I have nothing substantive to say, but I thought it might be helpful to
include an example of random
diagonals, which I have
drawn from an earlier MO question, "Shortest grid-graph paths with random diagonal shortcuts":
Random Diagonals 50x50 http://cs.smith.edu/%7Eorourke/MathOverflow/RandomDiagonals50.jpg
Joseph O'Rourke
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