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Maximum Overlap Area of a Convex Polyhedron and a Convex Polygon Under Translation
Authors
Honglin Zhu 
,
Hyuk Jun Kweon
-
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Volume:
39th International Symposium on Computational Geometry (SoCG 2023)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Computational Geometry (SoCG) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2023-06-09
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Acknowledgements
This paper is the result of the MIT SPUR 2022, a summer undergraduate research program organized by the MIT math department. The authors would like to thank the faculty advisors David Jerison and Ankur Moitra for their support and the math department for providing this research opportunity. We thank the anonymous referees for providing helpful comments that increased the quality of this paper.
Cite AsGet BibTex
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)
https://doi.org/10.4230/LIPIcs.SoCG.2023.61
https://doi.org/10.4230/LIPIcs.SoCG.2023.61
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.
Subject Classification
ACM Subject Classification
- Theory of computation → Computational geometry
Keywords
- computational geometry
- shape matching
- arrangement
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References
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