Asymptotic Direction

An asymptotic direction at a point p of a Regular Surface is a direction in which theNormal Curvature of vanishes.

1. There are no asymptotic directions at an Elliptic Point.

2. There are exactly two asymptotic directions at a Hyperbolic Point.

3. There is exactly one asymptotic direction at a Parabolic Point.

4. Every direction is asymptotic at a Planar Point.

References

Gray, A. Modern Differential Geometry of Curves and Surfaces.Boca Raton, FL: CRC Press, pp. 270 and 320, 1993.

• Upper Bound
• Upper Integral
• Upper Limit
• Upper Sum
• Upper-Trimmed Subsequence
• Upward Drawing
• Urchin
• Utility Graph
• Utility Problem
• Valence
• Valency
• Valuation
• Valuation Group
• Valuation Ring
• Valuation Theory
• Value
• Value (Game)
• Vampire Number
• van der Grinten Projection
• Vandermonde Determinant
• Vandermonde Identity
• Vandermonde Matrix
• Vandermonde's Sum
• Vandermonde Theorem
• van der Pol Equation