O. Aichholzer, E. Demaine, J. Erickson, F. Hurtado, M. Overmars,
M. Soss, and G. Toussaint
We prove that there is a motion from any convex polygon to any convex polygon
with the same counterclockwise sequence of edge lengths, that preserves the
lengths of the edges, and keeps the polygon convex at all times. Furthermore,
the motion is “direct” (avoiding any intermediate canonical configuration
like a subdivided triangle) in the sense that each angle changes
monotonically throughout the motion. In contrast, we show that it is
impossible to achieve such a result with each vertex-to-vertex distance
changing monotonically.
