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Abstract Morphing Using the Hausdorff Distance and Voronoi Diagrams

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

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Author Details

Lex de Kogel
  • Utrecht University, The Netherlands
Marc van Kreveld
  • Utrecht University, The Netherlands
Jordi L. Vermeulen
  • Utrecht University, The Netherlands

Funding

Research was funded by NWO TOP grant no. 612.001.651.

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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) https://doi.org/10.4230/LIPIcs.ESA.2022.74

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Morphing
  • Hausdorff distance
  • Voronoi diagrams

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