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

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