Overlap of Convex Polytopes under Rigid Motion

Authors Hee-Kap Ahn, Siu-Wing Cheng, Hyuk Jun Kweon, Juyoung Yon

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Hee-Kap Ahn
Siu-Wing Cheng
Hyuk Jun Kweon
Juyoung Yon

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Hee-Kap Ahn, Siu-Wing Cheng, Hyuk Jun Kweon, and Juyoung Yon. Overlap of Convex Polytopes under Rigid Motion. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 498-509, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


We present an algorithm to compute an approximate overlap of two convex polytopes P_1 and P_2 in R^3 under rigid motion. Given any epsilon in (0,1/2], our algorithm runs in O(epsilon^{-3}n log^{3.5}n) time with probability 1 - n^{-O(1)} and returns a (1-epsilon)-approximate maximum overlap, provided that the maximum overlap is at least lambda max(|P_1|,|P_2|) for some given constant lambda in (0,1].
  • convex polytope
  • overlap
  • approximation
  • rigid motion


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