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

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel-Aviv University, Israel

    Evgeny Lipovetsky & Nira Dyn

Authors
  1. Evgeny Lipovetsky
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  2. Nira Dyn
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Corresponding author

Correspondence to Evgeny Lipovetsky.

Additional information

Communicated by J. Carnicer and J.M. Peña

We wish our dear friend and colleague Mariano Gasca many more years of productive scientific work.

Mathematics subject classifications (2000)

65D18, 68U05.

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Lipovetsky, E., Dyn, N. An efficient algorithm for the computation of the metric average of two intersecting convex polygons, with application to morphing. Adv Comput Math 26, 269–282 (2007). https://doi.org/10.1007/s10444-005-7473-6

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  • DOI: https://doi.org/10.1007/s10444-005-7473-6

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