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May 6, 2013 at 18:30 comment added Benoît Kloeckner @Ori Gurel-Gurevich: you are certainly right, I was too optimistic. I guess the method works under certain regularity assumptions (smooth or convex should work).
May 6, 2013 at 17:13 comment added Ori Gurel-Gurevich Actually, I don't see how step 1 works in full generality. For example, if the domain $D$ is a "cone" with a vary pointy tip (not the regular quadratic surface, but one where the angle is 0), then a ring whose center is at the tip and is orthogonal to the cone's axis will not be connected to any ring whose center is inside the cone. However, it seems plausible that this method works for, say, any domain with a smooth boundary.
May 1, 2013 at 12:14 vote accept Joseph O'Rourke
Apr 28, 2013 at 16:07 comment added Joseph O'Rourke Nice idea to arrange that not-linking requires circles that are simultaneously nearly horizontal and nearly vertical!
Apr 28, 2013 at 7:34 history answered Benoît Kloeckner CC BY-SA 3.0