Geometric Representation of Swept Volumes with Application to Polyhedral Objects

Abstract

A formulation for developing a geometric repre sentation of swept volumes for compact n -manifolds undergo ing general sweeps in R ⁿ is presented. This formulation shows that the swept volume of a compact n-manifold in Rⁿ is equal to the union of the swept volume of its boundary with one location of the compact n-manifold in the sweep. This result is significant in that the problem of developing a geo metric representation of swept volumes for n-dimensional objects in Rⁿ is reduced to developing a geometric representa tion of swept volismes for (n - 1)-dimensional objects in Rⁿ. Based on this formulation, the swept volumes of polyhedral objects were generated from the swept volumes of their poly gonal faces.