3. Fun with weights

- Congratulations you're in the last step of this lesson. To finish our look at weighted averages recall that if I pick weights one one I get subdivision curves that look like this. And we learn that these shapes are pieces of degree two curves like Y equals X squared stitched together. And if I pick the weights one-two-one, I get curves that look smoother. Just like this. These curves turn out to be pieces of degree three curves like Y equals X cubed stitched together. In this example there are four different degree three pieces I can even get smoother curves by picking the weights one-three-three-one. Which are degree four curves like Y equals X to the fourth. And it turns out that the weights have to be chosen very carefully for the curves to be smooth. So what exactly does carefully mean? These numbers one-one, one-two-one, one-three-three-one all come from a pattern called Pascal's Triangle. Let's see what happens if I pick weights that aren't from Pascal's Triangle. I don't even have to pick positive weights, so supposed I pick one-negative two-three? Nothing new with split, it always just adds mid points. But when I do the averaging stuff, whoa! As I keep subdividing the curve gets less and less smooth. It's something called a fractal. We don't have all of the mathematical tools that we require to show this, there's some more advanced concepts from linear algebra and something called eigenanalysis. Eigenanalysis sounds kinda scary but mathematicians are just really good at coming up with names that are kinda scary. And just like we've done so far you just learn one step at a time. The main thing that I want you to walk away with is that the surfaces that you see in our films are actually pretty easy to create. The art department creates sketches for the modelers to refer to when determining control point positions. From there the software tools do the splitting and averaging to produce the beautiful surfaces that you see in the theater. Of course when you're watching one of our films we don't want you to think about any of that. We just want you to sit back, relax, and let the movie take you away. So play around with the weights. See what weird results you can get. And when you're done you can move onto the final exercise.