Main content

## 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

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# 4. Modeling grass

Next let's build a blade of grass using a parabolic arc as a spine.

Click here to review perpendicular lines.

Click here to review perpendicular lines.

## Want to join the conversation?

- How are the widths of the skeleton lines determined? Are they based on another parabola?(58 votes)
- Good question! They are determined using a sine wave in this example, but a parabola might have worked too. Then we could have added more control points so the width could also be controlled by the artists.(27 votes)

- How the skeleton works mathematically?(9 votes)
- He kind of glossed over that bit, didn't he? Here's one approach:

You can use the intersections of the individual line segments making up the curve to evenly distribute the skeleton lines along the curve. Say, every fourth intersection gets a displayed skeleton line.

Then you need to determine the angle of each skeleton line. The skeleton lines are all perpendicular to the curve. Trouble is, we've located them on the intersections, where there is a very shallow corner. Well, you can't actually get a line that's perpendicular to a corner, but what you**can**do is bisect the angle of that corner. Create a line that intersects with the corner such that the angles formed with the line segments on either side of the new line are equal. Or such that the angles on opposite sides of the new line are equal to 180 degrees. Either way gets the same result.

Now what about the length of the skeleton lines? If you look carefully at the endpoints of those lines, you might notice that they, like the main curve, describe the same kind of parabolic arc. The lower control points, where the base of the blade is, are offset from the center. There is probably a hidden parameter in the drawing program that determines the width of the base. The upper control point is in the same location as that of the main arc. Draw a line perpendicular to the curve that passes through the middle control point of the main arc, the middle control points of both skeleton curves will lie on that line. The width control determines the distance of those control points from the main arc.(10 votes)

- What kind of program is this?(6 votes)
- The program is to teach you how to make models for making movies or something(0 votes)

- What about modeling something like ferns? Couldn't we simply adjust the
`skeleton`

algorithm? Looks like we'd need to have user inputs for tweaking the amplitude and period of the sine wave. I mean, sure, it is an increase in complexiy, but it would allow the artists to create other species of underbrush, right?(4 votes)- Yes, grass is pretty much the simplest object to model, but you can tweak the basic idea to make more complex objects. By changing the how the skeleton is determined, you can more interesting leaves. Going further, you can use a recursive system to generate branches you can make pretty realistic plants. One such system is the L-system: https://en.wikipedia.org/wiki/L-system(3 votes)

- what link was he talking about?(2 votes)
- Do you mean perpendicular lines? You'll always find the links directly beneath each video(3 votes)

- Which Software I need to use for this ?(2 votes)
- You don't need any software other than your browser.(3 votes)

- what app or software can i install in my system for me to be able to do animations(2 votes)
- You have a wide variety of tools to choose, from commercial ones to open source tools. I would recommend using Blender to start, because it's free and it contains pretty much everything you need to learn, from modeling tools to rigging, texturing, animating and rendering your work and move on to some commercial software if you intend to become a professional 3D artist. However it's not really about the tools, it's more about studying, a lot, understanding the way the computer works to calculate various simulations, studying the main techniques, etc. For example, when modeling, once you learn the proper way to distribute the polygons on a model (proper topology) in one software you will know how to do that in any other related software, you'll just have to accommodate with the key bindings and commands.(2 votes)

- How do you create millions and millions of blades of grass?(2 votes)
- What are the usual widths parameters used in Brave or other movies for creating grass? This is amazing!(2 votes)
- Do artists have to make each blade of grass or is there a program that makes them for the artist.(1 vote)

## Video transcript

(clicking) Great work! Now we've got all the math we
need for a computer program to draw as many lines as we need to create a good
approximation to a parabola. Let's return to some of the
artistic aspects of grass starting with the width. In this interactive, I
can move the points around and I haven't drawn the
legs of the control polygon just to make it look a little bit simpler and, let's see, that kind of shape for the
spine looks pretty good. So let me move on to the next step which is to define the width. I'm going to do that using
something we'll call a Skeleton. The Skeleton is a set
of lines, like these, that cut across the blade
of grass at 90 degree angles so here's a Skeleton line,
here's a Skeleton line and so on. If I connect all the left
sides of the Skeleton lines and the right side of the Skeleton lines, I create a region, let me fill that in, and that region looks a lot
more like a blade of grass. (click)
(tinkling) I can control the width
using this slider here so that's just adjusting the
length of those Skeleton lines and that width there looks pretty good. Finally, I can control the color. I can go from a deep green to a lighter green to a really light green. Our artists control parameters like this to create the kind of convincing grass that you see in "Brave." Use this interactive to see what kinds of blades of grass you can create and then, in the next video, we'll talk about how to animate it.