Reconfiguring planar dihedral chains
نویسندگان
چکیده
We consider the dihedral model of motion for chains with fixed edge lengths, in which the angle between every pair of successive edges remains fixed. A chain is flat-state connected if every planar configuration can be transformed to any other via a series of dihedral motions which maintain simplicity. Here we prove that three classes of chains are flat-state connected. The first class is that of chains with unit-length edges and all angles in the range (60, 150). The second is the class of chains for which a planar monotone configuration exists. The third class includes, but is not limited to, chains for which every angle is in the range (δ, 2δ), for δ ≤ π
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