Parametric representation of a surface pencil with a common asymptotic curve

Authors:
Ergin Bayram;Fatma Güler;Emin Kasap
Affiliations:
-;-;-
Venue:
Computer-Aided Design
Year:
2012

Citing 1
Cited 2

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Abstract

In this paper, we study the problem of finding a surface pencil from a given spatial asymptotic curve. We obtain the parametric representation for a surface pencil whose members have the same curve as a given asymptotic curve. Using the Frenet frame of the given asymptotic curve, we present the surface as a linear combination of this frame and analyse the necessary and sufficient condition for that curve to be asymptotic. We illustrate this method by presenting some examples.