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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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# 1. Mathematics of linear interpolation

First we'll use the slope intercept form of a line to define each frame along a straight line.

Click here to review slope-intercept form of a line.

Click here to do the Environment Modeling topic if you haven't already.

Click here to review slope-intercept form of a line.

Click here to do the Environment Modeling topic if you haven't already.

## Want to join the conversation?

- I'm sorry I really just wanted to come on here to learn how to animate. I have never used khan academy until now and I'm not the best in math. I just want to know if I can still continue learning to animate without having to know all the math behind it.(6 votes)
- You do not need any of this to learn how to animate, you can get very far knowing none of it.

Source: I work in the games industry(4 votes)

- i'm 8+ am i to young to understand(5 votes)
- NO! noones too "young" to understand it (yes noone is a real word, it means no one.)(2 votes)

- I don't get it and their so many numbers(3 votes)
- It's called the 'Mathematics of animation curves,' so if you need to review, you should(2 votes)

- i did slope in school before and i already know about the formula but this is hard and doesn't make any sense, doesn't explain ANYTHING that i get.(2 votes)
- It helps you figure out where the ball is at that time, luckily, you don't always have to use this way of animating. There are some, where you just draw different frames, but you have to draw them.(3 votes)

- isn't a video just the computer animating itself?(3 votes)
- This is hard!Can any body help me understand(3 votes)
- im in 1st grade and im lernig this(2 votes)
- I'm 8 what to do I'm in grade 3 I dunno anything here(2 votes)
- This course is intended for all ages. You can follow the directions provided in the videos. If you need help feel free to ask :)(1 vote)

- yes please be little more specific(1 vote)
- Is it me or did it meant to be 3 seconds long?(1 vote)

## Video transcript

- So, we've seen two ways
to calculate in-betweens: linear interpolation and Bézier curves. Now let's get into the math behind them. We're gonna build on
some of what we learned in the environment modeling lesson, so if you need to review,
click on this link. Let's start with the simpler
version, linear interpolation. Let's focus on this segment. We know the value of y at frame 4 is 750 and the value at frame 8 is 190, but what's the value of
y at frame 5, 6, or 7? The picture tells us
that y can be represented as a linear function of x,
where x is the frame number. Linear functions can be written
in slope-intercept form: y = mx + b, where m is the slope and
b is the y-intercept. Now we don't know the slope
and intercept directly, but we do have two points on the line, which is enough information
to calculate them. Now, once we have m and b, we can figure out y for any frame. Try out this next exercise
to test your understanding of linear interpolation using
the slope-intercept form.