  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.
