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so far in this lesson we've learned how to model curves in two dimensions and now it's time to go back to the real problem that we want to address how to model the fun part characters using surfaces in three dimensions and that is where subdivision really shines the same ideas of splitting and averaging still apply in three dimensions and that means that subdivision applies as well for example suppose that I start with a cube I can look at the cube from different angles by clicking on the background and dragging the splitting step is a little bit more complicated than four curves in addition to adding midpoints of edges like this one I also need to add midpoints of the facets like this one midpoints of facets are computed by averaging all of the coordinates of the control points surrounding that facet for instance this midpoint is computed as the average of these four points and this one is the average of these four points the averaging step is a little bit more complicated than the curve case too each point is again repositioned using averaging but now it is in a straight average we need to use the weighted average of all of the points next to the one that we are repositioning we'll talk more about weighted averages in the next lesson and just like the curves we can combine split and average into a subdivide operation and if we subdivide enough times the shape becomes a smooth surface now let's try this on a doughnut shape subdividing ones gives me this subdividing again gives me that in practice we subdivide as many times as we need to to create a smooth image subdivision was first used to create the character named Jerry from the short film jerry's game here's jerry's han before the subdivision here it is after subdivision since Jerry's game we've used subdivision to create practically all of our characters we even use subdivision for things besides characters like the buildings in The Incredibles because subdivision surfaces are so easy for artists to use next up we have a simplified 3d program for you to play with really go play try anything and everything you can think of you can't break it and you can always restart once you start to feel comfortable with how the subdivision operation behaves move on and we'll try the final exercise after that you can check out the next lesson which goes a bit deeper into the mathematics of subdivision go do something awesome