Right, but I think that definition falls apart if you look at pathological shapes instead of nice convex ones. If you just randomly generate polygons, the thick

Right, but I think that definition falls apart if you look at pathological shapes instead of nice convex ones. If you just randomly generate polygons, the thickest part of the shape can appear anywhere, including a very far off edge. And if you cut a tiny opening into that part of the shape, the center would completely move.