Refolding Planar Polygons
This paper describes an algorithm for generating a guaranteed intersection-free interpolation sequence between any pair of compatible polygons. Our algorithm builds on prior results from linkage unfolding, and if desired it can ensure that every edge length changes monotonically over the course of the interpolation sequence. The computational machinery that ensures against self-intersection is independent from a distance metric that determines the overall character of the interpolation sequence. This decoupled approach provides a powerful control mechanism for determining how the interpolation should appear, while still assuring against intersection and guaranteeing termination of the algorithm. Our algorithm also allows additional control by accommodating a set of algebraic constraints that can be weakly enforced throughout the interpolation sequence.
Hayley N. Iben, James F. O'Brien, and Erik D. Demaine. "Refolding Planar Polygons". Discrete and Computational Geometry, 41(3):444–460, April 2009.
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This is an expanded version of an earlier paper that was published in SoCG 2006. As recipients of the SoCG Award for Best Paper, the authors were invited to submit an extended version to the journal Discrete and Computational Geometry.