Generalized Cylinder with Geodesic and Line of Curvature Parameterizations

Abstract

Constructing a surface with geodesic or line of curvature parameterization is an important problem in many practical applications. The present paper aims to design a generalized cylinder that is parametrized along the geodesics and lines of curvature curves in Euclidean 3- space. The main results show that the generalized cylinder with geodesic or line of curvature parameterization is a rectifying cylinder or a right cylinder respectively.