Directional tubular surfaces

In this paper, we introduce a new version of tubular surfaces. We rst dene a new adapted frame along a space curve, and denote this the q-frame. We then reveal the relationship between the Frenet frame and the q-frame. We give a parametric representation of a directional tubular surface using the q-frame. Finally, some comparative examples are shown to conrm the eectiveness of the proposed method. Mathematics Subject Classication: 53A04, 53A05