Compaction algorithm for non-convex polygons and its application

Research output: Chapter in Book/Report/Conference proceedingConference contribution

18 Scopus citations


Given a two dimensional, non-overlapping layout of convex and non-convex polygons, compaction can be thought of as simulating the motion of the polygons as a result of applied 'forces.' Compaction can be modeled as a motion of the polygons that reduces the value of some linear functional on their positions. Optimal compaction, planning a motion that finds the global minimum reachable value, is shown to be NP-complete. We give a compaction algorithm that finds a local minimum by direct calculation of the new polygon positions via linear programming. We also consider the related problem of separating overlapping polygons using a minimal amount of motion and show it to be NP-complete. A locally optimum version of this problem is solved using a slight modification of the compaction algorithm. The compaction algorithm and the separation algorithm have been applied to marker making: the task of packing polygonal pieces on a sheet of cloth of fixed width so that total length is minimized. The compaction algorithm has improved cloth utilization of human generated pants markers. The separation algorithm together with a database of human-generated markers can be used to automatically generate markers that are close to human performance.

Original languageEnglish (US)
Title of host publicationProceedings of the 9th Annual Symposium on Computational Geometry
Editors Anon
PublisherPubl by ACM
Number of pages10
ISBN (Print)0897915828
StatePublished - Dec 1 1993
Externally publishedYes
EventProceedings of the 9th Annual Symposium on Computational Geometry - San Diego, CA, USA
Duration: May 19 1993May 21 1993

Publication series

NameProceedings of the 9th Annual Symposium on Computational Geometry


OtherProceedings of the 9th Annual Symposium on Computational Geometry
CitySan Diego, CA, USA

ASJC Scopus subject areas

  • Engineering(all)


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