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

SURFACE FAMILY WITH COMMON LINE OF CURVATURE IN 3-DIMENSIONAL GALILEAN SPACE

In this paper we study to find parametric presentation of a surface family with common line of curvature in 3-dimensional Galilean space. We obtain necessary and sufficient conditions for the curve to be a common line of curvature on this surface. We state examples to visualize our results and we obtain some results for a torsion free curve