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EWCG 2006, Delphi, March 2729, 2006 Reconfiguring planar dihedral chains

Summary: EWCG 2006, Delphi, March 27­29, 2006
Reconfiguring planar dihedral chains
Greg Aloupis
Henk Meijer
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 (, 2), for


Source: Aloupis, Greg - Département d'Informatique, Université Libre de Bruxelles


Collections: Mathematics; Computer Technologies and Information Sciences