Why Flc-Frame is Better than Frenet Frame on Polynomial Space Curves?

Abstract

It is well known that the binormal and normal vectors of Frenet frame rotate around the tangent vector. That is why the Frenet frame is not suitable for some applications such as tube surfaces. However, there is not enough information about why the vectors of the Frenet frame rotate around the tangent vector. In this paper we will deal with this problem. Moreover we show the advantages of Flc-frame over the Frenet frame.