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# Introduction to subdivision surfaces

Video transcript

- 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!