Abstract Morphing Using the Hausdorff Distance and Voronoi Diagrams
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.
Morphing
Hausdorff distance
Voronoi diagrams
Theory of computation~Computational geometry
74:1-74:16
Regular Paper
Research was funded by NWO TOP grant no. 612.001.651.
https://hausdorff-morphing.github.io/
https://arxiv.org/abs/2206.15339
Lex
de Kogel
Lex de Kogel
Utrecht University, The Netherlands
Marc
van Kreveld
Marc van Kreveld
Utrecht University, The Netherlands
Jordi L.
Vermeulen
Jordi L. Vermeulen
Utrecht University, The Netherlands
10.4230/LIPIcs.ESA.2022.74
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Lex de Kogel, Marc van Kreveld, and Jordi L. Vermeulen
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