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DOI: 10.4230/LIPIcs.SoCG.2023.61

Maximum Overlap Area of a Convex Polyhedron and a Convex Polygon Under Translation

Authors: Honglin Zhu and Hyuk Jun Kweon

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract

Let P be a convex polyhedron and Q be a convex polygon with n vertices in total in three-dimensional space. We present a deterministic algorithm that finds a translation vector v ∈ ℝ³ maximizing the overlap area |P ∩ (Q + v)| in O(n log² n) time. We then apply our algorithm to solve two related problems. We give an O(n log³ n) time algorithm that finds the maximum overlap area of three convex polygons with n vertices in total. We also give an O(n log² n) time algorithm that minimizes the symmetric difference of two convex polygons under scaling and translation.

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Honglin Zhu and Hyuk Jun Kweon. Maximum Overlap Area of a Convex Polyhedron and a Convex Polygon Under Translation. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 61:1-61:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{zhu_et_al:LIPIcs.SoCG.2023.61,
  author =	{Zhu, Honglin and Kweon, Hyuk Jun},
  title =	{{Maximum Overlap Area of a Convex Polyhedron and a Convex Polygon Under Translation}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{61:1--61:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.61},
  URN =		{urn:nbn:de:0030-drops-179116},
  doi =		{10.4230/LIPIcs.SoCG.2023.61},
  annote =	{Keywords: computational geometry, shape matching, arrangement}
}

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Maximum Overlap Area of a Convex Polyhedron and a Convex Polygon Under Translation

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