2. Subdivide operation

one of the cool things about splitting and averaging is that it's pretty easy to program so we just need to find the midpoint which is just averaging coordinates this makes it pretty easy for the people that write our software to create intuitive tools for artists like myself to create characters kind of like used on the smiley face in this next version of the interactive we've replaced the split and average buttons with a single button called subdivide clicking it simply does split followed by average focus your attention on this region of the curve now let's extend these lines until they hit the control polygon hmm doesn't this look suspiciously like the string art construction we saw in the parabolic arcs now watch what happens when I subdivide again the string art pattern continues to emerge now every time you hit subdivide you get twice as many strings and that means that the curve that we're creating is a parabolic arc in this region and there's another parabolic arc over here and over here and over here but magically these four arcs are smoothly blending from one to another I think that's just so cool and someone interested in mathematics this is the kind of surprise that I find exciting this next exercise will test how well you understand this concept