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DOI: 10.4230/LIPIcs.ESA.2022.74

Abstract Morphing Using the Hausdorff Distance and Voronoi Diagrams

Authors: Lex de Kogel, Marc van Kreveld, and Jordi L. Vermeulen

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract

This paper introduces two new abstract morphs for two 2-dimensional shapes. The intermediate shapes gradually reduce the Hausdorff distance to the goal shape and increase the Hausdorff distance to the initial shape. The morphs are conceptually simple and apply to shapes with multiple components and/or holes. We prove some basic properties relating to continuity, containment, and area. Then we give an experimental analysis that includes the two new morphs and a recently introduced abstract morph that is also based on the Hausdorff distance [Van Kreveld et al., 2022]. We show results on the area and perimeter development throughout the morph, and also the number of components and holes. A visual comparison shows that one of the new morphs appears most attractive.

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Lex de Kogel, Marc van Kreveld, and Jordi L. Vermeulen. Abstract Morphing Using the Hausdorff Distance and Voronoi Diagrams. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 74:1-74:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dekogel_et_al:LIPIcs.ESA.2022.74,
  author =	{de Kogel, Lex and van Kreveld, Marc and Vermeulen, Jordi L.},
  title =	{{Abstract Morphing Using the Hausdorff Distance and Voronoi Diagrams}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{74:1--74:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.74},
  URN =		{urn:nbn:de:0030-drops-170120},
  doi =		{10.4230/LIPIcs.ESA.2022.74},
  annote =	{Keywords: Morphing, Hausdorff distance, Voronoi diagrams}
}

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Abstract Morphing Using the Hausdorff Distance and Voronoi Diagrams

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