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Documents authored by Parepally, Nithin

Artifact
Software
DOI: 10.4230/artifacts.23340
Ipelets for Points and Polygons

Authors: Klint Faber, Auguste H. Gezalyan, Adam Martinson, Aniruddh Mutnuru, Nithin Parepally, Ryan Parker, Mihil Sreenilayam, Aram Zaprosyan, and David M. Mount

Abstract
Cite as

Klint Faber, Auguste H. Gezalyan, Adam Martinson, Aniruddh Mutnuru, Nithin Parepally, Ryan Parker, Mihil Sreenilayam, Aram Zaprosyan, David M. Mount. Ipelets for Points and Polygons (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-23340,
   title = {{Ipelets for Points and Polygons}}, 
   author = {Faber, Klint and Gezalyan, Auguste H. and Martinson, Adam and Mutnuru, Aniruddh and Parepally, Nithin and Parker, Ryan and Sreenilayam, Mihil and Zaprosyan, Aram and Mount, David M.},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:8d9d49631e2688049de55f2c874e85e56cb50620;origin=https://github.com/nithin1527/onion-soup;visit=swh:1:snp:c055d63f5a6fe8fb1d9092a820512b5f1eea62fa;anchor=swh:1:rev:698a000737b45477597e7ffc8f17e59072bfe7f3}{\texttt{swh:1:dir:8d9d49631e2688049de55f2c874e85e56cb50620}} (visited on 2025-06-20)},
   url = {https://github.com/nithin1527/onion-soup},
   doi = {10.4230/artifacts.23340},
}
Artifact
Software
DOI: 10.4230/artifacts.23291
Software For the Thompson and Funk Geometry

Authors: Hridhaan Banerjee, Carmen Isabel Day, Auguste H. Gezalyan, Olga Golovatskaia, Megan Hunleth, Sarah Hwang, Nithin Parepally, Lucy Wang, and David M. Mount

Abstract
Cite as

Hridhaan Banerjee, Carmen Isabel Day, Auguste H. Gezalyan, Olga Golovatskaia, Megan Hunleth, Sarah Hwang, Nithin Parepally, Lucy Wang, David M. Mount. Software For the Thompson and Funk Geometry (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-23291,
   title = {{Software For the Thompson and Funk Geometry}}, 
   author = {Banerjee, Hridhaan and Day, Carmen Isabel and Gezalyan, Auguste H. and Golovatskaia, Olga and Hunleth, Megan and Hwang, Sarah and Parepally, Nithin and Wang, Lucy and Mount, David M.},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:074df2e40eb974083f969981c7b82f83a059488b;origin=https://github.com/nithin1527/funk-geo-visualizer;visit=swh:1:snp:e75b8a08dc088518d55d404013d3f75417e891e7;anchor=swh:1:rev:1d259b6d2d7bb2d3c8f23ee785fde413d9a38430}{\texttt{swh:1:dir:074df2e40eb974083f969981c7b82f83a059488b}} (visited on 2025-06-20)},
   url = {https://github.com/nithin1527/funk-geo-visualizer},
   doi = {10.4230/artifacts.23291},
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2025.82
Software for the Thompson and Funk Polygonal Geometry (Media Exposition)

Authors: Hridhaan Banerjee, Carmen Isabel Day, Auguste H. Gezalyan, Olga Golovatskaia, Megan Hunleth, Sarah Hwang, Nithin Parepally, Lucy Wang, and David M. Mount

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Metric spaces defined within convex polygons, such as the Thompson, Funk, reverse Funk, and Hilbert metrics, are subjects of recent exploration and study in computational geometry. This paper contributes an educational piece of software for understanding these unique geometries while also providing a tool to support their research. We provide dynamic software for manipulating the Funk, reverse Funk, and Thompson balls in convex polygonal domains. Additionally, we provide a visualization program for traversing the Hilbert polygonal geometry.
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Hridhaan Banerjee, Carmen Isabel Day, Auguste H. Gezalyan, Olga Golovatskaia, Megan Hunleth, Sarah Hwang, Nithin Parepally, Lucy Wang, and David M. Mount. Software for the Thompson and Funk Polygonal Geometry (Media Exposition). In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 82:1-82:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{banerjee_et_al:LIPIcs.SoCG.2025.82,
  author =	{Banerjee, Hridhaan and Day, Carmen Isabel and Gezalyan, Auguste H. and Golovatskaia, Olga and Hunleth, Megan and Hwang, Sarah and Parepally, Nithin and Wang, Lucy and Mount, David M.},
  title =	{{Software for the Thompson and Funk Polygonal Geometry}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{82:1--82:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.82},
  URN =		{urn:nbn:de:0030-drops-232349},
  doi =		{10.4230/LIPIcs.SoCG.2025.82},
  annote =	{Keywords: Thompson metric, Hilbert metric, Funk metric, balls}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2025.83
French Onion Soup, Ipelets for Points and Polygons (Media Exposition)

Authors: Klint Faber, Auguste H. Gezalyan, Adam Martinson, Aniruddh Mutnuru, Nithin Parepally, Ryan Parker, Mihil Sreenilayam, Aram Zaprosyan, and David M. Mount

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
There are many structures, both classical and modern, involving point-sets and polygons whose deeper understanding can 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 structures based on point sets and polygons. These include quadtrees, trapezoidal maps, beta skeletons, floating bodies of convex polygons, onion graphs, fractals (Sierpiński triangle and carpet), simple polygon triangulations, and random point sets in simple polygons. All our Ipelets are programmed in Lua and are freely available.
Cite as

Klint Faber, Auguste H. Gezalyan, Adam Martinson, Aniruddh Mutnuru, Nithin Parepally, Ryan Parker, Mihil Sreenilayam, Aram Zaprosyan, and David M. Mount. French Onion Soup, Ipelets for Points and Polygons (Media Exposition). In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 83:1-83:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{faber_et_al:LIPIcs.SoCG.2025.83,
  author =	{Faber, Klint and Gezalyan, Auguste H. and Martinson, Adam and Mutnuru, Aniruddh and Parepally, Nithin and Parker, Ryan and Sreenilayam, Mihil and Zaprosyan, Aram and Mount, David M.},
  title =	{{French Onion Soup, Ipelets for Points and Polygons}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{83:1--83:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.83},
  URN =		{urn:nbn:de:0030-drops-232350},
  doi =		{10.4230/LIPIcs.SoCG.2025.83},
  annote =	{Keywords: Hilbert metric, Macbeath Regions, Polar Bodies, convexity}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2024.92
Ipelets for the Convex Polygonal Geometry (Media Exposition)

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

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

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).
Cite as

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)

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@InProceedings{parepally_et_al:LIPIcs.SoCG.2024.92,
  author =	{Parepally, Nithin and Chatterjee, Ainesh and Gezalyan, Auguste H. and Du, Hongyang and Mangla, Sukrit and Wu, Kenny and Hwang, Sarah and Mount, David M.},
  title =	{{Ipelets for the Convex Polygonal Geometry}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{92:1--92:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.92},
  URN =		{urn:nbn:de:0030-drops-200375},
  doi =		{10.4230/LIPIcs.SoCG.2024.92},
  annote =	{Keywords: Hilbert metric, Macbeath Regions, Polar Bodies, Convexity}
}
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