Minimum Convex Container of Two Convex Polytopes under Translations

نویسندگان

  • Hee-Kap Ahn
  • Sang Won Bae
  • Otfried Cheong
  • Dongwoo Park
  • Chan-Su Shin
چکیده

Given two convex d-polytopes P and Q in R for d ≥ 3, we study the problem of bundling P and Q in a smallest convex container. More precisely, our problem asks to find a minimum convex set containing P and Q that are in contact under translations. For dimension d = 3, we present the first exact algorithm that runs in O(n) time, where n denotes the number of vertices of P and Q. Our approach easily extends to any higher dimension d > 3, resulting in the first exact algorithm.

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تاریخ انتشار 2014