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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 ,,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