An approach for designing a developable surface through a sweeping surface

Document Type: Research articles


Faculty of Science, University of Assiut, Assiut 71516 , EGYPT.


This paper studies the problem to construct a developable surface through a sweeping surface, using a special orthonormal frame of the spine curve, namely the (so--called) rotation minimizing frame (RMF for short). As a result, the necessary and sufficient condition for the sweeping surface to be a developable ruled surface is derived. In particular, we mainly focus on the study for the resulting developable surface to be cylinder, cone or tangent surface. Finally, we give some representative examples.