论文标题
纺织品的编码和拓扑计算
Encoding and Topological Computation on Textiles
论文作者
论文摘要
纺织结构是在增厚平面中螺纹的周期性排列。纺织结构的拓扑分类要比经典结和非周期性且仅限于有限区域的经典结和链接要难。第一个重要的问题是以简单的组合方式编码所有纺织结构。本文在经典结理论中扩展了高斯代码的概念，为这些结构提供了拓扑计算的工具。作为第一个应用程序，我们提出了一种线性时间算法，用于确定代码是否代表物理意义上的纺织品。该算法以及纺织结构不变的算法使我们首次将所有方向的纺织结构分类为从单个组件编织到复杂性五。
A textile structure is a periodic arrangement of threads in the thickened plane. A topological classification of textile structures is harder than for classical knots and links that are non-periodic and restricted to a bounded region. The first important problem is to encode all textile structures in a simple combinatorial way. This paper extends the notion of the Gauss code in classical knot theory, providing a tool for topological computation on these structures. As a first application, we present a linear time algorithm for determining whether a code represents a textile in the physical sense. This algorithm, along with invariants of textile structures, allowed us for the first time to classify all oriented textile structures woven from a single component up to complexity five.
