arXiv subjects

Gulnur Saffak Atalay

Publications and source records attributed to Gulnur Saffak Atalay.

2 recordsLinked to original sources

arXiv2015

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

Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface interpolating a given curve as the geodesic curve of it. Also, we analyze the conditions when the resulting surface is a ruled surface. In addition, developablity along the common geodesic of the members of surface family are discussed. Finally, we illustrate this method by presenting some examples.

math.DG↗

arXiv2014

Surfaces Family With Common Null Asymptotic

We analyzed the problem of finding a surfaces family through an asymptotic curve with Cartan frame. We obtain the parametric representation for surfaces family whose members have the same as an asymptotic curve. By using the Cartan frame of the given null curve, we present the surface as a linear combination of this frame and analysed the necessary and sufficient condition for that curve to satisfy the asymptotic requirement. We illustrate the method by giving some examples.

math.DG↗