Rotational polygon overlap minimization and compaction

Victor J. Milenkovic

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P1, P2, P3, . . . , Pk in a container polygon Q, translate and rotate the polygons to diminish their overlap to a local minimum. A (local) overlap minimum has the property that any perturbation of the polygons increases the overlap. Overlap minimization is modified to create a practical algorithm for compaction: starting with a non-overlapping layout in a rectangular container, plan a non-overlapping motion that diminishes the length or area of the container to a local minimum. Experiments show that both overlap minimization and compaction work well in practice and are likely to be useful in industrial applications.

Original languageEnglish (US)
Pages (from-to)305-318
Number of pages14
JournalComputational Geometry: Theory and Applications
Issue number4
StatePublished - Jul 1998
Externally publishedYes


  • Compaction
  • Containment
  • Layout
  • Linear programming
  • Minimum enclosure
  • Packing or nesting of irregular polygons

ASJC Scopus subject areas

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


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