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A point traced out twice as a closed curve is traversed. The maximum number of double points for a nondegenerate Quartic Curve is three. An Ordinary Double Point is called a Node.
Arnold (1994) gives pictures of spherical and Plane Curves with up to five double points, as well as other curves.
See also Biplanar Double Point, Conic Double Point, Crunode, Cusp, Elliptic Cone Point, Gauss's Double Point Theorem, Node (Algebraic Curve), Ordinary Double Point, Quadruple Point, Rational Double Point, Spinode, Tacnode, Triple Point, Uniplanar Double Point
References
Aicardi, F. Appendix to ``Plane Curves, Their Invariants, Perestroikas, and Classifications.'' In
Singularities & Bifurcations (V. I. Arnold). Providence, RI: Amer. Math. Soc., pp. 80-91, 1994.
Fischer, G. (Ed.). Mathematical Models from the Collections of Universities and Museums.
Braunschweig, Germany: Vieweg, pp. 12-13, 1986.