Abstract
A chain is a sequence of rigid rods or links consecutively connected at their endjoints, about which they may rotate freely. A planar chain is a chain whose rods lie in the plane, with rods allowed to pass over one another as they move. A convex obtuse polygon P is a convex polygon with each interior angle not less than π/2. We consider the following reconfiguration problem.
Given: an n-link planar chain Γ confined inside a convex obtuse polygon P whose sides are all longer that the longest link of Γ; a point p ε P; and an endjoint of Γ. Question: Can Γ be moved within P so that the specified endjoint of Γ reaches p?
We give a necessary and sufficient condition for a “yes” answer, and in this case we further give an algorithm for reaching p. The necessary and sufficient condition is independent of the initial configuration of Γ and is checkable in time proportional to the number of links in the real RAM model of computation.
Supported by FCAR and NSERC.
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© 1996 Springer-Verlag Berlin Heidelberg
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Whitesides, S., Pei, N. (1996). On the reconfiguration of chains. In: Cai, JY., Wong, C.K. (eds) Computing and Combinatorics. COCOON 1996. Lecture Notes in Computer Science, vol 1090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61332-3_172
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DOI: https://doi.org/10.1007/3-540-61332-3_172
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