Crunode

In mathematics, a crunode (archaic) or node is a point where a curve intersects itself so that both branches of the curve have distinct tangent lines at the point of intersection. A crunode is also known as an "ordinary double point".
For a plane curve, defined as the locus of points "f"("x", "y") = 0, where "f"("x", "y") is a smooth function of variables "x" and "y" ranging over the real numbers, a crunode of the curve is a singularity of the function "f", where both partial derivatives formula_1 and formula_2 vanish. Further the Hessian matrix of second derivatives will have both positive and negative eigenvalues.