Parametric representation of a surface pencil with a common asymptotic curve

In this paper, we study the problem of finding a surface pencil from a given spatial asymptotic curve. We obtain the parametric representation for a surface pencil whose members have the same curve as a given asymptotic curve. Using the Frenet frame of the given asymptotic curve, we present the surface as a linear combination of this frame and analyse the necessary and sufficient condition for that curve to be asymptotic. We illustrate this method by presenting some examples.

► Surface family accepting a given curve as an asymptotic is expressed parametrically.
► Conditions on marching-scale functions are given for a surface to be a member of the family.
► The method is illustrated by examples.