Abstract

Packing is a topic of interest in many fields. During our research on the underhood-packing problem, we observed that to bring components together — without switching their relative position — one could use the analogy of a rubber object stretched around the artifacts. In two-dimensional space, that object is a rubber band, and in three-dimensions, it is a balloon. Using this analogy, the convex hull can be used to determine the direction of forces applied to a single component, and a motion can result from the application of such forces. The objects can then be moved until contact occurs, at which point the forces become moments, and the objects can rotate with respect to each other. This technique can guarantee locally optimal packing, and displays a very intuitive behavior that might lead to further advances in optimization. This paper introduces the methodology for optimizing the packing of 2-dimensional geometric entities (polygons) in a plane and of 3-dimensional objects in space using the Rubber band Analogy.

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