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Documents authored by Wagger, Andrew


Artifact
Software
Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry

Authors: Hridhaan Banerjee, Soren Brown, June Cagan, Auguste H. Gezalyan, Megan Hunleth, Veena Kailad, Chaewoon Kyoung, Rowan Shigeno, Yasmine Tajeddin, Andrew Wagger, Kelin Zhu, and David M. Mount


Abstract

Cite as

Hridhaan Banerjee, Soren Brown, June Cagan, Auguste H. Gezalyan, Megan Hunleth, Veena Kailad, Chaewoon Kyoung, Rowan Shigeno, Yasmine Tajeddin, Andrew Wagger, Kelin Zhu, David M. Mount. Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry (Software, Web Application). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@misc{dagstuhl-artifact-25998,
   title = {{Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry}}, 
   author = {Banerjee, Hridhaan and Brown, Soren and Cagan, June and Gezalyan, Auguste H. and Hunleth, Megan and Kailad, Veena and Kyoung, Chaewoon and Shigeno, Rowan and Tajeddin, Yasmine and Wagger, Andrew and Zhu, Kelin and Mount, David M.},
   note = {Software (visited on 2026-05-27)},
   url = {https://andrew.wagger.net/hilbert/},
   doi = {10.4230/artifacts.25998},
}
Artifact
Audiovisual
Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry

Authors: Hridhaan Banerjee, Soren Brown, June Cagan, Auguste H. Gezalyan, Megan Hunleth, Veena Kailad, Chaewoon Kyoung, Rowan Shigeno, Yasmine Tajeddin, Andrew Wagger, Kelin Zhu, and David M. Mount


Abstract

Cite as

Hridhaan Banerjee, Soren Brown, June Cagan, Auguste H. Gezalyan, Megan Hunleth, Veena Kailad, Chaewoon Kyoung, Rowan Shigeno, Yasmine Tajeddin, Andrew Wagger, Kelin Zhu, David M. Mount. Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry (Audiovisual, Video). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@misc{dagstuhl-artifact-25999,
   title = {{Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry}}, 
   author = {Banerjee, Hridhaan and Brown, Soren and Cagan, June and Gezalyan, Auguste H. and Hunleth, Megan and Kailad, Veena and Kyoung, Chaewoon and Shigeno, Rowan and Tajeddin, Yasmine and Wagger, Andrew and Zhu, Kelin and Mount, David M.},
   note = {Audiovisual (visited on 2026-05-27)},
   url = {https://youtu.be/yhJn--3Qgks},
   doi = {10.4230/artifacts.25999},
}
Document
Media Exposition
Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry (Media Exposition)

Authors: Hridhaan Banerjee, Soren Brown, June Cagan, Auguste H. Gezalyan, Megan Hunleth, Veena Kailad, Chaewoon Kyoung, Rowan Shigeno, Yasmine Tajeddin, Andrew Wagger, Kelin Zhu, and David M. Mount

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)


Abstract
Higher-order Voronoi diagrams and Delaunay mosaics in polygonal metrics have only recently been studied, yet no tools exist for visualizing them. We introduce a tool that fills this gap, providing dynamic interactive software for visualizing higher-order Voronoi diagrams and Delaunay mosaics along with clustering and tools for exploring overlap and outer regions in the Hilbert polygonal metric. We prove that k-th order Voronoi cells are not always star-shaped and establish complexity bounds for our algorithm, which generates all order Voronoi diagrams at once. Our software unifies and extends previous tools for visualizing the Hilbert, Funk, and Thompson geometries.

Cite as

Hridhaan Banerjee, Soren Brown, June Cagan, Auguste H. Gezalyan, Megan Hunleth, Veena Kailad, Chaewoon Kyoung, Rowan Shigeno, Yasmine Tajeddin, Andrew Wagger, Kelin Zhu, and David M. Mount. Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry (Media Exposition). In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 100:1-100:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{banerjee_et_al:LIPIcs.SoCG.2026.100,
  author =	{Banerjee, Hridhaan and Brown, Soren and Cagan, June and Gezalyan, Auguste H. and Hunleth, Megan and Kailad, Veena and Kyoung, Chaewoon and Shigeno, Rowan and Tajeddin, Yasmine and Wagger, Andrew and Zhu, Kelin and Mount, David M.},
  title =	{{Visualizing Higher Order Structures, Overlap Regions, and Clustering in the Hilbert Geometry}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{100:1--100:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.100},
  URN =		{urn:nbn:de:0030-drops-259062},
  doi =		{10.4230/LIPIcs.SoCG.2026.100},
  annote =	{Keywords: Hilbert metric, Funk metric, Voronoi diagrams}
}
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