Search Results

Documents authored by Cagan, June

Artifact
Software
DOI: 10.4230/artifacts.25998
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)

Copy BibTex To Clipboard

@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
DOI: 10.4230/artifacts.25999
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)

Copy BibTex To Clipboard

@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},
}
Artifact
Software
DOI: 10.4230/artifacts.25979
Proximity Alert: Ipelets for Neighborhood Graphs and Clustering

Authors: Gitan Balogh, June Cagan, Bea Fatima, Auguste H. Gezalyan, Danesh Sivakumar, Arushi Srinivasan, Yixuan Sun, Vahe Zaprosyan, and David M. Mount

Abstract
Cite as

Gitan Balogh, June Cagan, Bea Fatima, Auguste H. Gezalyan, Danesh Sivakumar, Arushi Srinivasan, Yixuan Sun, Vahe Zaprosyan, David M. Mount. Proximity Alert: Ipelets for Neighborhood Graphs and Clustering (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@misc{dagstuhl-artifact-25979,
   title = {{Proximity Alert: Ipelets for Neighborhood Graphs and Clustering}}, 
   author = {Balogh, Gitan and Cagan, June and Fatima, Bea and Gezalyan, Auguste H. and Sivakumar, Danesh and Srinivasan, Arushi and Sun, Yixuan and Zaprosyan, Vahe and Mount, David M.},
   note = {Software (visited on 2026-05-27)},
   url = {https://github.com/Otcavo/Ipelets-Full-Library},
   doi = {10.4230/artifacts.25979},
}
Artifact
Audiovisual
DOI: 10.4230/artifacts.25983
Proximity Alert: Ipelets for Neighborhood Graphs and Clustering

Authors: Gitan Balogh, June Cagan, Bea Fatima, Auguste H. Gezalyan, Danesh Sivakumar, Arushi Srinivasan, Yixuan Sun, Vahe Zaprosyan, and David M. Mount

Abstract
Cite as

Gitan Balogh, June Cagan, Bea Fatima, Auguste H. Gezalyan, Danesh Sivakumar, Arushi Srinivasan, Yixuan Sun, Vahe Zaprosyan, David M. Mount. Proximity Alert: Ipelets for Neighborhood Graphs and Clustering (Audiovisual, Video). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@misc{dagstuhl-artifact-25983,
   title = {{Proximity Alert: Ipelets for Neighborhood Graphs and Clustering}}, 
   author = {Balogh, Gitan and Cagan, June and Fatima, Bea and Gezalyan, Auguste H. and Sivakumar, Danesh and Srinivasan, Arushi and Sun, Yixuan and Zaprosyan, Vahe and Mount, David M.},
   note = {Audiovisual (visited on 2026-05-27)},
   url = {https://youtu.be/NQr-SY1x2qc},
   doi = {10.4230/artifacts.25983},
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2026.99
Proximity Alert: Ipelets for Neighborhood Graphs and Clustering (Media Exposition)

Authors: Gitan Balogh, June Cagan, Bea Fatima, Auguste H. Gezalyan, Danesh Sivakumar, Arushi Srinivasan, Yixuan Sun, Vahe Zaprosyan, and David M. Mount

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

Abstract
Neighborhood graphs and clustering algorithms are fundamental structures in both computational geometry and data analysis. Visualizing them can help build insight into their behavior and properties. The Ipe extensible drawing editor, developed by Otfried Cheong, is a widely used software system for generating figures. One particular aspect of Ipe is the ability to add Ipelets, which extend its functionality. Here we showcase a set of Ipelets designed to help visualize neighborhood graphs and clustering algorithms. These include: ε-neighbor graphs, furthest-neighbor graphs, Gabriel graphs, k-nearest neighbor graphs, k-th-nearest neighbor graphs, k-mutual neighbor graphs, k-th-mutual neighbor graphs, asymmetric k-nearest neighbor graphs, asymmetric k-th-nearest neighbor graphs, relative-neighbor graphs, sphere-of-influence graphs, Urquhart graphs, Yao graphs, and clustering algorithms including complete-linkage, DBSCAN, HDBSCAN, k-means, k-means++, k-medoids, mean shift, and single-linkage. Our Ipelets are all programmed in Lua and are freely available.
Cite as

Gitan Balogh, June Cagan, Bea Fatima, Auguste H. Gezalyan, Danesh Sivakumar, Arushi Srinivasan, Yixuan Sun, Vahe Zaprosyan, and David M. Mount. Proximity Alert: Ipelets for Neighborhood Graphs and Clustering (Media Exposition). In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 99:1-99:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{balogh_et_al:LIPIcs.SoCG.2026.99,
  author =	{Balogh, Gitan and Cagan, June and Fatima, Bea and Gezalyan, Auguste H. and Sivakumar, Danesh and Srinivasan, Arushi and Sun, Yixuan and Zaprosyan, Vahe and Mount, David M.},
  title =	{{Proximity Alert: Ipelets for Neighborhood Graphs and Clustering}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{99:1--99:8},
  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.2026.99},
  URN =		{urn:nbn:de:0030-drops-259058},
  doi =		{10.4230/LIPIcs.SoCG.2026.99},
  annote =	{Keywords: neighborhood graphs, clustering, proximity graphs, Ipelets, visualization}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2026.100
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)

Copy BibTex To Clipboard

@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}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact