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Journal of Applied Mathematics and Computation

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

Author:Fatma Güler, Gülnur Şaffak Atalay, Ergin Bayram Date:July 17,2019 Hits:

Abstract

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

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

Fatma Güler, Gülnur Şaffak Atalay, Ergin Bayram
Emin Kasap Ondokuz Mayıs University, Arts and Science Faculty, Department of Mathematics, 55139, Samsun, Turkey 

*Corresponding author:Fatma Güler. Ondokuz Mayıs University, Arts and Science Faculty, Department of Mathematics, 55139, Samsun, Turky.
Email: f.guler@omu.edu.tr
How to cite this paper: Güler F, Atalay G, Ş, Bayram E, Kasap E. (2019). An approach for designing a surface pencil through a given asymptotic curve*. Journal of Applied Mathematics and Computation, 3(4), 606-615.
DOI: 10.26855/jamc.2019.06.002  
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