The Sweep surface is usually described by using the Local moving Frame along the spine. But the construction of the moving frame is strongly limited by the properties of spine. A problem is arisen: can we describe the Sweep surface to avoid using the moving frame? In this paper

a projected based approach is proposed which possesses two advantages: Firstly

the Sweep surface can be presented exactly if spine is line segment or arc curve. Secondly

the Sweep surface can be directly described by projected transform so we can avoid using the local moving frame

then the limitation of continuity of spine for the local moving frame is not necessary. On the other hand

the error control can be simplified to the error estimating of the offset of the spine. Three types of spine

such as line segment

arc curve and NURBS curve

are considered with different methods in the projection algorithm. Furthermore

3D NURBS offset approximation algorithm is presented for 3D NURBS curve

and the projection algorithm of the sweep surface is introduced. Finally

the robustness and efficiency of the algorithm is verified by a lot of examples.