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Computation of the Metric Average of Two Simple Polygons and Extensions

Modified Metric Average of Several Polygons
The Modified Metric Average of a SimplePolygon with Several Contained Polygons with Holes

 Abstract

 In this work we present an algorithm that applies segment Voronoi diagrams and planar arrangements to the computation of the metric average of two simple polygons. The idea to apply segment Voronoi diagrams is due to E. Lipovetsky. The implementation of the algorithm is described and a collection of computational examples is presented. Based on the computational framework of the algorithm, the connectedness of the metric average of two simple polygons is studied. Furthermore an artifact produced by the metric average of two simple polygons is identified and a modified averaging operation that avoids this artifact is suggested and implemented. Finally, we extend the algorithm to compute the metric average of two sets that are each a collection of simple polygons with simple polygonal holes.

 

Links

  • Shay Kels
  • An Algorithm for the Computation of the Metric Average of Two Simple Polygons and Extensions,
    M.Sc. thesis. Tel-Aviv University, 2008. [pdfppt]
  • N. Dyn and A. Mokhov
    Approximations of Set-Valued Functions Based on the Metric Average
    Rendiconti di Mathematica e delle sue Applicazioni Series 7 (26) , 249-266 (2006) [pdf, website]

 

Contact

Shay Kels http://www.cs.tau.ac.il/~kelsisha kelsisha@post.tau.ac.il
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