TY - JOUR
T1 - Densest translational lattice packing of non-convex polygons
AU - Milenkovic, Victor J.
N1 - Funding Information:
✩Expanded version of paper presented at the 16th Annual ACM Symposium on Computational Geometry (Hong Kong, June 2000). E-mail address: vjm@cs.miami.edu (V.J. Milenkovic). URL address: http://www.cs.miami.edu/∼vjm (V.J. Milenkovic). 1This research was funded by the Alfred P. Sloan Foundation through a subcontract from the Harvard Center for Textile and Apparel Research and by NSF grant NSF-CCR-97-12401.
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
KW - Lattice packing
KW - Layout
KW - Linear programming
KW - Nesting
KW - Packing
KW - Quadratic programming
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U2 - 10.1016/S0925-7721(01)00051-7
DO - 10.1016/S0925-7721(01)00051-7
M3 - Conference article
AN - SCOPUS:31244437676
VL - 22
SP - 205
EP - 222
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
SN - 0925-7721
IS - 1-3
T2 - 16th ACM Symposium on Computational Geometry
Y2 - 12 June 2000 through 14 June 2000
ER -