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. (C) 2012 Elsevier Ltd. All rights reserved.