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

(1) |

(2) |

(3) |

**References**

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.

© 1996-9

1999-05-25