License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2020.13
URN: urn:nbn:de:0030-drops-133572
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13357/
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van Kreveld, Marc ; Miltzow, Tillmann ; Ophelders, Tim ; Sonke, Willem ; Vermeulen, Jordi L.

Between Shapes, Using the Hausdorff Distance

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LIPIcs-ISAAC-2020-13.pdf (0.8 MB)

Abstract

Given two shapes A and B in the plane with Hausdorff distance 1, is there a shape S with Hausdorff distance 1/2 to and from A and B? The answer is always yes, and depending on convexity of A and/or B, S may be convex, connected, or disconnected. We show a generalization of this result on Hausdorff distances and middle shapes, and show some related properties. We also show that a generalization of such middle shapes implies a morph with a bounded rate of change. Finally, we explore a generalization of the concept of a Hausdorff middle to more than two sets and show how to approximate or compute it.

BibTeX - Entry

@InProceedings{vankreveld_et_al:LIPIcs:2020:13357,
  author =	{Marc van Kreveld and Tillmann Miltzow and Tim Ophelders and Willem Sonke and Jordi L. Vermeulen},
  title =	{{Between Shapes, Using the Hausdorff Distance}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{13:1--13:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Yixin Cao and Siu-Wing Cheng and Minming Li},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13357},
  URN =		{urn:nbn:de:0030-drops-133572},
  doi =		{10.4230/LIPIcs.ISAAC.2020.13},
  annote =	{Keywords: computational geometry, Hausdorff distance, shape interpolation}
}

Keywords: computational geometry, Hausdorff distance, shape interpolation
Collection: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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