[2206.15339] Abstract morphing using the Hausdorff distance and Voronoi diagrams
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Computer Science > Computational Geometry

arXiv:2206.15339 (cs)
[Submitted on 30 Jun 2022]

Title:Abstract morphing using the Hausdorff distance and Voronoi diagrams

Authors:Lex de Kogel, Marc van Kreveld, Jordi L. Vermeulen
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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. Between shapes, using the Hausdorff distance. Computational Geometry 100:101817, 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.
Subjects: Computational Geometry (cs.CG)
Cite as: arXiv:2206.15339 [cs.CG]
  (or arXiv:2206.15339v1 [cs.CG] for this version)
  https://doi.org/10.48550/arXiv.2206.15339

Submission history

From: Jordi Vermeulen [view email]
[v1] Thu, 30 Jun 2022 15:12:18 UTC (883 KB)
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