4 Search Results for "Devadoss, Satyan"

Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2022.67
Visualizing and Unfolding Nets of 4-Polytopes (Media Exposition)

Authors: Satyan L. Devadoss, Matthew S. Harvey, and Sam Zhang

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
Over a decade ago, it was shown that every edge unfolding of the Platonic solids was without self-overlap, yielding a valid net. Recent work has extended this property to their higher-dimensional analogs: the 4-cube, 4-simplex, and 4-orthoplex. We present an interactive visualization that allows the user to unfold these polytopes by drawing on their dual 1-skeleton graph.
Cite as

Satyan L. Devadoss, Matthew S. Harvey, and Sam Zhang. Visualizing and Unfolding Nets of 4-Polytopes (Media Exposition). In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 67:1-67:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{devadoss_et_al:LIPIcs.SoCG.2022.67,
  author =	{Devadoss, Satyan L. and Harvey, Matthew S. and Zhang, Sam},
  title =	{{Visualizing and Unfolding Nets of 4-Polytopes}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{67:1--67:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.67},
  URN =		{urn:nbn:de:0030-drops-160759},
  doi =		{10.4230/LIPIcs.SoCG.2022.67},
  annote =	{Keywords: unfoldings, nets, polytopes}
}
Document
Multimedia Exposition
DOI: 10.4230/LIPIcs.SoCG.2018.75
Geometric Realizations of the 3D Associahedron (Multimedia Exposition)

Authors: Satyan L. Devadoss, Daniel D. Johnson, Justin Lee, and Jackson Warley

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
The associahedron is a convex polytope whose 1-skeleton is isomorphic to the flip graph of a convex polygon. There exists an elegant geometric realization of the associahedron, using the remarkable theory of secondary polytopes, based on the geometry of the underlying polygon. We present an interactive application that visualizes this correspondence in the 3D case.
Cite as

Satyan L. Devadoss, Daniel D. Johnson, Justin Lee, and Jackson Warley. Geometric Realizations of the 3D Associahedron (Multimedia Exposition). In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 75:1-75:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{devadoss_et_al:LIPIcs.SoCG.2018.75,
  author =	{Devadoss, Satyan L. and Johnson, Daniel D. and Lee, Justin and Warley, Jackson},
  title =	{{Geometric Realizations of the 3D Associahedron}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{75:1--75:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.75},
  URN =		{urn:nbn:de:0030-drops-87886},
  doi =		{10.4230/LIPIcs.SoCG.2018.75},
  annote =	{Keywords: associahedron, secondary polytope, realization}
}
Document
Multimedia Exposition
DOI: 10.4230/LIPIcs.SoCG.2018.76
Star Unfolding of Boxes (Multimedia Exposition)

Authors: Dani Demas, Satyan L. Devadoss, and Yu Xuan Hong

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
Given a convex polyhedron, the star unfolding of its surface is obtained by cutting along the shortest paths from a fixed source point to each of its vertices. We present an interactive application that visualizes the star unfolding of a box, such that its dimensions and source point locations can be continuously toggled by the user.
Cite as

Dani Demas, Satyan L. Devadoss, and Yu Xuan Hong. Star Unfolding of Boxes (Multimedia Exposition). In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 76:1-76:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{demas_et_al:LIPIcs.SoCG.2018.76,
  author =	{Demas, Dani and Devadoss, Satyan L. and Hong, Yu Xuan},
  title =	{{Star Unfolding of Boxes}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{76:1--76:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.76},
  URN =		{urn:nbn:de:0030-drops-87890},
  doi =		{10.4230/LIPIcs.SoCG.2018.76},
  annote =	{Keywords: star unfolding, source unfolding, Voronoi diagram}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2016.66
Visualizing Scissors Congruence

Authors: Satyan Devadoss, Ziv Epstein, and Dmitriy Smirnov

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract
Consider two simple polygons with equal area. The Wallace-Bolyai-Gerwien theorem states that these polygons are scissors congruent, that is, they can be dissected into finitely many congruent polygonal pieces. We present an interactive application that visualizes this constructive proof.
Cite as

Satyan Devadoss, Ziv Epstein, and Dmitriy Smirnov. Visualizing Scissors Congruence. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 66:1-66:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{devadoss_et_al:LIPIcs.SoCG.2016.66,
  author =	{Devadoss, Satyan and Epstein, Ziv and Smirnov, Dmitriy},
  title =	{{Visualizing Scissors Congruence}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{66:1--66:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.66},
  URN =		{urn:nbn:de:0030-drops-59585},
  doi =		{10.4230/LIPIcs.SoCG.2016.66},
  annote =	{Keywords: polygonal congruence, geometry, rigid transformations}
}
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