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## Pixar in a Box

### Course: Pixar in a Box > Unit 3

Lesson 2: Mathematics of subdivision- Start here!
- Weighted average of three points
- Weighted average intuition
- Weighted average of three points
- 2. Weighted subdivision
- Weighted subdivision
- 3. Fun with weights
- Interativo: subdivisão ponderada
- Subdivision weights
- Bonus: Equations for points in subdivision

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# 2. Weighted subdivision

Next let's extend the averaging step from the previous lesson to include multiple points. Now we'll need to calculate positions using a weighted average.

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## Video transcript

- Hopefully now, you have a good idea of
how weighted averages work for both two points and three points. Next, we're gonna see what happens when you replace the
averaging step using midpoints with weighted averages. So here we are again with a curved subdivision interactive, except now, we have this
field that allows us to change the weights used
in the averaging step. The one, one over here means that we're doing straight averaging. So I split it as usual
by inserting midpoints. And the averaging step moves the points to the midpoint of their
clockwise neighbor. Watch what happens when I
change the weights to two, one. Now let's generalize to the case of averages of three points. Watch what happens when
I change the weights to one, two, one. And now I split as before but when I do the averaging step, each point will move to the position that takes itself with the
weight to its left neighbor with the weight one, and the right neighbor
with the weight one. This point should move about here as we saw in the weighted average example, and if we split an average
again, it looks like this. This next exercise will
give you some practice with the idea of weighted subdivisions. Good luck.