Given a Regular Surface , an asymptotic curve is formally defined as a curve on such that the
Normal Curvature is 0 in the direction for all in the domain of . The differential equation
for the parametric representation of an asymptotic curve is
See also Ruled Surface
Gray, A. ``Asymptotic Curves,'' ``Examples of Asymptotic Curves,'' ``Using Mathematica to Find Asymptotic Curves.''
§16.1, 16.2, and 16.3 in Modern Differential Geometry of Curves and Surfaces.
Boca Raton, FL: CRC Press, pp. 320-331, 1993.