释义 |
Asymptotic CurveGiven 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) |
where , , and are second Fundamental Forms. The differential equation for asymptotic curves on aMonge Patch is
 | (2) |
and on a polar patch is
 | (3) |
The images below show asymptotic curves for the Elliptic Helicoid, Funnel, Hyperbolic Paraboloid, and Monkey Saddle.See also Ruled Surface 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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