Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of knot diagram itself without any underlying three-dimensional structure, that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

翻译：纽结图是拓扑学中最常见的可视化工具之一。计算机程序现已能够实现纽结图的数字化绘制、操控和渲染，这在纽结理论的教学与研究中被证明颇具实用价值。然而，目前尚缺乏一款可公开获取的、支持实时交互式纽结图操作的工具。本文提出一种直接作用于纽结图几何本身的操控方法，无需借助任何底层三维结构，从而为此类应用奠定基础。该方法使我们能够直接与矢量图形格式的纽结图进行交互，同时依据前人提出的方式计算纽结不变量。文中还提供了该方法的具体实现。