Main content

## Pixar in a Box

### Unit 11: Lesson 2

Calculating parabolas- Start here!
- Weighted average of two points
- Weighted averages
- 2. Where is the touching point?
- Exploring the parabola construction
- 3. Compute the touching point
- Calculating the touching point
- 4. How can we prove this?
- Touching point
- Bonus: Completing the proof

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Start here!

Overview of this lesson

## Ready to dive into some math?

In this lesson, we're going to develop a powerful formula that will allow us to easily calculate points along a parabolic arc.

To get there, we first need to develop our understanding of

**weighted averages**. This is really important concept to understand since several other lessons will build on it—you can do this step without finishing the entire lesson. Next we'll discover de Casteljau's algorithm, which will allow us to calculate points on any parabolic curve. This results in a really simple set of equations computers can use to draw parabolic arcs.

# What do I need to know before starting?

- You should be able to calculate midpoints using this exercise from the first lesson.
- You should also be familiar with basic ratios and proportions, which you can review in this exercise.

## Want to join the conversation?

- Is de casteljau's algorithm a formula or a topic on it's own?(25 votes)
- Its an algorithm.(22 votes)

- I know that this lesson is focused on parabolas, and is using grass as an example for what parabolas can be used for. What else are parabolas used for when dealing with animation?(11 votes)
- You can also use it for leaves as well, since if you make a blade of grass thick enough, it looks similar to a leaf.(4 votes)

- This is great, but why is math in the lesson?(8 votes)
- I literally need medicine right now, I'm suffering from the MathaVirus(9 votes)

- ❤ I love khan academy.:📚📘(10 votes)
- how douse this relate(2 votes)

- how long dose it take to make a hour film?(6 votes)
- BY the time I am in college, I will need medicine for my frustration(3 votes)
- Who else is in 6th grade?(3 votes)
- Is it hard to make a movie?(2 votes)
- Yes. It involves producing something new and requires both technical skills and creativity. There is a huge crew of people behind the creation of just a single animated movie. So, we can conclude that it is very difficult and also takes a lot of hard work and effort to just make a single Animated movie.

And on average it can take anywhere from four to seven years to make an animated movie. Time varies for animated films because there are a few different ways to film an animated movie.(1 vote)

- Why should we use math for animation(2 votes)
- Math in animation is necessary to calculate viewpoints, aspect ratios, character movement, artificial lighting, and color balance. Furthermore, animators use math to calculate movement and frame rates in animation.(1 vote)

- this gave me a bigger understanding, but is this the process for all the animations(2 votes)