Stacking and Bundling Two Convex Polygons

  • Hee-Kap Ahn
  • Otfried Cheong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3827)


Given two compact convex sets C 1 and C 2 in the plane, we consider the problem of finding a placement ϕC 1 of C 1 that minimizes the area of the convex hull of ϕC 1 ∪ C 2. We first consider the case where ϕC 1 and C 2 are allowed to intersect (as in “stacking” two flat objects in a convex box), and then add the restriction that their interior has to remain disjoint (as when “bundling” two convex objects together into a tight bundle). In both cases, we consider both the case where we are allowed to reorient C 1, and where the orientation is fixed. In the case without reorientations, we achieve exact near-linear time algorithms, in the case with reorientations we compute a (1 + ε)-approximation in time  O(ε − 1/2 log n + ε − 3/2 log ε − 1/2), if two sets are convex polygons with n vertices in total.


Convex Hull Convex Polygon Rigid Motion Supporting Line Convex Object 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Otfried Cheong
    • 1
  1. 1.Division of Computer ScienceKorea Advanced Institute of Science and TechnologyDaejeonKorea

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