3D中锁定和解锁的多边形链
Locked and Unlocked Polygonal Chains in 3D
摘要：
本文研究了简单多边形链在三维空间中的运动。我们说，一个开放的，简单的多边形链可以被拉直，如果它可以连续地重新配置为一个直线序列的片段，以这种方式，每个环节的长度和简单的链保持整个运动。闭链的类似概念是凸化：重构为平面凸多边形。不能伸直或弯曲的链称为锁定链。虽然有开放的链在3D锁定，我们表明，如果一个开放的链有一个简单的正交投影到一些平面上，它可以被拉直。对于闭链，我们表明，有unknotted，但锁定的闭链，我们提供了一个算法，凸化一个平面简单的多边形在3D与多项式数量的移动。
英文摘要：
In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are maintained throughout the movement. The analogous concept for closed chains is convexification: reconfiguration to a planar convex polygon. Chains that cannot be straightened or convexified are called locked. While there are open chains in 3D that are locked, we show that if an open chain has a simple orthogonal projection onto some plane, it can be straightened. For closed chains, we show that there are unknotted but locked closed chains, and we provide an algorithm for convexifying a planar simple polygon in 3D with a polynomial number of moves.
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