Densest translational lattice packing of non-convex polygons

Victor J. Milenkovic

Research output: Contribution to journalConference articlepeer-review

8 Scopus citations


A translationallattice packing of £polygons P1, P2, Pk, ..., Pk is a (non-overlapping) packing of the k polygons which is replicated without overlap at each point of a lattice /oo + /1 i>i, where i>o and v\ are vectors generating the lattice and /o and i\ range over all integers. A densest translational lattice packing is one which minimizes the area |vo x vi | 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.

Original languageEnglish (US)
Pages (from-to)205-222
Number of pages18
JournalComputational Geometry: Theory and Applications
Issue number1-3
StatePublished - 2002
Event16th ACM Symposium on Computational Geometry - Hong Kong, China
Duration: Jun 12 2000Jun 14 2000


  • Lattice packing
  • Layout
  • Linear programming
  • Nesting
  • Packing
  • Quadratic programming

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


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