The Construction of Projected-Based Sweep Surface
基于投影变换的Sweep曲面构造方法

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.