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Rotational polygon overlap minimization and compaction. (English) Zbl 0904.68174
Summary: An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons $P_1, P_2, P_3, \dots, P_k$ in a container polygon $Q$, translate and rotate the polygons to diminish their overlap to a local minimum. A (local) overlap minimum has the property that any perturbation of the polygons increases the overlap. Overlap minimization is modified to create a practical algorithm for compaction: starting with a non-overlapping layout in a rectangular container, plan a non-overlapping motion that diminishes the length or area of the container to a local minimum. Experiments show that both overlap minimization and compaction work well in practice and are likely to be useful in industrial applications.

MSC:
68U05Computer graphics; computational geometry
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References:
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