Swept volumes generated by the natural quadric surfaces

Abstract

The swept volume of a moving object (generator) can be constructed from the envelope surfaces of its boundary. These envelope surfaces are the collections of the characteristic curves which are the point sets on the boundary of the generator at different times. In this study, the characteristic curves of the natural quadric surfaces (planes, circular cylinders, circular cones and spheres) are derived from the envelope theorem. The instantaneous screw axis is used to describe the sweep motion of the generators and to solve the characteristic curves. The faceted model of a swept volume is then established by warping the corresponding characteristic curves together with the partial bouncaries of the generator at the initial and final positions.