Pixar's senior scientist explains how math makes the movies and games we love | Hacker News Reader

Pixar's senior scientist explains how math makes the movies and games we love

theverge.com

148 pointsColinWright16 comments

Not only was the hair in Brave modeled with math, all of the vegetation was procedurally generated by Íñigo Quílez of http://shadertoy.com fame.

http://www.cgw.com/Publications/CGW/2012/Volume-35-Issue-4-J...

Inigo Quilez also has an awesome site with very accessible articles: iquilezles.org (I think the articles section is the most interesting part).

Here is their publication on hair simulation if y'all are interested: http://graphics.pixar.com/library/CurlyHairB/paper.pdf

There is some wild stuff in their library!

The article states the guy says when you have n objects you have n^2 possible collisions, if you're assuming just one on one interaction and an object cannot collide with itself shouldn't it be n*(n-1)? Am I missing something here?

Since collisions between two objects are symmetric (object one colliding with object two is the same event as object two colliding with object one) there are n(n-1)/2 possible collisions. The guy's probably short handing this as O(n^2), which is the important relationship as he's motivating the example by the need to handle collisions between large numbers of particles in hair, and modeling hair with as large a number of separate elements as possible is probably the key to realistic simulation.

I see what you mean. The symmetric part is noted. Thank you for the reply

It's definitely a shorthand since a typical solution for collision detection is a space partitioning recursive data structure which reduces collision tests to O(n log n)

That point is actually covered in the article:

Merida's hair is made of 100,000 individual elements. "If you know any combinatorics, you know that if you have n objects, you have n² possible collisions," he says, or 10 billion. How can you render so many collisions quickly enough to be usable? You have to create a new spatial data structure that culls extraneous collisions without being too lossy.

So he's saying that naively with n objects there are n² possible collisions, but they have to do clever things - such as you suggest, or even cleverer - to reduce that. Already there. In the article.

But the GGP's point is that there aren't n² possible collisions, there are only n(n-1)/2 if you allow for the symmetries. But is still grows quadratically, and that's the point being made. Quadratic is too fast.

For rigid bodies, given reasonably temporally coherent motion between time steps, you can get it down to O(n) with sweep and prune approaches [1]. These might not be the best choice for hair simulation, though.

[1] https://en.wikipedia.org/wiki/Sweep_and_prune

He's just thinking asymptotically. f(n) = n(n-1)/2 = O(n^2).

As others have pointed out, it's order n^2, not meant to be interpreted as exactly n^2. I will add that, having done hair simulation for DreamWorks, it's likely that their collision simulations are done on guide hairs, rather than interpolated hairs. So n is usually more like 1k, not 100k. Complete accuracy of hair simulations in film isn't required, nobody will notice individual hairs crossing each other, but you might notice big clumps behaving badly.

Is Pixar hiring computational mathematicians at the moment?

Looks like it!

Software Engineer, Simulation: https://pixar.wd5.myworkdayjobs.com/en-US/Pixar_External_Car...

Research Scientist: https://pixar.wd5.myworkdayjobs.com/en-US/Pixar_External_Car...

This reminded me of a really fun article from an AMS publication a few years back about harmonic functions and animation in Ratatouille: http://www.ams.org/publicoutreach/feature-column/fcarc-harmo.... Turns out it was the same guy, Tony DeRose!

From 2013, which might be why the most recent movie referenced is Brave.

If you're interested in a slightly more concrete example of the math going into Pixar movies, here's a Numberphile interview with Tony DeRose from around the same time:

https://news.ycombinator.com/item?id=8610626

> "Somewhere out there, a brilliant kid and their friends are working in their garage" using and improving on tools like Blender, DeRose tells the assembled children and adults at MoMath. "They will be the next Pixar."

Nope. I love Pixar because of the stories and storytelling. First ten minutes of Up? Inside Out? As long as they looked slightly better than ass I bet I'd still love them.

Reply on news.ycombinator.com