Introduction to subdivision surfaces

- Hi, I'm Tony DeRose. I'm a computer scientist here at Pixar. In Pixar films, the way our characters look and act varies wildly. But one thing they have in common is they don't look computery. They have an organic believable look. The first step in creating that organic look is called modeling. Modeling is creating a virtual three-dimensional shape in the computer. One of the biggest problems of modeling a character that looks believable is getting their forms to appear to be smooth no matter how close or far away they are from the camera. The computer works most easily with simple shapes likes planes and cylinders, but we need to create much more complicated shapes. This sounds like a complex problem. But we were able to break it down into two simple steps that are easy to calculate on a computer. We discovered we could use a mathematical algorithm called subdivision to make smooth shapes. Here's how it works. Let's start with a simple two-dimensional example made of straight lines like this, defined by four points. The first thing I'm going to do is add midpoints along each line. I'll call this the split step. Next I'm gonna make the shape a little smoother by sliding each point halfway to its right neighbor, then I'll connect all eight points. I'll call that the averaging step. And that's a good start, but I can make this curve even smoother by doing it again. Split and then average, and then another time. And I can even put these two steps, split and average, together into a combined step called subdivision. That's easier still. The really cool thing about this solution is that it allows you to animate the whole curve just by moving the original four points. Now our characters are not just curves in two dimensions. There's surfaces and three-dimensional space. But the same principles of splitting and averaging apply in three dimensions. And you can still animate it using just a couple of points. So we've solved the complex problem of creating curves by breaking it down into steps we can solve with math. - Oh!