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## Pixar in a Box

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

Lesson 2: Mathematics of subdivision

# 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.

## 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.