Abstract
A tiling of the plane is a set of figures, called tiles, that cover the plane without gaps or overlaps. On tiling we consider “Escherization problem": Given a closed figure in the plane, find a new closed figure that is similar to the original and can tile the plane. In this study, we give a new formulation of the problem with the weighted Procrustes distance and an algorithm to solve the problem optimally. We conduct computational experiments with animal shape tiles to confirm the effectiveness of the proposed method.
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Acknowledgments
This work was partly supported by JSPS Grant-in-Aid for Scientific Research (B) (No. 24360039) and (C) (No. 25330024). The authors would like to thank the anonymous reviewers for their valuable comments.
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Imahori, S., Kawade, S., Yamakata, Y. (2016). Escher-like Tilings with Weights. In: Akiyama, J., Ito, H., Sakai, T., Uno, Y. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2015. Lecture Notes in Computer Science(), vol 9943. Springer, Cham. https://doi.org/10.1007/978-3-319-48532-4_12
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DOI: https://doi.org/10.1007/978-3-319-48532-4_12
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