An efficient algorithm for the computation of the metric average of two intersecting convex polygons, with application to morphing

Evgeny Lipovetsky*, Nira Dyn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by the method for the reconstruction of 3D objects from a set of parallel cross sections, based on the binary operation between 2D sets termed "metric average", we developed an algorithm for the computation of the metric average between two intersecting convex polygons in 2D. For two 1D sets there is an algorithm for the computation of the metric average, with linear time in the number of intervals in the two 1D sets. The proposed algorithm has linear computation time in the number of vertices of the two polygons. As an application of this algorithm, a new technique for morphing between two convex polygons is developed. The new algorithm performs morphing in a non-intuitive way.

Original languageEnglish
Pages (from-to)269-282
Number of pages14
JournalAdvances in Computational Mathematics
Volume26
Issue number1-3
DOIs
StatePublished - Jan 2007

Keywords

  • Convex polygons
  • Linear time complexity
  • Metric average
  • Morphing

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