1. String art

welcome to Pixar I'm Tony DeRose one of the computer scientists who works on our film here and conveniently enough behind me is Mark Andrews director of brave good the same so we're talking today about some of the ways that Nath was used to create the flushed brand and I was wondering what it's like as a director to work with the technical staff here oh I love them I mean everything that you see on a screen on a Pixar movie we couldn't put up there without the technical staff it's our movies are so complex the movie like brave the organics in a dress the forest her hair I mean everything that just up is the game when it comes to the numbers that you're crunching in the computer so we rely completely on mathematics to make these movies that makes my heart warm you thank you so much absolutely and we're going to be talking about some of that complexity and the rest of this lesson we saw in the previous video how parabolas are used to model grass and brave a complete parabola is actually an infinite curve but we just want a little piece that's called a parabolic arc and to create believable grass we have to create other attributes such as how the width varies up the blade its color and how it moves in response to things like horse hooves and wind and we'll get to all of that later in the lesson but for now let's just focus on the basic shape come on inside I'll show you more so the question is how are we going to represent parabolic arcs in a way that artists can deal with what computers can - well they're variety of ways of representing parabolic arcs you may have seen them for instance as graphs of quadratic functions the problem with quadratic functions is they're not very intuitive for artists a more artist friendly way is to use three points let me show you okay so I have three points and as I move them around the parabola updates accordingly and in computer graphics these three points like this are called a control polygon so if I'm only going to store the three points I somehow I have to recover that parabolic arc so the question is how do I go from these three points to recovering my parabola the idea is pretty simple the first thing we're going to do is lay out some evenly spaced points the same number on each leg and then next what I'm going to do is start connecting dots and as I continue to connect these dots you'll see the curves start to emerge almost magically now you can do the same construction in real life it's called a string art construction you take a piece of paper you draw some lines on it you spread out some evenly spaced points and then with needle and thread you start making these connections as I've done here so we'll call this the string art construction for parabolic arcs in the next exercise you'll have an opportunity to connect the dots yourself