Interpolation of surfaces with asymptotic curves in Euclidean 3-space

In this paper, we investigate the interpolation of surfaces which are obtained from an isoasymptotic curve in 3D-Euclidean space. We prove that there exist a unique $C^0$-Hermite surface interpolation related to an isoasymptotic curve under some special conditions on the marching scale functions. Finally, we present some examples and plot their graphs

CONSTRUCTION OF OFFSET SURFACES WITH A GIVEN NON-NULL ASYMPTOTIC CURVE

In the present work, we study construction of offset surfaces with a givennon-null asymptotic curve. Let $\alpha \left( s\right)$ be a spacelike ortimelike unit speed curve with non-vanishing curvature and $\varphi \left(s,t\right)$ be a surface pencil accepting $\alpha \left( s\right)$ as acommon asymptotic curve. We obtain conditions such that the offset surfacepossesses the image of $\alpha \left( s\right)$ as an asymptotic curve. Wevalidate the method with illustrative examples