Paper by Erik D. Demaine

Reference:

Hayley N. Iben, James F. O'Brien, and Erik D. Demaine, “Refolding Planar Polygons”, in Proceedings of the 22nd Annual ACM Symposium on Computational Geometry (SoCG 2006), Sedona, Arizona, June 5–7, 2006, pages 71–79.

Abstract:

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 set of algebraic constraints that can be weakly enforced throughout the interpolation sequence.

Comments:

See also animations of this algorithm.

Availability:

The paper is available in PDF (327k).

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Refolding_DCG (Refolding Planar Polygons)

Refolding_SIGGRAPH2004 (Refolding Planar Polygons)

ForceLinkage_SoCG2004 (An Energy-Driven Approach to Linkage Unfolding)