Rigid isotopy classification of real degree-4 planar rational curves with only real nodes (An elementary approach)

We prove an elementary method to classify, up to rigid isotopy, all nodal degree 4 real rational curves in ${\mathbb{R}\mathbb{P}}^2$ that have only real double points. We show how to associate a chord diagram to a nodal real degree 4 planar rational curve and prove that such curves are defined up to rigid isotopy by their chord diagrams.