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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 the curve 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 weight to one to one and now I split as before but when I do the averaging step each point will move to a 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 up out 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