License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.SoCG.2017.67
URN: urn:nbn:de:0030-drops-72443
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Nielsen, Frank ; Shao, Laetitia

On Balls in a Hilbert Polygonal Geometry (Multimedia Contribution)

LIPIcs-SoCG-2017-67.pdf (0.7 MB)


Hilbert geometry is a metric geometry that extends the hyperbolic Cayley-Klein geometry. In this video, we explain the shape of balls and their properties in a convex polygonal Hilbert geometry. First, we study the combinatorial properties of Hilbert balls, showing that the shapes of Hilbert polygonal balls depend both on the center location and on the complexity of the Hilbert domain but not on their radii. We give an explicit description of the Hilbert ball for any given center and radius. We then study the intersection of two Hilbert balls. In particular, we consider the cases of empty intersection and internal/external tangencies.

BibTeX - Entry

  author =	{Frank Nielsen and Laetitia Shao},
  title =	{{On Balls in a Hilbert Polygonal Geometry (Multimedia Contribution)}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{67:1--67:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-72443},
  doi =		{10.4230/LIPIcs.SoCG.2017.67},
  annote =	{Keywords: Projective geometry, Hilbert geometry, balls}

Keywords: Projective geometry, Hilbert geometry, balls
Collection: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 20.06.2017

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