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## Mathematics of subdivision

Current time:0:00Total duration:1:53

# 2. Weighted subdivision

## Video transcript

- Hopefully, now, you
have a good idea of how weighted averages work for both
two points and three points. Next, we're gunna see what happens when you replace that 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 1:1, 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 2:1. Now, let's generalize to the
case of averages of 3 points. Watch what happens when I
change the weights to 1:2:1. And, now, I split, as before, but, when I do the averaging step, each point will move to a position that takes itself with a weight 2, its left neighbor with a weight 1, and the right neighbor with the weight 1. 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!