Locked and Unlocked Polygonal Chains in Three Dimensions

T. Biedl, University of Waterloo
E. Demaine, University of Waterloo
M. Demaine, University of Waterloo
S. Lazard, INRIA Nancy
A. Lubiw, University of Waterloo
J. O'Rourke, Smith College
M. Overmars, Universiteit Utrecht
S. Robbins, Université McGill
I. Streinu, Smith College
G. Toussaint, Université McGill
S. Whitesides, Université McGill

Archived as published.

Abstract

This paper studies movements of polygonal chains in three dimensions whose links are not allowed to cross or change length. Our main result is an algorithmic proof that any simple closed chain that initially takes the form of a planar polygon can be made convex in three dimensions. Other results include an algorithm for straightening open chains having a simple orthogonal projection onto some plane, and an algorithm for making convex any open chain initially configured on the surface of a polytope. All our algorithms require only O (n) basic "moves.".