earticle

영어

This paper describes a computational analysis of various parameterizations of a surface of revolution. The idea is to generate the parameterization of the surface by using different (not necessarily planar) curves with varying curvature. The approach to the practical case of obtaining the parameterization of a torus through different planar curves other than circles, such as planar lemniscates. The analysis is also extended to the interesting case of non-planar curves. Our work relies on the intensive use of Mathematica, a powerful computational system very well suited for symbolic calculations while also providing valuable numerical and graphical options, a user-friendly graphical interface and a compact and efficient programming language. All calculations in this paper have been carried out with Mathematica v8.0.