An asymptotic direction at a point **p** of a Regular Surface is a direction in which the
Normal 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.

© 1996-9

1999-05-25