License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2023.48
URN: urn:nbn:de:0030-drops-178980
URL: https://drops.dagstuhl.de/opus/volltexte/2023/17898/
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Löffler, Maarten ; Ophelders, Tim ; Silveira, Rodrigo I. ; Staals, Frank

Shortest Paths in Portalgons

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LIPIcs-SoCG-2023-48.pdf (5 MB)


Abstract

Any surface that is intrinsically polyhedral can be represented by a collection of simple polygons (fragments), glued along pairs of equally long oriented edges, where each fragment is endowed with the geodesic metric arising from its Euclidean metric. We refer to such a representation as a portalgon, and we call two portalgons equivalent if the surfaces they represent are isometric.
We analyze the complexity of shortest paths. We call a fragment happy if any shortest path on the portalgon visits it at most a constant number of times. A portalgon is happy if all of its fragments are happy. We present an efficient algorithm to compute shortest paths on happy portalgons.
The number of times that a shortest path visits a fragment is unbounded in general. We contrast this by showing that the intrinsic Delaunay triangulation of any polyhedral surface corresponds to a happy portalgon. Since computing the intrinsic Delaunay triangulation may be inefficient, we provide an efficient algorithm to compute happy portalgons for a restricted class of portalgons.

BibTeX - Entry

@InProceedings{loffler_et_al:LIPIcs.SoCG.2023.48,
  author =	{L\"{o}ffler, Maarten and Ophelders, Tim and Silveira, Rodrigo I. and Staals, Frank},
  title =	{{Shortest Paths in Portalgons}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{48:1--48:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17898},
  URN =		{urn:nbn:de:0030-drops-178980},
  doi =		{10.4230/LIPIcs.SoCG.2023.48},
  annote =	{Keywords: Polyhedral surfaces, shortest paths, geodesic distance, Delaunay triangulation}
}

Keywords: Polyhedral surfaces, shortest paths, geodesic distance, Delaunay triangulation
Collection: 39th International Symposium on Computational Geometry (SoCG 2023)
Issue Date: 2023
Date of publication: 09.06.2023


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