On the reconfiguration and reachability of chains

• Main Author: Pei, Naixun.
• Other Authors: Whitesides, Sue H. (advisor)
• Format: Others
• Language: en
• Published: McGill University 1996
• Subjects: Computer Science.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=42115

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 links lie in the plane, with links allowed to cross over one another. For a chain $ Gamma$ constrained to lie in a confining region P, the reachability problem for $ Gamma$ is to determine, given a point $p in P$ and an initial configuration of $ Gamma$ inside P, whether $ Gamma$ can be moved within P so that the endjoint of $ Gamma$ reaches p, and if so, how this can be done. === This thesis solves the reachability problem of a planar chain $ Gamma$ confined within a convex obtuse polygon P, a convex polygon whose interior angles each measure $ pi$/2 or more. In particular, we propose a uniform approach in which the geometry of $ Gamma$ and its confining region P are studied together. We use this to obtain a family of pairs $( Gamma, P),$ which is largest possible in some sense, so that the reachability problem for each pair in the family can be solved quickly. We also examine the properties of the reachable region of $ Gamma$ in such a pair. === This thesis also presents reconfiguration results for an n-link planar chain $ Gamma$ inside a circle. We show that if each link of $ Gamma$ is less than the radius of its confining circle, then $ Gamma$ can be moved between any of its configurations inside the circle in $O(n sp2)$ time. === Our results demonstrate how to design short link chains within a given confining environment in order to ensure fast reconfiguration.