Aligning Two Convex Figures to Minimize Area or Perimeter

  title={Aligning Two Convex Figures to Minimize Area or Perimeter},
  author={Hee-Kap Ahn and Otfried Cheong},
Given two compact convex sets P and Q in the plane, we consider the problem of finding a placement ϕ P of P that minimizes the convex hull of ϕ P∪Q. We study eight versions of the problem: we consider minimizing either the area or the perimeter of the convex hull; we either allow ϕ P and Q to intersect or we restrict their interiors to remain disjoint; and we either allow reorienting P or require its orientation to be fixed. In the case without reorientations, we achieve exact near-linear time… CONTINUE READING

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