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## Pixar in a Box

### 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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# Introduction to parabolic arcs

What do parabolic arcs have to do with blades of grass?

## Want to join the conversation?

- What are parabolic arcs anyways?(7 votes)
- A parabolic arc is a section of a parabola. A parabola is a curve whose equation is in the form y = ax^2 + bx + c

You can learn more about parabolas here: https://www.khanacademy.org/math/algebra2/conics_precalc/parabolas_precalc(26 votes)

- Do you use coding to create images in movies?(7 votes)
- yeah, but only TD's and rendering engineers do that.(1 vote)

- Alright this is probably a stupid question for any of you who are a pro at this but .......How much math goes into each blade of grass, leaf, bark, rock, moss, mushroom, dirt, smoke, fire, and every ting like that? If anyone is willing to tell me then grate!!(5 votes)
- It is not a stupid question! It usually takes a lot of math if you really want it to look good and realistic.(3 votes)

- How much math goes into one blade of grass?(4 votes)
- The term "computational power" describes how much work a computer has to work to get to the wanted result. The more math involved, the harder it is.

The question 'how much math goes into one blade of grass" is a bit vague. We do have ways to calculate the overall efficiency of an computer algorithm, which we can calculative by counting the numbers of operations done in the program.

For more info on this, I'd suggest looking into algorithms on KA in their Computer Science (CS) section.

Hope this helps! :-)(3 votes)

- why is it called a parabola(6 votes)
- in0:11and0:12he says something very ture(4 votes)
- What is the beep on:1:10in the video??(3 votes)
- I was wondering, how would we animate something like a tree or a fish?(3 votes)
- at1:02how do you make the curves without bumps? isn't that really hard?(2 votes)
- No, not really. All it is is some maths and you can curve it out.(2 votes)

- Alright this is probably a stupid question for any of you who are a pro at this but ......... How much math goes into each single blade of grass, leaf, bark, dirt speck, and rock?(2 votes)
- A lot of basic processing power, for the rendering, for the theater/disc, and all that stuff.

Otherwise, one has to bit by bit move around the points to create ONE blade, and as shown here, over a hundred blades must be made.

Trees are probably made using 3-D models, while dirt and rocks share the same fate.(2 votes)

## Video transcript

- 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)