  We introduce the warping crossing polynomial of an oriented knot diagram by
using the warping degrees of crossing points of the diagram. Given a closed
transversely intersected plane curve, we consider oriented knot diagrams
obtained from the plane curve as states to take the sum of the warping crossing
polynomials for all the states for the plane curve. As an application, we show
that every closed transversely intersected plane curve with even crossing
points has two independent canonical orientations and every based closed
transversely intersected plane curve with odd crossing points has two
independent canonical orientations.
