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.
- Rabin-Miller Strong Pseudoprime Test
- Rabinovich-Fabrikant Equation
- Racah V-Coefficient
- Racah W-Coefficient
- Radau Quadrature
- Rademacher Function
- Radial Curve
- Radial Point
- Radian
- Radiant Point
- Radical
- Radical Axis
- Radical Center
- Radical Integer
- Radical Line
- Radicand
- Radius
- Radius (Graph)
- Radius of Convergence
- Radius of Curvature
- Radius of Gyration
- Radius of Torsion
- Radius Vector
- Radix
- Radon-Nikodym Theorem