On the exact representation of the boundary surfaces ofthe swept volume of a cylinder undergoing rational bézier and b–spline motions

This paper develops methods for the exact analysis and representation of the swept volume of a circular cylinder undergoing rational Bézier and B-spline motions. Instead offollowing the traditional approach of analyzing the point trajectory of an object motion for swept volume analysis, this paper develops a new method for swept volume analysis by studying the plane trajectory of a rational motion. It brings together recent work in swept volume analysis, plane representation of developable surfaces, as well as computer aided synthesis of freeform rational motions. The results have applications in design and approximation of freeform surfaces as well as tool path planning for 5-axis machining of freeform surfaces.