# Computation of the Metric Average of Two Simple Polygons and Extensions

### 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
- 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]

**An Algorithm for the Computation of the Metric Average of Two Simple Polygons and Extensions,**

M.Sc. thesis. Tel-Aviv University, 2008. [pdf, ppt]

### Contact

Shay Kels | ||