Densest translational lattice packing of non-convex polygons

AbstractA translational lattice packing of k polygons P1,P2,P3,…,Pk is a (non-overlapping) packing of the k polygons which is replicated without overlap at each point of a lattice i0v0+i1v1, where v0 and v1 are vectors generating the lattice and i0 and i1 range over all integers. A densest translational lattice packing is one which minimizes the area |v0×v1| of the fundamental parallelogram. An algorithm and implementation is given for densest translational lattice packing. This algorithm has useful applications in industry, particularly clothing manufacture