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 the 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、操作与渲染，这在纽结理论的教学与研究中被证明极为有用。然而，目前仍缺乏一种可公开获取、支持实时交互式操作的纽结图工具。本文提出一种直接作用于纽结图几何结构的方法，无需依赖任何底层三维结构即可支持此类应用。该方法使我们能够直接操作矢量图形纽结图，同时沿用前人工作提出的方式计算纽结不变量。本文还提供了该方法的实现方案。