Densest translational lattice packing of non-convex polygons

Authors:
Victor J. Milenkovic
Affiliations:
University of Miami, Department of Computer Science, P.O. Box 248154, Coral Gables, FL 33124-4245, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2002

Citing 2
Cited 2

Double-lattice packings of convex bodies in the plane

Discrete & Computational Geometry
Translational polygon containment and minimal enclosure using linear programming based restriction

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An approximate arrangement algorithm for semi-algebraic curves

Proceedings of the twenty-second annual symposium on Computational geometry
An efficient solution method for relaxed variants of the nesting problem

CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65

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Abstract

A translational lattice packing of k polygons P"1,P"2,P"3,...,P"k is a (non-overlapping) packing of the k polygons which is replicated without overlap at each point of a lattice i"0v"0+i"1v"1, where v"0 and v"1 are vectors generating the lattice and i"0 and i"1 range over all integers. A densest translational lattice packing is one which minimizes the area |v"0xv"1| 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.