Abstract: A novel algorithm is proposed to fast approximate the swept volume of a general cutter. This algorithm is based on envelope theory and solid modeling techniques. The pipeline of this approximation consists of four stages：1. sampling points on the cutter; 2. sweeping the sample points of the cutter along the curved trajectory to create primitive curves; 3. creating planar slices along the trajectory, making planar meshes from the intersecting points between slices and primitive curves and approximating envelop curves through the outer boundary vertices of planar meshes; 4. making an envelope surface of the swept volume by lofting the envelope curves. Experimental results show that the presented algorithm is simple, efficient and accurate, so it can be widely applied in manufacturing.

Key words: Cutter swept volume, Envelop surface, General cutter, Primitive, Self-intersection