Refolding Planar Polygons

Authors:
Hayley N. Iben;James F. O’Brien;Erik D. Demaine
Affiliations:
University of California, Berkeley, Berkeley, CA, USA and Pixar Animation Studios, Emeryville, CA, USA;University of California, Berkeley, Berkeley, CA, USA;Massachusetts Institute of Technology, Cambridge, MA, USA
Venue:
Discrete & Computational Geometry
Year:
2009

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