An asymptotic direction at a point p of a regular surface M element R^3 is a direction in which the normal curvature of M 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.

asymptotic curve