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### Course: Pixar in a Box > Unit 11

Lesson 1: Modeling grass with parabolas- Start here!
- Introduction to parabolic arcs
- 1. String art
- String art construction
- 2. Midpoint formula
- Midpoint formula
- 3. Parabolic arcs
- Parabolic curve matching
- 4. Modeling grass
- Design challenge: Modeling grass
- 5. Animating grass
- Design challenge: Animating grass
- Getting to know Tony DeRose
- Hands-on activity

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# 1. String art

Find out how we can make curved lines using straight ones using the string art construction.

Click here to see Vi Hart's video on this technique.

Click here to see Vi Hart's video on this technique.

## Want to join the conversation?

- wait, they color and draw and create EVERY SINGLE BLADE!(18 votes)
- They likely use combinatorics once they design every blade and colour type that they desire. After that, the artist will use this to paint the background like a patchwork tool.(17 votes)

- How can a complete parabola be an infinite curve? Wouldn't it soon come back to the beginning and form a circle?(6 votes)
- No, parabolas keep going forever, never looping back on themselves. They are one of the conic sections, along with circles and ellipses (which do loop back on themselves) and hyperbolae (which don't). See https://www.khanacademy.org/math/algebra2/conics_precalc for more information.(11 votes)

- So, how is this string art going to help us make a animated grass?(6 votes)
- It is just a tool to use to see how the curve can be modeled in the computer.(3 votes)

- What programs do I need on my computer to be able to practice with lessons of the videos?(5 votes)
- Hi Ingrid: As Brit said in the comment on your question, you don't need to install anything on your computer to do these lessons. You just need the internet browser on your computer you're using right now! Good luck! --Blue Leaf(2 votes)

- About how many animators does it take to make a 90 minute movie?(2 votes)
- According to IMDB, there were 29 animators who worked on Inside Out (2015). There were plenty more working technical, sound and visual effects department. Pixar movies are surely a team effort! http://www.imdb.com/title/tt2096673/fullcredits/(5 votes)

- In the beginning of the video, was Mark Andrews sparring with a real sword?(3 votes)
- no, it's blunted. like what they use in historical sword fighting classes (yes that is a real thing)(2 votes)

- HI Sir

which software i need to install for this course?(2 votes)- You don't need to install anything, it all works in your browser.(3 votes)

- Is that a real sword?(3 votes)
- So being a math genius would be a must if you want to study animation?(2 votes)
- no, you just have to understand high school math (from what I've seen so far) quadratics are algebra 1.(0 votes)

- Is anyone gonna talk about how the director could've decapitated himself holding the sword like that(2 votes)
- We are all insane now(1 vote)

## Video transcript

(swords clanking) - 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. (whoosh) - Good to see you. - So we're talking today
about some of the ways that math was used to create
the forest in Brave. 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
it out there without the technical staff. Our movies are so complex. The movie like Brave, the
organics, and the grass, the forest, her hair, I mean everything. That just ups the game when
it comes to the numbers that you're crunching in a computer
so we rely completely on mathematics to make these movies. - That makes my heart warm.
(Andrew laughs) Thank you so much.
- Absolutely - And we're gonna be talking
about some of that complexity in the rest of this lesson. We saw in the previous
video, how parabolas are used to model grass in 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, but computers can too. Well, there are a variety
of ways of representing parabolic arcs. You may have seen them
for instance, as grass in quadratic functions. The problem with quadratic
functions is they're not very intuitive for artists. A more artist friendly way,
it 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 the control polygon. So if I'm only gonna store
the three points, I some how 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 gonna do
is lay out some evenly spaced points, the same number on each leg. And then next, what I'm gonna
do is start connecting dots. And as I continue to connect
these dots, you'll see the curve start to
emerge almost magically. Now you can do this same
construction in real life. It's called the string art construction. You take a pice 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 like down here. So we'll call this the
strong art construction for parabolic arcs. In the next exercise
you'll have an opportunity to connect the dots yourself.