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Oct 3, 2012 at 6:03 comment added Will Sawin I am not convinced this is optimal in general. Suppose I take one figure where a certain direction is optimal (and the difference between optimal and suboptimal is large), and another figure where a quite different direction is optimal (and the difference is again large) and connect them by a thin tube. It seems clear that the best way to cover this figure is with one region with the first direction, one region with the second direction, and a number of smaller regions.
Oct 1, 2012 at 7:01 history edited Cristi Stoica CC BY-SA 3.0
added 80 characters in body
Oct 1, 2012 at 6:49 history answered Cristi Stoica CC BY-SA 3.0