Densest translational lattice packing of non-convex polygons

Victor J. Milenkovic

doi:10.1016/S0925-7721(01)00051-7

Densest translational lattice packing of non-convex polygons

Victor J. Milenkovic

Computer Science

Research output: Contribution to journal › Conference article › peer-review

8 Scopus citations

Abstract

A translationallattice packing of £polygons P₁, P₂, P_k, ..., 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 language	English (US)
Pages (from-to)	205-222
Number of pages	18
Journal	Computational Geometry: Theory and Applications
Volume	22
Issue number	1-3
DOIs	https://doi.org/10.1016/S0925-7721(01)00051-7
State	Published - 2002
Event	16th ACM Symposium on Computational Geometry - Hong Kong, China Duration: Jun 12 2000 → Jun 14 2000

Keywords

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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title = "Densest translational lattice packing of non-convex polygons",

abstract = "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.",

keywords = "Lattice packing, Layout, Linear programming, Nesting, Packing, Quadratic programming",

author = "Milenkovic, {Victor J.}",

note = "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.; 16th ACM Symposium on Computational Geometry ; Conference date: 12-06-2000 Through 14-06-2000",

year = "2002",

doi = "10.1016/S0925-7721(01)00051-7",

language = "English (US)",

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pages = "205--222",

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issn = "0925-7721",

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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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DO - 10.1016/S0925-7721(01)00051-7

M3 - Conference article

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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 -

Densest translational lattice packing of non-convex polygons

Abstract

Keywords

ASJC Scopus subject areas

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