyway

I have aids

I took computer graphics. Why am I watching this

Good 😮😮😮matematics are very important to do movies 😀😀😀😀😀

I really love math

He has Arduino IDE installed xD

Hah im an artist i dont need math

o shiㅡ

I love math and making comics so I think Pixar would be perfect for me….

Wow! the 1997 video Geri's game was the first to use subdivision & midpoints, and it's plain to see how this simple mathematical technique really made animated film so much better! and that is one good short movie!

SHOW!!!! that´s great, syn! #FATORSYN!

#RTXon

"The door is there"?

How rude!

What a wuss!

Thanks for almost ruining Pixar AND Math for me, Tony!

Profe ramsés ya lo vi🤣

Ya vi el video profe

Saludos para Ramses! ✌🏻 Es el mejor profe huuuuu….! 🤙🏻 Pongame 10 en el parcial profe 🤘🏻🤣

Haaaa ya lo vi profe 🤣

Visualizado profe Ramsés 🤙

Visualizado profe Ramsés

Entonces, literalmente para todo usamos las matemáticas sin estar conscientes. Genial.

Visualizado profe ramses

Ya lo vi profe 👍

我看了視頻 profe Ramsés

Utilizamos las matemáticas para todo, a pesar de que a veces no nos damos cuenta. Las películas animadas son un claro ejemplo.

Profe Rances ya lo vi

SMH