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 who appear to be smooth no matter how close or far away they are from the camera the computer works most easily with simple shapes like 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 going to 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 now 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 an average together into a combined step called subdivision that's easier still the really cool thing about the solution is 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 they're surfaces in 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