We can make an intial space by pushing the midpoint in any three vertices to the left, going counter- clockwise. This gives us a potenital fourth point, unless this point is too close to the two other two endpoints, our initial and then our final point, in which case we drop it and make a triangle. Otherwise we get a quad/triangle pair which will be further subdivided if the edges are too long, adding and splicing in one or two more new points. I'm going make a bit of a place holder tonight, no surprise...
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