Geometric Representation of Swept Volumes with Application to Polyhedral Objects
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.
J. D. Weld and M. Leu, "Geometric Representation of Swept Volumes with Application to Polyhedral Objects," International Journal of Robotics Research, SAGE Publications, Jan 1990.
The definitive version is available at https://doi.org/10.1177/027836499000900507
Mechanical and Aerospace Engineering
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