Asymptotic Curve
Given a Regular Surface 
, an asymptotic curve is formally defined as a curve 
on such that theNormal Curvature is 0 in the direction 
for all 
in the domain of 
. The differential equationfor the parametric representation of an asymptotic curve is
 | (1) |
, 
, and 
are second Fundamental Forms. The differential equation for asymptotic curves on aMonge Patch 
is | (2) |
is | (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.
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