Densest translational lattice packing of non-convex polygons (extended abstract)

A translation lattice packin9 of k polygons/ '1, P2 , / ' 3 , . . . , Pk is a (non-overlapping) packing of the k polygons which can be replicated without overlap at each point of a lattice iovo + i~v~, where vo and vt are vectors generating the lattice and io and il range over all integers. A densest translational lattice packing is one which minimizes the area [vo x vl I of the fundamental parallelogram. An algorithm and implementation is given for densest translation lattice packing. This algorithm has useful applications in industry, particularly clothing manufacture.

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