Introduction to parabolic arcs

- Hi. My name is Inigo Quilez, and I work in Brave making all the trees, the forest, and all the natural environments of the movie. I use a lot of mathematics to do this. (arrow hits target) I think most people think of maths as something boring and mechanical, but that's not the way we see mathematics at Pixar. For us, maths are a tool to create images, movement, richness, and fun. This lesson, we'll talk about one of the ways we use mathematics to create the landscapes of Brave. So let's start with the most simple thing we can find in this landscape: one blade of grass. One blade of grass is something that starts in a point, grows in a direction, and bends down. It looks like a small, thin curve. This is great news, because in mathematics, we have a lot of tools to describe curves. In this case, we choose the parabola, which is a very specific curve. The curve, however, only gives us the spine of the blade. We still need to add a thickness to it and a color to make a blade of grass. And in order to populate the whole forest, we need to create millions of such curves, and then give them the right thicknesses and colors in order to create something organic and natural. Do you want to know more? Stay with us for the rest of the lesson. (beep)