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## Pixar in a Box

### Unit 10: Lesson 2

Mathematics of animation curves- Start here!
- 1. Mathematics of linear interpolation
- Linear interpolation
- 2. Repeated linear interpolation
- 3. De Casteljau's algorithm
- Constructing curves using repeated linear interpolation
- 4. What degree are these curves?
- Bonus: Equations from de Casteljau's algorithm

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# Start here!

Overview of this lesson

# Ready to dive into some math?

In this lesson we are going to uncover a really useful way to construct

**Bezier curves**of various degrees using de Casteljau's algorithm.We'll begin by reviewing how to do linear interpolation using the slope intercept form of a line.

Then we'll revisit de Castlejau's algorithm using the three points that were covered in the Environment modeling topic.

Finally we'll extend this construction to

**cubic curves**which are used in animation at Pixar. We'll even see how it works for curves of*any degree*.# What do I need to know before starting?

- You should know slope intercept form—click here to review with Sal.
- It would help to complete the calculating parabolas lesson as well.

## Want to join the conversation?

- Oh no... Am I gonna pass? I am kinda horrible at math like this! Probably cause I'm a fifth grader. :V(22 votes)
- I'm an 8th grader and I'm not that good at math! No need to worry(3 votes)

- How long does it take to make an {cartoon} movie?(7 votes)
- **a

It depends. A action movie would take some time. If you are just practicing -like the ball, just under an hour.(5 votes)

- Ready to dive into some math?(7 votes)
- Wow i love it but dont get it relly ? im n 3 grade my kaitlyn name(6 votes)
- I love this because I like anime.So I want to create anime.(2 votes)

- I agree with Sofiya. You can never be too young or to old to do anything.(6 votes)
- ur ima grade 5 is this good for me?

pls awnser(4 votes)- it matters if you know the math involved and if you are good at math(1 vote)

- Is fourth grade to young for this because, I finished everything(1 vote)
- I'm having a little hard time understanding this, may I get some help?(4 votes)
- I would help you if i could but i dont understand it either ;((1 vote)

- You destored my anime mine(4 votes)
- Is third grade to young to start learning these kinds of things(3 votes)