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Acquiring periodic tilings of regular polygons from images

Abstract

We describe how we have acquired geometrical models of many periodic tilings of regular polygons from two large collections of images. These models are based on a simplification of the representation recently proposed by us that uses complex numbers. We also describe an algorithm for deciding when two representations give the same tiling, which was used to identify coincidences in these collections.

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Acknowledgements

We thank Sá and Sá and Galebach for making their collections of tilings freely available at their websites. The first author is partially supported by a CNPq doctoral scholarship. The third author is partially supported by a CNPq research grant. This research was done in the Visgraf Computer Graphics laboratory at IMPA. Visgraf is supported by the funding agencies FINEP, CNPq, and FAPERJ, and also by gifts from IBM Brasil, Microsoft, NVIDIA, and other companies.

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Correspondence to Luiz Henrique de Figueiredo.

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Soto Sánchez, J.E., Medeiros e Sá, A. & de Figueiredo, L.H. Acquiring periodic tilings of regular polygons from images. Vis Comput 35, 899–907 (2019). https://doi.org/10.1007/s00371-019-01665-y

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Keywords

  • Tilings
  • Tessellations
  • Geometrical models