An approach for designing a surface pencil through a given asymptotic curve

Abstract

Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve has attracted much interest. In the present paper, we propose a new method to construct a surface interpolating a given curve as the asymptotic curve of it. Also, we analyze the conditions when the resulting surface is a ruled surface. Furthermore, we prove that there exists no developable surface possessing a given curve as an asymptotic curve except plane. Finally, we illustrate this method by presenting some examples.

Interpolation of surfaces with asymptotic curves in Euclidean 3-space

“…Moreover, Güler at al. constructed a surface interpolating a given curve as the asymptotic curve of it [11]. Similar to geodesics, the asymptotic curves also have many applications in related sciences.…”