I remember back in high school math class, wondering aloud (to the teacher, no less- I was not shy) why I needed to take math. I was absolutely certain that I would never be entering a profession that required any sort of mathematical manipulation and thus it was clearly a waste of my time and brain power. To me, math was something that only statisticians used, or people who worked in the lab. Professions that involved any type of calculation did not appeal to me.
I was right; until about a month ago, when I found myself at the “Science Behind Pixar” exhibit at the California Science Center. Twenty years into my math-less life and I was proven completely wrong. I soon discovered that without science, technology, engineering, and math (the “STEM” fields as they are known in academia) there would be no animated movies. No animated characters. In essence, no childhood memories implanted in movie theatres. It suddenly dawned on me. Here is a good enough reason to learn math.
Let’s start with Woody and Buzz of the beloved Toy Story series, the two animated characters that really kick-started the whole Pixar movement. They move effortlessly, smoothly, jumping around all over the screen. Or so it seems. Actually, there is a great deal of effort involved. Every one of those jumps, skips, and hops involves a calculation called “splining”, which is used to connect all these hops, skips, and jumps together. The animator draws the main poses of the character, translates it into a spreadsheet, and then a computer calculates the “in between” poses. Of course, these splines are all done based on what the Director of the movie wants, but each spline dictates how the movement will appear. For example, there is a scene in The Incredibles when Mr. Incredible is lifting a train. Now in order for the train to appear heavy, the animators knew that Mr. Incredible’s movements would have to appear as if he was exerting effort. So, in this case, they calculated the spline accordingly and the points on the graph were plotted further apart from one another. If they were plotted close to one another, then the train would have appeared to weigh nothing, thereby minimizing the believability of the scene (well, as believable as a scene could be with a man lifting a train).
Surprisingly, the use of light is also heavily calculated. Finding Nemo was the first of the animated movies where the animators had to create an underwater environment. Not only create it, but make it seem completely believable. To research this, the animation team embarked upon diving excursions in California, Hawaii, and Australia to get a real feel for the sea. There, they were able to analyze the light as it hits various surfaces and how different particles surge and swell depending on the water’s depth and murkiness. Without all of this texturized light, Nemo and his friends would look as if they are simply swimming in air.
In Cars too, the animators had to deal with light. Not underwater, as they did with Finding Nemo, but this time on the surfaces of the cars themselves. Using a calculation called Bidirectional Reflectance Distribution Functions (BRDF), animators were able to come up with the exact colour of the surface. In the simplest of terms, this calculation is used to describe how light scatters off a surface. This, in turn, is then used by the animators to produce a colour emulating the many surfaces we see in real life, such as glass, human skin, etc. Every surface is defined by BRDF. And in the case of Cars, this is why a rusty older car will appear differently than that of a more modern one. It all traces back to the light.
Then there’s “simulation”, which allows for a perfect bounce factor on Princess Merida’s bright red curly hair in Brave; and “subdivision”, a process that smooths out surfaces, like Woody’s human-like hands in Toy Story, so they do not appear jagged and crooked; and even (the biggest surprise) trigonometry, which is used to move Sulley’s mouth in Monsters, Inc. by a process called “rigging.” Hmm, I thought to myself as I left the museum, if I would have paid more attention in math class, could I be working at PIXAR?! (Let’s be honest, probably not).
A few days later, back to Montreal I flew. As we all do, I scrolled and scrolled through the list of TV shows and movies for something to watch. I landed upon Hidden Figures, the Oscar-nominated film showcasing three women who were instrumental in making the critical calculations required for the US’s first orbital space missions. Wow, talk about brilliant minds. These women were fierce with equations. Hmmm…if I put up less of a fuss in math class, could I be working at NASA?! Again, let’s be honest, probably not; but it doesn’t hurt to dream…
If only my math teacher could see me now.
"The Science Behind Pixar" exhibition runs until April 16, 2017 at the California Science Center.