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

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

Surfaces with constant gaussian curvature along a given curve

Bu çalışmada, verilen bir eğriden geçen ve bu eğri boyunca Gauss eğriliği sabit olan yüzeyler elde edildi. Verilen eğrinin Frenet vektör alanları kullanılarak bu eğriden geçen yüzeyler parametrik olarak ifade edildi. Ayrıca, verilen eğriden geçen ve Gauss eğriliği sabit regle yüzeyler için yeterli şartlar verildi. Bazı örnekler verilerek elde edilen yöntem görsel hale getirildi.In this study, we find surfaces with constant Gaussian curvature along a given curve. The parametric representation of the surfaces possessing the given curve expressed using the Frenet vector fields of the curve. Also, we give conditions for ruled surfaces passing through the given curve and having constant Gaussian curvature. We present some illustrative examples validating the presented method