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Ipelets for the Convex Polygonal Geometry (Media Exposition)

Authors Nithin Parepally, Ainesh Chatterjee, Auguste H. Gezalyan , Hongyang Du, Sukrit Mangla, Kenny Wu, Sarah Hwang, David M. Mount

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Author Details

Nithin Parepally
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Ainesh Chatterjee
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Auguste H. Gezalyan
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Hongyang Du
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Sukrit Mangla
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Kenny Wu
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Sarah Hwang
  • Department of Computer Science, University of Maryland, College Park, MD, USA
David M. Mount
  • Department of Computer Science, University of Maryland, College Park, MD, USA

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Nithin Parepally, Ainesh Chatterjee, Auguste H. Gezalyan, Hongyang Du, Sukrit Mangla, Kenny Wu, Sarah Hwang, and David M. Mount. Ipelets for the Convex Polygonal Geometry (Media Exposition). In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 92:1-92:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SoCG.2024.92

Abstract

There are many structures, both classical and modern, involving convex polygonal geometries whose deeper understanding would be facilitated through interactive visualizations. The Ipe extensible drawing editor, developed by Otfried Cheong, is a widely used software system for generating geometric figures. One of its features is the capability to extend its functionality through programs called Ipelets. In this media submission, we showcase a collection of new Ipelets that construct a variety of geometric objects based on polygonal geometries. These include Macbeath regions, metric balls in the forward and reverse Funk distance, metric balls in the Hilbert metric, polar bodies, the minimum enclosing ball of a point set, and minimum spanning trees in both the Funk and Hilbert metrics. We also include a number of utilities on convex polygons, including union, intersection, subtraction, and Minkowski sum (previously implemented as a CGAL Ipelet).

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Hilbert metric
  • Macbeath Regions
  • Polar Bodies
  • Convexity

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