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Sep 23, 2012 at 13:31 comment added Joseph O'Rourke @Alexandre: You (and Ben Crowell) are correct, in that rolling plays no role, even though that was my original motivation: to "paint" the surface with a rolling "paint ball." And $r$-convexity is a nice viewpoint, because of course if $r \rightarrow \infty$, $S$ must be convex.
Sep 23, 2012 at 3:48 history answered Alexandre Eremenko CC BY-SA 3.0