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Proceedings of CAD'14, 2014, 35-37
A Computational Framework for the Boundary Representation of Solid Sweeps
Abstract. This paper is about the theory and implementation of the solid sweep as a primitive solid modeling operation. A special case of this, viz., blends is already an important operation and prospective uses for the sweep are in NC-machining verification , collision detection, assembly planning and in packaging. The solid sweep is the envelope surface E of the swept volume generated by a given solid M moving along a one-parameter family h of rigid motions in R3. We use the industry standard brep format to input the solid M and to output the envelope E. The brep of course has the topological data of vertices, edges and co-edges, loops bounding the faces and orientation of these, and the underlying geometric data of the surfaces and curves. As we show, the brep of E, while intimately connected to that of M, has several intricate issues of orientation and parametrization. Much of the mathematics of self-intersection, of passing body-check and of overall geometry have been described in the companion paper. This paper uncovers the topological aspects of the solid sweep and its construction as a solid model. Here, we restrict ourselves to the simple generic case, i.e., smooth M and, therefore smooth E which is free from self-intersections, to illustrate our approach and its implementation.
Keywords. Solid sweep, swept volume, solid modeling, boundary representation, parametric curves and surfaces